Consumption risk sharing under private information when earnings are persistent

In this paper we quantitatively investigate the implications of a model of consumption risk sharing where infinitely-lived households are subject to exogenous idiosyncratic shocks to their earnings, and where the realization of these shocks are private information. Our theoretical contribution relative to the existing literature is to allow for persistence in earnings. This creates some formidable obstacles to recursive computation of the optimal contract. If the earnings process follows a Markov chain whose state space has N elements, the state space for the optimal dynamic contracting problem has N continuous dimensions and is a nontrivial subset W in RN . Such a problem is prohibitively complex, first because of the dimension of the dimensionality of the state space and, second, because it is difficult to solve for W itself.