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On the Design of Optimal Health Insurance Contracts under Ex Post Moral Hazard

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  • Pierre Martinon

    (Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems - CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique)

  • Pierre Picard

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

  • Anasuya Raj

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

Abstract

We analyze the design of optimal medical insurance under ex post moral haz- ard, i.e., when illness severity cannot be observed by insurers and policyholders decide for themselves on their health expenditures. The trade-o¤ between ex ante risk sharing and ex post incentive compatibility is analyzed in an optimal revelation mechanism under hidden information and risk aversion. The optimal contract provides partial insurance at the margin, with a deductible when in- surers' rates are affected by a positive loading, and it may also include an upper limit on coverage. The potential to audit the health state leads to an upper limit on out-of-pocket expenses.

Suggested Citation

  • Pierre Martinon & Pierre Picard & Anasuya Raj, 2018. "On the Design of Optimal Health Insurance Contracts under Ex Post Moral Hazard," Post-Print hal-01348551, HAL.
    • Handle: RePEc:hal:journl:hal-01348551
    DOI: 10.1057/s10713-018-0034-y
    Note: View the original document on HAL open archive server: https://polytechnique.hal.science/hal-01348551v3
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    References listed on IDEAS

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    1. Bond, Eric W. & Crocker, Keith J., 1997. "Hardball and the soft touch: The economics of optimal insurance contracts with costly state verification and endogenous monitoring costs," Journal of Public Economics, Elsevier, vol. 63(2), pages 239-264, January.
    2. Amy Finkelstein & Erzo F. P. Luttmer & Matthew J. Notowidigdo, 2013. "What Good Is Wealth Without Health? The Effect Of Health On The Marginal Utility Of Consumption," Journal of the European Economic Association, European Economic Association, vol. 11, pages 221-258, January.
    3. Jacques Drèze & Erik Schokkaert, 2013. "Arrow’s theorem of the deductible: Moral hazard and stop-loss in health insurance," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 147-163, October.
    4. Dionne, G. & St-Michel, P. & Gibbens, A., 1993. "An Economic Analysis of Insurance Fraud," Cahiers de recherche 93010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    5. Lollivier, Stefan & Rochet, Jean-Charles, 1983. "Bunching and second-order conditions: A note on optimal tax theory," Journal of Economic Theory, Elsevier, vol. 31(2), pages 392-400, December.
    6. Blomqvist, Ake, 1997. "Optimal non-linear health insurance," Journal of Health Economics, Elsevier, vol. 16(3), pages 303-321, June.
    7. Laffont, Jean-Jacques & Rochet, Jean-Charles, 1998. "Regulation of a Risk Averse Firm," Games and Economic Behavior, Elsevier, vol. 25(2), pages 149-173, November.
    8. Evans, William N & Viscusi, W Kip, 1991. "Estimation of State-Dependent Utility Functions Using Survey Data," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 94-104, February.
    9. Viscusi, W Kip & Evans, William N, 1990. "Utility Functions That Depend on Health Status: Estimates and Economic Implications," American Economic Review, American Economic Association, vol. 80(3), pages 353-374, June.
    10. Cutler, David M. & Zeckhauser, Richard J., 2000. "The anatomy of health insurance," Handbook of Health Economics, in: A. J. Culyer & J. P. Newhouse (ed.), Handbook of Health Economics, edition 1, volume 1, chapter 11, pages 563-643, Elsevier.
    11. Ching‐To Albert Ma & Michael H. Riordan, 2002. "Health Insurance, Moral Hazard, and Managed Care," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 11(1), pages 81-107, March.
    12. Ebert, Udo, 1992. "A reexamination of the optimal nonlinear income tax," Journal of Public Economics, Elsevier, vol. 49(1), pages 47-73, October.
    13. Zeckhauser, Richard, 1970. "Medical insurance: A case study of the tradeoff between risk spreading and appropriate incentives," Journal of Economic Theory, Elsevier, vol. 2(1), pages 10-26, March.
    14. Georges Dionne (ed.), 2013. "Handbook of Insurance," Springer Books, Springer, edition 2, number 978-1-4614-0155-1, January.
    15. Rees, Ray & Wambach, Achim, 2008. "The Microeconomics of Insurance," Foundations and Trends(R) in Microeconomics, now publishers, vol. 4(1–2), pages 1-163, February.
    16. Feldstein, Martin S, 1973. "The Welfare Loss of Excess Health Insurance," Journal of Political Economy, University of Chicago Press, vol. 81(2), pages 251-280, Part I, M.
    17. Pierre Picard, 2016. "A Note on Health Insurance under Ex Post Moral Hazard," Risks, MDPI, vol. 4(4), pages 1-9, October.
    18. Pierre Picard, 2012. "Economic Analysis of Insurance Fraud," Working Papers hal-00725561, HAL.
    19. Kevin E. Pflum, 2015. "Physician Incentives and Treatment Choice," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 24(4), pages 712-751, October.
    20. Weymark, John A., 1986. "A reduced-form optimal nonlinear income tax problem," Journal of Public Economics, Elsevier, vol. 30(2), pages 199-217, July.
    21. Ellis, Randall P. & Jiang, Shenyi & Manning, Willard G., 2015. "Optimal health insurance for multiple goods and time periods," Journal of Health Economics, Elsevier, vol. 41(C), pages 89-106.
    22. Picard, Pierre, 2000. "On the Design of Optimal Insurance Policies under Manipulation of Audit Cost," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1049-1071, November.
    23. GOLLIER, Ch., 1985. "Pareto-optimal risk sharing with fixed costs per claim," LIDAM Discussion Papers CORE 1985046, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    24. Feldman, Roger & Dowd, Bryan, 1991. "A New Estimate of the Welfare Loss of Excess Health Insurance," American Economic Review, American Economic Association, vol. 81(1), pages 297-301, March.
    25. Townsend, Robert M., 1979. "Optimal contracts and competitive markets with costly state verification," Journal of Economic Theory, Elsevier, vol. 21(2), pages 265-293, October.
    26. Feldstein, Martin & Friedman, Bernard, 1977. "Tax subsidies, the rational demand for insurance and the health care crisis," Journal of Public Economics, Elsevier, vol. 7(2), pages 155-178, April.
    27. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    28. Bernard Salanié, 1990. "Sélection adverse et aversion pour le risque," Annals of Economics and Statistics, GENES, issue 18, pages 131-149.
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    Cited by:

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    3. Peng Yang & Zhiping Chen, 2023. "Optimal Private Health Insurance Contract towards the Joint Interests of a Policyholder and an Insurer," Mathematics, MDPI, vol. 11(10), pages 1-28, May.
    4. Sun, Huan & Wang, Haiyan & Steffensen, Sonja, 2022. "Mechanism design of multi-strategy health insurance plans under asymmetric information," Omega, Elsevier, vol. 107(C).

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    More about this item

    Keywords

    optimal control; health insurance; ex post moral hazard; audit; background risk;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private

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