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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," LIDAM Discussion Papers CORE 2012027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2012027
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

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    2. Justina Klimaviciute & Pierre Pestieau, 2020. "Insurance with a deductible: a way out of the long term care insurance puzzle," Journal of Economics, Springer, vol. 130(3), pages 297-307, August.
    3. Flores, Gabriela & O’Donnell, Owen, 2016. "Catastrophic medical expenditure risk," Journal of Health Economics, Elsevier, vol. 46(C), pages 1-15.
    4. 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.
    5. Westerhout, Ed & Folmer, Kees, 2018. "The Effects of Capping Co-Insurance Payments," Discussion Paper 2018-050, Tilburg University, Center for Economic Research.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Marianne Tenand & Pieter Bakx & Bram Wouterse, 2021. "The impact of co-payments for nursing home care on use, health, and welfare," CPB Discussion Paper 430, CPB Netherlands Bureau for Economic Policy Analysis.
    11. Chi, Yichun & Zhuang, Sheng Chao, 2022. "Regret-based optimal insurance design," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 22-41.
    12. Owen (O.A.) O'Donnell, 2019. "Financial Protection Against Medical Expense," Tinbergen Institute Discussion Papers 19-010/V, Tinbergen Institute.
    13. 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.
    14. Bram Wouterse & Arjen Hussem & Albert Wong, 2022. "The risk protection and redistribution effects of long‐term care co‐payments," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(1), pages 161-186, March.
    15. 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.
    16. 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.
    17. Westerhout, Ed & Folmer, Kees, 2018. "The Effects of Capping Co-Insurance Payments," Other publications TiSEM 828746fb-4fb0-465b-bdff-3, Tilburg University, School of Economics and Management.

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    More about this item

    Keywords

    optimal health insurance; deductible stop-loss; moral hazard;
    All these keywords.

    JEL classification:

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

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