Updating Subjective Risks in the Presence of Conflicting Information: An Application to Climate Change

Willingness to support public programs for risk management often depends on individual subjective risk perceptions in the face of uncertain science. As part of a larger study concerning climate change, we explore individual updated subjective risks as a function of individual priors, the nature of external information, and individual attributes. We examine several rival hypotheses about how subjective risks change in the face of new information (Bayesian updating, alarmist learning, and ambiguity aversion). The source and nature of external information, as well as its collective ambiguity, can have varying effects across the population, in terms of both expectations and uncertainty.JEL Classification  D8, Q51, Q54     

The value of improved road safety

We report the results of a contingent valuation study for finding a conservative estimate of the value-of-statistical-life in an urban road safety context in Sweden. We estimate the value of both a private-good device and a public-good safety program. The reduction of risk is communicated with a “community analogy” representation of the “Vision Zero” target of the national traffic-safety policy. According to this target, the road-traffic system should be designed so as to prevent accidents when they happen to lead to fatalities or severe injuries. We use the “certainty approach” for ex-post correction of results to remove or mitigate hypothetical bias of responses. As expected we find insensitivity of responses in the full sample to the size of the risk reduction being valued. By our approach we can compute a conservative estimate, based on answers from fully confident respondents, of the value of the largest possible safety enhancement (i.e. fulfilment of the “Vision Zero”). This lower bound estimate indicates a higher average willingness-to-pay for public safety-improving measures than currently assumed in benefit-cost assessments. We also find that the willingness to pay is considerably lower within a public-good than a private-good framework and a weak indication of sensitivity to scale among the most confident respondents. JEL Codes H43 · I18 · Q51     

Willingness to pay for mortality risk reductions: Does latency matter?

Using results from two contingent valuation surveys conducted in Canada and the U.S., we explore the effect of a latency period on willingness to pay (WTP) for reduced mortality risk using a structural model. We find that delaying the time at which the risk reduction occurs by 10 to 30 years reduces WTP by more than 60% for respondents in both samples aged 40 to 60 years. The implicit discount rates are equal to 3.0–8.6% for Canada and 1.3–5.6% for the U.S. JEL Classification Q51 · Q58 The findings, interpretations and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the USEPA or of the World Bank, its Executive Directors or the countries they represent.     

Is imprecise knowledge better than conflicting expertise? Evidence from insurers’ decisions in the United States

This paper reports the results of the first experiment in the United States designed to distinguish between two sources of ambiguity: imprecise ambiguity (expert groups agree on a range of probability, but not on any point estimate) versus conflict ambiguity (each expert group provides a precise probability estimate which differs from one group to another). The specific context is whether risk professionals (here, insurers) behave differently under risk (when probability is well-specified) and different types of ambiguity in pricing catastrophic risks (floods and hurricanes) and non-catastrophic risks (house fires). The data show that insurers charge higher premiums when faced with ambiguity than when the probability of a loss is well specified (risk). Furthermore, they tend to charge more for conflict ambiguity than imprecise ambiguity for flood and hurricane hazards, but less in the case of fire. The source of ambiguity also impacts causal inferences insurers make to reduce their uncertainty.     

Recursive expected utility and the separation of attitudes towards risk and ambiguity: an experimental study

We use the multiple price list method and a recursive expected utility theory of smooth ambiguity to separate out attitude towards risk from that towards ambiguity. Based on this separation, we investigate if there are differences in agent behaviour under uncertainty over gain amounts vis-a-vis uncertainty over loss amounts. On an aggregate level, we find that (i) subjects are risk averse over gains and risk seeking over losses, displaying a “reflection effect” and (ii) they are ambiguity neutral over gains and are mildly ambiguity seeking over losses. Further analysis shows that on an individual level, and with respect to both risky and ambiguous prospects, there is limited incidence of a reflection effect where subjects are risk/ambiguity averse (seeking) in gains and seeking (averse) in losses, though this incidence is higher for ambiguous prospects. A very high proportion of such cases of reflection exhibit risk (ambiguity) aversion in gains and risk (ambiguity) seeking in losses, with the reverse effect being significantly present in the case of risk but almost absent in case of ambiguity. Our results suggest that reflection across gains and losses is not a stable individual characteristic, but depends upon whether the form of uncertainty is precise or ambiguous, since we rarely find an individual who exhibits reflection in both risky and ambiguous prospects. We also find that correlations between attitudes towards risk and ambiguity were domain dependent.      

Learning under compound risk vs. learning under ambiguity – an experiment

We design and conduct an economic experiment to investigate the learning process of agents under compound risk and under ambiguity. We gather data for subjects choosing between lotteries involving risky and ambiguous urns. Agents make decisions in conjunction with a sequence of random draws with replacement, allowing us to estimate the agents’ beliefs at different moments in time. For each type of urn, we estimate a behavioral model for which the standard Bayesian updating model is a particular case. Our findings suggest an important difference in updating behavior between risky and ambiguous environments. Specifically, even after controlling for the initial prior, we find that when learning under ambiguity, subjects significantly overweight the new signal, while when learning under compound risk, subjects are essentially Bayesian.     

The strength of sensitivity to ambiguity

We report an experiment where each subject’s ambiguity sensitivity is measured by an ambiguity premium, a concept analogous to and comparable with a risk premium. In our design, some tasks feature known objective risks and others uncertainty about which subjects have imperfect, heterogeneous, information (“ambiguous tasks”). We show how the smooth ambiguity model can be used to calculate ambiguity premia. A distinctive feature of our approach is estimation of each subject’s subjective beliefs about the uncertainty in ambiguous tasks. We find considerable heterogeneity among subjects in beliefs and ambiguity premia; and that, on average, ambiguity sensitivity is about as strong as risk sensitivity.     

Discount rates and risky sexual behaviors among teenagers and young adults

This article examines the relationship between personal discount rates and sexual behaviors in a sample of teenagers and young adults. We find that higher discount rates (an indication of less willingness to forego current consumption for future consumption) are significantly associated with a range of sexual behaviors, including ever having sex, having sex before age 16 years, and past or current pregnancy. These associations are consistent with previous studies showing a link between discounting and other, non-sexual health behaviors. JEL Classification D80 · D90 · I10     

Cumulative prospect theory's functional menagerie

Many different functional forms have been suggested for both the value function and probability weighting function of Cumulative Prospect Theory (Tversky and Kahneman, 1992). There are also many stochastic choice functions available. Since these three components only make predictions when considered in combination, this paper examines the complete pattern of 256 model variants that can be constructed from twenty functions. All these variants are fit to experimental data and their explanatory power assessed. Significant interaction effects are observed. The best model has a power value function, a risky weighting function due to Prelec (1998), and a Logit function. JEL Classification C52 · D81     

Communication of ambiguous risk information

This paper reports on the responses of 646 individuals to environmental risk information involving different forms of risk ambiguity. Recipients of more than one set of risk information do not simply average the risk levels provided. Rather, a variety of aspects of the nature of the risks that are communicated influence their probabilistic beliefs. Individuals' perceptions of the risk levels to which they are exposed are likely to be greater: (i) for more ambiguous risks, (ii) for risks for which the unfavorable risk evidence is presented last even when there is no temporal order, (iii) for risks for which the most unfavorable risk studies have been performed most recently, and (iv) for risks where there is asymmetry in the risk ambiguity that imposes substantial potential downside risks. Although these effects are modest for the median individual, the potential for extreme responses that reflect only the most adverse or the most favorable piece of information provided is quite prevalent. These findings are of interest more generally in that they indicate how individuals form their risk perceptions in the presence of risk ambiguity.The authors would like to thank the U.S. Environmental Protection Agency for support of this work under Cooperative Agreements Number CR-815445-01-2 and Number CR-814388-02-1. Dr. Alan Carlin and Dr. Ann Fisher provided valuable guidance in the design of the project, and Dr. Doyle Graham and Dr. Douglas Anthony offered generous assistance in communicating the medical consequences of nerve disease to subjects. Jon LaScala assisted superbly in the administration and analysis of the survey, and Patricia Born provided additional computer programming assistance.     

Risk Perceptions and Value of a Statistical Life for Air Pollution and Traffic Accidents: Evidence from Bangkok,Thailand

This paper presents results of two contingent valuation surveys conducted in Bangkok measuring individuals’ willingness to pay (WTP) to reduce mortality risk arising from two risk contexts: air pollution traffic accidents Results from the risk perception survey disclose that respondents view the two risks differently. WTP to reduce air pollution risk is influenced by degrees of dread, severity, controllability and personal exposure, while WTP to reduce traffic accident risk is influenced by perceived immediate occurrence. Nevertheless, the value of a statistical life (VSL) for both air pollution and traffic accidents are comparable (US$0.74 to $1.32 million and US$0.87 to $1.48 million, respectively). This indicates that the risk perception factor alone has little impact on the VSL, a finding similar to previous studies using program choice indifferences.JEL Classification: I18, D61, J17, J28     

An experimental investigation of imprecision attitude and its relation with risk attitude and impatience

We report in this article the result of three experiments on risk, ambiguity, and time attitude. The first two differed by the population considered (students vs. general population) while the third one used a different protocol and concerned students and portfolio managers. We find quite a lot of heterogeneity at the individual level. Of principal interest was the elicitation of risk, time, and ambiguity attitudes and the relationship among these (model free) measures. We find that on the student population, there is essentially no correlation. A non-negligible fraction of the population behaves in an extremely cautious manner in the risk and ambiguity domain. When we drop this population from the sample, the correlation between our measures is also non-significant. We also raise three questions linked to measurement of ambiguity attitudes that come out from our data sets.     

Heterogeneous and Correlated Risk Preferences in Commercial Fishermen: <Emphasis Type="Italic">The Perfect Storm</Emphasis> Dilemma

Commercial fishing involves both physical and financial risks. This combination questions whether fishermen are inherently risk-loving, whether physical and financial risk preferences are correlated, and how much preferences vary across fishermen. This paper addresses these questions with a panel data set of daily participation decisions in the California sea urchin dive fishery. Weather buoy data and the prevalence of great white sharks at a particular fishing site proxy for physical risk. Overall, urchin fishermen are not risk-loving on average, risk preferences are heterogeneous, and there is some evidence that risk preferences are positively correlated across physical and financial domains.JEL Classification: Q22, D81     

A simplified axiomatic approach to ambiguity aversion

This paper takes the Anscombe–Aumann framework with horse and roulette lotteries, and applies the Savage axioms to the horse lotteries and the von Neumann–Morgenstern axioms to the roulette lotteries. The resulting representation of preferences yields a subjective probability measure over states and two utility functions, one governing risk attitudes and one governing ambiguity attitudes. The model is able to accommodate the Ellsberg paradox and preferences for reductions in ambiguity.     

Investigating Risky Choices Over Losses Using Experimental Data

We conduct a battery of experiments in which agents make choices from several pairs of all-loss-lotteries. Using these choices, we estimate a representation of individual preferences over lotteries. We find statistically and economically significant departures from expected utility maximization for many subjects. We also estimate a preference representation based on summary statistics for behavior in the population of subjects, and again find departures from expected utility maximization. Our results suggest that public policies based on an expected utility approach could significantly underestimate preferences and willingness to pay for risk reduction.JEL Classification: C91, D81     

Hopes and Fears: the Conflicting Effects of Risk Ambiguity

The Ellsberg Paradox documented the aversion to ambiguity in the probability of winning a prize. Using an original sample of 266 business owners and managers facing risks from climate change, this paper documents the presence of departures from rationality in both directions. Both ambiguity-seeking behavior and ambiguity-averse behavior are evident. People exhibit fear effects of ambiguity for small probabilities of suffering a loss and hope effects for large probabilities. Estimates of the crossover point from ambiguity aversion (fear) to ambiguity seeking (hope) place this value between 0.3 and 0.7 for the risk per decade lotteries considered, with empirical estimates indicating a crossover mean risk of about 0.5. Attitudes toward the degree of ambiguity also reverse at the crossover point.     

Insurer ambiguity and market failure

A series of studies investigate the decision processes of actuaries, underwriters, and reinsurers in setting premiums for ambiguous and uncertain risks. Survey data on prices reveal that all three types of these insurance decision makers are risk averse and ambiguity averse. In addition, groups appear to be influenced in their premium-setting decisions by specific reference points such as expected loss and the concern with insolvency. This behavior is consistent with a growing analytical and empirical literature in economics and decision processes that investigates the role that uncertainty plays on managerial choices. Improved risk-assessment procedures and government involvement in providing protection against catastrophic losses may induce insurers to reduce premiums and broaden available coverage.This article is part of a larger effort supported by the National Science Foundation on The Role of Insurance, Compensation, Regulation, and Protective Behavior in Decision Making about Risk and Misfortune. We greatly appreciate the many helpful comments and suggestions by our colleagues on the project: Jon Baron, Colin Camerer, Neil Doherty, Jack Hershey, Eric Johnson, and Paul Kleindorfer. Support from NSF Grant #SES8809299 is gratefully acknowledged.     

Assessing multiple prior models of behaviour under ambiguity

The recent spate of theoretical models of behaviour under ambiguity can be partitioned into two sets: those involving multiple priors and those not involving multiple priors. This paper provides an experimental investigation into the first set. Using an appropriate experimental interface we examine the fitted and predictive power of the various theories. We first estimate subject-by-subject, and then estimate and predict using a mixture model over the contending theories. The individual estimates suggest that 24% of our 149 subjects have behaviour consistent with Expected Utility, 56% with the Smooth Model, 11% with Rank Dependent Expected Utility and 9% with the Alpha Model; these figures are close to the mixing proportions obtained from the mixture estimates where the respective posterior probabilities of each of them being of the various types are 25%, 50%, 20% and 5%; and using the predictions 22%, 53%, 22% and 3%. The Smooth model appears the best.