Abstract
Choice behavior is typically evaluated by assuming that the data is generated by one latent decision-making process or another. What if there are two (or more) latent decision-making processes generating the observed choices? Some choices might then be better characterized as being generated by one process, and other choices by the other process. A finite mixture model can be used to estimate the parameters of each decision process while simultaneously estimating the probability that each process applies to the sample. We consider the canonical case of lottery choices in a laboratory experiment and assume that the data is generated by expected utility theory and prospect theory decision rules. We jointly estimate the parameters of each theory as well as the fraction of choices characterized by each. The methodology provides the wedding invitation, and the data consummates the ceremony followed by a decent funeral for the representative agent model that assumes only one type of decision process. The evidence suggests support for each theory, and goes further to identify under what demographic domains one can expect to see one theory perform better than the other. We therefore propose a reconciliation of the debate over two of the dominant theories of choice under risk, at least for the tasks and samples we consider. The methodology is broadly applicable to a range of debates over competing theories generated by experimental and non-experimental data.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Andersen, S., Harrison, G. W., & Rutström, E. E. (2006a). Choice behavior, asset integration, and natural reference points (Working Paper 06-07). Department of Economics, College of Business Administration, University of Central Florida.
Andersen, S., Harrison, G. W., Lau, M. I., & Rutström, E. E. (2006b). Dual criteria decisions (Working Paper 06-11). Department of Economics, College of Business Administration, University of Central Florida.
Andersen, S., Harrison, G. W., Lau, M. I., & Rutström, E. E. (2008). Eliciting risk and time preferences. Econometrica, 76(3), 583–618.
Araña, J. E., & León, C. J. (2005). Flexible mixture distribution modeling of dichotomous choice contingent valuation with heterogeneity. Journal of Environmental Economics & Management, 50(1), 170–188.
Atkinson, A. C. (1970). A method for discriminating between models. Journal of the Royal Statistical Society, Series B, 32, 323–344.
Bardsley, N., & Moffatt, P. G. (2007). The experimetrics of public goods: inferring motivations from contributions. Theory and Decision, 62(2), 161–193.
Benartzi, S., & Thaler, R. H. (1995). Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics, 111(1), 75–92.
Benhabib, J., & Bisin, A. (2005). Modeling internal commitment mechanisms and self-control: a neuroeconomics approach to consumption-saving decisions. Games and Economic Behavior, 52, 460–492.
Brandstätter, E., Gigerenzer, G., & Hertwig, R. (2006). The priority heuristic: making choices without trade-offs. Psychological Review, 113(2), 409–432.
Bruhin, A., Fehr-Duda, H., & Epper, T. F. (2007). Risk and rationality: uncovering heterogeneity in probability distortion (Working Paper 0705). Socioeconomic Institute, University of Zurich.
Camerer, C. F. (1995). Individual decision making. In J. H. Kagel & A. E. Roth (Eds.), The handbook of experimental economics. Princeton: Princeton University Press.
Camerer, C. F., & Ho, T.-H. (1994). Violations of the betweeness axiom and nonlinearity in probability. Journal of Risk and Uncertainty, 8, 167–196.
Cherry, T. L., Frykblom, P., & Shogren, J. F. (2002). Hardnose the dictator. American Economic Review, 92(4), 1218–1221.
Clarke, K. A. (2003). Nonparametric model discrimination in international relations. Journal of Conflict Resolution, 47(1), 72–93.
Clarke, K. A. (2007). A simple distribution-free test for non-nested model selection. Political Analysis, 15(3), 347–363.
Cohen, J. D. (2005). The vulcanization of the human brain: a neural perspective on interactions between cognition and emotion. Journal of Economic Perspectives, 19(4), 3–24.
Conte, A., Hey, J. D., & Moffatt, P. G. (2007). Mixture models of choice under risk (Discussion Paper No. 2007/06). Department of Economics and Related Studies, University of York.
Cox, D. R. (1961). Tests of separate families of hypotheses. In E. G. Charatsis (Ed.), Proceedings of the fourth Berkeley symposium on mathematical statistics and probability (Vol. 1, pp. 105–123). Berkeley: University of California Press.
Cox, D. R. (1962). Further results on tests of separate families of hypotheses. Journal of the Royal Statistical Society, Series B, 24, 406–424.
Cox, J. C., & Sadiraj, V. (2006). Small- and large-stakes risk aversion: implications of concavity calibration for decision theory. Games & Economic Behavior, 56(1), 45–60.
Davidson, R., & MacKinnon, J. G. (1993). Estimation and inference in econometrics. New York: Oxford University Press.
El-Gamal, M. A., & Grether, D. M. (1995). Are people Bayesian? Uncovering behavioral strategies. Journal of the American Statistical Association, 90(432), 1137–1145.
Everitt, B. S. (1996). An introduction to finite mixture distributions. Statistical Methods in Medical Research, 5, 107–127.
Fudenberg, D., & Levine, D. K. (2006). A dual-self model of impulse control. American Economic Review, 96(5), 1449–1476.
George, J. G., Johnson, L. T., & Rutström, E. E. (2007). Social preferences in the face of regulatory change. In T. Cherry, S. Kroll, & J. F. Shogren (Eds.), Experimental methods, environmental economics. Oxford: Routledge.
Geweke, J., & Keane, M. (1999). Mixture of normals probit models. In C. Hsio, K. Lahiri, L.-F. Lee, & M. H. Pesaran (Eds.), Analysis of panel and limited dependent variables: a volume in honor of G.S. Maddala. New York: Cambridge University Press.
Goodman, L. A. (1974a). The analysis of systems of qualitative variables when some of the variables are unobservable: Part I. A modified latent structure approach. American Journal of Sociology, 79, 1179–1259.
Goodman, L. A. (1974b). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215–231.
Grether, D. M., & Plott, C. R. (1979). Economic theory of choice and the preference reversal phenomenon. American Economic Review, 69(4), 623–648.
Haigh, M., & List, J. A. (2005). Do professional traders exhibit myopic loss aversion? An experimental analysis. Journal of Finance, 60(1), 523–534.
Harless, D. W., & Camerer, C. F. (1994). The predictive utility of generalized expected utility theories. Econometrica, 62, 1251–1289.
Harrison, G. W., & List, J. A. (2004). Field experiments. Journal of Economic Literature, 42(4), 1013–1059.
Harrison, G. W., & Rutström, E. E. (2008). Risk aversion in the laboratory. In J. C. Cox & G. W. Harrison (Eds.), Research in experimental economics : Vol. 12. Risk aversion in experiments. Bingley: Emerald.
Harrison, G. W., Humphrey, S. J., & Verschoor, A. (2005). Choice under uncertainty: evidence from Ethiopia, India and Uganda (Working Paper 05-29). Department of Economics, College of Business Administration, University of Central Florida.
Haruvy, E., Stahl, D. O., & Wilson, P. W. (2001). Modeling and testing for heterogeneity in observed strategic behavior. Review of Economics and Statistics, 83(1), 146–157.
Heckman, J., & Singer, B. (1984). A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica, 52(2), 271–320.
Hey, J. D., & Orme, C. (1994). Investigating generalizations of expected utility theory using experimental data. Econometrica, 62(6), 1291–1326.
Holt, C. A., & Laury, S. K. (2002). Risk aversion and incentive effects. American Economic Review, 92(5), 1644–1655.
Hosmer, D. W., & Lemeshow, S. (2000). Applied logistic regression (2nd edn.). New York: Wiley.
Hurley, T. M., & Shogren, J. F. (2005). An experimental comparison of induced and elicited beliefs. Journal of Risk & Uncertainty, 30(2), 169–188.
Johnson, L. T., Rutström, E. E., & George, J. G. (2006). Income distribution preferences and regulatory change in social dilemmas. Journal of Economic Behavior & Organization, 61(2), 181–198.
Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47(2), 263–291.
Kirman, A. P. (1992). Whom or what does the representative individual represent? Journal of Economic Perspectives, 6(2), 117–136.
Köbberling, V., & Wakker, P. P. (2005). An index of loss aversion. Journal of Economic Theory, 122, 119–131.
Kumbhakar, S. C., & Lovell, C. A. K. (2000). Stochastic frontier analysis. New York: Cambridge University Press.
Liang, K.-Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22.
List, J. A. (2002). Preference reversals of a different kind: the more is less phenomenon. American Economic Review, 92, 1636–1643.
List, J. A. (2003). Does market experience eliminate market anomalies. Quarterly Journal of Economics, 118, 41–71.
List, J. A. (2004). Neoclassical theory versus prospect theory: evidence from the marketplace. Econometrica, 72(2), 615–625.
Loomes, G., & Sugden, R. (1998). Testing different stochastic specifications of risky choice. Economica, 65, 581–598.
Lopes, L. L. (1995). Algebra and process in the modeling of risky choice. In J. R. Busemeyer, R. Hastie, & D. L. Medin (Eds.), Decision making from a cognitive perspective. San Diego: Academic Press.
Lopes, L. L., & Oden, G. C. (1999). The role of aspiration level in risky choice: a comparison of cumulative prospect theory and SP/A theory. Journal of Mathematical Psychology, 43, 286–313.
Luce, R. D., & Suppes, P. (1965). Preference, utility, and subjective probability. In R. D. Luce, R. R. Bush, & E. Galanter (Eds.), Handbook of mathematical psychology (Vol. 3, pp. 249–410). New York: Wiley.
Marschak, J. (1960). Binary choice constraints on random utility indications. In K. Arow (Ed.), Stanford symposium on mathematical models in the social sciences. Stanford: Stanford University Press.
McLachlan, G., & Peel, D. (2000). Finite mixture models. New York: Wiley.
Oehlert, G. W. (1992). A note on the delta method. The American Statistician, 46(1), 27–29.
Papke, L. E., & Wooldridge, J. M. (1996). Econometric methods for fractional response variables with an application to 401(K) plan participation rates. Journal of Applied Econometrics, 11, 619–632.
Pearson, K. (1894). Contribution to the mathematical theory of evolution. Philosophical Transactions A, 185, 71–110.
Pesaran, M. H. (1981). Pitfalls of testing non-nested hypotheses by the Lagrange multiplier method. Journal of Econometrics, 17, 323–331.
Pollak, R. A., & Wales, T. J. (1991). The likelihood dominance criterion: a new approach to model selection. Journal of Econometrics, 47, 227–242.
Prelec, D. (1998). The probability weighting function. Econometrica, 66(3), 497–527.
Quandt, R. E. (1974). A comparison of methods for testing nonnested hypotheses. Review of Economics and Statistics, 56, 92–99.
Rogers, W. H. (1993). Regression standard errors in clustered samples. Stata Technical Bulletin, 13, 19–23.
Schoemaker, P. (1982). The expected utility model: its variants, purposes, evidence and limitations. Journal of Economic Literature, 20(2), 529–563.
Stahl, D. O. (1996). Boundedly rational rule learning in a guessing game. Games and Economic Behavior, 16, 303–330.
Stahl, D. O. (1998). Is step-j thinking an arbitrary modelling restriction or a fact of human nature? Journal of Economic Behavior & Organization, 37, 33–51.
Stahl, D. O., & Wilson, P. W. (1995). On players’ models of other players: theory and experimental evidence. Games and Economic Behavior, 10, 218–254.
Starmer, C. (2000). Developments in non-expected utility theory: the hunt for a descriptive theory of choice under risk. Journal of Economic Literature, 38, 332–382.
Titterington, D. M., Smith, A. F. M., & Makov, U. E. (1985). Statistical analysis of finite mixture distributions. New York: Wiley.
Train, K. E. (2003). Discrete choice methods with simulation. New York: Cambridge University Press.
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: cumulative representations of uncertainty. Journal of Risk & Uncertainty, 5, 297–323.
Vermunt, J. K., & Magidson, J. (2003). Latent class models for classification. Computational Statistics & Data Analysis, 41, 531–537.
Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57(2), 307–333.
Wang, M., & Fischbeck, P. S. (2004). Incorporating framing into prospect theory modeling: a mixture-model approach. Journal of Risk & Uncertainty, 29(2), 181–197.
Werner, M. (1999). Allowing for zeros in dichotomous choice contingent valuation models. Journal of Business and Economic Statistics, 17, 479–486.
Williams, R. L. (2000). A note on robust variance estimation for cluster-correlated data. Biometrics, 56, 645–646.
Wooldridge, J. (2003). Cluster-sample methods in applied econometrics. American Economic Review (Papers & Proceedings), 93, 133–138.
Wu, G., & Gonzalez, R. (1996). Curvature of the probability weighting function. Management Science, 42, 1676–1690.
Author information
Authors and Affiliations
Corresponding author
Additional information
We thank the U.S. National Science Foundation for research support under grants NSF/IIS 9817518, NSF/HSD 0527675 and NSF/SES 0616746; Ryan Brossette, Harut Hovsepyan, David Millsom and Bob Potter for research assistance; and Steffen Andersen, Vince Crawford, Curt Eaton, John Hey, Peter Kennedy, Jan Kmenta, Peter Wakker, two referees, and numerous seminar participants for helpful comments. Supporting data and instructions are stored at the ExLab Digital Library at http://exlab.bus.ucf.edu.
Rights and permissions
About this article
Cite this article
Harrison, G.W., Rutström, E.E. Expected utility theory and prospect theory: one wedding and a decent funeral. Exp Econ 12, 133–158 (2009). https://doi.org/10.1007/s10683-008-9203-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10683-008-9203-7