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

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  • Jacques Drèze
  • Erik Schokkaert

Abstract

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”, resulting 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 a predefined ceiling on expenses, 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. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
  • Handle: RePEc:kap:jrisku:v:47:y:2013:i:2:p:147-163
    DOI: 10.1007/s11166-013-9177-5
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    2. 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.
    3. Tan, Ken Seng & Wei, Pengyu & Wei, Wei & Zhuang, Sheng Chao, 2020. "Optimal dynamic reinsurance policies under a generalized Denneberg’s absolute deviation principle," European Journal of Operational Research, Elsevier, vol. 282(1), pages 345-362.
    4. 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.
    5. Flores, Gabriela & O’Donnell, Owen, 2016. "Catastrophic medical expenditure risk," Journal of Health Economics, Elsevier, vol. 46(C), pages 1-15.
    6. 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.
    7. 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.
    8. 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.
    9. Justina Klimaviciute & Pierre Pestieau, 0. "Insurance with a deductible: a way out of the long term care insurance puzzle," Journal of Economics, Springer, vol. 0, pages 1-11.
    10. Westerhout, Ed & Folmer, Kees, 2018. "The Effects of Capping Co-Insurance Payments," Discussion Paper 2018-050, Tilburg University, Center for Economic Research.
    11. Owen (O.A.) O'Donnell, 2019. "Financial Protection Against Medical Expense," Tinbergen Institute Discussion Papers 19-010/V, Tinbergen Institute.
    12. 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.
    13. Bram Wouterse & Arjen Hussem, 2019. "The welfare effects of co-payments in long term care," CPB Discussion Paper 394, CPB Netherlands Bureau for Economic Policy Analysis.

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    More about this item

    Keywords

    Optimal health insurance; Deductible; Stop-loss; Moral hazard; I13;
    All these keywords.

    JEL classification:

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

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