barriers to capital, subsistence consumption, and child labor · barriers to capital, subsistence...
TRANSCRIPT
Barriers to Capital Subsistence Consumption and Child Labor
DEGIT
St Petersburg Russia
8 September 2011
Richard C Barnett
Drexel University
Outline of the Talk
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Main Results
Can capital barriers impact on the child laborschooling decision
Can barriers be one explanation behind the observed negative
relationship between output and child labor
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Main Results
Can capital barriers impact on the child laborschooling decision
Can barriers be one explanation behind the observed negative
relationship between output and child labor
Conclusions
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Introduce child labor and schooling into a modified Diamond growth model
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Outline of the Talk
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Main Results
Can capital barriers impact on the child laborschooling decision
Can barriers be one explanation behind the observed negative
relationship between output and child labor
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Main Results
Can capital barriers impact on the child laborschooling decision
Can barriers be one explanation behind the observed negative
relationship between output and child labor
Conclusions
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Introduce child labor and schooling into a modified Diamond growth model
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Main Results
Can capital barriers impact on the child laborschooling decision
Can barriers be one explanation behind the observed negative
relationship between output and child labor
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Main Results
Can capital barriers impact on the child laborschooling decision
Can barriers be one explanation behind the observed negative
relationship between output and child labor
Conclusions
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Introduce child labor and schooling into a modified Diamond growth model
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Main Results
Can capital barriers impact on the child laborschooling decision
Can barriers be one explanation behind the observed negative
relationship between output and child labor
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Main Results
Can capital barriers impact on the child laborschooling decision
Can barriers be one explanation behind the observed negative
relationship between output and child labor
Conclusions
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Introduce child labor and schooling into a modified Diamond growth model
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Main Results
Can capital barriers impact on the child laborschooling decision
Can barriers be one explanation behind the observed negative
relationship between output and child labor
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Main Results
Can capital barriers impact on the child laborschooling decision
Can barriers be one explanation behind the observed negative
relationship between output and child labor
Conclusions
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Introduce child labor and schooling into a modified Diamond growth model
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Outline of the Talk Background and Motivation
― Evidence from World Bank
― Objectives
― Related literature
The Model― Model overview
― Agentsrsquo problem equilibrium
Main Results
Can capital barriers impact on the child laborschooling decision
Can barriers be one explanation behind the observed negative
relationship between output and child labor
Conclusions
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Introduce child labor and schooling into a modified Diamond growth model
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Introduce child labor and schooling into a modified Diamond growth model
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Background
Some 206 million children workpart-or full-time in developingcountries (ILO estimates 2002)
The World Bank documents aninverse relationship between per-capita incomes and child laborparticipation rates
Barriers to capital seem to playan important role in explainingsome stylized differences ineconomic development
Introduce child labor and schooling into a modified Diamond growth model
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Introduce child labor and schooling into a modified Diamond growth model
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Introduce child labor and schooling into a modified Diamond growth model
Two main questionsmdash Do capital barriers have
i) Positive impact on child labor and
ii) A negative impact on output
mdash What are some implications for policy
Paperrsquos Objectives
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
3 Important Features
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Binding non-negativity constraint on bequestsParents face binding credit restrictions which prevent them from amassing debt to pay for or compensate the family for the loss of a childs earnings and then passing this debt obligation onto the child later in life
― 0 lt λ lt 1 lsquoimpure altruismrsquo ― 1β lt rπ lt 1βλ
Barriers to capital formationBribes bureaucratic red tape or other capital market distortions common to
many developing economies
― Reduces capital input― Maymay not affect labor allocation
Minimum consumption requirement (MCR)Elasticity of intertemporal substitution depends on wealth
3 Important Features
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Barriers
Parente et al (JPE 2000) Ngai (JME 2004)
Child Labor and Human Capital
Basu and Van (AER 1998) Baland and Robinson (JPE 2000) Ranganzas (JME 2000) Aiyagari et al (JET 2002) Das and Deb (BE Press 2006) Doepke and Krueger (2008) Soares (2008) Bell and Gersbach (MD 2009)
Minimum Consumption Requirements
Basu and Van (AER 1998) Chatterjee and Ravikumar (MD 1999)
Related Studies
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Overview
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
The Model
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Overview
OG model with 2 period lived decision-makers Parents make time allocation for children
Single consumption good with Cobb-Douglas production using capital and labor inputs
Agents work each period of life Childrsquos time is divided between work lt and schooling 1- lt
Schooling increases the productivity of an agentrsquos labor input when middle-aged and old
Barrier-to-capital agrave la Parente et al (2000) The effective gross return on capital is MPKπ
MCR γ
The Model
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Preferences
Ut equiv u(c1t ) + β u(c2t+1 ) + βλ Ut+1
where u(c ) = (c ndash γ )1-σ (1 - σ) 0 le β λ le 1
c1t parentrsquos consumption (when middle age)
c2t+1 parentrsquos consumption (when old)
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
The Agentrsquos Problem
U(θt Ωt ) equiv max u(c1t ) + β u(c2t+1 ) + βλ U(θt +1 Ωt +1 )
Subject to
a) c1t + xt + bt le wt lt + wt h(1 ndash lt -1 ) + rt-1 bt - 1 π
b) c2t+1 le wt +1 h(1 ndash lt -1) + rt xt π
c) c1t c2t+1 ge γ xt bt ge 0
d) θt equiv bt - 1 lt - 1 is given
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Marginal Conditions Agentrsquos Problem
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Marginal Conditions Agentrsquos Problem
Savings uprime( c1t ) = (rt π ) β uprime( c2t+1 )
Bequest uprime(c1t ) ge (rt π ) λ β uprime(c1t +1 )
Schooling wt uprime( c1t ) ge wt+1 hprime( 1 - lt ) λβ uprime(c1t+1 )+ wt + 2 hprime( 1- lt ) λ β 2 uprime(c2t+2 )
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Aggregate Investment
X = +[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ ]
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Factors and Technologies
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Factors and Technologies
Output Yt = AKtα Lt
1-α
Factorsa) Labor of parent and child L1t = lt + h(1 ndash lt - 1 )b) Labor of the old L2t = h(1 ndash lt -2 )c) Capital Kt+1 = xt π + bt π
Human CapitalAssumption 1 h has lsquonice propertiesrsquo and h(0)= 1
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Given K0 b0 h(1- l0 ) h(1- l-1 ) an equilibrium consists of sequences for prices wt rt t ge 1 and allocations c1t c2t+1t ge 1and Xt Kt+1 lt t ge 1 such that
a) Agents optimize
b) Factor payments w = (1 - α) A Kα L-α
r = α A Kα -1 L1-α
c) All markets clear Labor Lt = lt + h(1 - lt -1 ) + h(1 - lt -2 ) Capital xt + bt = π Kt +1 Goods c1t + c2t + Xt = Yt
Equilibrium
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Approach
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Approach
Steady-State with Nonbinding Non-negativity Constraint on Bequests
Steady-State with Binding Non-negativity Constraint on Bequestsmdash MCR = 0
mdash MCR gt 0
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Savings uprime( c1t ) = β (rt π ) uprime( c2t+1 )
Bequest uprime(c1t ) ge β λ (rt π ) uprime(c1t+1 )
Schooling wt uprime( c1t ) gewt+1 hprime( 1 - lt ) β λ uprime(c1t+1 ) + wt+2 hprime( 1- lt ) β2 λ uprime(c2t+2 )
The Child Labor Decision
Steady State
uprime( c1 ) β uprime( c2 ) = rπ
1β λ ge r π
1 = hprime( 1 - l ) βλ[1 + βλ]
1 = hprime( 1 - l ) βλ[1 + πr]
uprime( c1t )β uprime( c2t+1 ) = rt π uprime( c1t )β λ uprime( c1t+1 ) ge rt π-- intertemporal link -- -- intergenerational link --
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
hprime( 1 - l ) = 1
βλ (1 + π r)
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Policy-induced changes in factors
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Policy-induced changes in factors
Result 1 (Child Labor and Aggregate Supply of LaborSuppose dl gt 0 Then dL lt 0 where L = l + 2h(1 ndash l ) is the steady-state supply of labor
Result 2 (Policy induced changes in l)dl ge 0 whenever drr ge dππ
Result 3 (Policy induced changes in K)Suppose drr ge dππ Then dK lt 0
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Proposition 2 (Nonbinding Constraint on Bequests)
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Proposition 2 (Nonbinding Constraint on Bequests)
If bequests bt gt 0 barriers to capital have no impact on child labor in the steady-state
Reason In the steady-state 1βλ = rπ if bt gt 0
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Proposition 4 (Binding Constraint on Bequests I)
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Proposition 4 (Binding Constraint on Bequests I)
If the MCR γ = 0 barriers to capital have no impact on child labor in the steady-state
Reasonndash When γ = 0 investment dXX = dwwndash But factor payments rarr dww = drr + dKKndash From the clearing condition X = π K so
dXX = dKK + dππ there4 drr = dππ
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Aggregate Investment (γ = 0)
X = +[wh(1- l)][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ)1σ]
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Proposition 5 (Binding Constraint on Bequests II)
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Proposition 5 (Binding Constraint on Bequests II)
Suppose the minimum consumption requirement γ gt 0 anddπ gt 0 Then drr gt dππ
Intuition Barrier does same sort of thing it does in the previous case ie reduces K (wealth and wages) But now hellip investment falls proportionally more than wages Why With lower wealth agent is less willing substitute intertemporally (invests less)
One consequence Effective return rπ rises child labor increases
dK + dππ = dXX lt dww = drr + dKK ndash dLL
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Bottom Line The increase in child labor accompanying an increase in π is a consequence of the reduction in the agentrsquos willingness to substitute intertemporally
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Steady State
+ = π K[wh(1- l) ndash γ ][(β rπ)1σ ndash 1 ]
[rπ + (β rπ)1σ]
wl (β rπ)1σ
[rπ + (β rπ) 1σ]
( )( )
( )( ) =
Γ
+minusminusminus
minus
Γminus
+minus+minusminus
παα
πππαα r
llhlhrrr
llhllh
)1211
)1211
( )( ) 11
1
1minus+
equivΓσββ z
z
( ) ( )( )
Γminus
minus
+minus+
minus
minus
πππαα
α
γ
α
αα
rrr
llhA
r 1
)121
11
1
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Simple Extension
Consider a capital externality in the human capital production function h(1 ndash lt ndash 1 Kt )
Why of interest Allows the human capital production function to
evolve over the course of development in an convenient manner
If you assume a lsquosmall countryrsquo assumption rπ is fixed and changes in the barrier have no effect on child labor
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Pedagogical Examples
Variable β λ σ γ α π hValue 397 25 964 475 30 1 to 3 h(x) = 1 + 10x84
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
1
11
12
13
14
15
16
17
18
19
04 05 06 07 08 09 1
Relative Output
Rela
tive
Parti
cipa
tion
Rate
s
Example 1 (Observations Across Steady-States)
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Example 2 (Dynamic Response to Lower Barrier)
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
γ gt 0 γ = 0
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Why the difference
The transitional effect of a lower barrier on child labor is felt through one of three channels Wages Return rπ Marginal rate of substitution across consumption of
middle-age decisionmakers
Fig 42a Case where γ gt 0
28
29
3
31
32
33
34
35
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
005
01
015
02
025
03
035
04
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Fig 42b Case where γ = 0
4
41
42
43
44
45
46
0 10 20 30 40 50 60 70 80 90 100Time
Out
put
0
002
004
006
008
01
012
014
Chi
ld L
abor
Cap
ital
OutputChild LaborCapital
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Conclusions
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
Conclusions
Paper provides a general equilibrium model of child labor andphysical and human capital
Paper focuses on the critical role MCRs may play in explainingobserved differences in output and child labor participationrates across countries
We make the argument that under certain conditions highercapital barriers can lsquodeepenrsquo child labor participation rates
The model also suggests that by reducing capital barriersdeveloping countries can reduce child labor Without areduction in capital barriers not clear that imposing stricterbarriers to child labor participation rates will improve the lotof a country
- Barriers to Capital Subsistence Consumption and Child Labor
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Outline of the Talk
- Background
- Background
- Slide Number 9
- Slide Number 10
- Slide Number 11
- 3 Important Features
- 3 Important Features
- 3 Important Features
- 3 Important Features
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Preferences
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- The Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Marginal Conditions Agentrsquos Problem
- Aggregate Investment
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Factors and Technologies
- Slide Number 39
- Approach
- Approach
- Approach
- Slide Number 43
- Slide Number 44
- Slide Number 45
- Slide Number 46
- Slide Number 47
- Steady State
- Steady State
- Steady State
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Policy-induced changes in factors
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 2 (Nonbinding Constraint on Bequests)
- Proposition 4 (Binding Constraint on Bequests I)
- Proposition 4 (Binding Constraint on Bequests I)
- Aggregate Investment (g = 0)
- Proposition 5 (Binding Constraint on Bequests II)
- Proposition 5 (Binding Constraint on Bequests II)
- Slide Number 62
- Steady State
- Simple Extension
- Simple Extension
- Simple Extension
- Slide Number 67
- Pedagogical Examples
- Example 1 (Observations Across Steady-States)
- Example 2 (Dynamic Response to Lower Barrier)
- Slide Number 71
- Conclusions
- Conclusions
- Conclusions
- Conclusions
- Conclusions
-
⎟⎠⎞
⎜⎝⎛
primeprime
+rπβλ 1
1
hprime(1 ndash l Kprime )
⎟⎠⎞
⎜⎝⎛ +
rπβλ 1
1
l
hprime(1 ndash l K )
l l prime
Chart1
Sheet1
Sheet1
Sheet2
Sheet3
| y | l | ratio y | ratio l | ||||||
| 1 | 5103837338 | 0196324827 | 1 | 1 | |||||
| 11 | 4846566344 | 02035560085 | 09495926345 | 1036832741 | |||||
| 12 | 4618839709 | 02106742213 | 09049739251 | 1073090064 | |||||
| 13 | 4414915419 | 02177155064 | 08650188333 | 1108955549 | |||||
| 14 | 423047326 | 02247115765 | 08288808949 | 1144590727 | |||||
| 15 | 4062184154 | 02316914036 | 07959078404 | 1180143169 | |||||
| 16 | 390742778 | 02386824584 | 07655862679 | 1215752801 | |||||
| 17 | 3764101166 | 0245711763 | 07375041398 | 1251557262 | |||||
| 18 | 3630484915 | 02528068757 | 07113245731 | 1287696923 | |||||
| 19 | 3505146855 | 02599969094 | 06867669603 | 1324320074 | |||||
| 2 | 3386870309 | 02673136922 | 06635929175 | 1361588833 | |||||
| 21 | 3274598498 | 02747932035 | 06415953882 | 1399686467 | |||||
| 22 | 3167388932 | 02824774842 | 06205897097 | 1438827114 | |||||
| 23 | 3064372843 | 02904173333 | 06004056634 | 1479269523 | |||||
| 24 | 296471464 | 02986763333 | 05808795311 | 152133756 | |||||
| 25 | 2867564887 | 03073372094 | 0561844882 | 1565452592 | |||||
| 26 | 2771995899 | 03165125252 | 05431199537 | 1612187974 | |||||
| 27 | 2676897761 | 03263641013 | 05244872796 | 1662367955 | |||||
| 28 | 2580781446 | 03371419529 | 0505655113 | 1717266013 | |||||
| 29 | 248133507 | 03492740545 | 04861704842 | 1779062077 | |||||
| 3 | 2374158982 | 03636235186 | 04651713652 | 1852152497 | |||||
| 31 | 2247263191 | 03826037427 | 04403085448 | 1948830153 | |||||
| 32 | |||||||||
| 33 | |||||||||
| 34 | |||||||||
| 35 |
| 1 | |
| 09495926345 | |
| 09049739251 | |
| 08650188333 | |
| 08288808949 | |
| 07959078404 | |
| 07655862679 | |
| 07375041398 | |
| 07113245731 | |
| 06867669603 | |
| 06635929175 | |
| 06415953882 | |
| 06205897097 | |
| 06004056634 | |
| 05808795311 | |
| 0561844882 | |
| 05431199537 | |
| 05244872796 | |
| 0505655113 | |
| 04861704842 | |
| 04651713652 |
Sheet1
Sheet1
Sheet2
Sheet3
| y | l | ratio y | ratio l | ||||||
| 1 | 5103837338 | 0196324827 | 1 | 1 | |||||
| 11 | 4846566344 | 02035560085 | 09495926345 | 1036832741 | |||||
| 12 | 4618839709 | 02106742213 | 09049739251 | 1073090064 | |||||
| 13 | 4414915419 | 02177155064 | 08650188333 | 1108955549 | |||||
| 14 | 423047326 | 02247115765 | 08288808949 | 1144590727 | |||||
| 15 | 4062184154 | 02316914036 | 07959078404 | 1180143169 | |||||
| 16 | 390742778 | 02386824584 | 07655862679 | 1215752801 | |||||
| 17 | 3764101166 | 0245711763 | 07375041398 | 1251557262 | |||||
| 18 | 3630484915 | 02528068757 | 07113245731 | 1287696923 | |||||
| 19 | 3505146855 | 02599969094 | 06867669603 | 1324320074 | |||||
| 2 | 3386870309 | 02673136922 | 06635929175 | 1361588833 | |||||
| 21 | 3274598498 | 02747932035 | 06415953882 | 1399686467 | |||||
| 22 | 3167388932 | 02824774842 | 06205897097 | 1438827114 | |||||
| 23 | 3064372843 | 02904173333 | 06004056634 | 1479269523 | |||||
| 24 | 296471464 | 02986763333 | 05808795311 | 152133756 | |||||
| 25 | 2867564887 | 03073372094 | 0561844882 | 1565452592 | |||||
| 26 | 2771995899 | 03165125252 | 05431199537 | 1612187974 | |||||
| 27 | 2676897761 | 03263641013 | 05244872796 | 1662367955 | |||||
| 28 | 2580781446 | 03371419529 | 0505655113 | 1717266013 | |||||
| 29 | 248133507 | 03492740545 | 04861704842 | 1779062077 | |||||
| 3 | 2374158982 | 03636235186 | 04651713652 | 1852152497 | |||||
| 31 | 2247263191 | 03826037427 | 04403085448 | 1948830153 | |||||
| 32 | |||||||||
| 33 | |||||||||
| 34 | |||||||||
| 35 |
Sheet1
Sheet2
Sheet3
Sheet2
Sheet3
