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

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  • 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.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2012027.

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Date of creation: 25 Jul 2012
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Handle: RePEc:cor:louvco:2012027

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

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  1. 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.
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  11. Gaertner,Wulf & Schokkaert,Erik, 2011. "Empirical Social Choice," Cambridge Books, Cambridge University Press, number 9781107013940, October.
  12. 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 251-77, June.
  13. Christian Gollier & Harris Schlesinger, 1996. "Arrow's theorem on the optimality of deductibles: A stochastic dominance approach (*)," Economic Theory, Springer, vol. 7(2), pages 359-363.
  14. 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.
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  16. Blomqvist, Ake, 1997. "Optimal non-linear health insurance," Journal of Health Economics, Elsevier, vol. 16(3), pages 303-321, June.
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