The Equivalence of Lending Equilibria and Signalling-Based Insurance under Asymmetric Information

I present a model in which a continuum of individuals have stochastic idiosyncratic income shocks. Complete insurance is physically feasible but unattainable due to an information asymmetry; income shocks are observable only by the individuals receiving them. Any insurance institution must therefore rely on self-repoorting of income innovations. Two ways of achieving incentive-compatible self-reporting are presented. The first is a debt market with an explicit lending restriction. The second is an insurance contract that linearly filters a signal transmitted by individuals. The two are then demonstrated to be identical. Equilibrium consumption fluctuates in a random walk, which is inefficient given the physical potential for complete insurance, but is efficient given the information constraints. The results are complementary to those of Green (1987) but permit more general stochastic processes of income to be analyzed. Serial correlation of income reduces the efficiency of the insurance.