Recovering Risk Preferences

The work proposed here will develop experimental methods and tools for the analysis of behavior under uncertainty in economically important settings. The research is motivated by types of questions commonly asked in demand analysis: (i) Consistency. Is behavior under conditions of uncertainty consistent with a model of utility maximization? (ii) Structure. Is the observed data consistent with a utility function with some special structural properties? (iii) Recoverability. Can underlying preferences be recovered from observed choices? (iv) Heterogeneity. To what degree do preferences over risky alternatives differ across subjects? For the most part, experimental investigations use several pairwise choices, à la Allais, to test von Neumann and Morgenstern (1947) Expected Utility Theory (EUT) and its various generalizations, such as weighted utility, implicit expected utility, and prospect theory, among others (see, respectively, Chew (1983), Dekel (1986), and Kahneman and Tversky (1979)). Each of the different theories of decisions under uncertainty gives rise to indifference curves with distinctive shapes in some part of the Marschak (1950) and Machina (1982, 1987) probability triangle, so each theory can be tested against the others by choosing alternatives that the various theories rank differently. In most studies, the criterion used to evaluate a theory is the fraction of choices it predicts correctly. Very few studies have also estimated parametric utility functions for individual subjects (see, Hey and Orme (1994)). Generally speaking, previous experimental work has, on the one hand, collected only a few decisions from each subject and, on the other, presented subjects with an “extreme” binary choice, designed to discover violations of specific theories, rather than “typical” decision problems. Camerer (1995) and Starmer (2000) review the experimental and theoretical work that focuses on evaluating non-EUT theories. In order to provide this more general account of choice under uncertainty, we have developed experimental methods and theoretical techniques that provide fundamental innovations over existing work. We employ graphical representations of portfolio choice problems that allow for the collection of richer individual-level data than has heretofore been possible. This allows us to apply statistical models to estimate preferences at the level of the individual subject rather than pooling data or assuming homogeneity across subjects. Moreover, our experimental technique allows us to confront subjects with choice problems that span a broad range of natural scenarios, rather than, as in existing methods, with stylized and extreme choices designed to test a particular theory. This enables us to avoid imposing theoretical preconceptions on the data and instead to recover preferences from the ground up. The data set produced by our experimental design has several advantages over data sets from earlier experiments. First, the choice of a portfolio subject to a budget constraint provides more information about preferences than a binary choice. Second, because of the user-friendly interface, each subject faces a large menu of highly heterogeneous budget sets, and the large amount of data generated by this design allows us to apply statistical models to individual data rather than pooling data or assuming homogeneity across subjects. Hence, we may generate better individuallevel estimates of risk aversion than has heretofore been possible. Third, these decision problems are representative, both in the statistical sense and in the economic sense, rather than being “tailored” to capture a particular “pathology.” Finally, the graphical representation does not emphasize any particular portfolio and, critically, does not offer subjects discrete choices that might suggest prototypical preference types.