Insurance demand and social comparison: An experimental analysis

This paper analyzes whether social comparison can explain the low take-up of disaster insurance usually reported in field studies. We argue that risks in the case of disasters are highly correlated between subjects whereas risks for which high insurance take-up can be observed (e.g. extended warranties or cell phone insurance) are typically idiosyncratic. We set up a simple model with social reference points and show that in the presence of inequality aversion social comparison makes insurance indeed less attractive if risks are correlated. In addition we conducted a simple experiment which confirms these theoretical results. The average willingness to pay for insurance is significantly higher for idiosyncratic than for correlated risks.     

How Much Internalization of Nuclear Risk Through Liability Insurance?

An important source of conflict surrounding nuclear energy is that with a very small probability, a large-scale nuclear accident may occur. One way to internalize the associated financial risks is through mandating nuclear operators to have liability insurance. This paper presents estimates of consumers' willingness to pay for increased financial security provided by an extension of coverage, based on the 'stated choice' approach. A Swiss citizen with median characteristics may be willing to pay 0.14 US cents per kwh to increase coverage beyond the current CHF 0.7 billion (bn.) (US$ 0.47 bn.). Marginal willingness to pay declines with higher coverage but exceeds marginal cost at least up to CHF 4 bn.(US$ 2.7 bn.). An extension of nuclear liability insurance coverage therefore may be efficiency-enhancing.     

Comparing risk preferences over financial and environmental lotteries

This paper investigates whether preferences over environmental risks are best modeled using probability-weighted utility functions or can be reasonably approximated by expected utility (EU) or subjective EU models as is typically assumed. I elicit risk attitudes in the financial and environmental domains using multiple-price list experiment. I examine how subjects?? behavioral, attitudinal, and demographic characteristics affect their probability weighting functions first for financial risks, then for oil-spill risks. I find that most subjects tend to overweight extreme positive outcomes relative to expected utility in both the environmental and financial domains. Subjects are more likely to overemphasize low probability, extreme environmental outcomes than low probability, extreme financial outcomes, leading subjects to offer more support for mitigating environmental gambles than financial gambles with the same odds and equivalent outcomes. I conclude that EU models are likely to underestimate subjects?? willingness to pay for environmental cleanup programs or policies with uncertain outcomes.     

Probabilistic Insurance

Probabilistic insurance is an insurance policy involving a small probability that the consumer will not be reimbursed. Survey data suggest that people dislike probabilistic insurance and demand more than a 20% reduction in the premium to compensate for a 1% default risk. While these preferences are intuitively appealing they are difficult to reconcile with expected utility theory. Under highly plausible assumptions about the utility function, willingness to pay for probabilistic insurance should be very close to willingness to pay for standard insurance less the default risk. However, the reluctance to buy probabilistic insurance is predicted by the weighting function of prospect theory. This finding highlights the potential role of the weighting function to explain insurance.     

Confusion of Relative and Absolute Risk in Valuation

Subjects were less willing to pay for government medical insurance for diseases when the number of people who could not be cured was higher, holding constant the number who could be cured. In a second experiment, willingness to pay (from a hypothetical government windfall) for risk reduction was unaffected by whether the risk was described in terms of percentage or number of lives saved, even though subjects knew that the risks in question differed in prevalence. These results are consistent with the findings of Fetherstonhaugh et al., Jenni and Loewenstein, and others. I suggest that these results can be explained in terms of a general tendency to confuse proportions and differences, a confusion that is analogous to other confusions of quantitative dimensions in children, adults, the news media, and perhaps even the epidemiological literature.     

Catastrophic responses to catastrophic risks

Socializing risks from catastrophic losses is difficult even in an ideal political environment, owing to different estimates of low probability risks, solvency constraints, dangers of moral hazard, and high loss correlation. However, these intrinsic contracting problems do not justify invalidating ordinary insurance contracts or forcing insurers to cover catastrophic losses. Yet, political pressures forcing insurance subsidies now induce inefficient decisions in siting and construction, with high expected social losses. Ordinary contract solutions are always imperfect, but superior to the regulatory maze. Unfortunately, patterns of legislation and court decisions are running in the wrong direction.     

Self-protection against repeated low probability risks

This paper reports the results of experiments designed to test the effect of experience on preferences for self-protection against low and high probability losses. Subjects gained experience by repeatedly making choices about whether or not to invest in a protective activity and then observing the result of their choice. Half of the subjects faced a low probability risk while the other half faced a higher probability risk with the severity of loss scaled down to hold expected value constant. Protection was more common against the high probability risk. Despite receiving full information about the risks in advance, most subjects made choices in response to prior outcomes. This led to a great deal of experimentation when losses were common (the high probability risk) but very little experimentation when losses were infrequent (the low probability risk).     

The impact of governmental assistance on insurance demand under ambiguity: a theoretical model and an experimental test

This article deals with the impact of governmental assistance on insurance demand under ambiguity, i.e., in situations where probabilities are uncertain. First, using a model of insurance demand under ambiguity, we derive theoretical predictions about the impact of several governmental assistance programmes on optimal insurance demand. For example, governmental assistance through a fixed public support scheme implies that partial insurance is always optimal under fair insurance with ambiguity. Second, we present the results of an experiment designed to test these predictions. We find support for several of our theoretical predictions. For example, the presence of governmental assistance through a fixed public support scheme decreases individuals’ willingness to pay to be fully insured. Finally, we compare these results with those obtained for a risk situation. We find that, regardless of the form of governmental assistance, participants in the ambiguity context are consistently willing to pay more to be fully insured than participants in the risk situation.     

How do people value extended warranties? Evidence from two field surveys

Extended warranties are popular but expensive. This paper examines how consumers value these warranties, and asks whether economic considerations alone can account for their popularity. Results from two field surveys show that consumers greatly overestimate both the likelihood and the cost of product breakdown. However, these biases alone do not explain their willingness to buy warranties. In fact, we find evidence of probability neglect, in which warranty purchase decision depends on the magnitude of the possible consequences of not having insurance and not on the probability of having to suffer these consequences. The expected emotional benefits from having a warranty was the best predictor of purchase decision and willingness to pay. We also found that people with higher cognitive skills are less likely to overestimate the economic determinants of warranty value, yet are still highly influenced by emotional considerations when deciding whether to purchase a warranty.     

Loss aversion leading to advantageous selection

Some insurance markets are characterized by “advantageous selection”, that is, ex-post risk and coverage are negatively correlated. We show that expectation-based loss aversion as in K?szegi and Rabin (Quarterly Journal of Economics, 121(4), 1133–1165, 2006; The American Economic Review, 97(4), 1047–1073, 2007) provides a natural explanation for this phenomenon in environments in which risk aversion models do not, e.g., when agents face modest-scale risks and/or in absence of moral hazard. More exposure to risk has two competing effects on an agent’s willingness to pay for insurance: a positive effect, as in standard expected utility models; and a negative one, due to a reference effect. We determine conditions under which an insurance provider optimally sets a high price at which only low risk agents buy.     

Anglo and Latino Differences in Willingness to Pay for Urban Public Services*

Objective. This research explores Anglo and Latino differences in willingness to pay for urban public services, assuming differences will impact service delivery in local government as the Latino population increases and becomes more visible. Methods. Survey data from a probability sample of Phoenix residents, now the nation's fifth largest city, are analyzed across 28 city services using multiple mechanisms that included a logit multivariate model. Results. Latinos are substantially more likely than Anglos to report willingness to pay for urban public services. These differences cut across services and are not mitigated by Latino income levels. Conclusions. Latinos are prepared to be full partners in improving service delivery in local government, even at the expense of out‐of‐pocket payment for services. Moreover, while increases in the Latino population will carry greater demand for more and high‐quality city services by Latinos, it is unlikely to alter the menu of preferred services along class or race/ethnic lines. The fact that Latinos seem generally more willing to pay for services also raises the possibility that Latinos are interested in investing in their communities, seeking more opportunities, and perhaps remaining in those communities.     

Ambiguity Aversion in the Field of Insurance: Insurers’ Attitude to Imprecise and Conflicting Probability Estimates

This article presents the results of a survey designed to test, with economically sophisticated participants, Ellsberg’s ambiguity aversion hypothesis, and Smithson’s conflict aversion hypothesis. Based on an original sample of 78 professional actuaries (all members of the French Institute of Actuaries), this article provides empirical evidence that ambiguity (i.e. uncertainty about the probability) affect insurers’ decision on pricing insurance. It first reveals that premiums are significantly higher for risks when there is ambiguity regarding the probability of the loss. Second, it shows that insurers are sensitive to sources of ambiguity. The participants indeed, charged a higher premium when ambiguity came from conflict and disagreement regarding the probability of the loss than when ambiguity came from imprecision (imprecise forecast about the probability of the loss). This research thus documents the presence of both ambiguity aversion and conflict aversion in the field of insurance, and discuses economic and psychological rationales for the observed behaviours.     

Average willingness to pay for disease prevention with personalized health information

Personal health related information modifies individuals’ willingness to pay for disease prevention programs inasmuch as it allows health status assessment based on intrinsic (instead of average) characteristics. In this paper, we examine the effect that personalized information about the baseline probability of disease has on the average willingness to pay for programs reducing either the probability of disease (self-protection) or the severity of disease (self-insurance). We show that such information raises the average willingness to pay for self-protection while it increases the average willingness to pay for self-insurance if health and wealth are complements (i.e. the marginal utility of wealth rises with health).     

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.     

Experimental markets for insurance

This article extends the large amount of research on double-oral auction markets to hazards that produce only losses. We report results from a series of experiments in which subjects endowed with low-probability losses can pay a premium for insurance protection. Insurers specify the price at which they are willing to assume the risk of a loss. Insurance prices approach expected value for a large range of probabilities and loss amounts. Subjects seem to realize losses are statistically independent. Prices are not affected by ambiguity about the probability of loss.     

The heterogeneity of the value of statistical life: Introduction and overview

The refinement in worker fatality risk data used in hedonic wage studies and evidence from new stated preference studies have facilitated the exploration of the heterogeneity of the value of statistical life (VSL). Although the median VSL estimate for workers is $7–$7–8 million, the VSL varies considerably within the worker population. New estimates of the income elasticity of VSL are 1.0 or above, which are consistent with theoretical models linking VSL to the coefficient of relative risk aversion. The specific relationship between VSL and risk aversion is, however, more complex than previously understood. Age differences in VSL are substantial, with young children being accorded especially high VSL amounts. The public’s willingness to pay to reduce risks is reduced if those being protected are perceived as being blameworthy due to their responsibility for contributing to the risk.     

To be,or not to be,that is the question: An empirical study of the WTP for an increased life expectancy at an advanced age

This study reports an attempt to measure the value of an increased survival probability at advanced ages. It turns out that the average willingness to pay for a program which would increase the expected length of life by one year, conditional on having survived to the age of 75 years, is lower than $1,500. The willingness to pay increases with a person's age, but at a low and seemingly constant rate (1–4 percent per year).     

Choices at various levels of uncertainty: An experimental test of the restated diversification theorem

Our “Restated diversification theorem” (Skogh and Wu, 2005) says that risk-averse agents may pool risks efficiently without assignment of subjective probabilities to outcomes, also at genuine uncertainty. It suffices that the agents presume that they face equal risks. Here, the theorem is tested in an experiment where the probability of loss, and the information about this probability, varies. The result supports our theorem. Moreover, it tentatively supports an evolutionary theory of the insurance industry—starting with mutual pooling at uncertainty, turning into insurance priced ex ante when actuarial information is available.     

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     

Willingness to accept equals willingness to pay for labor market estimates of the value of a statistical life

Our research clarifies the conceptual linkages among willingness to pay for additional safety, willingness to accept less safety, and the value of a statistical life (VSL). We present econometric estimates using panel data to analyze the VSL levels associated with job changes that may affect the worker’s exposure to fatal injury risks. Our baseline VSL estimates are $7.7 million and $8.3 million (Y$2001). There is no statistically significant divergence between willingness-to-accept VSL estimates associated with wage increases for greater risks and willingness-to-pay VSL estimates as reflected in wage changes for decreases in risk. Our focal result contrasts with the literature documenting a considerable asymmetry in tradeoff rates for increases and decreases in risk. An important implication for policy is that it is reasonable to use labor market estimates of VSL as a measure of the willingness to pay for additional safety.