Markov-perfect risk sharing, moral hazard and limited commitment

We define, characterize and compute Markov-perfect risk-sharing contracts in a dynamic stochastic economy with endogenous asset accumulation and simultaneous limited commitment and moral hazard frictions. We prove that Markov-perfect insurance contracts preserve standard properties of optimal insurance with private information and are not more restrictive than a long-term contract with one-sided commitment. Markov-perfect contracts imply a determinate asset time-path and a non-degenerate long-run stationary wealth distribution. Quantitatively, we show that Markov-perfect risk-sharing contracts provide sizably more consumption smoothing relative to self-insurance and that the welfare gains from resolving the commitment friction are larger than the gains from resolving the moral hazard friction at low asset levels, while the opposite holds for high asset levels.