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Expectation Traps, Intergenerational Redistribution and Child Labor
Patrick M. Emerson Department of Economics
University of Colorado at Denver Denver, CO 80217
Shawn D. Knabb Department of Economics
University of Colorado at Denver Denver, CO 80217
September 2004
Abstract
This paper develops a dynamic model with overlapping generations and child labor, where there are two possible equilibria. There is a ‘good’ equilibrium with a high level of education and no child labor, and a ‘bad’ equilibrium with a low level of education and positive child labor. It is first shown that a government program of intergenerational transfers, such as social security, can eliminate the low schooling-child labor equilibrium by replicating a missing intergenerational contracts market. This government intervention is Pareto improving in a deterministic setting. The model then introduces uncertainty to the dynamic system, where it is shown that if society does not believe that the government will implement the transfer program, then in fact it won’t, thus fulfilling society’s expectations. This is true even if the government would have implemented the Pareto improving transfer program in the absence of uncertainty. This result implies that governments may be powerless to prevent the low education-child labor equilibrium if the government lacks credibility, thus leaving the country in an expectations trap. (JEL classification numbers: D91, E60, J20, O20) (Keywords: Expectation Traps; Uncertainty; Intergenerational Transfers; Child Labor) Acknowledgements: For valuable comments and insight we would like to thank Kaushik Basu, Henning Bohn, David Stifel, seminar participants at Cornell University and two anonymous referees of this journal. This paper has also benefited from presentations at the 2003 Latin American and Caribbean Economics Association Conference and the 2003 Western Economic Association International Conference.
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Expectation Traps, Intergenerational Redistribution and Child Labor
I. Introduction
Child labor is widespread in the contemporary world. In fact, the International
Labor Organization estimates that 246 million of the world’s children aged 5 to 17, or 16
percent, are child laborers, most living in developing countries.1 Recently there has been
renewed interest in this topic among economists, which has led to a series of theoretical
studies with the aim of better understanding the causes and consequences of child labor in
order to help guide appropriate policy responses (see Gootaert and Kanbur (1995), Basu
(1999), and Basu and Tzannatos (2003) for useful literature surveys).
Typically, theoretical models designed to address the important policy issues
surrounding child labor posit that a family’s decision to send a child to the labor market is
taken only as a last resort in order to escape the dire consequences of poverty (e.g. Basu
and Van, 1998). Baland and Robinson (2000) show that this response on the part of the
family may be stronger in a dynamic setting because contracts between children and
adults are not self-enforcing, and capital markets are incomplete.2 In this case, an adult
decision maker may not only send their children to work to escape poverty in the present,
but do so to escape poverty in the future as well. This decision will hinder a child’s
ability to accumulate human capital and can lead to persistent cycles of poverty and child
labor across generations.3
1 ILO (2002). Child labor was also common in developed countries until fairly recently, see, e.g., Kruse and Mahony (2000). 2Other dynamic models studying child labor are Emerson and Souza (2003); Bell and Gersbach (2001); Lopez-Calva and Myiamoto (2004); Ranjan (2001); Hazan and Burdugo (2002); Jafarey and Lahiri (2002). 3 See Emerson and Souza (2003) and Wahba (2002) for the empirical support of child labor persistence.
2
This paper begins by showing that a benevolent government can address the
incidence of child labor that results from the non-enforceability of intergenerational
contracts and incomplete capital markets through the appropriate use of fiscal policy, and
that this policy is Pareto improving in a deterministic environment. It is then shown that
once uncertainty is introduced to the economy, this same fiscal policy may be rendered
ineffective. In other words, if households don’t believe that the government will follow
through on their policy promise, then in fact, it is quite possible that the government will
not be able to follow through on their promise as a result of these beliefs.4 This self-
fulfilling nature of fiscal policy in the presence of uncertainty can leave a country in an
expectations trap with a low level of human capital and child labor.5
To formally demonstrate this argument, we employ a three period overlapping
generations model in which child labor exists. This stylized setup will keep the dynamics
manageable and allow us to highlight the effects of uncertainty. Also, within this
framework we introduce a missing intergenerational contracts market, in conjunction
with a temporary increasing return to scale human capital production function, which
gives rise to two locally stable steady states. There is a ‘bad’ equilibrium where there is a
relatively low level of parental human capital, which results in a low level of income and
positive child labor (a poverty trap), and there is a ‘good’ equilibrium where there is a
4Rodrik (1989) uses a similar line of reasoning to demonstrate that expectations can affect the optimal design of trade policy reforms. As in the current paper, he interprets uncertainty in the context of an informational asymmetry between households and the government. In another related paper, Rodrik (1991) demonstrates that uncertainty can also affect (international) capital flows using a partial equilibrium model of investment in a developing country context. 5 It is important to distinguish the arguments made in this paper form those made in the time-consistency literature established by Kydland and Prescott (1977), Calvo (1978), and Fischer (1980). We argue that it is the perception of uncertainty by households that potentially renders a Pareto improving policy ineffective in a time-consistent framework. In other words, the government’s optimal decision rule is independent of time in our current setup but now depends on the households’ perception of the government’s willingness or ability to implement the program.
3
relatively high level of parental human capital, which results in a high level of income
and no child labor.
It is then shown that a benevolent government can replicate the missing
intergenerational contracts market with a pay-as-you-go social security program, thereby
eliminating this component of child labor in a deterministic environment. In addition, it
is also shown that this policy is Pareto improving in the sense that all generations are
strictly better off under this policy, except the initial old who are no worse off. The
reason why this policy is Pareto improving is because future generations benefit from a
human capital externality that is self-sustaining, as long as the human capital benefits are
greater than the implicit cost of maintaining the pay-as-you-go social security program.
The dynamics of this social security program are intuitive: if child labor is one
possible mechanism adults can use to redistribute resources from their children, then the
government can reduce this incentive by announcing a social security program that will
begin during the current adults’ old age (an institutional intergenerational contract). This
policy results in an increase in lifetime wealth for the initial generation because they
receive the social security transfer during their old age, but do not pay into the system
during their current working years. Thus, the adults of this initial generation will no
longer need to use their children’s labor to supplement current consumption and savings
for future consumption because of this increase in lifetime wealth. The subsequent
reduction in child labor that results from this increase in lifetime wealth increases the
child’s education, which in turn increases the child’s human capital, potentially setting
off a chain of events that allows the household and/or country to escape from poverty.
4
Therefore, the government can eliminate the ‘bad’ equilibrium, or poverty trap, through
the appropriate use of fiscal policy.6
The success of this intergenerational redistribution program, however, rests
critically on its ability to change people’s behavior in anticipation of this policy. In
developing countries, where there may be a high degree of uncertainty surrounding the
stability and intentions of the government, the deterministic results above may not carry
over to a more realistic setting that takes this type of uncertainty into account.7 To
formally demonstrate this possibility we add a specific form of uncertainty to the model
that is the result of asymmetric information between the households and the government,
which is similar to the approach taken by Engel and Kletzer (1991), and Rodrik (1991,
1989). Consider the following motivational scenario. The public believes there are two
possible government types. The first type is a benevolent government with a Rawlsian
social welfare function that assigns an equal weight to each generation. By assumption,
this government is in power, or is the ‘true’ government type. This government type will
implement the program or policy as long as it does not reduce the welfare of any
generation, that is, the policy is Pareto improving. The second type is a ‘false’
government that is not in power. The public believes that this government type will keep
the tax revenue for itself. Therefore, households do not expect to receive the social
security transfer during their retirement in this counterfactual case. Based on these
6 The idea that an intergenerational transfer program, along with the regulation of the child labor market (mandatory schooling or the banning of child labor), may be Pareto improving is informally discussed in Becker and Murphy (1988) and formalized in Hazan and Berdugo (2002). We show that the regulation requirement is unnecessary with an appropriately designed intergenerational transfer program in a deterministic environment. Bell and Gersbach (2001) also study redistribution policy, but in their case they examine an iterative series of within-generation transfers through time. 7 Even in more stable democratic countries uncertainty necessarily exists over long-term policies and programs due to the regularly changing leadership of the government. The United States and its Social Security program is a perfect example.
5
perceived government types households optimally choose current consumption, savings,
and child labor (human capital) based on the expected value of the social security transfer
from the government.
These subjective beliefs might arise because a new reformist government has
been installed but a portion of the population do not believe or trust that it is indeed
committed to reforms. Another possibility is that the uncertainty is purely extrinsic and
unrelated to the current fundamentals of the economy (see e.g. Azariadis, 1981; Cass and
Shell, 1983; and Farmer, 1999). Regardless of the interpretation, this paper demonstrates
that there exists a minimum level of confidence in government that is necessary for the
Pareto improving social security program to be successful. If the level of confidence is
below this minimum, then a benevolent government will not be able to implement the
Pareto improving policy, although it would have in a deterministic environment or if
households had more confidence in their government. It is in this sense that the model
generates an endogenous expectations trap that is inherently self-fulfilling in nature.8 In
other words, the households’ subjective beliefs, in addition to the initial level of parental
human capital, serve as the equilibrium selection mechanism.
The rest of the paper is as follows: Section II presents the benchmark model of
child labor. Section III demonstrates that a pay-as-you-go social security program can
eliminate the ‘bad’ equilibrium with child labor under certain conditions. Section IV
adds uncertainty to the model and demonstrates the existence of a minimum level of
confidence in government, which is sufficient to render the government’s transfer
program ineffective fulfilling the households’ pessimistic expectations. Section V
8Typically, expectation traps are discussed in the context of monetary economies. For monetary applications see Albanesi, et al. (2003), Chari, et al. (1998), and Weil (1987). Also see Cole and Kehoe (2000) for an application to sovereign debt.
6
describes our interpretation of uncertainty in greater detail and places our modeling
strategy in the existing literature. This section also discusses possible extensions to the
paper. Finally section VI concludes with a summary.
II. The Basic Model
The model consists of an infinite sequence of identical overlapping generations
living for three periods, where a household is defined as one child and one working age
adult. The last period of life is spent outside the household, thus the working age adults
have no filial responsibility to their elders.9 The population is constant and each
generation is normalized to unity. These simplifying demographic assumptions allow us
to concentrate on the key issue of the paper: the dynamic interaction between education,
child labor, government policy, and government credibility. Also imperfect capital
markets make it impossible for the adult to borrow against their child’s future earnings
and any future redistribution from the government.
In the first period of life the child receives an education and may work in the labor
market. If the child participates in the labor market he or she earns an adult equivalent
[ ]1,0∈a for physical labor only. Thus, a child is endowed with no human capital. The
decision to educate the child, [ ]1,0∈e , or have the child participate in the labor market,
( )e−1 , is made by the child’s parent. In the second period of life, the adult supplies
human capital h and one unit of physical labor to the labor market, has one child, and
9 This problem may be overcome if there exists a sufficient degree of reverse altruism or some sort of social norm of filial obligation on the part of the children, see, e.g., Lopez-Calva and Myiamoto (2004), although allowing some reverse altruism would not change our main results.
7
saves for retirement. Finally in the last period of life the adult consumes his or her
savings plus interest, where the gross return is 1>R .10
The representative adult of generation 1−t maximizes household utility,
(1) ( ) 1312111 lnlnln,, ++++ ++= tRt
Wtt
Rt
Wt hcchccU ααα ,
subject to the following constraints:
(2) ( ) ( )tttWt eahsc −++=+ 11
(3) tRt Rsc =+1
(4) ( ) ttt ehHh =+1 .
The parameters ( ) 3,2,1,1,0 =∈ iiα assign different weights to consumption utility
during the working years, Wtc , consumption utility during old age, R
tc 1+ , and the utility the
parent derives from the child’s human capital, 1+th . This form of paternalistic altruism
implies that the parent cares about the child’s potential for success.11,12 We also impose
the restriction 1321 =++ ααα on the preference parameters. The last constraint facing
the household is the education technology. 13
The solution provides us with the following optimal linear expenditure system:
(5) [ ]ahc tWt ++= 11α
10 Savings in our model does not necessarily include (or exclude) financial assets in the form of stocks and bonds. In developing countries with weak, or possibly absent financial markets, savings will more than likely take on different forms. As an example, a father maintains his family land holdings by investing his and his child’s time, and then promises to bequeath this land to his son in exchange for income during retirement. 11 The paternalistic form altruism appears to have more empirical support than the non-paternalistic form, see Altonji, et al. (1997, 1992). This is the same form of altruism implicitly employed in Baland and Robinson (2000) since they restrict their analysis to a single generation. 12 This paternalistic specification of the utility function is similar to that of Galor and Zeira (1993), but instead of measuring parental utility as a function of bequests we measure parental utility as a function of the child’s human capital. Galor and Weil (1996) and Glomm (1997) employ similar modeling strstegies. 13 These constraints are consistent with either a linear technology (Hansson and Stuart, 1989; Baland and Robinson, 2000) or a small open economy framework.
8
(6) [ ]ahRc tRt ++=+ 121 α
(7) [ ]aha
e tt ++= 13α.
A household allocates a proportional amount of total potential income, aht ++1 , to
consumption in both periods of life, and the child’s education. In particular, equation (7)
demonstrates that there is a positive relationship between the child’s time spent receiving
an education and parental human capital. This implies that children in poorer households
will spend more time in the labor market.
The child’s time spent receiving an education, described in equation (7), and the
education technology, described in equation (4), combine to determine the dynamic
behavior of human capital across generations:
(8) ( ) ( )
aahhH
h ttt
++=+
131
α.
For analytical purposes, we assume ( )thH takes the form of a threshold step-function:
(9) ( )⎪⎩
⎪⎨⎧
≥
<=
η
η
t
tt hiffA
hiffhH
1
This non-linearity captures any potential differences in the education technology for
various levels of parental human capital, see Azariadis and Drazen (1990), and is
responsible for the existence of a Pareto improving policy, which we discuss shortly.
This exact specification is not necessary – any human capital function that generates an s-
shaped curve (i.e. that intersects the 45 degree line twice) will produce the same
relationship. In fact, simple convexity could also generate multiple equilibra since we
9
have a defined upper bound.14 In any case, the non-linearity in the return to education
appears to be empirically well founded (see, e.g., Hungerford and Salon, 1987; Moretti,
2004).
Combining the threshold function (9) and the dynamic human capital
accumulation function (8) results in the following first order difference equation on
opposite sides of the threshold η :
(10)
( )
( )⎪⎪⎩
⎪⎪⎨
⎧
≥++
<++
=+
tanyforhiffha
Aa
aA
tallforhiffhaa
a
h
tt
tt
t
ηαα
ηαα
33
33
1 1
1
.
The steady states for these equilibrium paths are:
(11)
( )
⎪⎩
⎪⎨
⎧
≥=
<−+
==
tanyforhiffAh
tallforhiffa
ah
h
tH
tT
η
ηα
α
3
3 1
.
To impose stability on the low equilibrium and generate positive child labor ( )1,0∈Te we
assume ( ) 33 1 αα −<+ aa , which also implies that a<3α . To ensure that child labor is
zero in the high-income equilibrium, 1=He via equation (4), we assume aA >3α .
These dynamics properties are shown in Figure 1. For the case where initial parental
human capital is below the threshold value, η<0h , the economy converges to the low
human capital equilibrium Th since 13 <aα . For the case where initial human capital is
above or equal to the threshold value, η≥0h , the economy converges to the high human
capital equilibrium AhH = . This follows from the assumption 13 >aAα , which implies
divergence, and the fact that human capital is bounded from above at 1>A . An economy
14 We thank Kaushik Basu for pointing out this alternative interpretation.
10
that follows this human capital trajectory will reach the upper bound in finite time and
remain there in perpetuity. The (dark) horizontal line in figure 1 at the value A represents
the continual mapping back to this upper bound once it is reached.
Based on these dynamics, along with the following assumption pertaining to the
location of the threshold,
Assumption 2.1: The threshold value lies in the interval [ ]HT hh ,∈η ,
we have two important propositions in our stylized economy without government.
Proposition 2.1: A country with an initial level of parental human capital below the
threshold value η monotonically converges to the low human capital equilibrium Th . A
country with an initial level of human capital above or equal to the threshold value η
monotonically converges to the high human capital equilibrium Hh .15
This proposition demonstrates that an initially poor country will remain poor and an
initially wealthy country will remain wealthy in our stylized economy.
Proposition 2.2: A country with an initial level of parental human capital below the
threshold value monotonically converges to the positive child labor equilibrium. A
country with an initial level of human capital above or equal to the threshold value η
monotonically converges to the no child labor equilibrium.
15 The formal proofs for all the propositions in the paper are in the appendix.
11
This proposition demonstrates that child labor will persist if parental human capital is too
low and will disappear over time if parental human capital is sufficiently high. Also note
that these dynamics do not depend on the standard under-investment in education
argument or coordination failure that typically relies on increasing social returns alone.
Poor households may fully internalize the human capital externality, but the missing
capital market and poverty causes them to optimally choose a lower level of education for
their children with positive child labor.
III. The Model with Government Intergenerational Transfers
Given that there are two possible steady states and dynamic paths an economy can
follow, the question then becomes: what, if anything, can the government do to move a
country trapped in poverty, with child labor, out of this trap? This section demonstrates
that a government can announce a social security program that will begin transferring
resources from next period’s working generation to next period’s retirees (or old), the
current workers.16 This announcement reduces the current working generation’s need to
save for retirement (e.g. Feldstein, 1974) by replicating the missing intergenerational
contracts market, thus freeing up lifetime resources for current consumption and the
child’s education. If this increase in lifetime wealth is large enough, the social security
program can generate a critical mass of human capital that allows the economy to escape
from the poverty trap.
16 There are many other policy mechanisms that could accomplish this same redistribution across generations, such as issuing vouchers (pieces of paper) to the current working generation redeemable next period, or announcing the future issuance of debt to redistribute resources next period. We focus on social security for expositional reasons and because it replicates any other lump-sum intergenerational transfer scheme in our current deterministic environment.
12
3.1. Escaping the Poverty Trap
The only role for government in our stylized economy is to introduce and manage
the social security program using lump-sum transfers and taxes to operate the system.
Thus, we abstract from government purchases and operation costs. We also assume that
at time 0=T the benevolent government announces a plan to start the pay-as-you-go
social security program next period and that the country of interest starts in the low
income-child labor steady state of Th . The representative household maximizes the same
utility function (1) subject to the following modified household budget constraints, which
include working period taxes tT along with social security transfers 1+tTR :
(2’) ( ) ( ) ttttWt Teahsc −−++=+ 11
(3’) 11 ++ += ttRt TRRsc
This results in an optimal linear expenditure system that includes intergenerational
redistribution:
(5’) ⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ −+++= +
tt
tWt T
RTR
ahc 11 1α
(6’) ⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ −+++= +
+ tt
tRt T
RTR
ahRc 121 1α
(7’) ⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ −+++= +
tt
tt TR
TRah
ae 13 1
α.
The only difference between this system of equations, and the system of equations
without the government, is that the household now allocates any net resources (or net
losses) the program generates toward consumption and the child’s education.
The human capital dynamics are also similar, with the following modifications.
13
(10’)
⎪⎪⎩
⎪⎪⎨
⎧
≥+⎥⎦⎤
⎢⎣⎡ −+
<+⎥⎦⎤
⎢⎣⎡ −+
=+
tanyforhiffha
ATR
Rra
aA
tallforhiffha
TRRra
ah
tt
tt
t
ηαα
ηαα
33
33
1
1
1.
The steady states for these equilibrium paths are:
(11’) ⎪⎩
⎪⎨
⎧
≥=
<⎥⎦⎤
⎢⎣⎡ −+
−=
=
tanyforhiffAh
tallforhiffTRRra
ah
h
tH
tT
η
ηα
α1
3
3
.
Equations (10’) and (11’) assume the tax and transfer program is constant across
generations, TTR = . We will justify this constant tax and transfer assumption shortly.
Also, the parameter 1−= Rr defines the net return on savings.
Before determining the size of the transfer necessary to move the economy out
poverty and to achieve the critical mass of human capital ( ) η=TRh1 , we must first
formally define the threshold value.
Assumption 3.1: Let the threshold value equal a weighted average of the two steady
states, ( ) HT hh θθη −+= 1 , where [ ]1,0∈θ .
Using this threshold value we have the following proposition.
Proposition 3.1: There exists an intergenerational transfer ∗TR sufficient to induce the
current working generation to invest enough resources in their child’s education to reach
the threshold value η using the pay-as-you-go social security program.
14
More formally, we can see this result by looking at the education choice made by
the initial generation benefiting from the government transfer program:
(12) ( ) ( )TR
Raaa
TRh
Th
3
3
31
1 αα
α+⎥
⎦
⎤⎢⎣
⎡−+
=43421
.
This equation shows that when 0=TR human capital is mapped directly back to the low
income-child labor equilibrium, and if 0>TR , this increases the child’s education and
human capital. If the promise of a social security transfer to the current working
generation is large enough to increase the child’s human capital, so that ( ) η=TRh1 , the
country can escape from poverty as shown in Figure 2.
To find the necessary size of the transfer we equate equation (12) with the
threshold defined in assumption 3.1, ( ) HT hh θθη −+= 1 , and solve for TR :
(13) ( )( )TH hhRaTR −−=∗ θα
13
.
The size of the necessary transfer is increasing in the productivity of the child, the less
weight a parent assigns to the child’s human capital, the closer the threshold value is to
the high income - no child labor steady state (the closer θ is to zero), and the interest
differential between private savings and the social security program (the return from
social security is zero because the population is constant).
3.2. Feasibility of the Social Security Program (Deterministic Case)
When can a government implement such a program? To answer this question we
consider the case where the government behaves benevolently towards its population and
uses the following policy or decision rule, which is consistent with a Rawlsian social
welfare function with an equal weight assigned to each generation.
15
The Government’s Policy Rule: (i) Choose the minimum intergenerational transfer
necessary to reach the threshold value η . (ii) Implement and maintain the
intergenerational transfer program only if no generation is made strictly worse off.
The first part of this policy rule supposes that the government chooses the
minimum intergenerational transfer necessary to reach the threshold value. This is
consistent with the benevolence assumption. A larger transfer would reduce lifetime
consumption for future generations, relative to what it could have been, because the net
return to savings 01 >−= Rr is greater than the net return from the social security
system under our constant population assumption. Also from equation (10’) and (11’) we
can see that anything smaller will eventually return the household to a lower level of
human capital and income in the poverty equilibrium due to the lower return on social
security. Thus, part (i) of the government’s policy rule determines a unique transfer ∗TR
defined in equation (13) and proposition 3.1. The second part of the policy rule (ii)
implies that the government will only implement the program if no generation is made
strictly worse off, consistent with our Rawlsian social welfare function assumption.
To determine the feasibility of a program under this policy rule we can look at
each generation sequentially. Obviously the initial generation is strictly better off since it
receives only transfers. The first generation to actually pay taxes, 1T , is next period’s
working generation. This generation also benefits from the program in two ways: First
they receive transfers during their retirement years offsetting some of the tax burden.
Second, they receive more education and a higher level of human capital, increasing their
16
earnings during their working years. The problem here is that this generation does not
benefit from the human capital externality. Finally, since all future generations benefit
from the human capital externality and face the same tax burden under the above policy
rule, the transfer program is feasible for all future generations if it is feasible for next
period’s working generation (formalized shortly). Thus, we can use next period’s
working generation as a benchmark to determine whether or not the program is feasible.
To determine whether the program’s benefits outweigh the costs for next period’s
working generation we look at the household’s savings decision,
(14) ( ) ( )( )( )
( )4434421
444 3444 21
TRgTRz
TRR
raTRhTRs ⎟
⎠⎞
⎜⎝⎛ +
−++= 2121
11
αα ,
where ( )TRh1 is defined in equation (12). The first part of this savings equation, ( )TRz ,
demonstrates that the transfer program increases human capital and the earnings capacity
for this generation (the benefit), and is shown in Figure 3. The second part of the savings
equation reduces savings because lifetime income falls by ( )TRRr , which is shown as
( )TRg in Figure 3. The trade-off between these two effects provides us with a sufficient
condition, which is observable by the government, and determines whether or not the
program is feasible.
Proposition 3.2: There exists a positive range of government transfers
[ ]max,0 TRTTR ∈= ∗∗ where the pay-as-you-go social security program is feasible under
the defined policy rule. This feasible range has a finite upper bound that equals
( )( ) 322
2max 1
1ααα
α−+
++=
raahRaTR T , which satisfies the sufficient condition 0)( max1 =TRs .
17
If maxTRTR >∗ the government does not implement the program. If maxTRTR ≤∗ then the
program is feasible and the government implements the program.
We now generalize this result and formally argue that if the policy is feasible for
next period’s working generation it is feasible for all future generations as well. This
implies that if maxTRTR ≤∗ the intergenerational transfer program can generate a Pareto
superior outcome in a deterministic environment.
Proposition 3.3: If the social security program is feasible, then the current working
generation and next period’s working generation are strictly better off under the pay-as-
you-go social security program. This implies that all future generations are strictly better
off as well. Thus, the social security program is Pareto superior to the no program
equilibrium and dynamics.
This result holds because human capital and earnings capacity are higher for all future
generations relative to next period’s working generation. Recall that future generations
also benefit directly from the externality in the education technology.
3.3. A Child’s Human Capital and Parental Savings: A Graphical Approach
Before turning to the issue of government credibility in an uncertain environment
we first translate our model into the following graphical representation. This approach
simplifies the analysis in the next section. The first order conditions from the household’s
optimization problem, with respect to savings ts and education te , are as follows:
18
(15) ( ) TRRsR
seahT +=
−−++ 0
2
00
1
11αα
(16) ( ) 0
3
00
1
11 eseaha
T
αα=
−−++.
Equation (15) equates the marginal utility loss from an increase in savings (decrease in
first period consumption) to the marginal utility gain from an increase in savings
(increase in consumption next period). Equation (15) also shows how an increase in
transfers reduces the marginal gain in utility from an additional unit of savings. This
reduces the household’s desire to save, freeing up resources for current consumption and
the child’s education. Equation (16) equates the marginal loss in utility from an increase
in the child’s education with the direct marginal benefit of more human capital.
After eliminating 0e from (15) using (16) we have:
(17) ( )
( ) ( )4342144 344 21
TRsfsg
T TRRsR
sah;
0
2
0
2
00
11
+=
−++− αα .
Figure 4 shows ( )0sg is an upward sloping function of the initial working generation’s
savings and ( )TRsf ;0 is a downward sloping function of the initial generation’s savings
for a given level of social security transfers. If 0=TR , the solution is identical to the no
government case where ( )ahs T ++= 120 α . Using equation (16), after solving for 0e as a
function of 0s , we can determine the level of human capital accumulation for next
period’s working generation following the announcement of the social security program.
If the government chooses an initial transfer of ∗TR savings will fall, as shown in
equation (17). This decrease in savings in response to ∗TR increases the human capital of
19
next period’s working generation so that ( ) η=∗TRh1 placing the economy in the high
income - no child labor equilibrium’s basin of attraction.
IV. Credibility and the Effectiveness of Government Policy
If this type of intergenerational redistribution program is feasible and can lead to a
Pareto superior outcome, then why don’t we observe its implementation around the world
in developing countries? One possible answer is that governments lack credibility. If
today’s working generation does not believe that the government will follow through on
this transfer program their response will be different than it would have been in a
deterministic environment. In other words, it is the perception of a dynamic policy that
alters an individual’s behavior not the policy itself. For our specific example, it is shown
that the mere perception of uncertainty, or lack of government credibility, can render the
Pareto improving government transfer program infeasible leaving the country in an
expectations trap that is self-fulfilling in nature.
4.1 Adding Uncertainty to the Stylized Economy
We assume the only generation uncertain about the implementation of the social
security program is the current working generation. If the government implements the
program, the policy continues forever under the government’s policy rule. If the program
is not feasible because of society’s shared expectations that the program is unlikely to be
implemented, then the government does not implement the program, thus, fulfilling the
households’ pessimistic expectations. In this case, the policy will never be implemented.
Society therefore learns whether or not the government will implement the program.
20
To demonstrate the potentially self-fulfilling nature of this transfer program, or
perhaps more appropriately the success of the program, we consider the following
modified problem that incorporates the household’s subjective beliefs. The household’s
objective function now takes the following form:
(1’) ( ) 1310201110 lnlnln,,~ hcEchccU RWRW ααα ++=
All of the parameters in the utility function are the same as in equation (1) except for the
addition of the expectations operator 0E . Households in the initial working generation
now form expectations over whether or not they believe the government will follow
through on their promise to implement the social security program. There are two
perceived possible states of nature. Households believe that the government will either
implement the program with probability q or will not implement the program with
probability q−1 . We summarize the households’ subjective probability distribution in
the following equation.
(18) ⎪⎩
⎪⎨⎧
=−
==
dimplementenotpolicyiifq
dimplementepolicyiifqi
1)(0π
We define the value [ ]1,0∈q as the level of confidence society has in its government. As
q gets smaller society has less faith in their government.
Since our model assumes that the government in power is benevolent and would
implement the Pareto improving social security program in a deterministic environment
we interpret uncertainty as follows. Households believe there are two possible
government types: The first type of government is the ‘true’ government, which is
currently in power, but households believe this government is power with probability q .
21
The second type of government is a ‘false’ government that will keep the tax revenue for
itself. Households believe this government type is in power with probability q−1 . It is
important to note that these are perceived probabilities not actual probabilities because
the benevolent government is already in power. Thus, implicit in the model’s
construction is an informational asymmetry between the government and the households.
Given that households believe there is a positive probability that the government
will not implement the program, the next step is to demonstrate that these beliefs can in
fact become self-fulfilling. To formally demonstrate this result we use the first order
conditions for savings and education, respectively, in the presence of uncertainty:
(19) ( )( )
0
2
0
2
00
1 111 s
qTRRsqR
seahT
−+
+=
−−++ααα
(20) ( ) 0
3
0
1
11 eseaha
T
αα=
−−++.
Note that equation (20) is identical to equation (16), and equation (19) is identical to
equation (15), if the household believes the government will implement the program with
certainty, 1=q . Also, when 0=q , equation (19) captures the deterministic case without
transfers. This demonstrates that when society does not believe their government at all,
the outcome is the same as having no policy at all. These two extreme cases nest all other
possible scenarios, where ( )1,0∈q .
We once again we represent this dynamic system graphically in Figure 5.
(21) ( )
( )
( )
( )444 3444 2144 344 21
qTRsfsg
T sq
TRRsqR
sah,,
0
2
0
2
0
2
010
11
1 −+
+=
−++− ααα
(22) ( )( ) ( ) 0
2
3
2
3001 11
1)( s
aaah
seh T
αα
αα
−−
−++
==
22
The left-hand side of equation (21) is identical to equation (17), where ( )0sg is an
upward sloping function of savings. The right-hand side nests the two cases discussed
above. First, when 0=q government policy is completely ineffective regardless of the
size of the social security transfer payment and we have ( )0,,01∗TRsf . Second, under
certainty when 1=q , the necessary transfer ∗TR is sufficient to reach the threshold value
η by assumption. This deterministic transfer scheme also pins down the savings ∗0s
necessary to achieve the critical mass of education and the child’s human capital via (22).
Graphically, this case is represented by ( )1,,01∗∗ TRsf .
From the lower figure in Figure 5 we see that for ( )0,,01∗TRsf the human capital
accumulation equation maps directly back to the low income - child labor steady state.
For the case when ( )1,,01∗∗ TRsf , the country crosses the threshold η and falls into the
high income - no child labor equilibrium’s basin of attraction and converges to Hh . In
Figure 5 we also show an intermediate case when the probability ( )1,0∈q . In this case,
the level of confidence society has in their government is not complete and shows how
the size of the transfer ∗> TRTR A must increase as q falls to reach the threshold. This
discussion yields the following proposition:
Proposition 4.1: There exists a minimum level of confidence in government minq where
the pay-as-you-go social security program is no longer feasible if minqq < .
23
We demonstrate this argument graphically in Figure 6. From equation (21) we know
that as the level of confidence in the government falls, the necessary size of the transfer
increases at an increasing rate, and approaches infinity as the level of confidence
approaches zero. From proposition 3.2 we know there exists a finite maximum transfer,
maxTR . This implies that there exists a minimum level of confidence, minq , at which
point the necessary size of the transfer is just feasible, or maxTRTR N = . Below minq the
policy is no longer feasible under the policy rule. We can also see this result implicitly in
Figure 5. As q gets smaller, ( )qTRsf ,,01∗∗ moves closer to ( )0,,01
∗TRsf , which implies
that transfers must increase by larger and larger amounts to reach the critical mass of
education that allows the child’s human capital to reach η .
Proposition 4.1 formally demonstrates the main point of the paper. If society’s
level of confidence in their government is so low that they do not believe that their
government will implement the social security program the benevolent government does
not implement the program. This is true even if the government could have, and would
have, implemented the program if q were greater than minq . In other words, even if the
social security program is feasible in a Pareto sense and the government policy could
eliminate the ‘bad’ equilibrium or poverty trap in the deterministic environment, it is no
longer feasible when minqq < . This formally defines what we refer to as an expectations
trap. The mere fact that households do not believe that their government will follow
through on the policy promise is sufficient to ensure that the government does not follow
through on the policy promise, thus fulfilling the households’ pessimistic expectations.
This suggests that the households’ subjective beliefs can also serve as an equilibrium
selection mechanism in the presence of uncertainty in a dynamic environment.
24
4.2 Empirical Evidence
The empirical evidence of the effectiveness of transfer programs in reducing child
labor and increasing schooling is still being received, but early studies suggest that these
programs are less effective at reducing child labor than they are at increasing schooling.
Unconditional cash transfer programs have been found to have relatively small marginal
effects on both child labor and school enrollment (e.g. Behrman and Knowles, 1999;
Nielsen, 1998). This could be the result of uncertainty surrounding future transfers. If the
adult of the household perceives this as a temporary transfer the permanent income
hypothesis comes into play. Ravallion and Wodon (2000) find that a food-for-education
program in Bangladesh did indeed increase schooling among the participants, but the
concomitant reduction in child labor was quite small. Bourguignon, et al. (2002), in their
study of the Bolsa Escola educational subsidy program in Brazil, find similar results.
Skoufias and Parker (2001), however, find that the conditional transfer program,
PROGRESA, in Mexico showed significant effects on both school enrollment and child
labor. In this case perhaps the transfer programs were perceived as permanent and the
household responded accordingly.
Although the policies above are not identical in practice, the general idea carries
through. Even if countries implement identical policies, these programs may succeed in
some countries and fail in others as a result of government credibility. For policy design
this implies that only after the transfer program is implemented in a particular country
will we be able to determine whether or not the program is successful. Ex-ante analysis
from past policy successes or failures in different countries may not be appropriate for
determining a policy’s effectiveness for a particular country of interest.
25
V. Interpreting Uncertainty and Extensions
The expectations trap argument demonstrates that policy design and analysis for a
deterministic environment may be misleading if government’s lack credibility. By
assuming households form expectations over the future of the government’s policies, we
have demonstrated that these expectations can actually cause a Pareto improving policy
to fail, even if the government intends to follow through on their promises. This implies
that uncertainty can remove Pareto improving polices from a benevolent government’s
choice set. If the government is not truly benevolent then this can only exacerbate the
problem.
The key to this argument is that if households have a shared expectation that the
government will not follow through on their policy promise, that is, the government lacks
credibility, then households undertake actions that render the policy infeasible. In other
words, the mere fact that households do not believe that the government will implement
the Pareto improving policy with certainty can eliminate this policy from the benevolent
government’s choice set, thus fulfilling the households’ pessimistic subjective beliefs.
This modeling strategy, where subjective beliefs and expectations can in fact be
self-fulfilling, has been employed in a vast and diverse literature (see, e.g., early papers
by Azariadis,1981; and Cass and Shell, 1983; and more recent papers by Weil, 1987; and
Cole and Kehoe, 2000). In development, this strategy has similarly been used by Engel
and Kletzer (1991) and Rodrik (1989, 1991). Although these development papers do not
address the existence of a self-fulfilling expectations trap and the elimination of Pareto
26
improving policies from a benevolent government’s choice set as a result of society’s
subjective beliefs, the basic modeling of perceived uncertainty is the same.
One question remains: can an objective probability distribution develop over the
government’s type? This is another possible interpretation not highlighted in the current
paper.17 Suppose there are two competing factions within an incoming government: a
benevolent government faction with a Rawlsian social welfare function and a selfish
government faction that plans to keep any tax revenue for itself. The ex-ante (and known)
probability distribution is such that the benevolent faction of the government takes
control of policy with probability q and the selfish faction of the government takes
control of policy with probability q−1 . Next, suppose that the benevolent government
takes control of policy design and that this result is unobservable to the households in the
private sector. As a result of this asymmetric information, the perception of uncertainty
remains (the government type is no longer random). Ex-post, households still perceive
that the benevolent government (the “true” government) is in power with probability q ,
and that the selfish government (the “false” government) is in power with probability
q−1 .18 Although we do not formally use a game theoretic setting, given the objective of
the paper, we can still think of “nature” as selecting the type of government from the
following ex-ante objective probability distribution { }qq −1, .
However uncertainty is motivated, it is natural to wonder whether the benevolent
government can signal its type. Given the heterogeneous nature of the problem
(overlapping generations), we can no longer simply assume that the social welfare
17 Here the appropriate ex-ante interpretation is risk rather than uncertainty (by definition uncertainty implies that the agent’s beliefs are subjective). 18 This modeling strategy dates back to Harsanyi (1967).
27
function coincides with a representative agent’s utility function since the agents in this
type of stylized economy are alive at different points in time. Therefore, as already
mentioned, we motivate the government’s optimal behavior with a Rawlsian social
welfare function where each generation receives an equal weight. This implies that costly
policy signals will not be implemented by the benevolent government. In other words, if
any generation is made worse off by a particular “policy signal” that can identify the true
government type, then this policy signal is not available to the government. Thus, the
only type of policy signal that the benevolent government could possibly send would
have to be Pareto improving itself. In addition, if this policy has a dynamic component,
not only does the policy signal have to be Pareto improving for all generations, but it
must be immediate in nature. Whether or not a policy signal of this type exists is an
important question, but beyond the scope of this paper and is left for future research.
VI. Conclusion
This paper develops a model of child labor in a dynamic, general equilibrium,
setting. It is shown that lack of access to capital markets gives rise to a Pareto inferior
outcome that is characterized by the presence of child labor and a low level of human
capital. When a pay-as-you-go social security program is introduced in a deterministic
environment, it is shown that this type of intergenerational transfer program can move the
economy out of this inferior equilibrium by allowing families to redirect household
income, they would otherwise have saved for old age or consumed in the current period,
towards the education of their children.
28
It is also shown that the effectiveness of the intergenerational transfer program
relies critically on its ability to change the behavior of households through their
expectations. If there is uncertainty surrounding the government’s intention to follow
through on the program, we demonstrate that households may not change their behavior
sufficiently to move the economy from the ‘bad’ equilibrium with child labor to the
Pareto superior or ‘good’ equilibrium with no child labor leaving the country in an
expectations trap. This demonstrates that confidence in, and the trust of the government
is potentially a key element in effective policy design.
29
Appendix: proofs
Proof of Proposition 2.1: Using the parameter restriction ( ) 33 1 αα −<+ aa , which implies a<3α , along with equation
(10) produces a monotone sequence { }∞=0iih converging to low equilibrium Th . Using the
parameter restriction aA >3α implies 13 >a
Aα. Combining this result along with equation
(10) produces a monotone sequence { }∞=0iih converging to AhH = and 1=He via equation (4), the upper bound. ■ Proof of Proposition 2.2:
The parameter restriction ( ) 33 1 αα −<+ aa implies a
a+
<23α . This last condition implies
that ( )
11
3
3 <−+
=α
αa
aeT and 01 >− Te , positive child labor, in the low human capital steady
state. The restriction aA >3α implies that 1=He given AhH = in the high human capital steady state. The dynamics follow directly from proposition 2.1. ■ Proof of Proposition 3.1: By (A3.1) and equation (12) the government chooses the unique transfer that satisfies
η=)(1 TRh . Existence follows directly from (12) given that η is a constant and greater than zero by assumption, and ( ) 01 >′ TRh with ( ) 001 >h . ■ Proof of Proposition 3.2: Next period’s working generation, the first generation to pay taxes, savings equation is
( ) ( )( ) TRR
raTRhTRs ⎟
⎠⎞
⎜⎝⎛ +
−++= 2121
11
αα . Feasibility under the government’s policy rule
states that savings must remain positive ( ) TRR
rTR
aahT ⎟
⎠⎞
⎜⎝⎛ +
≥+++ 2322
11
αααα and that
ra>3α . This implies that there exists a unique maximum ( )
( ) 01
1
322
2max >
−+++
=ααα
αra
ahRaTR T
given ( )r232 1 ααα +< . ■ Proof of Proposition 3.3: First we assume that [ ]max,0 TRTR ∈∗ . Trivially, the current working generation is strictly better
off because they receive only transfers. Given that ∗TR is feasible, Thhh => 01 , and using the
government’s budget constraint ∗∗ = TTR , next period’s working generation is strictly better off
under the assumption that ar>3α because ⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ −
+++= ∗TRR
arahc T
W 311 1
αα ,
30
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ −
+++= ∗TRR
arahRc T
R 321 1
αα , and ( ) 01 ≥∗TRs . This implies all future generations
are also strictly better because the sequence of human capital satisfies the condition 011 hhhh tt >>>>+ L converging to the upper bound A . Also note, since the non-negativity
constraint is non-binding for 1h then it is non-binding for th when 1>t because ∗TR is constant. ■ Proof of Proposition 4.1: From equation (22) we have )( 001
∗∗ == sehη . Using this result, along with equation (21), we can pin down the necessary size of the transfer with uncertainty
( ) ( )∗∗∗
−+
+=
−++−
0
2
0
2
0
2 11
1s
qTRRsqR
sah NT
ααα for a given q . By the implicit function theorem,
after totally differentiating equation (21) with respect to NTR and q , we find
( )⎥⎦
⎤⎢⎣
⎡ +−=
∗
RqTRTRRs
dqdTR NNN
0 . In the limit as 0→q we have −∞→dq
dTR N
which implies
∞→NTR as 0→q given 0>∗TR when 1=q . From (P3.2) we know there exists a ∞<< max0 TR . This implies there must be some value minq satisfying
( ) ( )0
min2
max0
min2
0
2 11
1s
qTRsq
sahT
−+
+=
−++− ααα
with ( )1,0min ∈q . Below minq we have
maxTRTR N > , thus the policy is no longer feasible under the policy rule. ■
31
References Albanesi, Stefania, V.V. Chari, and Lawrence Christiano. (2003) “Expectation Traps and
Monetary Policy,” Review of Economic Studies, 70:4, pp. 715-741.
Altonji, Joseph G., Fumio Hayashi and Laurence J. Kotlikoff. (1997) “Parental Altruism
and Inter Vivos Transfers: Theory and Evidence,” Journal of Political Economy,
105:6, pp. 1121-66.
Altonji, Joseph G., Fumio Hayashi and Laurence J. Kotlikoff. (1992) “Is the Extended
Family Altruistically Linked? Direct Tests Using Micro Data,” American
Economic Review, 82:5, pp. 1177-98.
Azariadis, Costas. (1981) “Self-Fulfilling Prophecies,” Journal of Economic Theory, 25,
pp. 380-396.
Azariadis, Costas and Allan Drazen. (1990) “Threshold Externalities in Economic
Development,” Quarterly Journal of Economics, 105:2, pp. 501-526.
Baland, Jean-Marie, and James A. Robinson. (2000) “Is Child Labor Inefficient?”
Journal of Political Economy, 108:4, pp. 663-679.
Basu, Kaushik. (1999) “Child Labor: Cause, Consequence, and Cure,” Journal of
Economic Literature, 37:3, pp.1083-1119.
Basu, Kaushik, and Pham Hoang Van. (1998) “The Economics of Child Labor,”
American Economic Review, 88:3, pp. 412-427.
Basu, Kaushik, and Zafiris Tzannatos. (2003) “The Global Child Labor Problem: What
Do We Know and What Can We Do?” World Bank Economic Review, 17, pp.
147-173.
Becker, Gary and Kevin Murphy. (1988) “The Family and the State,” Journal of Law and
Economics, pp. 1-18.
Behrman, Jere, and John C. Knowles. (1999) “Household Income and Child
Schooling in Vietnam,” World Bank Economic Review 13:2, pp. 211–56.
Bell, Clive, and Hans Gersbach. (2001) “Child Labor and the Education of a Society.”
IZA Discussion Paper No 338.
Bourguignon, François, Francisco H. G. Ferreira, and Phillippe G. Leite. (2002) “Ex-
Ante Evaluation of Conditional Cash Transfer Programs: The Case of Bolsa
Escola,” mimeo, Pontifica Universidade Católica do Rio de Janeiro.
32
Calvo, Guillermo. (1978) “On the Time-Consistency of Optimal Policy in a Monetary
Economy,” Econometrica 46, pp. 1411-1428.
Cass, David and Karl Shell. (1983) “Do Sunspots Matter,” Journal of Political Economy,
91, pp. 193-227.
Chari, V.V., Lawrence Christiano, and Martin Eichenbaum. (1998) “Expectation Traps
and Discretion,” Journal of Economic Theory, 81:2, pp. 462-492.
Cole, Harold L., and Timothy J. Kehoe. (2000) “Self-Fulfilling Debt Crises,” Review of
Economic Studies, 67:1, pp. 91-116.
Emerson, Patrick M., and André Portela Souza. (2003) “Is there a Child Labor Trap?
Inter-Generational Persistence of Child Labor in Brazil,” Economic Development
and Cultural Change, 51:2, pp. 375 - 398.
Engel, Charles and Kenneth M. Kletzer (1991). “Trade Policy under Endogenous
Credibility,” Journal of Development Economics, 36, pp. 213-228.
Farmer, Roger. (1999) The Economics of Self-Fulfilling Prophecies, second edition. MIT
Press, Cambridge, MA.
Feldstein, Martin. (1974) “Social Security, Induced Retirement, and Aggregate Capital
Accumulation,” Journal of Political Economy, 82, pp. 905-926.
Fischer, Stanley. (1980) “Dynamic Inconsistency, Cooperation, and the Benevolent
Dissembling Government,” Journal of Economic Dynamics and Control, 2, pp.
93-107.
Galor, Oded, and David N. Weil. (1996) “The Gender Gap, Fertility and Growth,” The
American Economic Review, 86:3, pp. 374-387.
Galor, Oded , and Joseph Zeira. (1993) “Income Distribution and Macroeconomics,”
Review of Economic Studies, 60:1, pp. 35-52.
Glomm, Gerhard. (1997) “Parental Choice of Human Capital Investment,” Journal of
Development Economics, 53:1, pp. 99-114.
Grootaert, Christiaan, and Ravi Kanbur. (1995) “Child Labor: An Economic
Perspective,” International Labour Review, 134:2, pp. 187-203.
Hansson, Ingemar and Charles Stuart. (1989) “Social Security as Trade among Living
Generations,” American Economic Review, 79:5, pp. 1182-1195.
33
Harsanyi, John. (1967) “Games with Incomplete Information Played by Bayesian Players
Parts I, II, and III,” Management Science, 14, pp. 159-182, 320-334, 484-502.
Hazan, Moshe, and Binyamin Berdugo. (2002) “Child Labor, Fertility and Economic
Growth,” The Economic Journal, 112, pp. 810-828.
Hungerford, Thomas, and Gary Salon. (1987) “Sheepskin Effects in the Returns to
Education,” Review of Economics and Statistics, 69:1, pp. 175-177.
International Labour Organization. (2002) Every Child Counts: New Global Estimates on
Child Labour. (Geneva: International Labour Office).
Jafarey, Saqib, and Sajal Lahiri. (2002) “Will Trade Sanctions Reduce Child Labour?
The Role of Credit Markets,” Journal of Development Economics, 68:1, pp. 137-
156.
Kydland, Finn E., and Edward C. Prescott. (1977) “Rules Rather than Discretion: The
Inconsistency of Optimal Plans,” Journal of Political Economy, 85:3, pp. 437-
491.
Kruse, Douglas L., and Douglas Mahony. (2000) “Illegal Child Labor in the United
States: Prevalence and Characteristics,” Industrial and Labor Relations
Review, 54:1, pp. 17 - 40.
Lopez-Calva, Luis Felipe, and Koji Miyamoto. (2004) “Filial Obligations and Child
Labor,” Review of Development Economics, 8:3, pp. 489-504.
Moretti, Enrico. (2004) “Estimating the Social Return to Higher Education: Evidence
from Longitudinal and Repeated Cross-Sectional Data,” Journal of Econometrics,
121, pp. 175-212.
Nielsen, Helena Skyt. (1998) “Child Labor and School Attendance: Two Joint
Decisions.” Working Paper 98-15. Aarhus, Denmark: Center for Labor Market
and Social Research and the University of Aarhus School of Business.
Ranjan, Priya. (2001) “Credit Constraints and the Phenomenon of Child Labor,” Journal
of Development Economics, 64:1, pp. 81-102.
Ravallion, Martin, and Quentin Wodon. (2000) “Does Child Labour Displace Schooling?
Evidence on Behavioral Responses to an Enrollment Subsidy,” The Economic
Journal, 110:462, pp. C158 - C175.
34
Rodrik, Dani. (1991) “Policy Uncertainty and Private Investment in Developing
Countries,” Journal of Development Economics, 36, pp. 229-242.
Rodrik, Dani. (1989) “Promises, Promises: Credible Policy Reform via Signaling,” The
Economic Journal, 99:397, pp. 756-772.
Skoufias, Emmanuel, and Susan W. Parker. (2001) “Conditional Cash Transfers and
Their Impact on Child Work and Schooling: Evidence from the PROGRESA
Program in Mexico,” Economía, 2:1, pp. 45 – 96.
Weil, Philippe. (1987) “Confidence and the Real Value of Money in an Overlapping
Generations Economy,” Quarterly Journal of Economics, 102:1, pp. 1-22.
Wahba, Jackie. (2002) “The Influence of Market Wages and Parental History on Child
Labor and Schooling in Egypt,” mimeo: University of Southampton.
45o
A
ht
ht+1
tth
a
A
a
aAh
33
1
)1( ���
��
�
tth
aa
ah
33
1
)1( ���
��
�
Th
Figure 1: Human Capital Dynamics in a Deterministic Setting
�H
h
(upper bound)A
TR
TR
h(TR)
TR*
TR*TR
max
TR*
TR*
)1(2 ahT
���
322
2
)1(
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�
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ra
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Figure 3: Feasible and Infeasible Transfers
FeasibleNotFeasible
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�
TRa
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32
2 )1()(
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31
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Figure 4: The Effect of Transfers on Savings
�
s0
Ts
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)( 0sg
);( 0 TRsf
)0*,;( 0 �qTRsf
)1*,;( 0 �qTRsf
)( 0sg
Figure 5: The Effect of Transfers on Savings with Uncertianty
s '0
h <1
TR >TR*A
TR >TR*A
))1,0(*,;( 0 �qTRsf
TR>TR*
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