Insurance and Inequality with Persistent Private Information

101 Pages Posted: 2 Oct 2018 Last revised: 21 Feb 2019

See all articles by Alexander W. Bloedel

Alexander W. Bloedel

Stanford University - Department of Economics

R. Krishna

Florida State University

Oksana Leukhina

Federal Reserve Bank of St Louis

Multiple version iconThere are 2 versions of this paper

Date Written: 2018-09-07

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.

JEL Classification: C73, D30, D31, D80, D82, E61

Suggested Citation

Bloedel, Alexander W. and Krishna, R. and Leukhina, Oksana, Insurance and Inequality with Persistent Private Information (2018-09-07). FRB St. Louis Working Paper No. 2018-20. Available at SSRN: https://ssrn.com/abstract=3258970 or http://dx.doi.org/doi.org/10.20955/wp.2018.020

Alexander W. Bloedel (Contact Author)

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
STANFORD, CA 94305-6072
United States

R. Krishna

Florida State University

Oksana Leukhina

Federal Reserve Bank of St Louis ( email )

P.O. Box 442
St. Louis, MO 63166-0442
United States

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