Individual-level loss aversion in riskless and risky choices

Theory and Decision - Loss aversion can occur in riskless and risky choices. We present novel evidence on both in a non-student sample (660 randomly selected customers of a car manufacturer). We...     

The effects of loss aversion on deceptive advertising policies

We extend the deceptive advertising model of Piccolo et al. (RAND J Econ 46(3):611–624, 2015) to a framework in which consumers may be loss averse. There are two sellers, competing on prices and offering experience goods with some differences in quality. Prospective customers may be harmed by deceptive advertising: a marketing practice that can induce them to make bad purchases. We show that although deceptive advertising occurs depending on the degree of consumers’ loss aversion, this behavioral bias does not reflect on firms’ prices. Nevertheless, the presence of loss-averse consumers crucially changes the optimal deterrence rule that a Public Authority should adopt against false claims and misleading advertising. Unlike Piccolo et al. (2015), in this more general model, strong enforcements may improve the buyer welfare according to the degree of loss aversion.

     

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.     

Quantifying loss aversion: Evidence from a UK population survey

Journal of Risk and Uncertainty - We quantify differences in attitudes to loss from individuals with different demographic, personal and socio-economic characteristics. Our data are based on...     

On the definition of risk aversion

Two definitions of risk aversion have recently been proposed for non-expected utility theories of choice under uncertainty: the former refers the measure of risk aversion (Montesano 1985, 1986 and 1988) directly to the risk premium (i.e. to the difference between the expected value of the action under consideration and its certainty equivalent); the latter defines risk aversion as a decreasing preference for an increasing risk (introduced as mean preserving spreads) (Chew, Karni and Safra 1987, Machina 1987, Röell 1987, Yaari 1987).When the von Neumann-Morgenstern utility function exists both these definitions indicate an agent as a risk averter if his or her utility function is concave. Consequently, the two definitions are equivalent. However, they are no longer equivalent when the von Neumann-Morgenstern utility function does not exist and a non-expected utility theory is assumed. Examples can be given which show how the risk aversion of the one definition can coexist with the risk attraction of the other. Indeed the two definitions consider two different questions: the risk premium definition specifically concerns risk aversion, while the mean preserving spreads definition concerns the increasing (with risk) risk aversion.The mean preserving spreads definition of risk aversion, i.e. the increasing (with risk) risk aversion, requires a special kind of concavity for the preference function (that the derivatives with respect to probabilities are concave in the respective consequences). The risk premium definition of local risk aversion requires that the probability distribution dominates on the average the distribution of the derivatives of the preference function with respect to consequences. Besides, when the local measure of the first order is zero, there is risk aversion according to the measure of the second order if the preference function is concave with respect to consequences.Yaari's (1969) measure of risk aversion is closely linked to the r.p. measure of the second order. Its sign does not indicate risk aversion (if positive) or attraction (if negative) when the measure of the first order is not zero (i.e., in Yaari's language, when subjective odds differ from the market odds).     

A tractable method to measure utility and loss aversion under prospect theory

This paper provides an efficient method to measure utility under prospect theory. Our method minimizes both the number of elicitations required to measure utility and the cognitive burden for subjects, being based on the elicitation of certainty equivalents for two-outcome prospects. We applied our method in an experiment and were able to replicate the main findings on prospect theory, suggesting that our method measures what it is intended to. Our data confirmed empirically that risk seeking and concave utility can coincide under prospect theory. Utility did not depend on the probability used in the elicitation, which offers support for the validity of prospect theory.

On the axiomatisation of subjective probabilities

This paper essentially makes two remarks that are pertinent to many of the axiomatisations of subjective probability. First, the auxiliary experiment used to quantify qualitative feelings of relative likelihood is essentially distinct from the field of events of actual interest and may be kept so in the axiomatisation. Second, all theories of subjective probability agree that beliefs are conditional on the present state of knowledge and on the present mood and attitude of the individual concerned. As the individual moves through time this conditioning set, his knowledge and psychological state, change. This ever present change has implications for the conditions under which Bayes' Theorem may be invoked to prescribe how the individual should rationally update his beliefs in the light of a particular observation.     

On the intensity of downside risk aversion

The degree of downside risk aversion (or equivalently prudence) is so far usually measured by . We propose here another measure, , which has specific and interesting local and global properties. Some of these properties are to a wide extent similar to those of the classical measure of absolute risk aversion, which is not always the case for . It also appears that the two measures are not mutually exclusive. Instead, they seem to be rather complementary as shown through an economic application dealing with a simple general equilibrium model of savings.

Reevaluating evidence on myopic loss aversion: aggregate patterns versus individual choices

Investors who are more willing to accept risks when evaluating their investments less frequently are said to exhibit myopic loss aversion (MLA). Several recent experimental studies found that, on average, subjects bet significantly higher amounts on a risky lottery when they observe only a cumulative outcome of several realizations of the lottery (long evaluation period). In this article, we reexamine these empirical findings by analyzing individual rather than aggregate choice patterns. The behavior of the majority of subjects is inconsistent with the hypothesis of MLA: they bet an intermediate fraction of their initial endowment and these bets, on average, are not significantly different across two treatments with short and long evaluation period. We discuss several alternative explanations of this finding, including the Fechner model of random errors and the financial asset pricing model.     

On matrix probabilities in nonarchimedean decision theory

In an earlier paper, we axiomatized a lexicographic expected utility model for preference in decision under uncertainty that is patterned on the models of Ramsey and Savage but omits their Archimedean axioms. Our model has the unusual feature that subjective probabilities are matrices that premultiply utility vectors in the lexicographic representation of preference between acts. Our purpose here is to analyze the model in relation to the Ramsey-Savage theory along with other models that have a lexicographic feature. A point of departure is Savage's postulate P4, whose purpose is to weakly order hisis more probable than relation on events. This postulate does not hold in our model and we therefore encounter incomparability between events. The paper explores the nature of incomparability, which can be widespread in high-dimensional situations. We include special cases of our model that retain a lexicographic component but also satisfy P4.     

Uncertainty aversion and aversion to increasing uncertainty

According to the original Ellsberg (1961) examples there is uncertainty version if the decision maker prefers to bet on an urn of known composition rather than on an urn of unknown composition. According to another definition (Schmeidler, 1989), there is uncertainty aversion if any convex combination of two acts is preferred to the least favorable of these acts. We show that these two definitions differ: while the first one truly refers to uncertainty aversion, the second one refers to aversion to increasing uncertainty. Besides, with reference to Choquet Expected Utility theory, uncertainty aversion means that there exists the core of a capacity, while aversion to increasing uncertainty means that the capacity is convex. Consequently, aversion to increasing uncertainty implies uncertainty aversion, but the opposite does not hold. We also show that a completely analogous situation holds for the case of risk and we define a set of risk and uncertainty premiums according to the previous analysis.     

Personal probabilities of probabilities

By definition, the subjective probability distribution of a random event is revealed by the (‘rational’) subject's choice between bets — a view expressed by F. Ramsey, B. De Finetti, L. J. Savage and traceable to E. Borel and, it can be argued, to T. Bayes. Since hypotheses are not observable events, no bet can be made, and paid off, on a hypothesis. The subjective probability distribution of hypotheses (or of a parameter, as in the current ‘Bayesian’ statistical literature) is therefore a figure of speech, an ‘as if’, justifiable in the limit. Given a long sequence of previous observations, the subjective posterior probabilities of events still to be observed are derived by using a mathematical expression that would approximate the subjective probability distribution of hypotheses, if these could be bet on. This position was taken by most, but not all, respondents to a ‘Round Robin’ initiated by J. Marschak after M. H. De-Groot's talk on Stopping Rules presented at the UCLA Interdisciplinary Colloquium on Mathematics in Behavioral Sciences. Other participants: K. Borch, H. Chernoif, R. Dorfman, W. Edwards, T. S. Ferguson, G. Graves, K. Miyasawa, P. Randolph, L. J. Savage, R. Schlaifer, R. L. Winkler. Attention is also drawn to K. Borch's article in this issue.     

On risk aversion,classical demand theory,and KM preferences

Building on Kihlstrom and Mirman (Journal of Economic Theory, 8(3), 361–388, 1974)’s formulation of risk aversion in the case of multidimensional utility functions, we study the effect of risk aversion on optimal behavior in a general consumer’s maximization problem under uncertainty. We completely characterize the relationship between changes in risk aversion and classical demand theory. We show that the effect of risk aversion on optimal behavior depends on the income and substitution effects. Moreover, the effect of risk aversion is determined not by the riskiness of the risky good, but rather the riskiness of the utility gamble associated with each decision.     

On games under expected utility with rank dependent probabilities

Expected utility with rank dependent probabilities is a generalization of expected utility. If such preference representations are used for the payoffs in the mixed extension of a finite game, Nash equilibrium may fail to exist. Set-valued solutions, however, do exist even for those more general utility functions. But some set-valued solutions may have certain conceptual shortcomings. The paper thus proposes a new set-valued solution concept, called fixed sets under the best reply correspondence. All set-valued solution concepts are robust to perturbations of the expected utility hypothesis.     

Decreasing absolute risk aversion, prudence and increased downside risk aversion

Downside risk increases have previously been characterized as changes preferred by all decision makers u(x) with u????(x) > 0. For risk averse decision makers, u????(x) > 0 also defines prudence. This paper finds that downside risk increases can also be characterized as changes preferred by all decision makers displaying decreasing absolute risk aversion (DARA) since those changes involve random variables that have equal means. Building on these findings, the paper proposes using ??more decreasingly absolute risk averse?? or ??more prudent?? as alternative definitions of increased downside risk aversion. These alternative definitions generate a transitive ordering, while the existing definition based on a transformation function with a positive third derivative does not. Other properties of the new definitions of increased downside risk aversion are also presented.     

Risk aversion and religion

We use a dataset for a demographically representative sample of the Dutch population that contains a revealed preference risk attitude measure, as well as detailed information about participants’ religious background, to study three issues. First, we find strong confirmatory evidence that more religious people, as measured by church membership or attendance, are more risk averse with regard to financial risks. Second, we obtain some evidence that Protestants are more risk averse than Catholics in such tasks. Third, our data suggest that the link between risk aversion and religion is driven by social aspects of church membership, rather than by religious beliefs themselves.     

The impact of risk aversion and ambiguity aversion on annuity and saving choices

Journal of Risk and Uncertainty - We analyze the impact of risk aversion and ambiguity aversion on the competing demands for annuities and bequeathable savings using a lifecycle recursive utility...     

Risk aversion,downside risk aversion,and the transition to entrepreneurship

In this paper, we discuss the transition from secure employment to risky self-employment (entrepreneurship) caused by a small increase in wealth. Building on the apportioning risk literature, we prove that the transition from secure employment to risky entrepreneurship is based on a measure of the difference between the strength of downside risk aversion and the strength of risk aversion. This result highlights the idea that using the behavioral approach of risky lotteries to study entrepreneurship can produce different results from the traditional economic theory of entrepreneurship, which can have policy implications that must be considered with caution.