A triple test for behavioral economics models and public health policy

We propose a triple test to evaluate the usefulness of behavioral economics models for public health policy. Test 1 is whether the model provides reasonably new insights. Test 2 is on whether these have been properly applied to policy settings. Test 3 is whether they are corroborated by evidence. We exemplify by considering the cases of social interactions models, self-control models and, in relation to health message framing, prospect theory. Out of these sets of models, only a correctly applied prospect theory fully passes the tests at present. Specifically, in broad agreement with the evidence, a gain frame has positive implications for welfare encourages disease prevention activity, though this does not apply if the perceived probability of the bad health outcome is large enough. We see our tests as being useful to identify how much health policy weight policy makers should assign to specific behavioral economic models; they are also useful to verify what next steps would be most useful in further research.     

Arrow-Pratt Risk Aversion, Risk Premium and Decision Weights

This paper analyzes two issues: (a) the effect of decision-weights on risk premium, and (b) whether risk-aversion characterizes most investors. We theoretically show that cumulative prospect theory decision-weights systematically increase Arrow's risk premium, and may induce a positive risk premium even in the absence of risk-aversion. However, decision-weights may either increase or reduce Pratt's risk premium. We present three experiments revealing a striking result: a large proportion of the subjects' choices contradicts risk-aversion. This may be due to non-concave preferences, or to decision-weights. This result may have a dramatic impact on equilibrium models in economics and finance.     

The classification of parametric choices under uncertainty: analysis of the portfolio choice problem

This paper describes the admissible classes of parametric distribution functions of return portfolios and analyzes their consistency with the maximization of the expected utility. In particular, we present a general theory and a unifying framework with the following aims: (1) studying the implications of the classical market restrictions on the portfolio distributions; (2) establishing general rules of ordering, when the uncertain prospect depends by a finite number of parameters; (3) understanding how a dispersion measure has to be used, in order to obtain the investors' optimal portfolios.     

A genuine foundation for prospect theory

In most models of (cumulative) prospect theory, reference dependence of preferences is imposed beforehand and the location of the reference point is determined exogenously. This paper presents principles that provide critical tests and foundations for prospect theory preferences without assuming reference-dependent preferences a priori. Instead, reference dependence is derived from behavior and the reference point arises endogenously.     

Prospect theory for continuous distributions

We extend the original form of prospect theory by Kahneman and Tversky from finite lotteries to arbitrary probability distributions, using an approximation method based on weak-⋆ convergence. The resulting formula is computationally easier than the corresponding formula for cumulative prospect theory and makes it possible to use prospect theory in future applications in economics and finance. Moreover, we suggest a method how to incorporate a crucial step of the “editing phase” into prospect theory and to remove in this way the discontinuity of the original model.

On probabilities and loss aversion

This paper reviews the most common approaches that have been adopted to analyze and describe loss aversion under prospect theory. Subsequently, it is argued that loss aversion is a property of observable choice behavior and two new definitions of loss averse behavior are advocated. Under prospect theory, the new properties hold if the commonly used utility based measures of loss aversion are corrected by a probability based measure of loss aversion and their product exceeds 1. It is shown that prominent parametric families of weighting functions, while successful in accommodating empirical findings on probabilistic risk attitudes, may not fit well with the theoretical implications of the new loss averse behavior conditions.     

Testing Prospect Theories Using Probability Tradeoff Consistency

The two versions of prospect theory, original prospect theory (OPT; Kahneman and Tversky, 1979) and cumulative prospect theory (CPT; Tversky and Kahneman, 1992), use different composition rules to combine the value function and the probability weighting function and hence value gambles with two or more non-zero outcomes differently. Previous tests of OPT and CPT have yielded mixed results, with some investigations supporting OPT and some supporting CPT. We extend the probability tradeoff consistency axiom used in Abdellaoui (2002) for CPT to OPT, and develop a critical test of the two prospect theories based on their respective probability tradeoff consistency conditions. An empirical investigation of the critical test shows that choices are consistent with OPT, but not CPT, for gambles that do not involve a certainty effect, and consistent with both CPT and OPT for gambles that do involve a certainty effect, provided that an editing operation is invoked for OPT.     

Testing between alternative models of choice under uncertainty—Comment

Battaglio, Kagel, and Jiranyakul use experimental tests to compare rank-dependent expected utility (RDEU), regret theory, prospect theory, and Machina's generalized smooth preferences model. They conclude that none of these models consistently organizes the data. The purpose of this note is to point out that RDEU theory was tested in combination with a hypothesis on the choice of functional form that has been explicitly rejected by the original author of the model (Quiggin, 1982, 1987). When the original form of RDEU theory is tested, it performs quite well.     

Discriminating among probability weighting functions using adaptive design optimization

Probability weighting functions relate objective probabilities and their subjective weights, and play a central role in modeling choices under risk within cumulative prospect theory. While several different parametric forms have been proposed, their qualitative similarities make it challenging to discriminate among them empirically. In this paper, we use both simulation and choice experiments to investigate the extent to which different parametric forms of the probability weighting function can be discriminated using adaptive design optimization, a computer-based methodology that identifies and exploits model differences for the purpose of model discrimination. The simulation experiments show that the correct (data-generating) form can be conclusively discriminated from its competitors. The results of an empirical experiment reveal heterogeneity between participants in terms of the functional form, with two models (Prelec-2, Linear-in-Log-Odds) emerging as the most common best-fitting models. The findings shed light on assumptions underlying these models.     

Testing between alternative models of choice under uncertainty: Some initial results

Experiments have identified a number of well-known violations of expected utility theory, giving rise to alternative models of choice under uncertainty, all of which are able to explain these violations. In this article, predictions of several prominent rival formulations are examined. No single alternative consistently organizes choices. Among the more important inconsistencies, we identify conditions generating systematic fanning in of indifference curves in the unit probability triangle, and find risk-loving over a number of gambles with all positive payoffs, in cases where prospect theory predicts risk aversion.     

Normative, Gain and Hedonic Goal Frames Guiding Environmental Behavior

This article discusses new developments about goal-dependent framing and multiple goal frames (sometimes also called "multiple motives"), which are highly relevant for understanding environmental behavior. We introduce goal-framing theory, which postulates that goals "frame" the way people process information and act upon it. Three goal frames are distinguished: a hedonic, gain, and normative goal frame. In general, multiple goals are active at any given time, which may (or may not) be compatible; that is, the strength of the focal goal may be influenced by other goals that are in the background. Based on an extensive review of studies in environmental psychology, we suggest those conditions under which each goal frame may be dominant in influencing environmental behavior. In the environmental context, normative goal frames imply acting pro-environmentally, while gain and hedonic goal frames often result in not acting in an environmentally sound manner. Next, we argue that pro-environmental behavior may be promoted by strengthening normative goals or by making gain and hedonic goals less incompatible with normative goals. Finally, based on goal-framing theory, we suggest questions to be addressed in future research.     

Do financial professionals behave according to prospect theory? An experimental study

Prospect theory is increasingly used to explain deviations from the traditional paradigm of rational agents. Empirical support for prospect theory comes mainly from laboratory experiments using student samples. It is obviously important to know whether and to what extent this support generalizes to more naturally occurring circumstances. This article explores this question and measures prospect theory for a sample of private bankers and fund managers. We obtained clear support for prospect theory. Our financial professionals behaved according to prospect theory and violated expected utility maximization. They were risk averse for gains and risk seeking for losses and their utility was concave for gains and (slightly) convex for losses. They were also averse to losses, but less so than commonly observed in laboratory studies and assumed in behavioral finance. A substantial minority focused on gains and largely ignored losses, behavior reminiscent of what caused the current financial crisis.     

Prospect theory and the “forgotten” fourfold pattern of risk preferences

Markowitz (Journal of Political Economy 60:151–158, 1952) identified a fourfold pattern of risk preferences in outcome magnitude: When outcomes are large, people are risk averse in gains and risk seeking in losses, but risk preferences reverse when the outcomes are small, with people exhibiting risk seeking in gains and risk aversion in losses. This fourfold pattern was not addressed by either version of prospect theory (Kahneman and Tversky Econometrica 47:363–391, 1979; Tversky and Kahneman Journal of Risk and Uncertainty 5:297–323, 1992). We show how prospect theory can accommodate the pattern by combining an overweighting of low probabilities with a decreasingly elastic value function. We then examine the performance of prospect theory with two decreasingly elastic value functions: Prospect theory performs better, both quantitatively and qualitatively, with a normalized logarithmic value function than with a normalized exponential value function. We discuss several issues, and speculate about why Tversky and Kahneman did not address Markowitz’s fourfold pattern.     

Estimating cumulative prospect theory parameters from an international survey

We conduct a standardized survey on risk preferences in 53 countries worldwide and estimate cumulative prospect theory parameters from the data. The parameter estimates show that significant differences on the cross-country level are to some extent robust and related to economic and cultural differences. In particular, a closer look on probability weighting underlines gender differences, economic effects, and cultural impact on probability weighting. The data set is a useful starting point for future research that investigates the impact of risk preferences on the market level.     

What is Loss Aversion?

A behavioral definition of loss aversion is proposed and its implications for original and cumulative prospect theory are analyzed. Original prospect theory is in agreement with the new loss aversion condition, and there utility is capturing all effects of loss aversion. In cumulative prospect theory loss aversion is captured by both the weighting functions and the utility function. Further, some restrictions apply for the weighting functions involved in the latter model.We are indebted to Michèle Cohen and Peter Wakker for helpful comments. The suggestions of an anonymous referee have improved the presentation of the paper.     

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.