Advanced Search
MyIDEAS: Login to save this paper or follow this series

Optimal Insurance with Adverse Selection

Contents:

Author Info

  • Hector Chade
  • Edward Schlee

Abstract

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.)

Download Info

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

Bibliographic Info

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/

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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. Szalay, Dezsö, 2008. "Monopoly, Non-linear Pricing, and Imperfect Information : A Reconsideration of the Insurance Market," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 863, University of Warwick, Department of Economics.
  2. Pierre-André Chiappori & Bernard Salanié, 1997. "Testing for Asymmetric Information in Insurance Markets," Working Papers, Centre de Recherche en Economie et Statistique 97-11, Centre de Recherche en Economie et Statistique.
  3. Alberto Bennardo & Pierre-Andre Chiappori, 2003. "Bertrand and Walras Equilibria under Moral Hazard," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 111(4), pages 785-817, August.
  4. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, Springer, vol. 5(2), pages 209-27, March.
  5. 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, Elsevier, vol. 25(3), pages 329-369, December.
  6. 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, Max Planck Institute for Research on Collective Goods 2006_26, Max Planck Institute for Research on Collective Goods, revised Apr 2010.
  7. Pierre‐André Chiappori & Bruno Jullien & Bernard Salanié & François Salanié, 2006. "Asymmetric information in insurance: general testable implications," RAND Journal of Economics, RAND Corporation, RAND Corporation, vol. 37(4), pages 783-798, December.
  8. Alma Cohen & Liran Einav, 2005. "Estimating Risk Preferences from Deductible Choice," NBER Working Papers 11461, National Bureau of Economic Research, Inc.
  9. Jullien, Bruno, 2000. "Participation Constraints in Adverse Selection Models," Journal of Economic Theory, Elsevier, Elsevier, vol. 93(1), pages 1-47, July.
  10. Richard Arnott & Joseph E Stiglitz, 2010. "Randomization with Asymmetric Information," Levine's Working Paper Archive 2054, David K. Levine.
  11. Georg Noldeke & Larry Samuelson, 2006. "Optimal Bunching without Optimal Control," Levine's Bibliography 784828000000000502, UCLA Department of Economics.
  12. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
  13. Fudenberg, Drew & Tirole, Jean, 1990. "Moral Hazard and Renegotiation in Agency Contracts," Econometrica, Econometric Society, Econometric Society, vol. 58(6), pages 1279-1319, November.
  14. Steven Matthews & John Moore, 1985. "Monopoly Provision of Quality and Warranties: An Exploration in the Theory of Multidimensional Screening," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 661, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Bruno Biais & David Martimort & Jean-Charles Rochet, 2000. "Competing Mechanisms in a Common Value Environment," Econometrica, Econometric Society, Econometric Society, vol. 68(4), pages 799-838, July.
  16. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, Econometric Society, vol. 70(2), pages 583-601, March.
  17. Thiele, Henrik & Wambach, Achim, 1999. "Wealth Effects in the Principal Agent Model," Journal of Economic Theory, Elsevier, Elsevier, vol. 89(2), pages 247-260, December.
  18. John Cawley & Tomas Philipson, 1996. "An Empirical Examination of Information Barriers to Trade in Insurance," NBER Working Papers 5669, National Bureau of Economic Research, Inc.
  19. Rothschild, Michael & Stiglitz, Joseph E, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 90(4), pages 630-49, November.
  20. Spence, Michael, 1977. "Nonlinear prices and welfare," Journal of Public Economics, Elsevier, Elsevier, vol. 8(1), pages 1-18, August.
  21. Prescott, Edward C & Townsend, Robert M, 1984. "Pareto Optima and Competitive Equilibria with Adverse Selection and Moral Hazard," Econometrica, Econometric Society, Econometric Society, vol. 52(1), pages 21-45, January.
  22. 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, University of Chicago Press, vol. 109(2), pages 444-473, April.
  23. Jewitt, Ian, 1987. "Risk Aversion and the Choice between Risky Prospects: The Preservation of Comparative Statics Results," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 54(1), pages 73-85, January.
  24. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, Econometric Society, vol. 62(1), pages 157-80, January.
  25. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, Elsevier, vol. 18(2), pages 301-317, August.
  26. Stiglitz, Joseph E, 1977. "Monopoly, Non-linear Pricing and Imperfect Information: The Insurance Market," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 44(3), pages 407-30, October.
  27. Ormiston, Michael B & Schlee, Edward E, 2001. "Mean-Variance Preferences and Investor Behaviour," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 111(474), pages 849-61, October.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Daniel L. McFadden & Carlos E. Noton & Pau Olivella, 2012. "Remedies for Sick Insurance," NBER Working Papers 17938, National Bureau of Economic Research, Inc.
  2. Georges Dionne & Casey G. Rothschild, 2014. "Economic Effects of Risk Classification Bans," Cahiers de recherche, CIRPEE 1420, CIRPEE.
  3. Nathaniel Hendren, 2012. "Private Information and Insurance Rejections," NBER Working Papers 18282, National Bureau of Economic Research, Inc.

Lists

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

Statistics

Access and download statistics

Corrections

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.