IDEAS home Printed from https://ideas.repec.org/p/cor/louvco/2012027.html
   My bibliography  Save this paper

Arrow’s theorem of the deductible: moral hazard and stop-loss in health insurance

Author

Listed:
  • DREZE, Jacques

    () (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • SCHOKKAERT, Erik

    () (Department of Economics, KU Leuven, B-3000 Leuven, Belgium and Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

Abstract

We show that the logic of Arrow's theorem of the deductible, i.e. that it is optimal to focus insurance coverage on the states with largest expenditures, remains at work in a model with ex post moral hazard. The optimal insurance contract takes the form of a system of "implicit deductibles", i.e. it results in the same indemnities as a contract with full insurance above a variable deductible positively related to the elasticity of medical expenditures with respect to the insurance rate. In a model with an explicit stop-loss arrangement, i.e. with a predefined ceiling on the annual expenses of the insured, this stop-loss takes the form of a deductible, i.e. there is no reimbursement for expenses below the stop-loss amount. One motivation to have some insurance below the deductible arises if regular health care expenditures in a situation of standard health have a negative effect on the probability of getting into a state with large medical expenses.

Suggested Citation

  • DREZE, Jacques & SCHOKKAERT, Erik, 2012. "Arrow’s theorem of the deductible: moral hazard and stop-loss in health insurance," CORE Discussion Papers 2012027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2012027
    as

    Download full text from publisher

    File URL: http://uclouvain.be/cps/ucl/doc/core/documents/coredp2012_27web.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521715348, December.
    2. Louis Eeckhoudt & Maurice Marchand & Pierre Pestieau & Gwenaël Piaser, 2008. "Vaccination versus “wait and treat”: how to subsidize them?," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 9(1), pages 33-39, February.
    3. EECKHOUDT, Louis, 2012. "Beyond risk aversion: why, how and what's next?," CORE Discussion Papers RP 2514, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Manning, Willard G, et al, 1987. "Health Insurance and the Demand for Medical Care: Evidence from a Randomized Experiment," American Economic Review, American Economic Association, vol. 77(3), pages 251-277, June.
    5. Tomas J. Philipson & Dana Goldman, 2007. "Integrated Insurance Design in the Presence of Multiple Medical Technologies," American Economic Review, American Economic Association, vol. 97(2), pages 427-432, May.
    6. Gollier, Christian & Schlesinger, Harris, 1996. "Arrow's Theorem on the Optimality of Deductibles: A Stochastic Dominance Approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 359-363, February.
    7. Pauly, Mark V. & Blavin, Fredric E., 2008. "Moral hazard in insurance, value-based cost sharing, and the benefits of blissful ignorance," Journal of Health Economics, Elsevier, vol. 27(6), pages 1407-1417, December.
    8. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1991. "Increases in risk and deductible insurance," Journal of Economic Theory, Elsevier, vol. 55(2), pages 435-440, December.
    9. Blomqvist, Ake, 1997. "Optimal non-linear health insurance," Journal of Health Economics, Elsevier, vol. 16(3), pages 303-321, June.
    10. Louis Eeckhoudt & Christian Gollier, 2005. "The impact of prudence on optimal prevention," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 989-994, November.
    11. repec:adr:anecst:y:2006:i:83-84:p:11 is not listed on IDEAS
    12. Dionne, Georges & Eeckhoudt, Louis, 1985. "Self-insurance, self-protection and increased risk aversion," Economics Letters, Elsevier, vol. 17(1-2), pages 39-42.
    13. Manning, Willard G. & Marquis, M. Susan, 1996. "Health insurance: The tradeoff between risk pooling and moral hazard," Journal of Health Economics, Elsevier, vol. 15(5), pages 609-639, October.
    14. repec:cor:louvrp:-2514 is not listed on IDEAS
    15. David Bardey & Romain Lesur, 2006. "Optimal regulation of health system with induced demand and 'ex post' moral hazard," Annals of Economics and Statistics, GENES, issue 83-84, pages 279-293.
    16. Duranton, Gilles & Martin, Philippe & Mayer, Thierry & Mayneris, Florian, 2010. "The Economics of Clusters: Lessons from the French Experience," OUP Catalogue, Oxford University Press, number 9780199592203.
    17. DEHEZ, Pierre & DREZE, Jacques H., 1984. "State-dependent utility, the demand for insurance and the value of safety," CORE Discussion Papers RP 560, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Bardey, David & Lesur, Romain, 2005. "Optimal health insurance contract: Is a deductible useful?," Economics Letters, Elsevier, vol. 87(3), pages 313-317, June.
    19. 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.
    20. Ellis, Randall P. & Manning, Willard G., 2007. "Optimal health insurance for prevention and treatment," Journal of Health Economics, Elsevier, vol. 26(6), pages 1128-1150, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Flores, Gabriela & O’Donnell, Owen, 2016. "Catastrophic medical expenditure risk," Journal of Health Economics, Elsevier, vol. 46(C), pages 1-15.
    2. Justina Klimaviciute & Pierre Pestieau, 2018. "Long-term care social insurance: How to avoid big losses?," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 25(1), pages 99-139, February.
    3. Drèze, Jacques H. & Pestieau, Pierre & Schokkaert, Erik, 2016. "Arrow’s theorem of the deductible and long-term care insurance," Economics Letters, Elsevier, vol. 148(C), pages 103-105.
    4. repec:kap:geneva:v:43:y:2018:i:2:d:10.1057_s10713-018-0034-y is not listed on IDEAS
    5. Pierre Martinon & Pierre Picard & Anasuya Raj, 2018. "On the design of optimal health insurance contracts under ex post moral hazard," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(2), pages 137-185, September.
    6. Westerhout, Ed & Folmer, Kees, 2018. "The Effects of Capping Co-Insurance Payments," Discussion Paper 2018-050, Tilburg University, Center for Economic Research.
    7. Wouterse, B.; & Hussem, A.; & Wong, A.;, 2018. "The effect of co-payments in Long Term Care on the distribution of payments,consumption, and risk," Health, Econometrics and Data Group (HEDG) Working Papers 18/24, HEDG, c/o Department of Economics, University of York.
    8. Pierre Martinon & Pierre Picard & Anasuya Raj, 2017. "On the Design of Optimal Health Insurance Contracts under Ex Post Moral Hazard," Working Papers hal-01348551, HAL.
    9. Andreas Richter & Jörg Schiller & Harris Schlesinger, 2014. "Behavioral insurance: Theory and experiments," Journal of Risk and Uncertainty, Springer, vol. 48(2), pages 85-96, April.
    10. Owen (O.A.) O'Donnell, 2019. "Financial Protection Against Medical Expense," Tinbergen Institute Discussion Papers 19-010/V, Tinbergen Institute.

    More about this item

    Keywords

    optimal health insurance; deductible stop-loss; moral hazard;

    JEL classification:

    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private

    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:cor:louvco:2012027. 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: (Alain GILLIS). General contact details of provider: http://edirc.repec.org/data/coreebe.html .

    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.