Explaining Diversities in Age-Specific Life Expectancies and Values of Life Saving: A Numerical Analysis

To what extent can life protection account for observed diversities in age-specific life expectancies across individuals and over time? We provide answers via calibrated simulations of a life-cycle model where life’s end is stochastic, and age-specific mortality hazards are endogenous outcomes of life protection, set jointly with life insurance and annuities. Our model links mortality hazards and values of life saving (VLS) as “dual variables”, and offers new insights about the measurement of VLS. Life protection is estimated to account for non-trivial portions of observed levels and inequalities in life expectancies and empirical estimates of VLS by age and education, and over time.     

The Value of a Statistical Life: A Critical Review of Market Estimates Throughout the World

A substantial literature over the past thirty years has evaluated tradeoffs between money and fatality risks. These values in turn serve as estimates of the value of a statistical life. This article reviews more than 60 studies of mortality risk premiums from ten countries and approximately 40 studies that present estimates of injury risk premiums. This critical review examines a variety of econometric issues, the role of unionization in risk premiums, and the effects of age on the value of a statistical life. Our meta-analysis indicates an income elasticity of the value of a statistical life from about 0.5 to 0.6. The paper also presents a detailed discussion of policy applications of these value of a statistical life estimates and related issues, including risk-risk analysis.     

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.     

Measures of Mortality Risks

Different risks of death are not equivalent because of differences in timing. This paper develops measures of mortality risks that recognize the probability of death, the duration of life lost, and the role of discounting. These adjustments lead to a substantial reordering of the major causes of death. Recognition of duration-related issues explains much of the public's misperception of mortality risk probabilities, which may reflect duration-related concerns rather than biases in risk beliefs. Our estimates suggest that in forming their risk beliefs the public discounts years of life lost at a rate from 3.3–12.4 percent. Standardization of lifetimes at risk also alters the relative efficacy of regulatory policies for which we provide a variety of cost-effectiveness measures.     

Risk-risk analysis

Constraints on the use of benefit-cost tests have generated increased interest in risk-risk analysis as a regulatory test. The effect on individual mortality of the income losses arising from regulatory expenditures can be determined from direct empirical estimates, which this article surveys. The article proposes an alternative formulation based on information on the value of life and the marginal propensity to spend on health, which implies a loss of one statistical life for every $50 million in expenditures. Occupational injury and fatality costs caused by expenditures represent another type of risk tradeoff that could be considered within risk-risk analysis or, more generally, a benefit-cost test.     

On the Value of Changes in Life Expectancy: Blips Versus Parametric Changes

We estimate the value of a ‘blip’, i.e. an immediate small reduction, in the hazard rate for a random sample of Swedes. Since the risk reduction is age-independent (2 ‘extra saved lives’ out of 10,000 during the next year), we can examine how the value of a statistical life varies with age. We also show how blip data can be used to obtain a lower bound for the value of a permanent change in an individual's hazard rate. The value of a life exhibits an inverted-U shape with respect to age, peaking at the age of 40, and lies within the $3 to $7 million interval where most reasonable estimates are clustered according to Viscusi's (1992) survey.     

Changes in the Value of Life, 1940–1980

We present the first nationwide value of life estimates for the United States at more than one point in time. Our estimates are for every ten years between 1940 and 1980, a period when declines in fatal accident rates were historically unprecedented. Our estimated elasticity of value of life with respect to per capita GNP is 1.5 to 1.7. We illustrate the importance of rising value of life for policy evaluation by examining the benefits of improved longevity since 1900. Our estimated elasticity implies that the current marginal increase in longevity is more valuable than the large increase in the first half of the twentieth century.     

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 mortality risk in China: Comparing stated-preference estimates from 2005 and 2016

Journal of Risk and Uncertainty - We estimate the marginal rate of substitution of income for reduction in current annual mortality risk (the “value per statistical life” or VSL) using...     

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.     

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.     

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.     

On the Measurement of Job Risk in Hedonic Wage Models

We examine the incidence, form, and research consequences of measurement error in measures of fatal injury risk in U.S. workplaces using both Bureau of Labor Statistics and National Intitute of Occupational Safety and Health data. Of the various measures examined the NIOSH industry risk measure produces implicit value of life estimates most in line with both economic theory and the mode result for the existing literature. Because we find non-classical measurement error that differs across risk measures and is not independent of other regressors, innovative statistical procedures need be applied to obtain statistically improved estimates of wage-fatality risk tradeoffs.     

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 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.     

The Potential for Reducing Mortality in Russia

This article attempts to assess current national and regional reserves for reducing the mortality rate in Russia. It explores the potential to reduce the mortality rate in comparison to comparable international benchmarks in rates of growth and gains in life expectancy at birth, identifies a range of circumstances that have an adverse impact on the population’s health in post-Soviet Russia, and shows that the main reserve for reducing mortality remains the “lost health capital” that preceded the collapse of the Soviet Union and continued in the 1990s. Finally, it assesses the current regional potential for lowering the mortality rate, which is “hidden” in differences between regions leading in life expectancy (with the exception of extremes) and the country’s remaining territories. The conclusion presents data revealing the life expectancy of men and women.     

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.     

The Value of a Statistical Life and the Coefficient of Relative Risk Aversion

Individuals’ risk preferences are estimated and employed in a variety of settings, notably including choices in financial, labor, and product markets. Recent work, especially in financial economics, provides estimates of individuals’ coefficients of relative risk aversion (R’s) in excess of one, and often significantly higher. However, it can be shown that high R’s imply equally high values for the income elasticity of the value of a statistical life. Yet estimates of this elasticity, derived from labor and product markets, are in the range of 0.5 to 0.6. Furthermore, it turns out that even an R below one is difficult to reconcile with these elasticity estimates. Thus, there appears to be an important (additional) anomaly involving individuals’ risk-taking behavior in different market settings.JEL Classification: D80, G11, G12, I10, J17     

Mortality Risk Perceptions: A Bayesian Reassessment

"This study uses data on perceived and actual mortality risks to test several alternative Bayesian models of the factors influencing risk beliefs. The analysis...indicates that while the hazard rate for the individual age group is an influential factor, the overall population death rate and the discounted expected number of life years lost due to the cause of death are also influential in affecting risk perceptions.... The predictive power of a linear perception model increases with the level of the risk and is least accurate for very small risks."     

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