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

343231

3

xxx

X with 1,03 kx

111

,110

,101

,011

,100

,010

,001

,000

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

00

,01

,10

,11

1312

1 xxRanked

00

,01

,11

,10

2321

2 xxRanked

343231

3

xxx

Ranked

01

,00

,11

,10

4543

4 xxRanked

0,1545 xRanked

000

,010

,001

,011

,111

,100

,110

,101

Round 1 Round 2 Round 3 HH1: 2 No 2 No

3 Match 3 Match destablishe

10*

1X

HH2: 3 No 3 Match

10*

2X

HH3: 1 Match 1 Match

4 No 2 Match

011

*3X

HH4: 5 Match

10*

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

Basic simulation illustration

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

Different patterns for an autarkically mobile household

a a

a a

Different patterns for a household autarkically mobile given its S0

b b

b b

Different patterns for a household whose mobility depends on social links

c c

c c

Different patterns for a destitute, economically immobile household

ci ci

ci ci

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.

Targeted transfers and “crowding in” possibilities due to network endogeneity

hf

e fh

e

Targeted transfers and “crowding in” effect

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)

Thank you for your attention

Comments are greatly appreciated