Expected utility theory and prospect theory: one wedding and a decent funeral
- 3.8k Downloads
- 118 Citations
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.
Keywords
Expected utility theory Prospect theory Mixture modelsJEL Classification
D81 C91 C51 C12References
- 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. Google Scholar
- 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. Google Scholar
- Andersen, S., Harrison, G. W., Lau, M. I., & Rutström, E. E. (2008). Eliciting risk and time preferences. Econometrica, 76(3), 583–618. CrossRefGoogle Scholar
- 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. CrossRefGoogle Scholar
- Atkinson, A. C. (1970). A method for discriminating between models. Journal of the Royal Statistical Society, Series B, 32, 323–344. Google Scholar
- Bardsley, N., & Moffatt, P. G. (2007). The experimetrics of public goods: inferring motivations from contributions. Theory and Decision, 62(2), 161–193. CrossRefGoogle Scholar
- Benartzi, S., & Thaler, R. H. (1995). Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics, 111(1), 75–92. Google Scholar
- 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. CrossRefGoogle Scholar
- Brandstätter, E., Gigerenzer, G., & Hertwig, R. (2006). The priority heuristic: making choices without trade-offs. Psychological Review, 113(2), 409–432. CrossRefGoogle Scholar
- 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. Google Scholar
- Camerer, C. F. (1995). Individual decision making. In J. H. Kagel & A. E. Roth (Eds.), The handbook of experimental economics. Princeton: Princeton University Press. Google Scholar
- Camerer, C. F., & Ho, T.-H. (1994). Violations of the betweeness axiom and nonlinearity in probability. Journal of Risk and Uncertainty, 8, 167–196. CrossRefGoogle Scholar
- Cherry, T. L., Frykblom, P., & Shogren, J. F. (2002). Hardnose the dictator. American Economic Review, 92(4), 1218–1221. CrossRefGoogle Scholar
- Clarke, K. A. (2003). Nonparametric model discrimination in international relations. Journal of Conflict Resolution, 47(1), 72–93. CrossRefGoogle Scholar
- Clarke, K. A. (2007). A simple distribution-free test for non-nested model selection. Political Analysis, 15(3), 347–363. CrossRefGoogle Scholar
- 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. CrossRefGoogle Scholar
- 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. Google Scholar
- 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. Google Scholar
- Cox, D. R. (1962). Further results on tests of separate families of hypotheses. Journal of the Royal Statistical Society, Series B, 24, 406–424. Google Scholar
- 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. CrossRefGoogle Scholar
- Davidson, R., & MacKinnon, J. G. (1993). Estimation and inference in econometrics. New York: Oxford University Press. Google Scholar
- El-Gamal, M. A., & Grether, D. M. (1995). Are people Bayesian? Uncovering behavioral strategies. Journal of the American Statistical Association, 90(432), 1137–1145. CrossRefGoogle Scholar
- Everitt, B. S. (1996). An introduction to finite mixture distributions. Statistical Methods in Medical Research, 5, 107–127. CrossRefGoogle Scholar
- Fudenberg, D., & Levine, D. K. (2006). A dual-self model of impulse control. American Economic Review, 96(5), 1449–1476. CrossRefGoogle Scholar
- 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. Google Scholar
- 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. Google Scholar
- 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. CrossRefGoogle Scholar
- Goodman, L. A. (1974b). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215–231. CrossRefGoogle Scholar
- Grether, D. M., & Plott, C. R. (1979). Economic theory of choice and the preference reversal phenomenon. American Economic Review, 69(4), 623–648. Google Scholar
- Haigh, M., & List, J. A. (2005). Do professional traders exhibit myopic loss aversion? An experimental analysis. Journal of Finance, 60(1), 523–534. CrossRefGoogle Scholar
- Harless, D. W., & Camerer, C. F. (1994). The predictive utility of generalized expected utility theories. Econometrica, 62, 1251–1289. CrossRefGoogle Scholar
- Harrison, G. W., & List, J. A. (2004). Field experiments. Journal of Economic Literature, 42(4), 1013–1059. CrossRefGoogle Scholar
- 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. Google Scholar
- 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. Google Scholar
- 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. CrossRefGoogle Scholar
- 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. CrossRefGoogle Scholar
- Hey, J. D., & Orme, C. (1994). Investigating generalizations of expected utility theory using experimental data. Econometrica, 62(6), 1291–1326. CrossRefGoogle Scholar
- Holt, C. A., & Laury, S. K. (2002). Risk aversion and incentive effects. American Economic Review, 92(5), 1644–1655. CrossRefGoogle Scholar
- Hosmer, D. W., & Lemeshow, S. (2000). Applied logistic regression (2nd edn.). New York: Wiley. Google Scholar
- Hurley, T. M., & Shogren, J. F. (2005). An experimental comparison of induced and elicited beliefs. Journal of Risk & Uncertainty, 30(2), 169–188. CrossRefGoogle Scholar
- 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. CrossRefGoogle Scholar
- Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47(2), 263–291. CrossRefGoogle Scholar
- Kirman, A. P. (1992). Whom or what does the representative individual represent? Journal of Economic Perspectives, 6(2), 117–136. Google Scholar
- Köbberling, V., & Wakker, P. P. (2005). An index of loss aversion. Journal of Economic Theory, 122, 119–131. CrossRefGoogle Scholar
- Kumbhakar, S. C., & Lovell, C. A. K. (2000). Stochastic frontier analysis. New York: Cambridge University Press. Google Scholar
- Liang, K.-Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22. CrossRefGoogle Scholar
- List, J. A. (2002). Preference reversals of a different kind: the more is less phenomenon. American Economic Review, 92, 1636–1643. CrossRefGoogle Scholar
- List, J. A. (2003). Does market experience eliminate market anomalies. Quarterly Journal of Economics, 118, 41–71. CrossRefGoogle Scholar
- List, J. A. (2004). Neoclassical theory versus prospect theory: evidence from the marketplace. Econometrica, 72(2), 615–625. CrossRefGoogle Scholar
- Loomes, G., & Sugden, R. (1998). Testing different stochastic specifications of risky choice. Economica, 65, 581–598. CrossRefGoogle Scholar
- 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. Google Scholar
- 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. CrossRefGoogle Scholar
- 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. Google Scholar
- 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. Google Scholar
- McLachlan, G., & Peel, D. (2000). Finite mixture models. New York: Wiley. CrossRefGoogle Scholar
- Oehlert, G. W. (1992). A note on the delta method. The American Statistician, 46(1), 27–29. CrossRefGoogle Scholar
- 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. CrossRefGoogle Scholar
- Pearson, K. (1894). Contribution to the mathematical theory of evolution. Philosophical Transactions A, 185, 71–110. CrossRefGoogle Scholar
- Pesaran, M. H. (1981). Pitfalls of testing non-nested hypotheses by the Lagrange multiplier method. Journal of Econometrics, 17, 323–331. CrossRefGoogle Scholar
- Pollak, R. A., & Wales, T. J. (1991). The likelihood dominance criterion: a new approach to model selection. Journal of Econometrics, 47, 227–242. CrossRefGoogle Scholar
- Prelec, D. (1998). The probability weighting function. Econometrica, 66(3), 497–527. CrossRefGoogle Scholar
- Quandt, R. E. (1974). A comparison of methods for testing nonnested hypotheses. Review of Economics and Statistics, 56, 92–99. CrossRefGoogle Scholar
- Rogers, W. H. (1993). Regression standard errors in clustered samples. Stata Technical Bulletin, 13, 19–23. Google Scholar
- Schoemaker, P. (1982). The expected utility model: its variants, purposes, evidence and limitations. Journal of Economic Literature, 20(2), 529–563. Google Scholar
- Stahl, D. O. (1996). Boundedly rational rule learning in a guessing game. Games and Economic Behavior, 16, 303–330. CrossRefGoogle Scholar
- 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. CrossRefGoogle Scholar
- Stahl, D. O., & Wilson, P. W. (1995). On players’ models of other players: theory and experimental evidence. Games and Economic Behavior, 10, 218–254. CrossRefGoogle Scholar
- 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. Google Scholar
- Titterington, D. M., Smith, A. F. M., & Makov, U. E. (1985). Statistical analysis of finite mixture distributions. New York: Wiley. Google Scholar
- Train, K. E. (2003). Discrete choice methods with simulation. New York: Cambridge University Press. Google Scholar
- Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: cumulative representations of uncertainty. Journal of Risk & Uncertainty, 5, 297–323. CrossRefGoogle Scholar
- Vermunt, J. K., & Magidson, J. (2003). Latent class models for classification. Computational Statistics & Data Analysis, 41, 531–537. CrossRefGoogle Scholar
- Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57(2), 307–333. CrossRefGoogle Scholar
- Wang, M., & Fischbeck, P. S. (2004). Incorporating framing into prospect theory modeling: a mixture-model approach. Journal of Risk & Uncertainty, 29(2), 181–197. CrossRefGoogle Scholar
- Werner, M. (1999). Allowing for zeros in dichotomous choice contingent valuation models. Journal of Business and Economic Statistics, 17, 479–486. CrossRefGoogle Scholar
- Williams, R. L. (2000). A note on robust variance estimation for cluster-correlated data. Biometrics, 56, 645–646. CrossRefGoogle Scholar
- Wooldridge, J. (2003). Cluster-sample methods in applied econometrics. American Economic Review (Papers & Proceedings), 93, 133–138. CrossRefGoogle Scholar
- Wu, G., & Gonzalez, R. (1996). Curvature of the probability weighting function. Management Science, 42, 1676–1690. CrossRefGoogle Scholar