Risk Sharing Across Communities

This paper studies cross-community risk sharing. There is now a large body of theoretical and empirical work on informal insurance, where people mitigate risk by sharing income. A consistent empirical finding is that risk-sharing is not complete within villages, often the observed sets of individuals.2 One reason, researchers suspect, is that risk-sharing does not take place at the village level, but between individuals and families.3 We build a theoretical model where risksharing takes place between pairs of agents. There are idiosyncratic shocks to individual income and community-level shocks. We consider how the opportunity for cross-community links affects the shape and efficiency of risk sharing arrangements. We find that when links across villages form, there can be less risk sharing within a village. Welfare is higher for those directly or indirectly connected across villages, but lower for those with no path connecting them to the other village. Overall, welfare can be higher. Thus, empirical findings that insurance within a village is not complete is not necessarily evidence of an inefficient pattern of risk-sharing relations. Rather, the finding is consistent with risk-sharing patterns that involve cross-community relations, and such patterns may yield higher aggregate welfare despite incomplete insurance within a village. This paper makes two contributions. First, it demonstrates the importance of a network analysis. By examining pairwise incentives to form relations and the resulting pattern, we can see new risk sharing outcomes. Second, with this network model, we show how informal risk sharing across communities has both aggregate and distributional effects. To study network outcomes, we posit a simple two stage model. First, we provide a benchmark model for risk-sharing for a given network. Then, working backwards, we consider incentives to form risk-sharing links.4 To illustrate: Consider a rural population and ask how people might link