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Mixture Models of Choice Under Risk

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  • Anna Conte
  • John D Hey
  • Peter G Moffatt

Abstract

This paper is concerned with estimating preference functionals for choice under risk from the choice behaviour of individuals. We start from the observation that there is heterogeneity in behaviour between individuals and within individuals. By ‘heterogeneity between individuals’ we mean that people are different, not only in terms of which type of preference functional that they have, but also in terms of their parameters for these functionals. By ‘heterogeneity within individuals’ we mean that behaviour may be different even by the same individual for the same choice problem. Given the heterogeneity between individuals, the assumption of a ‘representative agent’ preference functional to represent the preference functional of all individuals may well lead to biased estimates. Given the heterogeneity within individuals, we should think carefully about the source of this heterogeneity and model it appropriately, for otherwise we get biased estimates. We propose solutions to both of these problems, concentrating particularly, but not exclusively, on using a Mixture Model to capture the heterogeneity of preference functionals across individuals.

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Bibliographic Info

Paper provided by Department of Economics, University of York in its series Discussion Papers with number 07/06.

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Date of creation: Apr 2007
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Handle: RePEc:yor:yorken:07/06

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Postal: Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom
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Fax: (0)1904 323759
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Web page: http://www.york.ac.uk/economics/
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Keywords: errors; expected utility theory; experimental economics; maximum simulated likelihood; mixture models; preference functionals; risky choice; rank dependent expected utility theory; unobserved heterogeneity;

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  1. Peter Moffatt, 2005. "Stochastic Choice and the Allocation of Cognitive Effort," Experimental Economics, Springer, vol. 8(4), pages 369-388, December.
  2. David Buschena & David Zilberman, 2008. "Generalized expected utility, heteroscedastic error, and path dependence in risky choice," Journal of Risk and Uncertainty, Springer, vol. 36(2), pages 201-201, April.
  3. Peter P. Wakker, 2008. "Explaining the characteristics of the power (CRRA) utility family," Health Economics, John Wiley & Sons, Ltd., vol. 17(12), pages 1329-1344.
  4. Ballinger, T Parker & Wilcox, Nathaniel T, 1997. "Decisions, Error and Heterogeneity," Economic Journal, Royal Economic Society, vol. 107(443), pages 1090-1105, July.
  5. Loomes, Graham & Moffatt, Peter G & Sugden, Robert, 2002. " A Microeconometric Test of Alternative Stochastic Theories of Risky Choice," Journal of Risk and Uncertainty, Springer, vol. 24(2), pages 103-30, March.
  6. David Buschena & David Zilberman, 2000. "Generalized Expected Utility, Heteroscedastic Error, and Path Dependence in Risky Choice," Journal of Risk and Uncertainty, Springer, vol. 20(1), pages 67-88, January.
  7. Peter Moffatt & Simon Peters, 2001. "Testing for the Presence of a Tremble in Economic Experiments," Experimental Economics, Springer, vol. 4(3), pages 221-228, December.
  8. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
  9. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387.
  10. Henry Stott, 2006. "Cumulative prospect theory's functional menagerie," Journal of Risk and Uncertainty, Springer, vol. 32(2), pages 101-130, March.
  11. Nathaniel T Wilcox, 2006. "Theories of Learning in Games and Heterogeneity Bias," Econometrica, Econometric Society, vol. 74(5), pages 1271-1292, 09.
  12. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
  13. Hey, John D., 1995. "Experimental investigations of errors in decision making under risk," European Economic Review, Elsevier, vol. 39(3-4), pages 633-640, April.
  14. Fabrizio Botti & Anna Conte & Daniela T. Di Cagno & Carlo D'Ippoliti, . "Risk attitude in real decision proBLEMs," Quaderni DEF 144, Dipartimento di Economia e Finanza, LUISS Guido Carli.
  15. Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, vol. 62(6), pages 1251-89, November.
  16. John Hey, 2001. "Does Repetition Improve Consistency?," Experimental Economics, Springer, vol. 4(1), pages 5-54, June.
  17. Loomes, Graham & Sugden, Robert, 1998. "Testing Different Stochastic Specifications of Risky Choice," Economica, London School of Economics and Political Science, vol. 65(260), pages 581-98, November.
  18. Pavlo Blavatskyy, 2007. "Stochastic expected utility theory," Journal of Risk and Uncertainty, Springer, vol. 34(3), pages 259-286, June.
  19. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  20. Glenn Harrison & E. Rutström, 2009. "Expected utility theory and prospect theory: one wedding and a decent funeral," Experimental Economics, Springer, vol. 12(2), pages 133-158, June.
  21. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  22. Hey, John D & Orme, Chris, 1994. "Investigating Generalizations of Expected Utility Theory Using Experimental Data," Econometrica, Econometric Society, vol. 62(6), pages 1291-1326, November.
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