Consumption Risk-sharing in Social Networks

Abstract

We develop a model of informal risk-sharing in social networks, where relationships between individuals can be used as social collateral to enforce insurance payments. We characterize incentive compatible risk-sharing arrangements and obtain two results. (1) The degree of informal insurance is governed by the expansiveness of the network, measured by the number of connections that groups of agents have with the rest of the community, relative to group size. Two-dimensional networks, where people have connections in multiple directions, are sufficiently expansive to allow very good risk-sharing. We show that social networks in Peruvian villages satisfy this dimensionality property; thus, our model can explain Townsend's (1994) puzzling observation that village communities often exhibit close to full insurance. (2) In second-best arrangements, agents organize in endogenous "risk-sharing islands" in the network, where shocks are shared fully within, but imperfectly across islands. As a result, network based risk-sharing is local: socially closer agents insure each other more. A B C D E F G H I J X Agricultural tool (74.3%) Other tool (7.3%) Animals (1.8%) Electric device (0.8%) Kitchen utensil (5.6%) Clothes (0.7%) Food (7.0%) Other (2.5%) 0 to 10 S/. 40.5% 11 to 20 S/. 15.6% 21 to 50 S/. 17.1% 51 to 100 S/. 11.0% 101 S/. or more 15.9% Huaraz Community Figure 1: Financial and real transactions between relatives and friends in a rural community in Peru, represented as lines between transacting parties in the village map. Thickness of line measures value of transaction in Peruvian New Soles.state of the world. This arrangement is subject to moral hazard: ex post, an agent who is expected to make a transfer to a network neighbor may prefer to deviate and withhold payment. In our model, such deviations result in the loss of the a¤ected link. Intuitively, network links serve as social collateral ensuring that agents live up to their obligations under the informal risk-sharing arrangement.Our …rst result is that an incentive-compatible risk-sharing arrangement always gives rise to a consumption allocation that is coalition-proof in the following sense: the net transfer from any group of agents to the rest of the community, de…ned as the di¤erence between the group's total endowment and consumption, cannot exceed the sum of the values of all links between the group and the community. Intuitively, individual obligations embedded in the value of links build up to group obligations represented by the total value of links connecting the group with the larger community. This equivalence between coalition-proof allocations and incentive compatible risk-sharingWe show that full insurance requires highly expansive networks like the in…nite binary tree. However, we do not …nd that real-world social networks in rural villages in Peru exhibit this large degree of expansiveness. Instead, these social networks are more similar to planar networks, possibly because people tend to have connections at close geographic distance. We next sh...

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