social network capital, economic mobility and poverty traps sommarat chantarat and chris barrett...
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Social Network Capital, Economic Mobility and Poverty Traps
Sommarat Chantarat and Chris BarrettCornell University
Seminar at Watson Institute, Brown University
October 13, 2010
Motivation: builds on two literatures 1. Poverty Traps
Do households face multiple equilibria, one of them associated with low well-being? If so what can be done, and how, to help poor households escape poverty traps?
Literature increasingly based on the study of intertemporal asset accumulation
Most poverty traps depend on financial market failures that impede investment in productive assets or technologies
(Loury 1981, Banerjee and Newman 1993, Galor and Zeira 1993, Mookherjee and Ray 2002-3, Carter and Barrett 2006, etc.)
Motivation: builds on two literatures2. Social Economics of Poverty
Multiple pathways of socially mediated growth Facilitate productivity growth and technological adoption
(Foster and Rosenzweig 1995, Conley and Udry 2010, Moser and Barrett 2006) Enhance access to (informal) finance and insurance
(Townsend 1994, Fafchamps and Lund 2003) Market intelligence, contract enforcement, etc.
(Fafchamps 1996, Fafchamps and Minten 2002)
Existence of exclusionary mechanisms that prevent some individuals from such socially mediated growth (Voluntary) social isolation or (involuntary) social exclusion from social
networks that otherwise can facilitate growth
(Carter and May 2001, Adato et at. 2006, Santos and Barrett 2006, etc.)
Most literature treats social networks as exogenous to one’s choices
Contribution of this paper
We provide a theoretical foundation of the mechanisms by which endogenous social network capital can facilitate or impede the poor’s escape from persistent poverty by…
Including “social network capital” as another productive asset that households can accumulate (by forming a network of social links) and use to enable intertemporal productivity growth
Treating each mutually consensual link as the result of individuals’ cost-benefit calculus with respect to prospective links with others, depending on social distance and the economy’s observable wealth distribution
Modeling endogenous network formation in the presence of financial market failures and a non-convex production technology set that generates multiple equilibria of long-run well being
Key Findings
Social network capital can either substitute for or complement real capital in facilitating escape from poverty depending on the poor’s initial capital endowment
Heterogeneous patterns of economic mobility can arise: (1) exit poverty without using social network, (2) exit poverty using social network capital, (3) social exclusion, (4) social isolation
A household’s welfare dynamics depend not only on its own initial endowment, but on the economy’s initial wealth distribution as well
Crowding-in transfers through endogenous social networks become possible in this setting
The Model: Assumptions
There are n heterogeneous households in this small agrarian economy: N = (1,2,…,n)
Each lives for two periods: t = 0,1
Each is born with two endowments: (A0 ,S0) Productive assets: A0
Social network capital: S0
Identical preferences
Absence of financial markets
Identical production technology set
The Model: Production technology
Two available production techniques at any period t:
High-return production requires fixed cost of :
Low-return production:
Assume: for , Inada and standard
concavity conditions are satisfied
Household i’s aggregate production function at any period t:
0tSF
MaxYit [ Lit
Hit YY , ] = Max [ )( ititH SFAf , itL Af ]
)( ttHH
t SFAfY with 0tSF , 01 tSF and 0F
tLL
t AfY
0tNA , 0'' iLtH NAfNAf
The Model: Production technology
This production technology set is non-convex and exhibits locally increasing return in the neighborhood of s.t.
ttt SAY , ttH SFAf
tSF tA tSA
tL Af
is the asset
threshold beyond
which a household
will optimally switch
to the high-return
production
The Model: Production technology
Social network capital reduces the productive asset stock necessary to make the high-return technology optimal
Value of social network capital will vary across households with heterogeneous endowment of productive assets
ttt SAY ,
ttH SFAf
tL Af
tA tSF 'tSA
'ttH SFAf
When acquiring
more social network
capital ,
and so
tt SS
tt SFSF '
tt SASA '
The Model: Household’s unilateral dynamic welfare maximization problem
Household i maximizes
Period 0: household allocates income Y(Ai0 , Si0) among Consumption: Ci0
Investment in A: Ii0 (unilateral choice)
Investment in S: Xi0 (bilateral choice) which costs
Period 1: individual consumes all income
He will consume Ci1 from all income Y(Ai1 , Si1)
Subsistence consumption constraint:
and
For any desired network , household i can derive the corresponding indirect utility by solving:
The Model: Household’s unilateral dynamic welfare maximization problem
subject to:
Endogenous network formation
Who in the economy will hh consider for a prospective link?
Consider those within the feasible social distance for interaction
How to choose with whom to link?
Complementarities and interdependence of links decisions Choose among possible networks of links rather than individual links
Intertemporal benefit-cost calculus of social links Rank all feasible networks based on the corresponding indirect utilities
Mutual consent requirement and equilibrium of social network Non-cooperative extensive form game with perfect information
Endogenous network formation1. Social distance, cost and benefit
Social distance between i and j:
Total costs to establish a network Xi0 is where Cost to i to establish a link with j:
Total benefits from an established network Xi0 is where Benefit to i from an established link with j:
Endogenous network formation 2. Social network structure
For a household i Denote binary link between i and j: ij
Household i’s network:
where
Set of i’s all possible network: Ωi
From the example: with
Consider an economy with N=(1,2,3,4,5) and 9d
34
32
31
3
x
x
x
X with 1,03 kx
1
1
1
,
1
1
0
,
1
0
1
,
0
1
1
,
1
0
0
,
0
1
0
,
0
0
1
,
0
0
0
3
9d
Endogenous network formation 3. Linking game with perfect information
Households form a ranking of networks based on their indirect utility.
Mutual consent requirement impedes use of off-the-shelf solutions . Need to use a noncooperative, extensive form game with a link formation protocol.
Players use their network ranking as
best response functions
Consider an economy with N=(1,2,3,4,5) and 9d
0
0,
0
1,
1
0,
1
1
13
121 x
xRanked
0
0,
0
1,
1
1,
1
0
23
212 x
xRanked
34
3231
3
x
xx
Ranked
0
1,
0
0,
1
1,
1
0
45
434 x
xRanked
0,1545 xRanked
0
0
0
,
0
1
0
,
0
0
1
,
0
1
1
,
1
1
1
,
1
0
0
,
1
1
0
,
1
0
1
Round 1 Round 2 Round 3 HH1: 2 No 2 No
3 Match 3 Match destablishe
1
0*1X
HH2: 3 No 3 Match
1
0*2X
HH3: 1 Match 1 Match
4 No 2 Match
0
1
1*3X
HH4: 5 Match
1
0*4X
HH5: 4 Match 1*
5 X
Endogenous network formation
Endogenous network formation 3. Linking game with perfect information
The benchmark case: no social network S0 = 0 and X0 = 0
A static asset poverty line exists at the asset threshold that defines the technology choice, distinguishing current poor and non-poor.
The dynamics – in particular the autarkic savings options – suggests the
existence of a dynamic asset poverty line such that the initially
poor with will save and escape poverty eventually
will be trapped in long-term poverty
Each household’s initial endowment of productive assets thus
determines its long-term well-being
*0A
*00 AAA i
*00 AAi
A
The possibilities of social network capital (S0 ≥ 0 and X0)
The static asset poverty line is now set at the general asset threshold
Social network capital reduces the assets needed to be non-poor.
A dynamic asset poverty line now depends not only on initial
endowments (Ai0 ,Si0) but also on the poor’s opportunity to establish a
productive social network, Xi0
A dynamic asset threshold exists. The initial poor
with escape poverty w/o needing new social
links
must form new networks to escape
0iSA such that Hf [ )( 00 ii SFSA ] = Lf [ 0iSA ]
0000*0 0/ iiii SAAXSA
000*00 0/ iiii SAXSAA
0/ 00*0 ii XSA
The initially poor who failed to meet (either because of inadequate endowment (Ai0 ,Si0) or there is no feasible productive network Xi0), will never consider establishing a network with others as
For them, social networks do not provide a viable escape from
persistent poverty.
They self-select out of social networks: “social isolation”
00*0 iHi XC
0*
0* 0 iiLiiL XUXU
, 00 iX
The limitations of social network capital (S0 ≥ 0 and X0)
Four patterns of social network-mediated economic mobility and immobility among initial poor
Households who escape from poverty without forming social networks:
Households who form social networks and escape from poverty
(using social network capital to either substitute for or complement to own assets)
Households involuntarily excluded from networks and trapped in poverty
Households who choose social isolation and remain trapped in poverty
0*0 iX and *
0**
iiHi XUU
0*0 iX and 0*
0** iiHi XUU ( either 00
*0
* iiHiiH XUXU
, 00 iiX
or he failed to establish 00ˆ
iiX such that 0ˆ0
*0
* iiHiiH XUXU
0*0 iX , 0*
0** iiLi XUU and 00
~iiX such that 0
~0
*0 iHi XC but no such
network arises in equilibrium
0*0 iX , 0*
0** iiLi XUU and 00
*0 iHi XC
� for all 00 iiX
� and so
. 0*0 iX is their top-ranked network choice in Ranked
i0
Initially poor
*0A
0/ 00*0 XSA
0SA
Never poor
A
B
C
D
Patterns of social network-mediated economic mobility and immobility
For the initial poor ( )
In A ( ), social network capital substitutes for own capital
In B and C ( ), social network capital complements own capital• Those in A and B are
endowed with enough that they are independently mobile
• Those in C need to accumulate more social network capital by forming new social networks
00*0 ii SAAA
*00 AAi
00 ii SAA
Network endogeneity, socio-economic structure and socially-mediated growth
- Greater wealth dispersion limits social links and thus socially mediated growth, trapping more people in poverty.
- But polarization can enable solidarity groupings and mobility.
Conclusions
Social network capital can facilitate escape from poverty by complementing own capital for those who lack sufficient assets or substituting and thus conserving scarce resources for those who would escape otherwise
But because social links are costly to establish and require mutual consent, there will commonly be social isolation and exclusion in the equilibrium
The equilibrium social network arrangements and the resulting well-being dynamics depend fundamentally on initial wealth distribution in the economy, not just on household endowments (but also on their social distance from others)
Implications
Empirical work establishing correlation between well-being dynamics and measures of social embeddedness typically seeks just one of these types of relations … highly context-specific
Work that finds no correlation can be an artifact of widespread social exclusion and social isolation
Crowding-in transfers are possible through endogenous network, in contrast to the widely claims of crowding-out effects (which typically treat social network as exogenous)
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