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Insurance and Inequality with Persistent Private Information

Alex Bloedel (), R. Vijay Krishna () and Oksana Leukhina ()
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Alex Bloedel: Stanford University
R. Vijay Krishna: Florida State University

No 2018-20, Working Papers from Federal Reserve Bank of St. Louis

Abstract: 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.

Keywords: Absolute immiseration; relative immiseration; dynamic contracting; recursive contracts; principal-agent problem; persistent private information. (search for similar items in EconPapers)
JEL-codes: C73 D30 D31 D80 D82 E61 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cta, nep-gth, nep-mic and nep-upt
Date: 2018-09-07
Note: This paper was previously circulated as “Misery, Persistence, and Growth” by Bloedel and Krishna.
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DOI: doi.org/10.20955/wp.2018.020

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