IDEAS home Printed from https://ideas.repec.org/p/mpg/wpaper/2004_06.html
   My bibliography  Save this paper

Risk Aversion in the Small and in the Large. When Outcomes are Multidimensional

Author

Listed:
  • Martin Hellwig

    (Max Planck Institute for Research on Collective Goods, Bonn, Germany)

Abstract

The paper discusses criteria for comparing risk aversion of decision makers when outcomes are multidimensional. A weak concept, ”commodity specific greater risk aversion”, is based on the comparison of risk premia paid in a specified commodity. A stronger concept, ”uniformly greater risk aversion” is based on the comparison of risk premia regardless of what commodities are used for payment. Neither concept presumes that von Neumann-Morgenstern utility functions are ordinally equivalent. Nonincreasing consumption specific risk aversion is shown to be sufficient to make randomization undesirable in an agency problem with hidden characteristics.

Suggested Citation

  • Martin Hellwig, 2004. "Risk Aversion in the Small and in the Large. When Outcomes are Multidimensional," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2004_6, Max Planck Institute for Research on Collective Goods.
    • Handle: RePEc:mpg:wpaper:2004_06
    as

    Download full text from publisher

    File URL: http://www.coll.mpg.de/pdf_dat/2004_06online.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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 441-467, March.
    2. Richard E. Kihlstrom & Leonard J. Mirman, 1981. "Constant, Increasing and Decreasing Risk Aversion with Many Commodities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(2), pages 271-280.
    3. Aaron S. Edlin & Chris Shannon, 1998. "Strict Single Crossing and the Strict Spence-Mirrlees Condition: A Comment on Monotone Comparative Statics," Econometrica, Econometric Society, vol. 66(6), pages 1417-1426, November.
    4. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    5. Brito, Dagobert L. & Hamilton, Jonathan H. & Slutsky, Steven M. & Stiglitz, Joseph E., 1995. "Randomization in optimal income tax schedules," Journal of Public Economics, Elsevier, vol. 56(2), pages 189-223, February.
    6. Stiglitz, Joseph E., 1982. "Self-selection and Pareto efficient taxation," Journal of Public Economics, Elsevier, vol. 17(2), pages 213-240, March.
    7. Joseph E. Stiglitz, 1969. "A Note on Behavior towards Risk with Many Commodities," Cowles Foundation Discussion Papers 262, Cowles Foundation for Research in Economics, Yale University.
    8. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    9. Mirrlees, J. A., 1976. "Optimal tax theory : A synthesis," Journal of Public Economics, Elsevier, vol. 6(4), pages 327-358, November.
    10. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    11. Stiglitz, Joseph E, 1969. "Behavior Towards Risk with Many Commodities," Econometrica, Econometric Society, vol. 37(4), pages 660-667, 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


    Cited by:

    1. Christoph Engel, 2006. "The Difficult Reception of Rigorous Descriptive Social Science in the Law," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2006_1, Max Planck Institute for Research on Collective Goods.
    2. Kannai, Yakar & Selden, Larry & Kang, Minwook & Wei, Xiao, 2016. "Risk neutrality regions," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 75-89.
    3. Sudhir A. Shah, 2016. "The Generalized Arrow-Pratt Coefficient," Working papers 254, Centre for Development Economics, Delhi School of Economics.
    4. Hellwig, Martin F., 2007. "The undesirability of randomized income taxation under decreasing risk aversion," Journal of Public Economics, Elsevier, vol. 91(3-4), pages 791-816, April.
    5. Martin Hellwig, 2008. "A Maximum Principle for Control Problems with Monotonicity Constraints," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2008_04, Max Planck Institute for Research on Collective Goods.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hellwig, Martin F., 2007. "The undesirability of randomized income taxation under decreasing risk aversion," Journal of Public Economics, Elsevier, vol. 91(3-4), pages 791-816, April.
    2. Martin Hellwig, 2010. "Utilitarian mechanism design for an excludable public good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(3), pages 361-397, September.
    3. Hellwig, Martin F., 2007. "A contribution to the theory of optimal utilitarian income taxation," Journal of Public Economics, Elsevier, vol. 91(7-8), pages 1449-1477, August.
    4. Huh, Sungjun & Kim, Insu, 2021. "Real estate and relative risk aversion with generalized recursive preferences," Journal of Macroeconomics, Elsevier, vol. 68(C).
    5. Philippe Chone & Guy Laroque, 2010. "Negative Marginal Tax Rates and Heterogeneity," American Economic Review, American Economic Association, vol. 100(5), pages 2532-2547, December.
    6. Sudhir A. Shah, 2009. "Duality Mappings For The Theory of Risk Aversion with Vector Outcomes," Working Papers id:2085, eSocialSciences.
    7. Craig Brett, 2007. "Optimal nonlinear taxes for families," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 14(3), pages 225-261, June.
    8. Eric T. Swanson, 2020. "Implications of Labor Market Frictions for Risk Aversion and Risk Premia," American Economic Journal: Macroeconomics, American Economic Association, vol. 12(2), pages 194-240, April.
    9. Sudhir A. Shah, 2007. "Duality mappings for the theory of risk aversion with vector outcomes," Working papers 160, Centre for Development Economics, Delhi School of Economics.
    10. Brito, Dagobert L. & Hamilton, Jonathan H. & Slutsky, Steven M. & Stiglitz, Joseph E., 1995. "Randomization in optimal income tax schedules," Journal of Public Economics, Elsevier, vol. 56(2), pages 189-223, February.
    11. Stiglitz, Joseph E., 2018. "Pareto efficient taxation and expenditures: Pre- and re-distribution," Journal of Public Economics, Elsevier, vol. 162(C), pages 101-119.
    12. Morten Nyborg Støstad & Frank Cowell, 2021. "Inequality as an Externality: Consequences for Tax Design," PSE Working Papers halshs-03495989, HAL.
    13. Arthur Charpentier & Alfred Galichon & Marc Henry, 2012. "Local Utility and Multivariate Risk Aversion," CIRJE F-Series CIRJE-F-836, CIRJE, Faculty of Economics, University of Tokyo.
    14. Brito, Dagobert L, et al, 1990. "Pareto Efficient Tax Structures," Oxford Economic Papers, Oxford University Press, vol. 42(1), pages 61-77, January.
    15. Jacobs, Bas & van der Ploeg, Frederick, 2019. "Redistribution and pollution taxes with non-linear Engel curves," Journal of Environmental Economics and Management, Elsevier, vol. 95(C), pages 198-226.
    16. Florian Scheuer, 2014. "Entrepreneurial Taxation with Endogenous Entry," American Economic Journal: Economic Policy, American Economic Association, vol. 6(2), pages 126-163, May.
    17. Sören Blomquist & Luca Micheletto, 2008. "Age‐related Optimal Income Taxation," Scandinavian Journal of Economics, Wiley Blackwell, vol. 110(1), pages 45-71, March.
    18. Robin Boadway, 1998. "The Mirrlees Approach to the Theory of Economic Policy," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 5(1), pages 67-81, February.
    19. Slemrod, Joel & Yitzhaki, Shlomo & Mayshar, Joram & Lundholm, Michael, 1994. "The optimal two-bracket linear income tax," Journal of Public Economics, Elsevier, vol. 53(2), pages 269-290, February.
    20. Saez, Emmanuel, 2002. "The desirability of commodity taxation under non-linear income taxation and heterogeneous tastes," Journal of Public Economics, Elsevier, vol. 83(2), pages 217-230, February.

    More about this item

    Keywords

    Multidimensional Risks; Risk Aversion; Risk Premia; Randomization in Incentive Schemes;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mpg:wpaper:2004_06. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Marc Martin (email available below). General contact details of provider: https://edirc.repec.org/data/mppggde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.