Insurance and Inequality with Persistent Private Information

We study optimal insurance contracts for an agent with Markovian private information. Our main results characterize the implications of constrained efficiency for long-run welfare and inequality. Under minimal technical conditions, there is Absolute Immiseration: in the long run, the agent’s consumption and utility converge to their lower bounds. When types are persistent and utility is unbounded below, there is Relative Immiseration: low-type agents are immiserated at a faster rate than high-type agents, and “pathwise welfare inequality� grows without bound. These results extend and substantially generalize the hallmark findings from the classic literature with iid types, suggesting that the underlying forces are robust to a broad class of private information processes. The proofs rely on novel recursive techniques and martingale arguments. When the agent has CARA utility, we also analytically and numerically characterize the short-run properties of the optimal contract. Persistence gives rise to qualitatively novel short-run dynamics and allocative distortions (or “wedges�) and, quantitatively, induces less efficient risk-sharing. We compare properties of the wedges to their counterparts in the dynamic taxation literature