Left-Side strong increases in risk and their comparative statics

This paper introduces a new concept of left-side strong increases in risk (L-SIR) that extends the definition of strong increases in risk (SIR). We also provide somewhat stronger restrictive set of risk-averse decision-makers with a non-negative third derivative utility (prudence) to obtain an appealing comparative statics result for L-SIR.The authors gratefully acknowledge the helpful comments and suggestions of an anonymous referee     

Ethical oxymora for risk assessment practitioners

We define working conditions faced by some practitioners of risk assessment that contradict their formal training and career expectations. Panels of expert risk scientists are used to assess the importance of these ethical oxymora. We offer recommendations aimed at helping risk scientists deal with these contradictions.

An oxymoron is a figure of speech combining contradictory ideas into a useful expression (e.g., sweet sorrow, silent thunder). In this paper we argue that some practitioners of quantitative risk assessment face working conditions that strongly contradict their professional ethos. In the first part of the paper, after briefly defining quantitative risk assessment, we describe four ethical oxymora faced by risk analysts. Second, we describe how we used panels of expert risk scientists to assess the importance of these ethical problems. We offer recommendations aimed at helping risk scientists deal with these oxymora in the last part.     

Non-expected utility risk premiums: The cases of probability ambiguity and outcome uncertainty

This paper discusses two problems. (a) What happens to the conditional risk premium that a decision maker is willing to pay out of the middle prize in a lottery to avoid uncertainty concerning the middle prize outcome, when the probabilities of other prizes change? (b) What happens to the increase that a decision maker is willing to accept in the probability of an unpleasant outcome in order to avoid ambiguity concerning this probability, when this probability increases? We discuss both problems by using anticipated utility theory, and show that the same conditions on this functional predict behavioral patterns that are consistent both with a natural extension of the concept of diminishing risk aversion and with some experimental findings.     

The effect of fast and slow decisions on risk taking

We experimentally compare fast and slow decisions in a series of experiments on financial risk taking in three countries involving over 1700 subjects. To manipulate fast and slow decisions, subjects were randomly allocated to responding within 7 seconds (time pressure) or waiting for at least 7 or 20 seconds (time delay) before responding. To control for different effects of time pressure and time delay on measurement noise, we estimate separate parameters for noise and risk preferences within a random utility framework. We find that time pressure increases risk aversion for gains and risk taking for losses compared to time delay, implying that time pressure increases the reflection effect of Prospect Theory. The results for gains are weaker and less robust than the results for losses. We find no significant difference between time pressure and time delay for loss aversion (tested in only one of the experiments). Time delay also leads to less measurement noise than time pressure and unconstrained decisions, and appears to be an effective way of decreasing noise in experiments.     

Assortative mating on risk attitude

Spousal correlation in risk attitude is estimated using data from the German Socio-Economic Panel over the period 2004–2009. We apply the bivariate panel ordered probit model to the analysis of the simultaneous determination of the male’s and the female’s risk attitude, using the survey question about general willingness to take risk, provided on a 0–10 Likert-scale. The correlations between both the individual-specific effects of the two partners and the two within-individual errors are separately estimated, and found to be +0.285 and +0.310, respectively. We consider the former to be a key parameter, since its positive sign may be interpreted in terms of positive assortative mating on risk attitude: individuals tend to form partnerships with others having a similar risk attitude. We also find evidence that this correlation increases with years of marriage, suggesting either a form of spousal socialization or a selection process in which marriage breakdown is more likely in poorly matched couples.     

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.     

Social comparison and risk taking behavior

This paper studies the effects of social comparison on risk taking behavior. In our theoretical framework, decision makers evaluate the consequences of their choices relative to both their own and their peers’ conditions. We test experimentally whether the position in the social ranking affects risk attitudes. Subjects interact in a simulated workplace environment where they perform a work task, receive possibly different wages, and then undertake a risky decision that may produce an extra gain. We find that social comparison matters for risk attitudes. Subjects are more risk averse in the presence of small social gain than social loss. In addition, risk aversion is decreasing in the size of the social gain.     

Mean utility preserving increases in risk for state dependent utility functions

This paper defines the concept of a mean utility preserving spread across states (MUPSAS) for state dependent utility functions and analyzes the behavioural impact of shifts in the probability distribution of wealth across states such that overall mean utility is preserved. The main result provides an alternative way of ranking state dependent utility functions according to their degree of risk aversion (thus extending Kami's theorem of comparative risk aversion) and establishes a link between increases in risk and risk aversion for state dependent preferences. In a portfolio problem where preferences and the rate of return of the risky venture are state dependent, we find sufficient conditions to determine the impact of a MUPSAS on the optimal share of the portfolio invested in the risky asset.

---

     

A tale of two tails: An alternative characterization of comparative risk

A characterization of comparative risk, parallel to but more restrictive than the Rothschild-Stiglitz (1970) characterization, is developed. As in Rothschild and Stiglitz, we develop a four-way characterization that consists of generating processes (a noise condition and generation by a sequence of special mean-preserving spreads), integral conditions, and preferences. The building blocks of this new order, Mean-preserving increases in risk about ν, where ν is any constant, are mean-preserving spreads whose centers have a nonempty intersection. If this intersection contains the mean of the distribution, the induced order, or mean-preserving increase in risk about the mean, conveys a particularly meaningful notion of an increase in risk as a buildup of the tails of the distribution.     

Changes in multiplicative background risk and risk-taking behavior

This article analyzes the conditions under which any change in a multiplicative background risk induces a more cautious behavior. We give necessary and sufficient conditions under which any change in the multiplicative background risk with respect to the Nth-degree stochastic dominance raises local risk aversion. Surprisingly, decreasing relative risk aversion of any order up to N in the sense of Pratt (Econometrica 32:122–136, 1964) coupled with decreasing relative risk aversion in the sense of Ross (Econometrica 49:631–638, 1981) are sufficient to guarantee an increase in local risk aversion after any deterioration of the multiplicative background risk thanks to the Nth-degree stochastic dominance. We link our results concerning second-order stochastic dominance with the concept of multiplicative risk vulnerability.     

Risk preferences and changes in background risk

We present two theorems that yield necessary and sufficient conditions for first- and second-degree stochastic dominance deteriorations of background risk to increase risk aversion with respect to foreground risk. We require that any change in a foreground risk that is undesirable remains so after a background risk changes in a way that is either unfair, undesirable in the sense of reducing expected utility, or undesirable in the sense of increasing expected marginal utility. Our results thus characterize utility functions that are, respectively, vulnerable, proper, or standard with respect to changes in background risk.

Reference-dependent valuations of risk: Why willingness-to-accept exceeds willingness-to-pay

The gap between willingness-to-pay (WTP) and willingness-to-accept (WTA) benefit values typifies situations in which reference points—and direction of movement from reference points—are consequential. Why WTA-WTP discrepancies arise is not well understood. We generalize models of reference dependence to identify separate reference dependence effects for increases and decreases in environmental health risk probabilities, for increases and decreases in costs, and reference dependence effects embodying the interaction of two changes. We estimate separate reference dependence effects for the four possible cost and health risk change combinations using data from our choice-based experiment for a nationally representative sample of 4,745 households. The WTA-WTP gap is due largely to the reference dependence effects related to costs. Standard models of reference dependence are not consistent with the results, as there is an interactive effect. Estimated income effects are under a penny and thus cannot account for higher values of WTA relative to WTP.     

Mothering and child protection practice: rethinking risk assessment

In recent years, across North America and the UK, child protective service agencies have increasingly begun to rely on bureaucratic, technocratic, and regulatory mechanisms for detecting and managing abuse and neglect. Coupled with a shift from concern for the general social welfare of children to a heightened preoccupation with risk or dangerousness to children, risk assessment systems are becoming integral to child protection practice.
Though risk assessment systems aim to enhance the effectiveness of child protection investigations and service provision, as well as filter out high risk cases from the rest, such systems may foster and reproduce often concealed relations of gender, race, and class. This paper presents a review of the risk assessment trend in child welfare, its general objectives, and some criticisms raised to date. Through a feminist analysis of the social construction of mothering, we re-examine risk assessment. We argue that the risk assessment trend has the potential to entrench oppressive relations of gender, race, and class in child welfare practice with mothers. We suggest that an approach to risk assessment which incorporates a 'mothering narrative' might offer a more thorough evaluation of the conditions that shape the context within which risk to children emerges.     

Framing effects in the evaluation of multiple risk reduction

We studied how evaluation of changes in low-probability risks are affected by reference points and framing effects. Subjects considered hypothetical situations with one or two low-probability risks. Different frames were used to describe changes in risk levels. In the first experiment, subjects chose between risk-reduction options that achieved the same overall risk reduction: large reduction of one risk vs. equal (smaller) reduction of two risks. When the risks were described as losses relative to the no-risk ideal, more subjects were indifferent between the options than when the same options were described as gains relative to the status quo. In the latter case subjects preferred equal reduction of both risks, unless one risk could be reduced to zero. In a related experiment, subjects were less willing to pay any price for a commodity that carried small increases in two risks than for a commodity carrying a comparable large increase in one risk. In other experiments, subjects evaluated single changes in risks rather than comparing or evaluating pairs of changes. Subjects again placed particularly high value on reducing any risks to zero, and they were even more inclined to do so when some other risk would also be reduced to zero. In a final experiment, elimination of risk was found to be less highly valued if its source was not fully eliminated, and a status-quo effect was found. The findings are interpreted in terms of reference theories of choice.     

Mean-preserving changes in risk with tail-dominance

In this paper, we consider a class of mean preserving increases in risk such that all risk-averse decision makers respond to an increase in risk by reducing the level of their risky activities. The type of increase in risk that we consider is based on the notion of tail dominance which generalizes other cases previously discussed in the literature.L. Eeckhoudt is Professor of Economics at the Catholic Faculties of Mons (Belgium) and Lille (France). P. Hansen is Professor of Operations Research at Ecole des Hautes Etudes Commerciales, Montréal. Both authors have benefited from comments by P. Caperaa, G. Dionne, J. Meyer and H. Varian. They also thank A. Coopman who carefully reviewed and improved the English style.     

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.     

Giving in the face of risk

Decisions about how to share resources with others often need to be taken under uncertainty regarding its allocational consequences. Although risk preferences are likely important, existing research is silent about how social and risk preferences interact in such situations. In this paper we provide experimental evidence on this question. In a first experiment givers are not exposed to risk while beneficiaries’ final earnings may be larger or smaller than the allocation itself, depending on the realized state of the world. In a second experiment, risk affects the earnings of givers but not of beneficiaries. We find that individuals’ risk preferences are predictive for giving in both experiments. Increased risk exposure of beneficiaries tends to decrease giving whereas increased risk exposure of givers has no effect. We propose a simple non-linear generalization of a model allowing for other-regarding preferences, ex-post and ex-ante fairness, and risk aversion. We find some support for it in our data when risk is on the beneficiaries’ side but less so when risk is on the givers’ side. Our results point to the importance of the further development of models of social preferences that also incorporate risk preferences.     

Utility Functions for Wealth

We specify all utility functions on wealth implied by four special conditions on preferences between risky prospects in four theories of utility, under the presumption that preference increases in wealth. The theories are von Neumann-Morgenstern expected utility (EU), rank dependent utility (RDU), weighted linear utility (WLU), and skew-symmetric bilinear utility (SSBU). The special conditions are a weak version of risk neutrality, Pfanzagl's consistency axiom, Bell's one-switch condition, and a contextual uncertainty condition. Previous research has identified the functional forms for utility of wealth for all four conditions under EU, and for risk neutrality and Pfanzagl's consistency axiom under WLU and SSBU. The functional forms for the other condition-theory combinations are derived in this paper.     

Heterogeneous risk and time preferences

Assessing individuals’ time and risk preferences is crucial in domains such as health-related decisions (e.g., dieting, addictions), environmentally-friendly practices, and saving opportunities. We propose a new method to jointly elicit and estimate risk attitudes and intertemporal choices. We use a novel individual level estimation procedure based on a hierarchical Bayes methodology, which can integrate different functional forms for discounting and risk attitudes. This method provides individual level estimates, and allows us to explore the heterogeneity in the data. In addition, we report a negative correlation between risk and time preferences, implying that risk-seeking individuals are less patient and less willing to defer consumption.     

The effects of spatial patterns of neighborhood risk factors on adverse birth outcomes

Neighborhood environments play an important role in shaping health. But how do the conditions of surrounding neighborhoods affect health? Specifically, how do the spatial patterns of neighborhood characteristics shape birth outcomes? Using Census and health data from Wyandotte County, Kansas, we analyze the relationship between spatial patterns of socio-demographic risk factors and incidence of low weight births in neighboring block groups. Using spatial filtering with eigenvectors we identify significant socio-demographic patterns and use them as predictors of low-weight births in a regression model. We identify several patterns that predict significant variability in birth outcomes and find that while some factors, like unemployment, have strong internal neighborhood effects on birth weight they may not have strong external neighborhood effects. We argue spatial filtering methods may improve our understanding of persistent inequalities in health by helping to identify the differential effects of proximate social conditions and spatial interdependencies.