Efficient and sustainable risk sharing with adverse selection

We analyze a model with two risk averse agents who engage in risk sharing over an infinite time horizon in the presence of asymmetric information: one agent’s stochastic income realizations are his private information. Both agents can opt out of the risk sharing agreement at any time. We prove existence and uniqueness of efficient and incentive compatible sharing rules. We find inefficient risk sharing across states at all times, and show history dependence of efficient sharing rules: consumption strictly increases over time for an agent who is repeatedly hit with a favorable income shock. Under some restrictions on agents ’ utility functions, we show that after a better history, an agent’s consumption is strictly larger. Agents’ consumption is therefore positively correlated with past income. We argue that these results can explain empirical findings of excess sensitivity to income changes and history dependence of agents ’ consumption. We also prove the existence of a unique stationary wealth distribution in which neither agent becomes impoverished. We provide an algorithm for numerical computation and compute examples for agents with CRRA utility and various values of risk aversion and impatience. ∗I thank Faruk Gul for invaluable help and advice and John Smith, Bruce Preston and Aureo de Paula for very helpful conversations