Social Network Capital, Economic Mobility and Poverty Traps

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Social Network Capital, Economic Mobility and
Poverty Traps

• Sommarat Chantarat and Chris Barrett
• Cornell University
• May 3, 2007 Seminar
• Ohio State University

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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 bas
ed on the study of state variable (assets)
accumulation overtime Most poverty traps depend o
n 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
2002-3, Carter and Barrett 2006, etc.)
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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) M
arket 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 e
xclusion (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 ones choices
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Contribution of this paper
We provide a theoretical foundation of the
mechanisms by which endogenous social network
capital can facilitate or impede the poors
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 economys
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
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Key Points
Social network capital can either substitute for
or complement real capital in facilitating
escape from poverty depending on the poors
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 households welfare dynamics may depend not
only on its initial endowment, but on the
economys initial wealth distribution as well
Crowding-in transfers through endogenous social
networks are possible in this setting
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Outline of the talk

• The model
• The optimal social network structure
• Households equilibria and patterns of mobility
• The simulations
• Conclusions

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The Model
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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 capita
l S0 Identical preferences Absence of financial
markets Identical production technology set
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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 is aggregate production function at
any period t
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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
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The Model Production technology
Social network capital reduces the productive
asset stock necessary to make the high-return
technology optimal Value of social network capita
l will vary across households with heterogeneous
endowment of productive assets
When acquiring more social network capital
,
and so
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The Model Households unilateral dynamic welfare
maximization problem
Household i maximizes Period 0 household alloca
tes income Y(Ai0 , Si0) among
Consumption Ci0 Investment in A Ii0 Investm
ent in S Xi0 (network of social links) which
costs Period 1 individual consumes all income
and He will consume Ci1 from all in
come Y(Ai1 , Si1) Subsistent consumption constra
int
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The Model Households unilateral dynamic welfare
maximization problem
For any desired network , household i can
derive the corresponding indirect utility by
solving
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Optimal Social Network Structure
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Determine a households optimal social network
Who in the economy will hh consider for a
prospective link? Consider those within the feasi
ble 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 benef
it-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 pa
irwise stability
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The optimal social network decision1. 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 lin
k with j A cost vector Total benefits from a
n established network Xi0 is where
Benefit to i from an established link with j
A benefit vector
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The optimal social network decision2. Social
network structure
For a household i Denote binary link between i a
nd j ij Household is network where Set o
f is all possible network Oi
From the example with
Consider an economy with N(1,2,3,4,5) and
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The optimal social network decision2. Social
network structure
For an economy N (1,2,,n) Set of all feasible
links An economys network g represents any s
et of links Set of an economys all feasible netw
ork For any economys network g, household is n
etwork is thus Net intertemporal benefit
Consider an economy with N(1,2,3,4,5) and
For example for g (13,23,45),
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The optimal social network decision3.
Non-cooperative game of network formation
For a finite set of players N (1,2,,n), a
non-cooperative game (A,?) can be represented by
Action space where
For every household i, Ai 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,?) if for every household ,
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The optimal social network decision4. Pairwise
Stable Network
As the game (A,?) 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 b
oth benefit (with at least one strictly
benefiting) from adding a link that is not in the
network Formally, a network is pa
irwise stable with respect to payoff structure ?
if
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Households equilibria and patterns of economic
mobility
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Characterize equilibrium of the model
The pairwise stable network structure g that
optimally arises from the non-cooperative game
will depict every household is optimal
network Household is equilibrium is thus cha
racterized 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 characte
rized by
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A simple case study of linear utility
We consider a simple case study where
This setting ensures the existence of multip
le equilibria such that

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A benchmark case with no social network S0 0
and X0 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 households ini
tial endowment of productive assets thus
determines its long-term well-being
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A case with social network application S0 0
and X0
A static asset poverty line is hypothetically set
at asset threshold For any household i, the tw
o possible equilibria are

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A case with social network application S0 0
and X0
The initially poor whose
thus can escape poverty through autarkic saving
iff or A dynamic asset pov
erty line thus will depend not only on initial
endowments (Ai0 ,Si0) but also on the poors
opportunity to establish a productive social
network, Xi0 A dynamic asset threshold
can be derived such that the
initial poor with and so will escape p
overty without the need to form new social
network thus forming new network is
needed
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A social network is not a panacea for every poor
household
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 viab
le escape from persistent poverty.
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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
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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 soci
al 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 remai
n trapped in poverty
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The Simulations
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Example of endogenous network formation protocol
in the simulation
Consider an economy with For

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Example of endogenous network formation protocol
in the simulation
Endogenous network formation

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Basic simulation illustration
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Different patterns for an autarkically mobile
household
a
a
a
a
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Different patterns for a household autarkically
mobile given its S0
b
b
b
b
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Different patterns for a household whose mobility
depends on social links
c
c
c
c
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Different patterns for a destitute, economically
immobile household
ci
ci
ci
ci
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Targeted transfers and crowding in
effect
e
f
f
e
h
h
f
f
h
e
e
h
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Targeted transfers and crowding in effect
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Conclusions
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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)
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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 thro
ugh endogenous network, in contrast to the widely
claims of crowding-out effects (which typically
treat social network as exogenous)
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Thank you for your attention

• Comments are greatly appreciated

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Equilibrium social networks and long-run
equilibria (100 randomly generated economy)
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Parameterization of the simulation
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Network simulation statistics
Sample proportion of those getting their first
best network vs. number of households feasible fo
r social link
(100 economies of 17 households)
Sample proportion of those getting their first
best network vs. number of households in the firs
t best network
(100 economies of 17 households)