IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Optimal Insurance with Adverse Selection

  • Hector Chade
  • Edward Schlee

We solve the principal-agent problem of a monopolist insurer selling to an agent whose riskiness (loss chance) is private information, a problem introduced in Stiglitz's (1977) seminal paper. For an \emph{arbitrary} type distribution, we prove several properties of optimal menus, such as efficiency at the top and downward distortions elsewhere. We show that these results extend beyond the insurance problem we emphasize. We also prove that the principal always prefers an agent facing a larger loss, and a poorer one if the agent's risk aversion decreases with wealth. For the standard case of a continuum of types and a smooth density, we show that, under the mild assumptions of a log-concave density and decreasing absolute risk aversion, the optimal premium is \emph{backwards-S shaped} in the amount of coverage, first concave, then convex. This curvature result implies that quantity discounts are consistent with adverse selection in insurance, contrary to the conventional wisdom from competitive models.

(This abstract was borrowed from another version of this item.)

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.dklevine.com/archive/refs4122247000000002175.pdf
Download Restriction: no

Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 122247000000002175.

as
in new window

Length:
Date of creation: 02 Jun 2008
Date of revision:
Handle: RePEc:cla:levarc:122247000000002175
Contact details of provider: Web page: http://www.dklevine.com/

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Martin Hellwig, 2006. "Incentive Problems with Unidimensional Hidden Characteristics: A Unified Approach," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2006_26, Max Planck Institute for Research on Collective Goods, revised Apr 2010.
  2. Pierre‐André Chiappori & Bruno Jullien & Bernard Salanié & François Salanié, 2006. "Asymmetric information in insurance: general testable implications," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 783-798, December.
  3. Guesnerie, Roger & Laffont, Jean-Jacques, 1984. "A complete solution to a class of principal-agent problems with an application to the control of a self-managed firm," Journal of Public Economics, Elsevier, vol. 25(3), pages 329-369, December.
  4. Alberto Bennardo & P.A. Chiappori, 2002. "Bertrand and Walras equilibria under moral hazard," CSEF Working Papers 87, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  5. Richard J. Arnott & Joseph E. Stiglitz, 1988. "Randomization with Asymmetric Information," NBER Working Papers 2507, National Bureau of Economic Research, Inc.
  6. Jullien, Bruno, 1997. "Participation Constraints in Adverse Selection Models," IDEI Working Papers 67, Institut d'Économie Industrielle (IDEI), Toulouse.
  7. Alma Cohen & Liran Einav, 2005. "Estimating Risk Preferences from Deductible Choice," Discussion Papers 04-031, Stanford Institute for Economic Policy Research.
  8. Chade, Hector & Vera de Serio, Virginia N., 2014. "Wealth effects and agency costs," Games and Economic Behavior, Elsevier, vol. 86(C), pages 1-11.
  9. Pierre-Andre Chiappori & Bernard Salanie, 2000. "Testing for Asymmetric Information in Insurance Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 56-78, February.
  10. Fudenberg, Drew & Tirole, Jean, 1990. "Moral Hazard and Renegotiation in Agency Contracts," Econometrica, Econometric Society, vol. 58(6), pages 1279-1319, November.
  11. Ian Jewitt, 1987. "Risk Aversion and the Choice Between Risky Prospects: The Preservation of Comparative Statics Results," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 73-85.
  12. Matthews, Steven & Moore, John, 1987. "Monopoly Provision of Quality and Warranties: An Exploration in the Theory of Multidimensional Screening," Econometrica, Econometric Society, vol. 55(2), pages 441-67, March.
  13. Georges Dionne & Christian Gourieroux & Charles Vanasse, 2001. "Testing for Evidence of Adverse Selection in the Automobile Insurance Market: A Comment," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 444-473, April.
  14. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
  15. Georg Noldeke & Larry Samuelson, 2006. "Optimal Bunching without Optimal Control," Levine's Bibliography 784828000000000502, UCLA Department of Economics.
  16. Biais, Bruno & Martimort, David & Rochet, Jean-Charles, 1998. "Competing Mechanisms in a Commun Value Environment," IDEI Working Papers 75, Institut d'Économie Industrielle (IDEI), Toulouse.
  17. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
  18. Szalay, Dezsö, 2008. "Monopoly, Non-linear Pricing, and Imperfect Information : A Reconsideration of the Insurance Market," The Warwick Economics Research Paper Series (TWERPS) 863, University of Warwick, Department of Economics.
  19. Prescott, Edward C & Townsend, Robert M, 1984. "Pareto Optima and Competitive Equilibria with Adverse Selection and Moral Hazard," Econometrica, Econometric Society, vol. 52(1), pages 21-45, January.
  20. Spence, Michael, 1977. "Nonlinear prices and welfare," Journal of Public Economics, Elsevier, vol. 8(1), pages 1-18, August.
  21. Tomas Philipson & John Cawley, 1999. "An Empirical Examination of Information Barriers to Trade in Insurance," American Economic Review, American Economic Association, vol. 89(4), pages 827-846, September.
  22. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  23. Joseph E. Stiglitz, 1977. "Monopoly, Non-linear Pricing and Imperfect Information: The Insurance Market," Review of Economic Studies, Oxford University Press, vol. 44(3), pages 407-430.
  24. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
  25. Page, Frank H, Jr, 1992. "Mechanism Design for General Screening Problems with Moral Hazard," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 265-81, April.
  26. Ormiston, Michael B & Schlee, Edward E, 2001. "Mean-Variance Preferences and Investor Behaviour," Economic Journal, Royal Economic Society, vol. 111(474), pages 849-61, October.
  27. Thiele, Henrik & Wambach, Achim, 1999. "Wealth Effects in the Principal Agent Model," Journal of Economic Theory, Elsevier, vol. 89(2), pages 247-260, December.
  28. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 209-27, March.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:cla:levarc:122247000000002175. 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: (David K. Levine)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.