IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01348551.html
   My bibliography  Save this paper

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

Author

Listed:
  • Pierre Martinon

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

  • Pierre Picard

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

  • Anasuya Raj

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

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://hal-polytechnique.archives-ouvertes.fr/hal-01348551v3
    as

    Download full text from publisher

    File URL: https://hal-polytechnique.archives-ouvertes.fr/hal-01348551v3/document
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Pierre Picard, 2016. "A Note on Health Insurance under Ex Post Moral Hazard," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-1, October.
    10. Pierre Picard, 2012. "Economic Analysis of Insurance Fraud," Working Papers hal-00725561, HAL.
    11. 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.
    12. Blomqvist, Ake, 1997. "Optimal non-linear health insurance," Journal of Health Economics, Elsevier, vol. 16(3), pages 303-321, June.
    13. Kevin E. Pflum, 2015. "Physician Incentives and Treatment Choice," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 24(4), pages 712-751, October.
    14. Weymark, John A., 1986. "A reduced-form optimal nonlinear income tax problem," Journal of Public Economics, Elsevier, vol. 30(2), pages 199-217, July.
    15. 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.
    16. 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.
    17. 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.
    18. 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).
    19. 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.
    20. 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.
    21. 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.
    22. Ebert, Udo, 1992. "A reexamination of the optimal nonlinear income tax," Journal of Public Economics, Elsevier, vol. 49(1), pages 47-73, October.
    23. 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.
    24. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    25. 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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    optimal control; health insurance; ex post moral hazard; audit; background risk;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-01348551. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.