Dynamic Optimal Insurance and Lack of Commitment

Fernando Martin and Alexander Karaivanov

No 793, 2007 Meeting Papers from Society for Economic Dynamics

Abstract: We analyze the role of commitment in a dynamic principal-agent model of optimal insurance with hidden effort and observable but non-contractible assets. We argue that the optimal contract under full commitment is time-inconsistent. Consequently, we solve for and analyze the optimal insurance contract when both the agent and the principal cannot commit (i.e., each can renege in each period) and contrast our results with the full commitment case studied by the existing literature. We find that the Markov-perfect contract under double-sided lack of commitment provides additional insurance relative to the self-insurance allocation and features a non-degenerate long-run asset and consumption distributions. Furthermore, the no commitment contract differs significantly from the full commitment contract in the time profiles of consumption and savings, insurance, and welfare. We solve numerically for the optimal insurance contract in several environments characterized by different degrees of market imperfections. We find that the welfare loss due to lack of commitment is very high relative to the welfare costs of moral hazard or savings non-contractibility.

Date: 2007
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Related works:
Journal Article: Dynamic Optimal Insurance and Lack of Commitment (2015)
Working Paper: Dynamic optimal insurance and lack of commitment (2011)
Working Paper: Dynamic Optimal Insurance and Lack of Commitment (2007)
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