Social Network Capital, Economic Mobility and Poverty Traps Sommarat Chantarat and Chris Barrett Cornell University May 3, 2007 Seminar Ohio State University

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 state variable (assets) accumulation overtime Most poverty traps depend on the existence of financial market failures that impede investment in productive assets or technologies Loury 1981, Banerjee and Newman 1993, Galor and Zeira 1993, Mookherjee and Ray , Carter and Barrett 2006, etc.)

Motivation: builds on two literatures 2. Social Economics of Poverty Multiple pathways of socially mediated growth Facilitate productivity growth and technological adoption (Foster and Rosenzweig 1995, Conley and Udry 2002, Moser and Barrett 2006) Enhance access to (informal) finance and insurance (Townsend 1994, Fafchamps and Lund) Market intelligence, contract enforcement, etc. (Fafchamps 1996, Fafchamps and Minten 2002) Existence of exclusionary mechanisms that prevent some individuals from such socially mediated growth Social isolation (voluntarily) or social exclusion (involuntarily) of some poor with certain identities from social networks that otherwise can facilitate growth (Carter and May 2001, Adato et at. 2006, Santos and Barrett 2006, etc.) Most literatures 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 Points 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 may depend not only on its initial endowment, but on the economy’s initial wealth distribution as well Crowding-in transfers through endogenous social networks are possible in this setting

Outline of the talk The model The optimal social network structure Households’ equilibria and patterns of mobility The simulations Conclusions

The Model

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: (A 0,S 0 ) Productive assets: A 0 Social network capital: S 0 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 are satisfied Household i’s aggregate production function at any period t:

The Model: Production technology This production technology set is non-convex and exhibits locally increasing return in the neighborhood of s.t. 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 When acquiring more social network capital, and so

The Model: Household’s unilateral dynamic welfare maximization problem Household i maximizes Period 0: household allocates income Y(A i0, S i0 ) among Consumption: C i0 Investment in A: I i0 Investment in S: X i0 (network of social links) which costs Period 1: individual consumes all income and He will consume C i1 from all income Y(A i1, S i1 ) Subsistent consumption constraint:

For any desired network, household i can derive the corresponding indirect utility by solving: The Model: Household’s unilateral dynamic welfare maximization problem

Optimal Social Network Structure

Determine a household’s optimal social network Who in the economy will hh consider for a prospective link? Consider those within the feasible social distance for interaction How to choose whom to link with? 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 game approach to endogenous network formation Apply concept of “pairwise stability”

The optimal social network decision 1. Social distance, cost and benefit Social distance between i and j: Total costs to establish a network X i0 is where Cost to i to establish a link with j: A cost vector Total benefits from an established network X i0 is where Benefit to i from an established link with j: A benefit vector

The optimal social network decision 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: Ω i From the example: with Consider an economy with N=(1,2,3,4,5) and

The optimal social network decision 2. Social network structure For an economy N = (1,2,…,n) Set of all feasible links: An economy’s network g represents any set of links Set of an economy’s all feasible network: For any economy’s network g, household i’s network is thus Net intertemporal benefit: Consider an economy with N=(1,2,3,4,5) and For example: for g* = (13,23,45),

The optimal social network decision 3. Non-cooperative game of network formation For a finite set of players N = (1,2,…,n), a non-cooperative game (A,Π) can be represented by… Action space where For every household i, A i is a set of unilateral actions they can take over all the feasible links: The resulting network from any action is thus given by The composite payoff function The payoff to i from any action is thus given by A network is supported by a Nash equilibrium with action a * in this game (A,Π) if for every household,

The optimal social network decision 4. Pairwise Stable Network As the game (A,Π) can have multiplicity of Nash equilibria, we choose to use “pairwise stability” to characterize the optimal network A network is pairwise stable if No household would be better off if it severed one of its links No pair of households would both benefit (with at least one strictly benefiting) from adding a link that is not in the network Formally, a network is pairwise stable with respect to payoff structure Π if

Households’ equilibria and patterns of economic mobility

Characterize equilibrium of the model The pairwise stable network structure g* that optimally arises from the non-cooperative game will depict every household i’s optimal network Household i’s equilibrium is thus characterized by its accumulation decisions, which determines current and future technology choice, consumption, and thus level of well-being The equilibrium of this model is thus characterized by

A simple case study of linear utility We consider a simple case study where This setting ensures the existence of multiple equilibria such that

A benchmark case with no social network S 0 = 0 and X 0 = 0 A static asset poverty line is hypothetically set at asset threshold The initialyl poor whose thus can escape poverty through autarkic saving iff This suggests the existence of a dynamic asset poverty line such that the initially poor with and thus will escape poverty eventually and will be trapped in long-term poverty Each household’s initial endowment of productive assets thus determines its long-term well-being

A case with social network application S 0 ≥ 0 and X 0 A static asset poverty line is hypothetically set at asset threshold For any household i, the two possible equilibria are

The initially poor whose thus can escape poverty through autarkic saving iff or A dynamic asset poverty line thus will depend not only on initial endowments (A i0,S i0 ) but also on the poor’s opportunity to establish a productive social network, X i0 A dynamic asset threshold can be derived such that the initial poor with and so will escape poverty without the need to form new social network thus forming new network is needed A case with social network application S 0 ≥ 0 and X 0

The initially poor who failed to meet (either because of inadequate endowment (A i0,S i0 ) or there is no feasible productive network X i0 ), will never consider establishing a network with others as For them, social networks do not provide a viable escape from persistent poverty. A social network is not a panacea for every poor household

Roles of social network in facilitating escape from poverty 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

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

The Simulations

Consider an economy with For Example of endogenous network formation protocol in the simulation

Endogenous network formation

Basic simulation illustration

Different patterns for an autarkically mobile household aa aa

Different patterns for a household autarkically mobile given its S 0 bb bb

Different patterns for a household whose mobility depends on social links cc c c

Different patterns for a destitute, economically immobile household cici cici cici cici

Targeted transfers and “crowding in” effect h h ee f f e f h e f h

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 established 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 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 the 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

Equilibrium social networks and long-run equilibria (100 randomly generated economy)

Parameterization of the simulation

Network simulation statistics Sample proportion of those getting their first best network vs. number of households feasible for social link (100 economies of 17 households) Sample proportion of those getting their first best network vs. number of households in the first best network (100 economies of 17 households)