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.     

Age,autos, and the value of a statistical life

The value of a statistical life (VSL) is used to assign a dollar value to the benefits of health and safety regulations. Many of those regulations disproportionately benefit older people, but most estimates of the VSL come from hedonic wage regressions with few older workers and no retirees. Using automobile purchase decisions, I estimate a VSL for individuals from the age of 18 up to the age of 85. Combining information on vehicle holdings and use, household attributes, used vehicle prices, crash test results, and yearly fatal accidents for each make, model, and vintage automobile, I calculate a separate willingness to pay for reduced mortality for different age groups. I find a significant inverted-U shape to the age-VSL function that ranges from $1.5 to $19.2 million (in 2009 dollars). The shape and magnitude of the vehicle-based age-VSL relationship corroborate labor market estimates and extend the age range of revealed preference evidence on the relationship between age and the VSL.     

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.

Policy relevant heterogeneity in the value of statistical life: New evidence from panel data quantile regressions

We examine differences in the value of statistical life (VSL) across potential wage levels in panel data using quantile regressions with intercept heterogeneity. Latent heterogeneity is econometrically important and affects the estimated VSL. Our findings indicate that a reasonable average cost per expected life saved cut-off for health and safety regulations is 7 million to7 million to 8 million per life saved, but the VSL varies considerably across the labor force. Our results reconcile the previous discrepancies between hedonic VSL estimates and the values implied by theories linked to the coefficient of relative risk aversion. Because the VSL varies elastically with income, regulatory agencies should regularly update the VSL used in benefit assessments, increasing the VSL proportionally with changes in income over time.     

Self Selection Bias in the Estimates of Compensating Differentials for Job Risks in India

This study contributes to the hedonic wage literature in developing countries by estimating the collective willingness to pay of a statistical life/injury, using an original data set from the Indian labor market. As self-selection by workers results in biased estimates of the wage premium for job risks, the study uses a modified selectivity bias correction technique. Empirical results indicate substantial heterogeneity in returns to risk. The estimated value of life without selectivity bias is Rs. 56 million (US $3 million), which is substantially larger than the value with selection bias. The estimates provided by the study can aid policy makers, international agencies and other researchers in evaluating health projects in India and other developing countries.     

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     

A Choice Experiment Approach to the Valuation of Mortality

This paper presents an integrated framework for evaluating the reduction of several types of mortality risk using a Choice Experiment (CE) approach, a type of stated preference technique. Using this approach, we can distinguish the marginal willingness to pay (MWTP) for the amount of risk reduction from the MWTP for the opportunity of risk reduction and therefore calculate the “Quantity-based” Value of a Statistical Life. The risks in our survey include mortality risks due to accident, cancer, and heart disease. The Quantity-based VSL is calculated to be 350 million JPY (in 2002 Japanese Yen, about 2.9 million US dollars). Furthermore, we analyzed the influence of subjective risk perception and population characteristics of the respondents on their MWTP. Estimated results suggest that it is unnecessary to adjust the VSL according to the differences in the type of risk if the VSL is calculated using an adequate approach. However, adjustments for the timing of risk reduction and population characteristics are found to be significant for the execution of benefit transfer.JEL Classification: I18, D81, J17     

Elicitation of health values from mortality risk reduction

There are concerns regarding uncertainty about the accuracy of applying available empirical willingness-to-pay (WTP) estimates for reducing accidental deaths to value changes in risks of pollution-related deaths. In this study, we develop a theoretical model on defining WTP, and its determinants, and derive WTP estimates for changes in pollution-related mortality risks with varying morbidity and timing attributes. A survey is designed and conducted with 100 subjects. Each subject was to complete five choice sets and provided a range of implicit values of statistical life (VSL). The choices are estimated using the logit procedure. And, using the results of estimated multinomial logit model, the VSL is estimated to about $6.2 million.     

Background Risks and the Value of a Statistical Life

We examine the effects of background mortality and financial risks on an individual's willingness to pay to reduce his mortality risk (the value of statistical life or VSL). Under reasonable assumptions about risk aversion and prudence with respect to wealth in the event of survival and with respect to bequests in the event of death, background mortality and financial risks decrease VSL. The effects of large mortality or financial risks on VSL can be substantial, but the effects of small background risks are negligible. These results suggest that the commonplace failure to account for background risk in evaluating VSL is unlikely to produce substantial bias in most applications.     

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.     

The value of job safety for railroad workers

The value of reducing job risk is estimated using a hedonic wage model and a risk variable that is matched by occupation and state of residence. This study is the first to use the hedonic wage approach to estimate the value of safety in a single industry. Industry-specific estimates will help researchers and labor policymakers better understand the distribution of compensating wage differentials across industries. Our estimated value of job safety for railroad workers is between $21,000 and $26,000 (1980 dollars) per statistical disabling injury, which is somewhat larger than the average of values estimated in previous studies that use cross-industry or crossoccupation aggregate risk data.     

Valuing the risk of workplace sexual harassment

Using data on sexual harassment charges filed with the Equal Employment Opportunity Commission, I calculate the risk of sexual harassment by gender, industry, and age and establish that white females, but not nonwhite females, receive a compensating wage differential for exposure to a higher risk of sexual harassment. I use this risk premium to calculate the value of statistical harassment (VSH) in a manner analogous to the calculation of the value of statistical life (VSL). The VSH is around $7.6 million, about three-quarters of the size of the most-commonly cited levels of the VSL, and far above the maximum damages award for sexual harassment available under federal law. Boosting the maximum damages award to equal the VSH would create the appropriate economic incentives for organizations to deter sexual harassment.     

Dirty money: Is there a wage premium for working in a pollution intensive industry?

Within a compensating wage differential framework we investigate whether there is a wage premium for working in a pollution intensive industry. Our results for the economy as a whole suggest a small wage premium of approximately one quarter of one percent associated with the risk of working in a dirty job. This premium rises to over fifteen percent for those individuals who work in one of the five dirtiest industries. We also find evidence of a fatal risk wage premium, providing estimates of the value of a statistical life of between ￡12 million and ￡19 million (2000 prices).     

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.     

Anchoring biases in international estimates of the value of a statistical life

U.S. labor market estimates of the value of a statistical life (VSL) were the first revealed preference estimates of the VSL in the literature and continue to constitute the majority of such market estimates. The VSL estimates in U.S. studies consequently may have established a reference point for the estimates that researchers analyzing data from other countries are willing to report and that journals are willing to publish. This article presents the first comparison of the publication selection biases in U.S. and international estimates using a sample of 68 VSL studies with over 1000 VSL estimates throughout the world. Publication selection biases vary across the VSL distribution and are greater for the larger VSL estimates. The estimates of publication selection biases distinguish between U.S. and international studies as well as between government and non-government data sources. Empirical estimates that correct for the impact of these biases reduce the VSL estimates, particularly for studies based on international data. This pattern of publication bias effects is consistent with international studies relying on U.S. estimates as an anchor for the levels of reasonable estimates. U.S. estimates based on the Census of Fatal Occupational Injuries constitute the only major set of VSL studies for which there is no evidence of statistically significant publication selection effects. Adjusting a baseline bias-adjusted U.S. VSL estimate of $9.6 million using estimates of the income elasticity of the VSL may be a sounder approach for generating international estimates of the VSL than relying on direct estimates from international studies.     

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.     

Imprecise preferences and the WTP-WTA disparity

This article reports the results of a study designed to elicit willingness to pay (WTP) and willingness to accept (WTA) values for changes in the risk of nonfatal road injuries. We examine the possibility that individuals' preferences over combinations of wealth, risk, and safety are imprecise, and that this imprecision might result in the observed disparity between WTP and WTA measures of value. The results confirm that individuals' preferences for safety are significantly imprecise, but that this alone is insufficient to explain more than part of the disparity. Indeed, respondents' estimates of the minimum that they would be prepared to accept for a risk increase frequently exceed the maximum that they would be prepared to pay for an equivalent risk reduction.     

The value of mortality risk reductions in Delhi,India

We interviewed commuters in Delhi, India, to estimate their willingness to pay (WTP) to reduce their risk of dying in road traffic accidents in three scenarios that mirror the circumstances under which traffic fatalities occur in Delhi. The WTP responses are internally valid: WTP increases with the size of the risk reduction, income, and exposure to road traffic risks, as measured by length of commute and whether the respondent drives a motorcycle. As a result, the value of a statistical life (VSL) varies across groups of beneficiaries. For the most highly-exposed individuals the VSL is about 150,000 Purchasing Power Parity (PPP) dollars.

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.     

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).