“Social Capital, Social Mobility”

by: Peter Q. Blair

MotivationsMotivations

Progress benefits everyone (conventional wisdom)

Reality: pockets of poverty still exist

Research Question: What role does social mobility play in transforming 'poor' communities?

Result: Increased social mobility has at best a positive or at worst a neutral effect on counteracting poverty.

Outline

Model of Social Interactions in Poor Community (Fryer, Harvard U.)

Understanding Cooperation

Effects of Social Mobility

Conclusions

Model: Social Interactions in Poor Community

Agents endowed with talent 'Ө' by nature

Agent invests in human capital 'h' and social capital 'c'

human capital: valued in both rich and poor community, e.g. college/high school education

social capital: valued in poor community only, e.g. native dialect, familial ties

subject to constraint: h+c=1

Community observes level of social capital investment by agent

Agent and Community engage in social interaction game

modeled as infinitely repeated prisoner's dilemma game

Pay-off Matrix

Parameters: 0 < α; µ > α; and β < 0

Cooperate Defect

Cooperate α,α β,µ

Defect µ, β 0,0

Understanding Cooperation

Cooperation a Nash Equilibrium of Game absent social mobility agents cooperate

probability of remaining in community δ(h) = 1

assume social mobility probability of remaining in poor community 0≤ δ(h) < 1

δ '(h) < 0: increased 'h' indicates lower probability of cooperating probability of remaining in poor community [1- δ(h)] > 0

v_p(h,Ө): return to 'h' in poor community, given Ө v_r(h,Ө): return to 'h' in rich community, given Ө v'(Ө) > 0: return to 'h' varies positively with Ө in both

communities ρδ(h): discount factor of future utility -- require 0 < ρδ(h) < 1

Maintaining Cooperation

Require Utility(C) ≥ Utility(D)

Result:

δ(h) ≥ δ(h*): cooperation an equilibrium above a

threshold probability of agent remaining in poor

community

h ≤ h*: cooperation limits 'h' investment

c ≥ c*: cooperation requires minimum social capital

investment (“litmus test of belonging”)

Effects of Social Mobility

Social mobility requires probability of remaining in poor community to decrease in time

δ(h*)_t ≥ δ(h*)_t+1:

h*_t+1 ≥ h*_t: poor community allows agents to invest in more human capital – increases utility of cooperating agents and counters the increased probability of defection

c*_t+1≤ c*_t : poor community lowers social capital threshold for signaling community commitment

Effects of Social Mobility

Depends on Marginal Utility (MU) of agent Cases:

Positive MU: greater investment in human capital (Positive Effect)

Negative MU: no change in human capital investment (Neutral Effect)

Zero Marginal Utility: no change in human capital investment (Neutral Effect)

Conclusion

Social progress encourages human capital investment in poor communities

Agents who value human capital investment benefit from increased social mobility

Agents who value human capital investment, negatively, or not at all, neither benefit nor lose due to increased social mobility

Education is Key!