An Experimental Investigation of the Disparity Between WTA and WTP for Lotteries

In this paper we experimentally investigate the disparity between willingness-to-accept (WTA) and willingness-to-pay (WTP) for risky lotteries. The direction of the income effect is reversed by endowing subjects with the highest price of a lottery when asking the WTP question. Our results show that the income effect is too small to be the only source of the disparity. Since the disparity concentrates on a subsample of subjects, parametric and nonparametric tests of the WTA-WTP ratio may lead to contradictory results. The disparity is significantly reduced when background risk is introduced. That is, putting subjects always into a risky position could improve the contingent valuation method, which is often concerned with the assessment of risky situations such as health risks, automobile safety, etc.      

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.     

Valuing Mortality-Risk Reduction: Using Visual Aids to Improve the Validity of Contingent Valuation

We investigate the validity of contingent valuation (CV) estimates of the value per statistical life (VSL). We test for sensitivity of estimated willingness to pay (WTP) to the magnitude of mortality-risk reduction and for the theoretically predicted proportionality of WTP to risk reduction using alternative visual aids to communicate risk. We find that WTP is sensitive to the magnitude of risk reduction for independent subsamples of respondents presented with each of three alternative visual aids, but not for the subsample presented with no visual aid. Estimated WTP is consistent with proportionality to risk reduction for the subsamples presented with a logarithmic scale or an array of 25,000 dots, but not for the subsample receiving a linear scale. These results suggest that CV can provide valid estimates of WTP for mortality-risk reduction if appropriate methods are used to communicate the risk change to respondents.     

Effects of Disease Type and Latency on the Value of Mortality Risk

We evaluate the effects of disease type and latency on willingness to pay (WTP) to reduce environmental risks of chronic, degenerative disease. Using contingent-valuation data collected from approximately 1,200 respondents in Taiwan, we find that WTP declines with latency between exposure to environmental contaminants and manifestation of any resulting disease, at a 1.5 percent annual rate for a 20 year latency period. WTP to reduce the risk of cancer is estimated to be about one-third larger than WTP to reduce risk of a similar chronic, degenerative disease. The value of risk reduction also depends on the affected organ, environmental pathway, or payment mechanism: estimated WTP to reduce the risk of lung disease due to industrial air pollution is twice as large as WTP to reduce the risk of liver disease due to contaminated drinking water.     

Age, Health and the Willingness to Pay for Mortality Risk Reductions: A Contingent Valuation Survey of Ontario Residents

We present the results of a contingent valuation survey eliciting willingness to pay (WTP) for mortality risk reductions. The survey was self-administered using a computer by 930 persons in Hamilton Ontario aged 40 to 75. Visual and audio aides were used to enhance risk comprehension. Mean WTP figures for a contemporaneous risk reduction imply a value of a statistical life of approximately C$l.2 to C$3.8 million (1999 C$). Mean WTP is constant with age up to 70 years, and is about 30 percent lower for persons aged 70 and older. WTP is unaffected by physical health status, but is affected by mental health.     

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.     

The value of private safety versus the value of public safety

In this study, one group of respondents is offered to purchase a safety device to be installed in their cars, while another group is offered a public safety program (improved road quality) which results in the same size risk reduction. In terms of the value of a statistical life, our results are very reasonable. However, the WTP for the private safety device ishigher than the WTP for the public safety measure. Drawing on a model developed by Jones-Lee (1991), we show that some types of altruists may, but need not, be willing to pay more for a private risk reduction than for a uniform risk reduction of the same magnitude. Still, our empirical results are surprising, and further empirical research seems warranted.     

Admissible utility functions for health, longevity, and wealth: integrating monetary and life-year measures

The value of reducing health and mortality risks is often measured using value per statistical life (VSL) or one of several life-year measures (e.g., life years, quality-adjusted life years, disability-adjusted life years). I derive the utility function that is admissible when preferences for health and longevity, conditional on wealth, are consistent with any life-year measure (LYM) and examine the implications for marginal willingness to pay (WTP) for increases in health, longevity, and current-period survival probability. I conclude that marginal WTP for any LYM is decreasing and that VSL is increasing in the LYM. These results imply that cost-effectiveness analysis using a fixed monetary value per LYM is not consistent with economic welfare theory and that the benefit of a health improvement cannot be calculated by multiplying the change in a LYM by a constant.     

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.     

Willingness-to-pay and willingness-to-accept for risky and ambiguous lotteries

Former studies have shown that people tend to give buying prices that are lower than selling prices. In our study, we investigate if this willingness-to-accept and willingness-to-pay disparity is affected by ambiguity. Using a Becker, DeGroot, and Marschak procedure, we elicit buying, selling, short-selling, and short-buying prices. The results indicate that subjects clearly distinguish between risky and ambiguous lotteries and the different ways in which lotteries are framed. However, the average WTA/WTP ratios are remarkably close for all lotteries considered, as well as for negative and positive framing.     

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     

Precautionary behavior and willingness to pay for a mortality risk reduction: Searching for the expected relationship

This paper examines within-sample correlation between six different precautionary behaviors and stated willingness to pay for a mortality risk reduction. The paper also shows estimates of the value of a statistical life based on seat belt and bicycle helmet use as well as based on the stated willingness to pay for a risk reduction in traffic mortality. Contrary to the theoretical expectations, no correlation is found between precautionary behavior and stated willingness to pay. One major explanation is that females and the elderly take more precaution, but state a lower WTP for a risk reduction. The estimates of VSL from the different approaches are $11.0 million, $5.0 million and $2.8 million from stated WTP, bicycle helmet use and seat belt use, respectively.

Valuing fatal risks to children and adults: Effects of disease,latency, and risk aversion

We examine heterogeneity of willingness to pay (WTP) to reduce risks of fatal disease and trauma to adults and children. Using a stated-preference survey fielded to a large, nationally representative internet panel, we find that WTP to reduce fatal-disease risks (caused by consuming pesticide residues on foods) are similar for several types of cancer and non-cancer diseases and similar to WTP to reduce motor-vehicle crashes. WTP to reduce risk to one’s child is uniformly larger than to reduce risk to another adult or to oneself. Estimated values per statistical life are $6–10 million for adults and $6–10 million for adults and 12–15 million for children.     

Common consequence effects in pricing and choice

This paper presents an experimental study of common consequence effects in binary choice, willingness-to-pay (WTP) elicitation, and willingness-to-accept (WTA) elicitation. We find strong evidence in favor of the fanning out hypothesis (Machina, Econometrica 50:277–323, 1982) for both WTP and WTA. In contrast, the choice data do not show a clear pattern of violations in the absence of certainty effects. Our results underline the relevance of differences between pricing and choice tasks, and their implications for models of decision making under risk.     

Does the WTA/WTP ratio diminish as the severity of a health complaint is reduced? Testing for smoothness of the underlying utility of wealth function

The aim of the study reported in this paper is to test the hypothesis that individual utility of wealth functions may violate the assumption of smoothness that underpins the standard analysis of the Value of Statistical Life (VSL) and safety. In order to do so we examine the way in which the Willingness to Accept/Willingness to Pay (WTA/WTP) ratio varies as the severity of a health complaint is reduced. We find that as the severity of the health effect is reduced, the WTA/WTP ratio converges across the sample and tends to a level that does not significantly exceed unity. While we acknowledge that this does not constitute conclusive evidence of smoothness, it does suggest that the case in favour of the assumption that individual utility of wealth functions tend to display a kink at the current level of wealth is less than wholly persuasive.     

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.     

Willingness to Pay for Health Protection: Inadequate Sensitivity to Probability?

Efficient investments in health protection require valid estimates of the public's willingness to forgo consumption for diminished probabilities of death, injury, and disease. Stated valuations of risk reduction are not valid measures of economic preference if the valuations are insensitive to probability variation. This article reviews the existing literature on CV studies of reductions in health risk and finds that most studies are poorly designed to assess the sensitivity of stated valuations to changes in risk magnitude. Replication of a recent study published in this journal by Johannesson et al. (1997) demonstrates how serious the problem of insensitivity can be, even for a study that reports plausible results. New empirical results are presented from telephone surveys designed to provide internal and external tests of how WTP responds to size of risk reduction. The effect of variations in instrument design on estimated sensitivity to magnitude is examined. Overall, estimated WTP for risk reduction is inadequately sensitive to the difference in probability, that is, the magnitude of the difference in WTP for different reductions in risk is typically smaller than suggested by standard economic theory. Additional research to improve methods for communicating changes in risk is needed, and future studies of stated WTP to reduce risk should include rigorous validity checks.     

The Value of Safety as Revealed in the Swedish Car Market: An Application of the Hedonic Pricing Approach

In this article the hedonic regression technique is used to estimate the value of traffic safety, using information from the Swedish market for automobiles. The results from the study show that the market price of an automobile is negatively correlated with its inherent risk level, i.e. Swedish car consumers pay a safety premium for safer cars. In comparison to previous Swedish stated-preference studies, this study reveals a lower willingness to pay for additional car safety, which might be a result of the interaction between government interventions and individual self-insurance and self-protection.JEL Classification: C51, D61, J28     

Scope insensitivity in health risk reduction studies: A comparison of choice experiments and the contingent valuation method for valuing safer food

Scope insensitivity and embedding are fundamental concerns in contingent valuation studies for health risk reductions. Recently, choice experiments have increasingly been used to obtain contingent willingness to pay (WTP) estimates. We juxtapose the WTP estimates of a choice experiment (CE) to those of the contingent valuation method (CVM) for different health risk reductions and compare them in the extent of scope insensitivity and embedding. WTP using CVM is scope sensitive for single health risks, but embedding is observed for multiple disease risks. In contrast, WTP based on the CE is highly scope sensitive and convex in risk reduction levels.

Time Insensitivity for Protective Investments

Investments in protective measures involve an initial immediate cost in exchange for a stream of potential benefits accruing over time in the form of reduced expected losses. This paper describes two studies in which individuals were asked both to make choices and indicate the maximum amount they were willing to pay (WTP) for such protective measures. By varying the number of years that the measures provided protection, we observed four different decision strategies that individuals use to determine their maximum WTP. The findings from these experiments strongly suggest that most individuals do not take into account the added benefits of having a protective measure in place over a longer period of time when determining the likelihood of purchasing protection or the maximum price they are willing to pay. The behavior of a relatively small proportion of the subjects was consistent with a discounted utility model. Most subjects were either myopic in their behavior or did not change their maximum WTP as the time horizon changed. Despite the fact that most subjects were insensitive to time changes, they were generally willing to purchase the protective measures. Implications of these results for investment in risk mitigation measures are briefly explored.