Stake effects on ambiguity attitudes for gains and losses

We test the effect of stake size on ambiguity attitudes. Compared to a baseline condition, we find subjects to be more ambiguity seeking for small-probability gains and large-probability losses under high stakes. They are also more ambiguity averse for large-probability gains and small-probability losses. We trace these effects back to stake effects on decisions under risk (known probabilities) and uncertainty (unknown probabilities). For risk, we replicate previous findings. For uncertainty, we find an increase in probabilistic insensitivity under high stakes that is driven by increased uncertainty aversion for large-probability gains and for small-probability losses.     

Accommodating stake effects under prospect theory

This paper investigates how letting people predict others’ choices under risk affects subsequent own choices. We find an improvement of strong rationality (risk neutrality) for losses in own choices, but no such improvement for gains. There is no improvement of weak rationality (avoiding preference reversals). Overall, risk aversion in own choices increases. Conversely, for the effects of own choices on predicting for others, the risk aversion predicted in others’ choices is reduced if preceded by own choices, for both gains and losses. Remarkably, we find a new probability matching paradox at the group level. Relative to preceding studies on the effects of predicting others’ choices, we added real incentives, pure framing effects, and simplicity of stimuli. Our stimuli were maximally targeted towards our research questions.     

Recursive expected utility and the separation of attitudes towards risk and ambiguity: an experimental study

We use the multiple price list method and a recursive expected utility theory of smooth ambiguity to separate out attitude towards risk from that towards ambiguity. Based on this separation, we investigate if there are differences in agent behaviour under uncertainty over gain amounts vis-a-vis uncertainty over loss amounts. On an aggregate level, we find that (i) subjects are risk averse over gains and risk seeking over losses, displaying a “reflection effect” and (ii) they are ambiguity neutral over gains and are mildly ambiguity seeking over losses. Further analysis shows that on an individual level, and with respect to both risky and ambiguous prospects, there is limited incidence of a reflection effect where subjects are risk/ambiguity averse (seeking) in gains and seeking (averse) in losses, though this incidence is higher for ambiguous prospects. A very high proportion of such cases of reflection exhibit risk (ambiguity) aversion in gains and risk (ambiguity) seeking in losses, with the reverse effect being significantly present in the case of risk but almost absent in case of ambiguity. Our results suggest that reflection across gains and losses is not a stable individual characteristic, but depends upon whether the form of uncertainty is precise or ambiguous, since we rarely find an individual who exhibits reflection in both risky and ambiguous prospects. We also find that correlations between attitudes towards risk and ambiguity were domain dependent.      

Stability of risk preferences and the reflection effect of prospect theory

Are risk preferences stable over time? To address this question we elicit risk preferences from the same pool of subjects at two different moments in time. To interpret the results, we use a Fechner stochastic choice model in which the revealed preference of individuals is governed by some underlying preference, together with a random error. We take cumulative prospect theory as the underlying preference model (Kahneman and Tversky, Econometrica 47:263–292, 1979; Tversky and Kahneman, Journal of Risk and Uncertainty 5:297–323, 1992). We observe that the aggregate pattern of preferences is very similar in both sessions, and it matches the results reported in the literature. Most subjects are risk averse for gains, and risk seeking for losses. However, the subjects that jointly agree with the reflection effect of prospect theory are around 50%. The percentage of individuals that change their responses across sessions is quite high, 63%. Estimating the stochastic choice model we find that 72% of the subjects have an underlying preference which agrees with the reflection effect of prospect theory. The remaining 28% are mainly classified as risk averse for both gains and losses. The results reinforce the empirical validity of the reflection effect. Deviations from the reflection effect can be attributed to noise, as well as to the existence of a fraction of risk averse subjects.     

Risk and choice: A research saga

The economic theory of decision making under risk has seen remarkable advances over the 50 years since Pratt’s (1964) characterization of risk aversion under expected utility. We review developments in three key areas to which Louis Eeckhoudt has made significant contributions: (1) increases in risk and risk taking; (2) self-protection and risk aversion; and (3) higher (and lower) order derivatives of utility. For each, we identify seminal papers, puzzles, and recent developments. The saga of research on these topics reveals that important contributions were made long ago and yet significant gains in understanding continue to be made. Recent advances often have roots in early results and researchers can profit by examining the old as well as the new papers.     

Advances in prospect theory: Cumulative representation of uncertainty

We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a distinctive fourfold pattern of risk attitudes: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability.This article has benefited from discussions with Colin Camerer, Chew Soo-Hong, David Freedman, and David H. Krantz. We are especially grateful to Peter P. Wakker for his invaluable input and contribution to the axiomatic analysis. We are indebted to Richard Gonzalez and Amy Hayes for running the experiment and analyzing the data. This work was supported by Grants 89-0064 and 88-0206 from the Air Force Office of Scientific Research, by Grant SES-9109535 from the National Science Foundation, and by the Sloan Foundation.     

Reference Wealth Effects in Sequential Choice

It is argued that in order to accommodate experimentally-observed choice patterns, it is not enough to model the utility function as being dependent on changes from a reference wealth point. Instead, individuals should be modeled as treating decisions as part of an identifiable sequence of decisions, and utility should be a function of reference wealth, income so far from the sequence, and payoffs from the current decision. The three-argument utility function allows for risk aversion over gains and risk seeking over losses for the first choice in the sequence, and for the house money and break-even effects in later decisions.     

Dynamic awareness and zero probability beliefs

We study behavioral patterns of insurance demand for low-probability large-loss events (catastrophic losses). Individual patterns of belief formation and risk attitude that were suggested in the behavioral decisions literature emerge robustly in the current set of insurance choices. However, social comparison effects are less robust. We do not find any evidence for peer effects (through social-loss aversion or imitation) on insurance take-up. In contrast, we find support for the prediction that people underweight others’ relevant information in their own decision making.     

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 theory.     

Commonalities in Time and Ambiguity Aversion for Long-Term Risks*

Optimal protective responses to long-term risks depend on rational perceptions of ambiguous risks and uncertain time horizons. Our study examined the joint influence of uncertain delay and risk in an original sample of business owners and managers. We found that many subjects disliked uncertainty in the timing of an outcome, a reaction we term ``lottery timing risk aversion.' Such aversion to uncertain timing was positively related to aversion to ambiguous probabilities for lotteries involving storm damage risks. This association suggests that uncertainty may be processed similarly in both the risk and time dimensions.     

Loss Averse Behavior

A behavioral condition of loss aversion is proposed and tested. Forty-nine students participated in experiments on binary choices among lotteries involving small scale real gains and losses. At the aggregate level, a significant proportion of the choices are in the direction predicted by loss aversion. Individuals can be classified as loss averse (28 participants), gain seeking (12), and unclassified (9). A comparison with risk behavior for binary choices on lotteries involving only gains shows that risk attitudes vary across these domains of lotteries. A gender effect is also observed: proportionally more women are loss averse. In contrast to the predictions of comonotonic independence, the size of common outcomes has systematic influence on choice behavior. JEL Classification: D81, C91     

An Empirical Investigation of the Assumptions of Risk-Value Models

Do participants make decisions consistent with risk-value tradeoffs? One hundred and five undergraduate business students made risk and preference judgments about lottery pairs in a series of paper surveys. The data indicate that the participants’ responses were generally consistent with the key assumptions of risk-value models, but that some extensions of the theory would improve this consistency. In particular, we find that modifying the risk assumptions of the risk-value theory so they are consistent the concept of the reflection of the risk attitude in the domains of gains and losses increases the agreement between the theory and the participants’ responses.     

Time preferences and risk aversion: Tests on domain differences

Understanding how individuals discount and evaluate the risks of environmental outcomes is a prime component in designing effective environmental policy. We use an incentivized experimental design to investigate whether subjects’ time preferences and risk aversion across the monetary and environmental domains differ. We find that subjects’ time preferences are not significantly different across the two domains. In contrast, subjects exhibit a higher degree of risk aversion in the environmental domain. Furthermore, we corroborate earlier results, documenting that women are more risk averse than men in the monetary domain, and show this finding to also hold in the environmental domain.     

Measuring risk aversion with lists: a new bias

Various experimental procedures aimed at measuring individual risk aversion involve a list of pairs of alternative prospects. We first study the widely used method by Holt and Laury (Am Econ Rev 92(5):1644–1655, 2002), for which we find that the removal of some items from the lists yields a systematic decrease in risk aversion and scrambles the ranking of individuals by risk aversion. This bias, that we call embedding bias, is quite distinct from other confounds that have been previously observed in the use of the HL method. It may be related to empirical phenomena and theoretical developments where better prospects increase risk aversion. Nevertheless, we also find that the more recent elicitation method due to Abdellaoui et al. (Theory Decis 71:63–80, 2011), also based on lists but using only one and the same probability in the list, does not display any statistically significant bias when the corresponding items of the list are removed. Our results suggest that methods other than the popular HL one may be preferable for the measurement of risk aversion.     

Action Bias and Environmental Decisions

Individuals have a penchant for action, often for good reasons. But action bias arises if that penchant is carried over to areas where those reasons do not apply, hence is nonrational. Action bias is explored theoretically, and then empirically, using data from surveys of hypothetical environmental decisions. Quite apart from agency considerations, individuals like to affect outcomes when gains are reaped. Given the ability to help one of two sites, we find that decision makers choose to foster improvement rather than prevent deterioration, despite framing that makes it arbitrary which site is improved, which preserved. Strong action bias—individuals choosing to reap gains even though they must impose losses—is also observed. These concepts are related to loss aversion, status quo bias, omission bias for losses, and bright-line behavior.     

Joint measurement of risk aversion,prudence, and temperance

Risk aversion—but also the higher-order risk preferences of prudence and temperance—are fundamental concepts in the study of economic decision making. We propose a method to jointly measure the intensity of risk aversion, prudence, and temperance. Our theoretical approach is to define risk compensations of different orders, and in an experiment we elicit these compensations with a price list technique. We find evidence for risk aversion, prudence, and temperance. These traits correlate within subjects. The compensations elicited for prudence are significantly larger than those for risk aversion and temperance. In contrast to commonly used utility functions, prospect theory can predict this behavioral pattern. In our experiment, risk-averse, risk-loving, and risk-neutral subjects are prudent. This supports a recent theoretical observation that prudence may be a more universal trait than previously realized.     

Risk aversion and physical prowess: Prediction,choice and bias

This paper reports on experiments where individuals are asked to make risky decisions for themselves, and to predict the risky decisions of others. Prior research shows that people predict women to be more risk averse than men, a result we confirm. We investigate whether differences in physical prowess underlie actual and perceived gender differences, a hypothesis suggested by both evolutionary and economic theories. Overall we find that perceptions of others’ risk attitudes reflect stereotypes about gender and strength but tend to exaggerate the underlying relationships. Physically stronger and taller people and those perceived as attractive are predicted to be more risk tolerant, while women are perceived to be more risk averse. The impact of gender and physical prowess measures on actual gamble choices is much weaker. Sources of prediction bias are examined, showing that specific characteristics of the target and predictor lead to systematic over-prediction or under-prediction of risk aversion.     

Temporal discounting of gains and losses of time: An experimental investigation

This paper investigates “asymmetries” between non-monetary gains and losses in intertemporal choice. We considered gains and losses of spare/working time with respect to a reference duration defined in a working contract. Specifically, we elicited a behavioral model of intertemporal choice that accounts for a gain/loss-dependent discounting function and a reference-dependent utility. Additionally, we did not impose preference for the present (positive discounting) and allowed for both decreasing and increasing impatience. While our results are standard regarding the discount of money (our baseline treatment), our subjects heavily discounted gains of time. More patience was observed for losses of time and a sizable portion of subjects even exhibited negative discounting, i.e. they preferred to expedite losses of time. Our econometric estimations also reveal a much larger heterogeneity of behavior in terms of both utility and discounting for gains and losses of spare time as compared to money.     

Reference points,loss aversion,and contingent values for auto safety

This article is concerned with the possible role of reference points and loss aversion (as suggested by prospect theory) in subjects' judgments about the value of increments and decrements in automobile safety. The contingent valuation method is employed in two experiments, both of which consider subjects' willingness-to-pay (WTP) for increased safety and compensation demanded (CD) for decreased safety in hypothetical new vehicle purchases. The results establish that disparities exist in subjects' WTP and CD values for the same increment of auto safety, even for a close-to-market context such as hypothetical new vehicle purchases. The results also indicate that evaluations can be manipulated by changing the perception of the reference point: losses can be recast as forgone gains and forgone gains as losses, altering (or even eliminating) differences between WTP and CD values.I would like to thank Mark Kamlet, Greg Fischer, and Granger Morgan for advice and help in structuring the research for the first experiment; Paul Slovic and Jack Knetsch for suggestions regarding the structure and content of the second experiment; Robin Gregory and two anonymous referees for insightful comments on earlier drafts; and the subjects who provided their time in the two experiments. Michael McNickle provided able research assistance for the second experiment. The survey for the first experiment was partially supported by the Program for Technology and Society at Carnegie Mellon University, with funds from the Andrew W. Mellon Foundation.     

Individual decision-making experiments with risk and intertemporal choice

Many decisions require tradeoffs over time and in the presence of risk. To examine interactions between risk and intertemporal effects we developed a laboratory experiment. In the experiment, subjects choose between payoffs that take place at different points in time. We find that very few subjects are consistently risk averse or risk loving. Instead, we find that subjects are less patient in the presence of risk. We also find that increased risk decreases subjects’ patience levels. However, we do not find evidence that the effect of risk on the intertemporal decision depends on the length of the temporal delay.