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Optimality and Equilibrium In a Competitive Insurance Market Under Adverse Selection and Moral Hazard

Author

Listed:
  • Joseph Stiglitz
  • Jungyoll Yun
Abstract
This paper analyzes optimal and equilibrium insurance contracts under adverse selection and moral hazard, comparing them with those under a single informational asymmetry. The complex interactions of self-selection and moral hazard constraints have important consequences. We develop an analytic approach that allows a characterization of equilibrium and optimal (Pareto Optimal (PO), and Utilitarian optimal (UO)) allocations. Among the results : (i) a PO allocation may involve "shirking" (not only less care in accident avoidance than is possible, but less care compared to the case of pure moral hazard) either by high risk individuals in the case of single-crossing preference or by one or both types in the case of multi-crossing preference (as may naturally be the case under the double informational asymmetry); and (ii) while an equilibrium, which is unique (even under multi-crossing preferences) if it exists, is more likely to exist as the non-shirking constraint for low-risk type gets more stringent (i.e. when low risk individuals shirk with lower levels of insurance). We also show that a pooling equilibrium, which is not feasible under pure adverse selection, may exist when individuals differ in risk aversion (as well as in accident probability) or when the provision of insurance is non-exclusive (i.e. individuals can purchase insurance from more than one firm). Furthermore, while with pure adverse selection, UO always entails pooling with complete insurance (in the standard model), with adverse selection and moral hazard, all PO allocations may entail separation and the UO may entail incomplete insurance. We show further that, in general, any PO allocation can be implemented by a basic pooling insurance provided by the government and a supplemental separating contracts that can be offered by the market, although, in the presence of moral hazard, a tax needs to be imposed upon the market provision. The analysis suggests that two commonly observed features of many countries' public insurance schemes are consistent with PO: (a) Some individuals (type H) shirk--contrary to widespread views, it is not a sign of a poorly designed system that some individuals shirk; and (b) there exists a hybrid provision of insurance by the government and the market.

Suggested Citation

  • Joseph Stiglitz & Jungyoll Yun, 2013. "Optimality and Equilibrium In a Competitive Insurance Market Under Adverse Selection and Moral Hazard," NBER Working Papers 19317, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:19317
    Note: TWP
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    References listed on IDEAS

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    1. Whinston, Michael D., 1983. "Moral hazard, adverse selection, and the optimal provision of social insurance," Journal of Public Economics, Elsevier, vol. 22(1), pages 49-71, October.
    2. Richard J. Arnott & Joseph E. Stiglitz, 1988. "The Basic Analytics of Moral Hazard," NBER Working Papers 2484, National Bureau of Economic Research, Inc.
    3. Spence, Michael, 1978. "Product differentiation and performance in insurance markets," Journal of Public Economics, Elsevier, vol. 10(3), pages 427-447, December.
    4. Richard Arnott & Joseph Stiglitz, 1991. "Equilibrium in Competitive Insurance Markets with Moral Hazard," NBER Working Papers 3588, National Bureau of Economic Research, Inc.
    5. Richard Arnott & Joseph E. Stiglitz, 1991. "Price Equilibrium, Efficiency, and Decentralizability in Insurance Markets," NBER Working Papers 3642, National Bureau of Economic Research, Inc.
    6. Chassagnon, A. & Chiappori, P.A., 1994. "Insurance Under Moral Hazard and Adverse Selection: The Case of Pure Competition," Papers 28, Laval - Laboratoire Econometrie.
    7. Andrei Bougrov & Robert Johnson & Benno Ndulo & Pedro Paez & Avinash Persaud & Heidemarie Wieczorek-Zeul & Akhtar Aziz Zeti & Charles Goodhart & Jomo Kwame Sundaram & Youssef Boutros-Ghali & José Anto, 2010. "The Stiglitz Report," SciencePo Working papers Main hal-03415638, HAL.
      • Andrei Bougrov & Robert Johnson & Benno Ndulo & Pedro Paez & Avinash Persaud & Heidemarie Wieczorek-Zeul & Akhtar Aziz Zeti & Charles Goodhart & Jomo Kwame Sundaram & Youssef Boutros-Ghali & José Anto, 2010. "The Stiglitz Report," Working Papers hal-03415638, HAL.
    8. Joseph E. Stiglitz & Andrew Weiss, 1987. "Macro-Economic Equilibrium and Credit Rationing," NBER Working Papers 2164, National Bureau of Economic Research, Inc.
    9. repec:bla:scandj:v:90:y:1988:i:3:p:383-413 is not listed on IDEAS
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    Cited by:

    1. Joseph E. Stiglitz & Jungyoll Yun & Andrew Kosenko, 2017. "Equilibrium in a Competitive Insurance Market Under Adverse Selection with Endogenous Information," NBER Working Papers 23556, National Bureau of Economic Research, Inc.
    2. Stiglitz, Joseph E., 2018. "Pareto efficient taxation and expenditures: Pre- and re-distribution," Journal of Public Economics, Elsevier, vol. 162(C), pages 101-119.
    3. Georges Dionne & Casey Rothschild, 2014. "Economic Effects of Risk Classification Bans," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 39(2), pages 184-221, September.
    4. Xinyan Shi & Lydia Gan, 2023. "Equilibrium in Competitive Insurance Markets with Medical Tourism," Studies in Microeconomics, , vol. 11(2), pages 246-269, August.
    5. Chen, Bingzheng & Feng, Frank Y. & Powers, Michael R. & Qiu, Joseph, 2019. "Risk-revealing contracts for government-sponsored microinsurance," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).

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    More about this item

    JEL classification:

    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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