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.