Risk Aversion in Experiments: Volume 12

Attitudes to risk play a central role in economics. Policy makers should know them in order to judge the certainty equivalent of the effects of policy on individuals. What might look like a policy improvement when judged by the average impact could easily entail a welfare loss for risk averse individuals if the variance of expected impacts is wide compared to the alternatives.

Much of the literature on theories of decision making under risk has emphasized differences between theories. One enduring theme has been the attempt to develop a distinction between “normative” and “descriptive” theories of choice. Bernoulli (1738) introduced log utility because expected value theory was alleged to have descriptively incorrect predictions for behavior in St. Petersburg games. Much later, Kahneman and Tversky (1979) introduced prospect theory because of the alleged descriptive failure of expected utility (EU) theory (von Neumann & Morgenstern, 1947).

We review the experimental evidence on risk aversion in controlled laboratory settings. We review the strengths and weaknesses of alternative elicitation procedures, the strengths and weaknesses of alternative estimation procedures, and finally the effect of controlling for risk attitudes on inferences in experiments.

Choice under risk has a large stochastic (unpredictable) component. This chapter examines five stochastic models for binary discrete choice under risk and how they combine with “structural” theories of choice under risk. Stochastic models are substantive theoretical hypotheses that are frequently testable in and of themselves, and also identifying restrictions for hypothesis tests, estimation and prediction. Econometric comparisons suggest that for the purpose of prediction (as opposed to explanation), choices of stochastic models may be far more consequential than choices of structures such as expected utility or rank-dependent utility.

Measuring risk aversion is sensitive to assumptions about the wealth in subjects’ utility functions. Data from the same subjects in low- and high-stake lottery decisions allow estimating the wealth in a pre-specified one-parameter utility function simultaneously with risk aversion. This paper first shows how wealth estimates can be identified assuming constant relative risk aversion (CRRA). Using the data from a recent experiment by Holt and Laury (2002a), it is shown that most subjects’ behavior is consistent with CRRA at some wealth level. However, for realistic wealth levels most subjects’ behavior implies a decreasing relative risk aversion. An alternative explanation is that subjects do not fully integrate their wealth with income from the experiment. Within-subject data do not allow discriminating between the two hypotheses. Using between-subject data, maximum-likelihood estimates of a hybrid utility function indicate that aggregate behavior can be described by expected utility from income rather than expected utility from final wealth and partial relative risk aversion is increasing in the scale of payoffs.

This paper investigates whether individuals’ risk-taking behavior is affected by background risk by analyzing individuals’ choices over a series of lotteries in a laboratory setting in the presence and absence of independent, uncorrelated background risks. Overall, our results were mixed. We found some support for the notion that individuals were more risk averse when faced with the introduction of an unfair or mean-preserving background risk than when no background risk was present, but this finding depends on how individuals incorporate endowments and background gains and losses into their utility functions and how error variance is modeled.

This paper reports findings from a series of laboratory asset markets. Although stakes in these markets are modest, asset prices display a substantial equity premium (risky assets are priced substantially below their expected payoffs) – indicating substantial risk aversion. Moreover, the differences between expected asset payoffs and asset prices are in the direction predicted by standard asset-pricing theory: assets with higher beta have higher returns. This work suggests ways to separate the effects of risk aversion from competing explanations in other experimental environments.

We review the use of behavior from television game shows to infer risk attitudes. These shows provide evidence when contestants are making decisions over very large stakes, and in a replicated, structured way. Inferences are generally confounded by the subjective assessment of skill in some games, and the dynamic nature of the task in most games. We consider the game shows Card Sharks, Jeopardy!, Lingo, and finally Deal Or No Deal. We provide a detailed case study of the analyses of Deal Or No Deal, since it is suitable for inference about risk attitudes and has attracted considerable attention.

This paper reports a new experimental test of the notion that behavior switches from risk averse to risk seeking when gains are “reflected” into the loss domain. We conduct a sequence of experiments that allows us to directly compare choices under reflected gains and losses where real and hypothetical payoffs range from several dollars to over $100. Lotteries with positive payoffs are transformed into lotteries over losses by multiplying all payoffs by –1, that is, by reflecting payoffs around zero. When we use hypothetical payments, more than half of the subjects who are risk averse for gains turn out to be risk seeking for losses. This reflection effect is diminished considerably with cash payoffs, where the modal choice pattern is to exhibit risk aversion for both gains and losses. However, we do observe a significant difference in risk attitudes between losses (where most subjects are approximately risk neutral) and gains (where most subjects are risk averse). Reflection rates are further reduced when payoffs are scaled up by a factor of 15 (for both real and hypothetical payoffs).