Mixed risk aversion and preference for risk disaggregation: a story of moments

In a recent article entitled “Putting Risk in its Proper Place,” Eeckhoudt and Schlesinger (2006) established a theorem linking the sign of the n-th derivative of an agent’s utility function to her preferences among pairs of simple lotteries. We characterize these lotteries and show that, in a given pair, they only differ by their moments of order greater than or equal to n. When the n-th derivative of the utility function is positive (negative) and n is odd (even), the agent prefers a lottery with higher (lower) n + 2p-th moments for p belonging to the set of positive integers. This result links the preference for disaggregation of risks across states of nature to the complete structure of moments preferred by mixed risk averse agents. It can be viewed as a generalization of a proposition appearing in Ekern (1980) which focused only on the differences in the n-th moments.     

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.     

Risk and risk aversion for state-dependent utility

This paper analyses risk and risk aversion in the state-dependent utility model, which is useful for modelling health or life insurance purchase. We use Karni's (1983) definition of risk aversion, and extend the class of risks to which it can be applied.Research supported by the ESRC postdoctoral fellowship scheme. I would like to thank Jerry Nordquist for arousing my interest in this subject. For helpful comments on an earlier draft I am grateful to an anonymous referee and the editor of this journal.     

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.     

Ambiguity aversion and the propensities for self-insurance and self-protection

Two models of ambiguity preferences that permit comparative statics analysis of greater ambiguity aversion yield definite predictions concerning propensities for self-insurance and self-protection: The levels of both activities that are optimal for an ambiguity-averse decision maker are higher in the presence of ambiguity than in its absence, and demands for both activities increase with greater ambiguity aversion. The reason is that, at levels optimal for one decision maker, an increase in either activity results in a mean-preserving contraction in the distribution of expected utility in the presence of ambiguity, which is valuable to anyone with the same risk preferences who is more ambiguity averse.     

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.

     

Risk aversion for losses and the Nash bargaining solution

Theory and Decision - We call a decision maker risk averse for losses if that decision maker is risk averse with respect to lotteries having alternatives below a given reference alternative in...     

Hard evidence and ambiguity aversion

This article shows that if an allocation rule can be implemented with unlimited information certification, then it can also be implemented with limited information certification if the designer can use ambiguous communication mechanisms, and if agents are averse to ambiguity in the sense of maxmin expected utility. The reverse implication is true if there is a single agent and a worst outcome.     

Inequality aversion and antisocial punishment

Antisocial punishment—punishment of pro-social cooperators—has shown to be detrimental for the efficiency of informal punishment mechanisms in public goods games. The motives behind antisocial punishment acts are not yet well understood. This article shows that inequality aversion predicts antisocial punishment in public goods games with punishment. The model by Fehr and Schmidt (Q J Econ 114(3): 817–868, 1999) allows to derive conditions under which antisocial punishment occurs. With data from three studies on public goods games with punishment I evaluate the predictions. A majority of the observed antisocial punishment acts are not compatible with inequality aversion. These results suggest that the desire to equalize payoffs is not a major determinant of antisocial punishment.     

Judged knowledge and ambiguity aversion

Competence has recently been proposed as an explanation for the degree of ambiguity aversion. Using general knowledge questions we presented subjects with simple lotteries in which they could bet on an event and against the same event. We show that the sum of certainty equivalents for both bets depends on the judged knowledge of the class of events. We also elicited the decision weights for events and complementary events. We found a similar effect of knowledge on the sum of decision weights.     

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.     

Experimental Cournot oligopoly and inequity aversion

This paper explores the role of inequity aversion as an explanation for observed behavior in experimental Cournot oligopolies. We show that inequity aversion can change the nature of the strategic interaction: quantities are strategic substitutes for sufficiently asymmetric output levels but strategic complements otherwise. We find that inequity aversion can explain why: (i) some experiments result in higher than Cournot–Nash production levels while others result in lower, (ii) collusion often occurs with only two players whereas with three or more players market outcomes are very close to Cournot–Nash, and (iii) players often achieve equal profits in asymmetric Cournot oligopoly.     

Set and revealed preference axioms for multi-valued choice

Theory and Decision - We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We...     

Varieties of commitment

This discussion of some aspects of the problem of conditional normative statements, conditional obligations, or commitments will first focus on some well-known pseudo-paradoxes, then state some different ways of symbolizing conditioned norm statements and, finally, end up with a remark concerning von Wright's interpretation of commitments by means of a logic of necessary and sufficient conditions.     

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.     

Separating marginal utility and probabilistic risk aversion

This paper is motivated by the search for one cardinal utility for decisions under risk, welfare evaluations, and other contexts. This cardinal utility should have meaningprior to risk, with risk depending on cardinal utility, not the other way around. The rank-dependent utility model can reconcile such a view on utility with the position that risk attitude consists of more than marginal utility, by providing a separate risk component: a probabilistic risk attitude towards probability mixtures of lotteries, modeled through a transformation for cumulative probabilities. While this separation of risk attitude into two independent components is the characteristic feature of rank-dependent utility, it had not yet been axiomatized. Doing that is the purpose of this paper. Therefore, in the second part, the paper extends Yaari's axiomatization to nonlinear utility, and provides separate axiomatizations for increasing/decreasing marginal utility and for optimistic/pessimistic probability transformations. This is generalized to interpersonal comparability. It is also shown that two elementary and often-discussed properties — quasi-convexity (aversion) of preferences with respect to probability mixtures, and convexity (pessimism) of the probability transformation — are equivalent.     

Explaining satisficing through risk aversion

Theory and Decision - This paper extends the analysis of the data from the experiment of Hey et al. (Theory and Decision 83(3): 337–353, 2017), which was designed to test Proposition 2 of the...