Social Insurance, Information Revelation, and Lack of Commitment

Abstract:

We study the optimal provision of insurance against unobservable idiosyncratic shocks in a setting in which a benevolent government cannot commit. A continuum of agents and the government play an infinitely repeated game. Actions of the government are constrained only by the threat of reverting to the worst subgame perfect equilibrium (SPE). We construct a recursive problem that characterizes the resource allocation and information revelation on the Pareto frontier of the SPE and show incentives to reveal information are provided by promised utilities. We prove a version of the Revelation Principle and find an upper bound on the maximum number of messages that are needed to achieve the optimal allocation. Agents play mixed strategies over that message set to limit the amount of information transmitted to the government. The central feature of the optimal contract is that it is optimal for agents who enter a period with low promised utility to provide no information to the government, and receive no insurance against shocks they experience in current period, while agents with high promised utility reveal precise information about their current shock and receive insurance as in economies with full commitment by the government.