Insurance and Inequality With Persistent Private Information

We study the implications of optimal insurance provision for long-run welfare and inequality in economies with persistent private information. A principal insures an agent whose private type follows an ergodic, finite-state Markov chain. The optimal contract always induces immiseration: the agent's consumption and utility decrease without bound. Under positive serial correlation, it also backloads high-powered incentives: the sensitivity of the agent's utility with respect to his reports increases without bound. These results extend-and help elucidate the limits of-the hallmark immiseration results for economies with i.i.d. private information. Numerically, we find that persistence yields faster immiseration, higher inequality, and novel short-run distortions. Our analysis uses recursive methods for contracting with persistent types and allows for binding global incentive constraints.