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Contracting under Ex Post Moral Hazard and Non-Commitment

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  • M. Martin Boyer

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Abstract

This paper characterizes the optimal insurance contract in an environment where an informed agent can misrepresent the state of the world to a principal who cannot credibly commit to an auditing strategy. Because the principal cannot commit, the optimal strategy of the agent is not to tell the truth all the time. Assuming that there are T > 1 possible losses, and that the agent cannot fake an accident (he is constrained only to misreport the size of the loss when a loss occurs), the optimal contract is such that higher losses are over-compensated while lower losses are on average under-compensated. The amount by which higher losses are over-compensated decreases as the loss increases. The optimal contract may then be represented as a simple combination of a deductible, a lump-sum payment and a coinsurance provision. Ce document de travail caractérise le contrat optimal dans une économie où un agent informé de l'état de la nature doit rapporter cet état à un principal qui ne peut se commettre de manière crédible dans une stratégie de vérification de l'annonce de l'agent. Puisque le principal ne peut se commettre, il devient optimal pour l'agent de mentir avec une certaine probabilité. En supposant qu'il existe T>1 pertes possibles en cas d'accident, que l'agent ne peut feindre un accident (il est restreint à rapporter la perte en cas d'accident,0501s la présence d'un accident est une information de nature commune), le contrat optimal est tel que les hautes pertes sont sur-indemnisées alors que les faibles pertes sont sous-indemnisées en moyenne. Le niveau de sur-indemnisation des hautes pertes diminue toutefois avec la perte elle-même. Le contrat optimal peut ainsi être représenté comme une simple combinaison d'une franchise, d'un paiement forfaitaire et de co-paiements.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2001s-30.

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Date of creation: 01 Apr 2001
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Handle: RePEc:cir:cirwor:2001s-30

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Keywords: Non-commitment; insurance; ex post moral hazard; contract theory; Absence d'engagement; assurance; aléa moral ex post; théorie des contrats;

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  1. Harrison, Glenn W, 1989. "Theory and Misbehavior of First-Price Auctions," American Economic Review, American Economic Association, vol. 79(4), pages 749-62, September.
  2. Robert Townsend, 1979. "Optimal contracts and competitive markets with costly state verification," Staff Report 45, Federal Reserve Bank of Minneapolis.
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  4. Khalil, Fahad & Parigi, Bruno M, 1998. "Loan Size as a Commitment Device," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(1), pages 135-50, February.
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  12. Bond, E.W. & Crocker, K.J., 1993. "Hardball and the Soft Touch: The Economics of Optimal Insurance Contracts with Costly State Verification and Endogenous Monitoring Costs," Papers 10-93-1b, Pennsylvania State - Department of Economics.
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  15. Picard, Pierre, 1996. "Auditing claims in the insurance market with fraud: The credibility issue," Journal of Public Economics, Elsevier, vol. 63(1), pages 27-56, December.
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Cited by:
  1. Schiller, Jörg, 2004. "Versicherungsbetrug als ökonomisches Problem: Eine vertragstheoretische Analyse," Working Papers on Risk and Insurance 13, University of Hamburg, Institute for Risk and Insurance.
  2. M. Martin Boyer, 2004. "On the Use of Hierarchies to Complete Contracts when Players Have Limited Abilities," CIRANO Working Papers 2004s-41, CIRANO.
  3. J Fran�ois Outreville, 2010. "The Geneva Risk and Insurance Review 2009: In Quest of Behavioural Insurance," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan, vol. 35(3), pages 484-497, July.
  4. Bénédicte Coestier & Nathalie Fombaron, 2003. "L'audit en assurance," THEMA Working Papers 2003-41, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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