Insurance and Inequality with Persistent Private Information

Bloedel, Alex; Krishna, R. Vijay; Leukhina, Oksana

doi:10.20955/wp.2018.020

Working Paper Revision

Insurance and Inequality with Persistent Private Information

Abstract: This paper studies the optimal tradeoff between insurance and inequality in economies with persistent private information.We consider a principal-agent model in which the principal insures the agent against privately-observed shocks to his endowment, which follows an ergodic finite-state Markov chain that may exhibit arbitrary serial correlation. The optimal contract always induces immiseration: the agent’s consumption and utility become arbitrarily negative in the long run. When the endowment is positively serially correlated, the optimal contract provides increasingly high-powered incentives: the sensitivity of the agent’s utility with respect to his report increases without bound. These results generalize the classic immiseration results established under the assumption of iid types, and extend to settings in which the agent’s private type concerns his tastes or productivity (as in optimal taxation). In a solved example, we additionally show that, with persistence, the optimal contract (i) is not renegotiation-proof and (ii) exhibits qualitatively novel short-run dynamics and quantitatively worse risk-sharing relative to the iid information benchmark.

Keywords: dynamic contracting; recursive contracts; principal-agent problems; persistent private information; inequality; high-powered incentives; Immiseration;

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

https://doi.org/10.20955/wp.2018.020