Risk seeking with diminishing marginal utility in a non-expected utility model

The present work takes place in the framework of a non-expected utility model under risk: the RDEU theory (Rank Dependent Expected Utility, first initiated by Quiggin under the denomination of Anticipated Utility), where the decision maker's behavior is characterized by two functionsu andf. Our first result gives a condition under which the functionu characterizes the decision maker's attitude towards wealth. Then, defining a decision maker as risk averter (respectively risk seeker) when he always prefers to any random variable its expected value (weak definition of risk aversion), the second result states that a decision maker who has an increasing marginal utility of wealth (a convex functionu) can be risk averse, if his functionf issufficiently below his functionu, hence if he is sufficientlypessimistic. Obviously, he can also be risk seeking with a diminishing marginal utility of wealth. This result is noteworthy because with a stronger definition of risk aversion/risk seeking, based on mean-preserving spreads, Chew, Karni, and Safra have shown that the only way to be risk averse (in their sense) in RDEU theory is to have, simultaneously, a concave functionu and a convex functionf.     

Comparative Risk Sensitivity with Reference-Dependent Preferences

Experimental evidence suggests that individuals are risk averse over gains and risk seeking over losses (i.e., they have S-shaped utility functions in an expected utility setting) and that they are loss averse. Furthermore, the evidence leads to a single definition of S-shaped utility, but it has led to several alternative specifications of loss aversion. This paper characterizes the relations more S-shaped than and more loss averse than for a utility function, and in so doing arrives at a new definition of loss aversion based on average instead of marginal utility.     

A parametric analysis of prospect theory’s functionals for the general population

This article presents the results of an experiment that completely measures the utility function and probability weighting function for different positive and negative monetary outcomes, using a representative sample of N = 1,935 from the general public. The results confirm earlier findings in the lab, suggesting that utility is less pronounced than what is found in classical measurements where expected utility is assumed. Utility for losses is found to be convex, consistent with diminishing sensitivity, and the obtained loss-aversion coefficient of 1.6 is moderate but in agreement with contemporary evidence. The estimated probability weighting functions have an inverse-S shape and they imply pessimism in both domains. These results show that probability weighting is also an important phenomenon in the general population. Women and lower educated individuals are found to be more risk averse, in agreement with common findings. In contrast to previous studies that ascribed gender differences in risk attitudes solely to differences in the degree utility curvature, however, our results show that this finding is primarily driven by loss aversion and, for women, also by a more pessimistic psychological response toward the probability of obtaining the best possible outcome.     

OSHA enforcement and workplace injuries: A behavioral approach to risk assessment

We develop a model of risk assessment that incorporates assumptions from the behavioral theory of the firm into conventional expected utility models of compliance, and test the model using data on injuries and OSHA inspections for 6842 manufacturing plants between 1979 and 1985. Four hypotheses are supported-the specific deterrence effect of an inspection, the importance of lagged effects of general deterrence, the asymmetrical effects of probability and amount of penalty on injuries, and the tendency of injury rates to self-correct over a few years. The model estimates that a 10% increase in enforcement activities will reduce injuries by about 1% for large, frequently inspected firms. Prior analyses reporting lower impacts (Smith, 1979; Viscusi, 1986a) are replicated to distinguish between sampling and modeling differences. The results suggest that further compliance theory needs more detailed models of risk-assessment processes to be tested on samples of firms most affected by enforcement.     

Adverse selection,moral hazard and propitious selection

We propose a simple model with preference-based adverse selection and moral hazard that formalizes the cherry picking/propitious selection argument. This argument assumes that individuals differ in risk aversion, potentially resulting in more risk averse agents buying more insurance while being less risky. The propitious selection argument is summarized by two properties: regularity (more risk averse agents exert more caution) and single-crossing (more risk averse agents have a higher willingness to pay for insurance). We show that these assumptions are incompatible with a pooling equilibrium, and that they do not imply a negative correlation between risk and insurance coverage at equilibrium.

Preference Reversals and Induced Risk Preferences: Evidence for Noisy Maximization

We combine two research lines: preference reversal research (Lichtenstein and Slovic, 1971) and research on lottery-based risk preference induction (Roth and Malouf, 1979). Our results are informative for both research lines. We show that inducing risk preferences in preference reversal experiments has dramatic effects. First, while our subjects still display reversals, they do not display the usual pattern of predicted reversals suggested by the compatibility hypothesis. By inducing risk averse and risk loving preferences, we can dramatically reduce reversal rates and even produce the opposite pattern of reversals. Our results are consistent with the assumption that subjects maximize expected utility with error. This provides evidence that Camerer and Hogarth's (1999) framework for incentive effects can be extended to include the risk preference induction reward scheme.     

Making social trade-offs among lives,disabilities, and cost

Applying cost/benefit techniques to issues of life and death generally requires a single index, comparable to gross domestic product, describing the welfare of any community in terms of the health, quality of life, wealth, and longevity of its population. While such indices, based on economic and multiattribute utility theory, do exist, they generally require detailed information on the preferences of the affected individuals. Since gathering such detailed information is often prohibitively expensive and time-consuming, this article derives a simpler index of community welfare. Our index evaluates any proposed government project using a weighted geometric average of the project's anticipated impact on

?per capita wealth less the weighted proportion of individuals with various disabilities, and

?per capita life expectancy adjusted to discount future years of life.

Since the criterion measures the overall utility of society, it can also be used to compare quality of life in various countries.     

Learning from mistakes: What do inconsistent choices over risk tell us?

We implement a risk experiment that allows for judgment errors to investigate who makes mistakes and whether it matters. The experiments are conducted with a random sample of the adult population in Rwanda, and data on financial decisions are collected. We find a high proportion of inconsistent choices, with over 50% of the participants making at least one mistake. Importantly, errors are informative. While risk aversion alone does not explain financial decisions, risk aversion and inconsistent choices interact in significant and sensible ways. As we would expect, risk-averse individuals are more likely to belong to a savings group and less likely to take out an informal loan. For those more likely to make mistakes, however, as they become more risk averse, they are less likely to belong to a savings group and more likely to take up informal credit, suggesting that mistakes correlate with less than optimal behavior.

The Social Composition of China's Private Entrepreneurs: Class and Cohort Differences*

On the basis of survey data on Chinese private enterprises over the years, we try to respond to the classic subject of “the social composition of private entrepreneurs (siyingqiyezhu 私营企业主).” In nearly forty years of development, the overall composition of private entrepreneurs has undergone major changes. The group contains a growing proportion of people who have a market background and higher education and are non-political CPCs. On further classifying the occupational mobility of private entrepreneurs into categories such as “xiahai 下海” (jump into business), “gaizhi 改制” (restructuring), “kuajie 跨界” (crossover), “tiaoban 跳板” (springboard) and “caogen 草 根” (grassroots), we find there are significant differences in the occupational mobility of entrepreneurs in large, medium, and small enterprises in terms of what they did before they founded their businesses. In particular, entrepreneurs in large enterprises are more likely to have “jumped into business” from inside the government system or after restructuring, while most small and medium entrepreneurs develop outside the system. Multiple regression and coefficient clustering analysis shows that education level and political status have varying effects on the occupational mobility of entrepreneurs in terms of class and cohort.     

The impact of self-protection and self-insurance on individual response to risk

We develop four experimental markets to examine how individuals respond to risk: self-protection and self-insurance in both private and collective auctions. First, we find evidence that the mechanism used to reduce risk is important. Results indicate that the upper and lower bounds on value were elicited by the private self-protection and the collective self-insurance markets, respectively. Second, the robustness of these results declined with low-probability lotteries. We find further evidence that individuals overestimate the impact of low-probability events. Overestimation decreased, however, with repeated market exposure. Third, the four markets induced rapid value formation. Usually only one or two additional market trials were necessary before an individual's perception and valuation of reduced risk stabilized.     

Approximations of rational criteria under complete ignorance and the independence axiom

Rational decision making under complete ignorance, a limit case of uncertainty, is defined. Through a concept of approximation, a meaning is given to a criterion almost possessing a property. Rational criteria depend almost on the sole bounds of the outcome range of each decision, they are almost continuous, they can almost possess a transitive indifference relation; however, under Savage's Independence Axiom, this last property restricts possible criteria to those which can be approximated, at least partly, by either the Maximin or the Maximax criterion.     

The impact of risk attitude,uncertainty and disequilibria on optimal production and inventory

Summary The empirical facts seem to indicate that in real economies the effect of uncertainty tends to decrease production. The limitations of empirical investigations presented should be stressed: they were performed mainly on an aggregate level, they mainly refer to Austrian manufacturing, they rely heavily on questionnaires. Above all empirical investigation will never be able to decide normative questions or to explain the behavior in the general equilibrium. Nevertheless in the short run, given all the rigidities and disequilibria which exist, uncertainty tends to lower optimal production even in absence of risk aversion. Risk aversion becomes important for large, for once-for-all decisions, but it is not the only channel through which uncertainty changes decisions.Technological concavity created by concave marginal revenues or by convex marginal costs, marginal costs of uncertainty in disequilibria model or asymmetric costs of revisions of the preliminary decision are able to bias the decision downward in a real world economy without invokingPaper presented to the 2nd Conference on the Foundations of Risk and Utility (FUR), Venezia, 1984.     

Normalized measures of concavity and Ross’s strongly more risk averse order

The Arrow-Pratt (A-P) definitions of absolute and relative risk aversion dominate the discussion of risk aversion and defining “more risk averse”. Ross (Econometrica 49:621–663, 1981) notes, however, that being A-P more risk averse is not sufficient for addressing many important comparative static questions. Consequently he introduces “a new and stronger measure for comparing two agents’ attitudes towards risk…”. Ross does not provide a corresponding measure of risk aversion. This paper uses a normalized measure of concavity to characterize the Ross definition of strongly more risk averse on bounded intervals. Other properties and uses of these normalized measures of concavity are also presented.     

Regret theory and risk attitudes

We examine risk attitudes under regret theory and derive analytical expressions for two components—the resolution and regret premiums—of the risk premium under regret theory. We posit that regret-averse decision makers are risk seeking (resp., risk averse) for low (resp., high) probabilities of gains and that feedback concerning the foregone option reinforces risk attitudes. We test these hypotheses experimentally and estimate empirically both the resolution premium and the regret premium. Our results confirm the predominance of regret aversion but not the risk attitudes predicted by regret theory; they also clarify how feedback affects attitudes toward both risk and regret.     

Conditional expected utility

Let \({\mathcal {E}}\) be a class of events. Conditionally Expected Utility decision makers are decision makers whose conditional preferences \(\succsim _{E}\), \(E\in {\mathcal {E}}\), satisfy the axioms of Subjective Expected Utility (SEU) theory. We extend the notion of unconditional preference that is conditionally EU to unconditional preferences that are not necessarily SEU. We study a subclass of these preferences, namely those that satisfy dynamic consistency. We give a representation theorem, and show that these preferences are Invariant Bi-separable in the sense of Ghirardato et al. (Journal of Economic Theory 118:133–173, 2004). We also show that these preferences have only a trivial overlap with the class of Choquet Expected Utility preferences, but there are plenty of preferences of the \(\alpha \)-Maxmin Expected Utility type that satisfy our assumptions. We identify several concrete settings where our results could be applied. Finally, we consider the special case where the unconditional preference is itself SEU, and compare our results with those of Fishburn (Econometrica 41:1–25, 1973).     

Comparative Mixed Risk Aversion: Definition and Application to Self-Protection and Willingness to Pay

We analyze the optimal choices of agents with utility functions whose derivatives alternate in sign, an important class that includes most of the functions commonly used in economics and finance (Mixed Risk Aversion, MRA, Caballé and Pomansky, 1996). We propose a comparative mixed risk aversion definition for this class of utility functions, namely, More Risk Averse MRA, and provide a sufficient condition to compare individuals. We apply the model to optimal prevention and willingness to pay. More risk averse MRA agents spend less to reduce accident probabilities that are above 1/2. They spend more only when accident probabilities are below 1/2. Explanations in terms of risk premiums are provided. The results presented also allow for the presence of background risk.     

Learning-by-doing in an ambiguous environment

How well do revealed ambiguity preferences predict how people choose to seek new information about uncertain events? In an economics experiment, we apply a new instrument to measure ambiguity preferences, and in a later session observe to what extent the measure predicts the choice to receive costly information in a learning-by-doing game. Ambiguity averse subjects are more willing to pay to receive information, while risk averse subjects are not. Holding ambiguity preferences constant, risk averse subjects tend to perform worse than risk loving subjects. The returns to experimentation, especially for ambiguity averse subjects, suggest a not-well studied but important role that ambiguity preferences play in decision-making under uncertainty.     

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.     

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.     

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.