Risk and Rationality: Uncovering Heterogeneity in Probability Distortion

It has long been recognized that there is considerable heterogeneity in individual risk taking behavior but little is known about the distribution of risk taking types. We present a parsimonious characterization of risk taking behavior by estimating a finite mixture regression model for three different experimental data sets, two Swiss and one Chinese, over a large number of real gains and losses. We find two distinct types of individuals: In all three data sets, the choices of roughly 80% of the subjects exhibit significant deviations from rational probability weighting consistent with prospect theory. 20% of the subjects weight probabilities linearly and behave essentially as expected value maximizers. Moreover, the individuals are assigned to one of these two groups with probabilities of close to one resulting in a low measure of entropy. The reliability and robustness of our classification suggest using a mix of preference theories in applied economic modeling.individual risk taking behavior, latent heterogeneity, finite mixture regression models

Rationality on the Rise: Why Relative Risk Aversion Increases with Stake Size

How does risk tolerance vary with stake size? This important question cannot be adequately answered if framing effects, nonlinear probability weighting, and heterogeneity of preference types are neglected. We show that, contrary to gains, no coherent change in relative risk aversion is observed for losses. The increase in relative risk aversion over gains cannot be captured by the curvature of the utility function. It is driven predominantly by a change in probability weighting of a majority group of individuals who exhibit more rational probability weighting at high stakes. These results not only challenge expected utility theory, but also prospect theory.Risk Aversion, Stake-Size Effect, Prospect Theory, Latent Heterogeneity

Viewing the future through a warped lens: Why uncertainty generates hyperbolic discounting

A large body of experimental research has demonstrated that, on average, people violate the axioms of expected utility theory as well as of discounted utility theory. In particular, aggregate behavior is best characterized by probability distortions and hyperbolic discounting. But is it the same people who are prone to these behaviors? Based on an experiment with salient monetary incentives we demonstrate that there is a strong and significant relationship between greater departures from linear probability weighting and the degree of decreasing discount rates at the level of individual behavior. We argue that this relationship can be rationalized by the uncertainty inherent in any future event, linking discounting behavior directly to risk preferences. Consequently, decreasing discount rates may be generated by people's proneness to probability distortion

Rationality on the rise: Why relative risk aversion increases with stake size

How does risk tolerance vary with stake size? This important question cannot be adequately answered if framing effects, nonlinear probability weighting, and heterogeneity of preference types are neglected. We show that the observed increase in relative risk aversion over gains cannot be captured by the curvature of the value function. Rather, it is predominantly driven by a change in probability weighting of a majority group of individuals who weight probabilities of high gains more conservatively. Contrary to gains, no coherent change in relative risk aversion is observed for losses. These results not only challenge expected utility theory, but also prospect theor

Uncertainty Breeds Decreasing Impatience: The Role of Risk Preferences in Time Discounting

Future events are uncertain by their very nature. Therefore, people's risk preferences are likely to play a role in the valuation of allegedly guaranteed future outcomes. We show that future uncertainty conjointly with people's proneness to nonlinear probability weighting generates a unifying framework for explaining many anomalies in intertemporal choice, such as hyperbolic discounting and subadditivity of discount factors. Moreover, our approach implies that higher uncertainty of future prospects increases the hyperbolicity of discount rates, suggesting that institutional deficiencies such as lack of contract enforcement, may be a source ofnhyperbolic discounting behavior. Based on an experiment with monetary incentives, we show that people's risk taking behavior is indeed a significant determinant of their time discounting behavior: Greater departures from linear probability weighting predict a stronger decline in impatience on the level of individual behavior

Risk and Rationality: Uncovering Heterogeneity in Probability Distortion

It has long been recognized that there is considerable heterogeneity in individual risk taking behavior but little is known about the distribution of risk taking types. We present a parsimonious characterization of risk taking behavior by estimating a finite mixture regression model for three different experimental data sets, two Swiss and one Chinese, over a large number of real gains and losses. We find two distinct types of individuals: In all three data sets, the choices of roughly 80% of the subjects exhibit significant deviations from rational probability weighting consistent with prospect theory. 20% of the subjects weight probabilities linearly and behave essentially as expected value maximizers. Moreover, the individuals are assigned to one of these two groups with probabilities of close to one resulting in a low measure of entropy. The reliability and robustness of our classification suggest using a mix of preference theories in applied economic modeling

RISK IN TIME: The Intertwined Nature of Risk Taking and Time Discounting

Standard economic models view risk taking and time discounting as two independent dimensions of decision making. However, mounting experimental evidence demonstrates striking parallels in patterns of risk taking and time discounting behavior and systematic interaction effects, which suggests that there may be common underlying forces driving these interactions. Here we show that the inherent uncertainty associated with future prospects together with individuals' proneness to probability weighting generates a unifying framework for explaining a large number of puzzling behavioral regularities: delay-dependent risk tolerance, aversion to sequential resolution of uncertainty, preferences for the timing of the resolution of uncertainty, the differential discounting of risky and certain outcomes, hyperbolic discounting, subadditive discounting, and the order dependence of prospect valuation. Furthermore, all these phenomena can be predicted simultaneously with the same set of preference parameters

The missing link: unifying risk taking and time discounting

Standard economic models view risk taking and time discounting as two independent dimensions of decision makers' behavior. However, mounting experimental evidence demonstrates the existence of robust and systematic interaction effects. There are striking parallels in patterns of risk taking and time discounting behavior, which suggests that there is a common underlying force driving these interactions. Here we show that decision makers' anticipation of something going wrong in the future conjointly with their proneness to probability weighting generates a unifying framework for explaining seven puzzling regularities: delay-dependent risk tolerance, aversion to sequential resolution of uncertainty, preferences for resolution timing, hyperbolic discounting, subadditive discounting, the differential discounting of risky and certain outcomes, and the order dependence of prospect valuation. Finally, we discuss the implications of our framework for understanding real-world behavior, such as the coexistence of underinsuring and overinsuring

Comment on "risk preferences are not time preferences": balancing on a budget line

In a recent experimental study of intertemporal risky decision making, Andreoni and Sprenger (2012) find that subjects exhibit a preference for intertemporal diversification, which is inconsistent with discounted expected utility theory. It was claimed that their results are also at odds with models involving probability weighting, such as rank-dependent utility and cumulative prospect theory. Here we demonstrate, however, that rank-dependent probability weighting explains intertemporal diversification if decision makers care about portfolio risk. Moreover, we provide a unified account of all of Andreoni and Sprenger's key findings