We analyze the role of commitment in a dynamic principal-agent model of optimal insurance with hidden effort and observable but non-contractible savings. We argue that the optimal contract under full commitment is time-inconsistent. Consequently, we analyze the optimal time-consistent Markov-perfect insurance contract when both the agent and the principal cannot commit for longer than one period and contrast our results with the full commitment case from the existing literature. We find that the optimal contract under lack of commitment provides additional insurance relative to the autarky allocation and features non-degenerate long-run asset and consumption distributions. Furthermore, the no-commitment contract differs significantly from the commitment contract in the time profiles of consumption, savings, and welfare. We solve for the optimal insurance contracts in several environments featuring different degrees of market incompleteness and find that the welfare loss due to lack of commitment can be very high relative to the welfare costs of moral hazard or savings non-contractibility.
