Skip to main content
SpringerLink
Log in

Estimating Risk Attitudes using Lotteries: A Large Sample Approach

  • Published:
Journal of Risk and Uncertainty Aims and scope Submit manuscript

Abstract

Attitudes towards risk play a major role in many economic decisions. In empirical studies it is quite often assumed that attitudes towards risk do not vary across individuals. This paper questions this assumption and analyses which factors influence an individual's risk attitude. Based on questions on lotteries in a large household survey we first semiparametrically estimate an index for risk aversion. We only make weak assumptions about the underlying decision process and our estimation method allows for generalisations of expected utility. We then estimate a structural model based on Cumulative Prospect Theory. Expected utility is strongly rejected and both the value function and the probability weighting function vary significantly with (among other things) age, income, and wealth of the individual.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abdellaoui, M. (1998). “Parameter-Free Eliciting of Utilities and Probability Weighting Functions,” forthcoming in Management Science.

  • Allais, M. (1953). “Le comportement de l'Homme Rationnel devant le Risque, Critique des Postulates et Axiomes de l'Ecole Americaine,” Econometrica 21, 503–546.

    Google Scholar 

  • Arrow, K. (1965). Aspects of the Theory of Risk-bearing. Helsinki: Yrjö Jahnssonin Säätiö.

    Google Scholar 

  • Beattie, J., and G. Loomes. (1997). “The Impact of Incentives upon Risky Choice Experiments',” Journal of Risk and Uncertainty 14, 155–168.

    Google Scholar 

  • Beetsma, R. M. W. J., and P. C. Schotman. (1997). “Measuring Risk Attitudes in a Natural Experiment: an Empirical Analysis of the Television Game Show LINGO., CentER discussion paper no 9808, Tilburg University, Tilburg.

    Google Scholar 

  • Bell, D. (1982) “Regret in Decision Making under Uncertainty,” Operations Research 30, 961–981.

    Google Scholar 

  • Bell, D. (1985). “Putting a Premium on Regret”, Management Science 31, 117–120.

    Google Scholar 

  • Bone, J., J. D. Hey, and J. Suckling. (1999). “Are Groups More (or less) Consistent Than Individuals?,” Journal of Risk and Uncertainty 18, 63–81.

    Google Scholar 

  • Camerer, C. F. (1989). “An Experimental Test of Several Generalized Utility Theories,” Journal of Risk and Uncertainty 2, 61–104.

    Google Scholar 

  • Camerer, C. F. (1995). “Individual Decision Making.” In J. H. Kagel and A. E. Roth (eds.), Handbook of Experimental Economics. Princeton, NJ: Princeton University.

    Google Scholar 

  • Camerer, C. F. and R. M. Hogarth. (1999). “The Effects of Financial Incentives in Experiments: A Review and Capital-Labor-Production Framework,” Journal of Risk and Uncertainty 19, 7–42.

    Google Scholar 

  • Carbone, E., and J. D. Hey. (1994). “Discriminating Between Preference Functionals.A Preliminary Monte Carlo Study,” Journal of Risk and Uncertainty 8, 23–242.

    Google Scholar 

  • Carbone, E., and J. D. Hey. (2000). “Which Error Story is Best?,” Journal of Risk and Uncertainty 20, 161–176.

    Google Scholar 

  • Cavanagh, C., and R. P. Sherman. (1998). “Rank Estimators for Monotonic Index Models,” Journal of Econometrics 84, 351–381.

    Google Scholar 

  • Conlisk, J. (1989). “Three Variants on the Allais Example,” American Economic Review 79, 392–407.

    Google Scholar 

  • Delecroix, M., W. Härdle, and M. Hristache. (1997). “Efficient Estimation in Single Index Regression,” mimeo, Humboldt Universität, Berlin.

    Google Scholar 

  • Delquie, P. (1997). “ 'Bi-Matching'—A New Preference Assessment Method to Reduce Compatibility Effects,” Management Science 43, 640–658.

    Google Scholar 

  • Fennema, H., and M. van Assen. (1999). “Measuring the Utility of Losses by Means of the Tradeoff Method,” Journal of Risk and Uncertainty 17, 277–295.

    Google Scholar 

  • Gonzalez, R., and G. Wu. (1999). “On the Shape of the Probability Weighting Function,” Cognitive Psychology 38, 129–166.

    Google Scholar 

  • Grether, D. M., and C. R. Plott. (1979). “Economic Theory of Choice and the Preference Reversal Phenomenon,. American Economic Review 85, 260–266.

    Google Scholar 

  • Guiso, L., T. Japelli, and D. Terlizzese. (1992). “Earnings Uncertainty and Precautionary Saving,” Journal of Monetary Economics 30, 307–337.

    Google Scholar 

  • Gul, F. (1991). “A Theory of Disappointment Aversion,” Econometrica 59, 667–686.

    Google Scholar 

  • Hajivassiliou, V. A. (1993). “Simulation Estimation Methods for Limited Dependent Variables Models.” In G. S. Maddala, C. R. Rao, and H. D. Vinod (eds.), Handbook of statistics, Vol 11. Amsterdam: North-Holland.

    Google Scholar 

  • Hall, P. (1990). “On the Bias of Variable Bandwidth Curve Estimators,” Biometrika 77, 529–535.

    Google Scholar 

  • Hall, P. and J. S. Marron. (1988). “Variable Window Width Kernel Estimates of Probability Density Estimates,” Probability Theory and Related Fields 80, 37–49.

    Google Scholar 

  • Han, A. K. (1987). “Non-parametric Analysis of Generalized Regression Model,” Journal of Econometrics 35, 303–316.

    Google Scholar 

  • Härdle, W., and O. Linton. (1994). “Applied Nonparametric Methods.” In R. Engle and D. McFadden (eds.), Handbook of Econometrics, Vol IV. Amsterdam: North-Holland.

    Google Scholar 

  • Harless, D. W., and C. F. Camerer. (1994). “The Predictive Utility of Generalized Expected Utility Theoreies,” Econometrica 62, 1251–1290.

    Google Scholar 

  • Hartog, J., N. Jonker, and H. Oosterbeek. (1997). “On a Simple Measure of Risk Aversion,” mimeo, University of Amsterdam, Amsterdam.

    Google Scholar 

  • Hershey, J. C., and P. J. H. Schoemaker. (1985). “Probability versus Certainty Equivalence Models in Utility Measurement,” Management Science 31, 1213–1231.

    Google Scholar 

  • Hey, J. D. and E. Carbone. (1995). “Stochastic Choice with Deterministic Preferences: An Experimental Investigation,. Economics Letters 47, 161–167.

    Google Scholar 

  • Horowitz, J. L. (1992). “A Smoothed Maximum Score Estimator for the Binary Response Model,” Econometrica 60, 505–531.

    Google Scholar 

  • Jullien, B., and Salanie. (1997). “The Attitudes Towards Risk of Racetrack Bettors,” mimeo, Universite des Sciences Sociales de Toulouse, Toulouse.

    Google Scholar 

  • Kahneman, D., J. L. Knetsch, and R. H. Thaler. (1991). “Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias,” Journal of Economic Perspectives 5, 193–206.

    Google Scholar 

  • Kahneman, D., P. Slovic, and A. Tversky (1982). Judgment Under Uncertainty: Heuristics and Biases. New York: Cambridge University Press.

    Google Scholar 

  • Kahneman, D., and A. Tversky. (1979). “Prospect Theory: An Analysis of Decision Under Risk,” Econometrica 47, 263–291.

    Google Scholar 

  • Klein, R. W., and R. H. Spady. (1993). “An Efficient Semiparametric Estimator for Binary Response Models,” Econometrica 61, 387–421.

    Google Scholar 

  • Lattimore, P. M. J., J. R. Baker, and A. D. Witte. (1992). “The Influence of Probability on Risky Choice,” Journal of Economic Behavior and Organization 17, 377–400.

    Google Scholar 

  • Lee, M.-J. (1996). Methods of Moments and Semiparametric Econometrics for Limited Dependent Variable Models. New York: Springer Verlag.

    Google Scholar 

  • Loomes, G., and R. Sugden. (1982). “Regret Theory: An Alternative Theory of Rational Choice Under Uncertainty,. Economic Journal 92, 805–824.

    Google Scholar 

  • Lusardi, A. (1997). “Precautionary Saving and Subjective Earnings Variance,” Economics Letters 57, 319–326.

    Google Scholar 

  • Machina, M. J. (1982). “Expected Utility Without the Independence Axiom,” Econometrica 50, 277–323.

    Google Scholar 

  • Machina, M. J. (1987), “Choice Under Uncertainty: Problems Solved and Unsolved,” Journal of Economic Perspectives 1, 121–154.

    Google Scholar 

  • Nyhus, E. K. (1996). “The VSB-CentER Savings Project: Data Collection Methods, Questionnaries and Sampling Orocedures,” mimeo, CentER, Tilburg.

    Google Scholar 

  • Pålsson, A.-M. (1996). “Does the Degree of Relative Risk Aversion Vary with Household Characteristics?,” Journal of Economic Psychology 17, 771–787.

    Google Scholar 

  • Pratt, J. (1964). “Risk Aversion in the Small and in the Large,” Econometrica 32, 122–136.

    Google Scholar 

  • Prelec, D. (1998). “The Probability Weighting Function,” Econometrica 66, 497–528.

    Google Scholar 

  • Quiggin, J. (1982). “A Theory of Anticipated Utility. Journal of Economic Behaviour and Organization 3, 323–343.

    Google Scholar 

  • Seidl, C., and S. Traub. (1997). “Assessment Biases in Utility Functions,” mimeo, Christian-Albrechts-Universität, Kiel.

    Google Scholar 

  • Tversky, A., and C. R. Fox. (1995). “Weighing Risk and Uncertainty,” Psychological Review 2, 269–283.

    Google Scholar 

  • Tversky, A., and D. Kahneman. (1992). “Advances in Prospect Theory: Cumulative Representation of Uncertainty,. Journal of Risk and Uncertainty 5, 297–323.

    Google Scholar 

  • Viscusi, K. W. (1989). “Prospective Reference Theory: Toward an Explanation of the Paradoxes,” Journal of Risk and Uncertainty 2, 235–264.

    Google Scholar 

  • Wakker, P. P. (1994). “Separating Marginal Utility and Probabilistic Risk Aversion,” Theory and Decision 36, 1–44.

    Google Scholar 

  • Wakker, P. P., and D. Deneffe. (1996). “Eliciting von Neuman-Morgenstern Utilities When Probabilities are Distorted or Unknown,” Management Science 8, 1131–1150.

    Google Scholar 

  • Warneryd, K. E. (1996). “Risk Attitudes and Risky Behavior,” Journal of Economic Psychology 17, 749–770.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Marketing, Erasmus University, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands

    Bas Donkers

  2. Tilburg University, The Netherlands

    Bertrand Melenberg & Arthur Van Soest

Authors
  1. Bas Donkers
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bertrand Melenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arthur Van Soest
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Donkers, B., Melenberg, B. & Van Soest, A. Estimating Risk Attitudes using Lotteries: A Large Sample Approach. Journal of Risk and Uncertainty 22, 165–195 (2001). https://doi.org/10.1023/A:1011109625844

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011109625844

Search

Navigation