The analysis of age variations in VSL is accompanied by a review of the Value of Statistical Life Year (VSLY) approach. The VSL number is not an accounting measure of the present value of lost earnings.
Heterogeneity of VSL Based on the Risk Level
Moreover, consideration of the heterogeneity of VSL is not a minor footnote to VSL. A key assumption in this analysis is that people select their job risk based on available market opportunities, independent of the choices of others.
Segmented Labor Markets
Whether smokers will simply be located further to the right on the flat portion of the market supply curve than nonsmokers or whether they will be on different labor market supply curves is an empirical issue. This issue of labor market segmentation also arises with respect to racial differences in compensation for risk.
Heterogeneity Based on Age
To sum up, what do we know about the age-LFS relationship based on labor market evidence?2 First, LFS does not peak at birth, as it would if only total remaining life expectancy mattered. Total remaining life expectancy is not the only factor influencing the VSL rating.
Value of a Statistical Life Year (VSLY)
The VSLY Approach
Viscusi and Aldy (2007), Aldy and Viscusi (2008), and Viscusi and Hersch (2008) analyze VSL and VSLY by age using a measure of occupational death rate specific to the worker's industry and the worker's age group. Note the cohort-adjusted VSLY estimates indicated by dashed lines in the figure. VSLY rises from around $125,000 for those in their late teens and peaks at approx.
After that, the VSLY expires, but nevertheless remains quite substantial, at a level of $350,000 for workers aged 62.
An Application of VSL and VSLY to the Private Cost of Cigarettes
Male smokers estimate the loss of life expectancy from smoking at 8.6 years, and female smokers at 13.2 years, each of which far exceeds the actual estimated loss of life expectancy.3 Thus, the perceived mortality effect is quite large. The presence of a high discount rate coupled with high life expectancy loss figures is why smoking is nevertheless attractive to smokers. Even the positive financial externalities, such as health costs from smoking, are below $1 per pack.
These calculations of the costs per package thus provides no new information for smokers who already overestimate the mortality risk and expected loss from smoking.
Income Effects
There were two main estimation strategies used to determine the income elasticity of the VSL. The meta-analysis approach estimates the income elasticity based on how the VSL responds to differences in the wage level in the studies. Notwithstanding these differences in the magnitude of the income elasticity, it is clear that the value of the income elasticity of VSL is positive and significant.
The influential role of the positive income elasticity of VSL also has implications for the age variations in VSL.
The Advent of Using VSL in the Policy Arena
I was asked to resolve the dispute between the two agencies by analyzing the merits of the proposal and OMB's criticisms. Using my value-of-life estimates, which have since been called VSL, I have shown that the benefits outweigh the costs. In particular, using my VSL estimates increases the value of the estimated benefits by a factor of ten.1 As a result of this analysis, the regulation became attractive on a benefit-cost basis.
The calculated benefits now exceeded the value of the costs, and the day after the White House received my report in support of the settlement, the settlement was issued.
The “Senior Discount” Controversy
It is important to note that this proposed ban on demographic adjustments for differences in VSL referred only to point-in-time differences and not to adjustments over time. Assume that the goal, to avoid disputes, is to evaluate policies based on fairness rather than using an efficiency-based measure of the VSL-age ratio. Such a reference to fairness consequently does not resolve the choice of an appropriate age adjustment of the VSL, as there are different and entirely legitimate views of what is fair.
But VSL is not a steadily decreasing function of age and does not decrease with age.
Should Income Levels Matter?
Although FAA did not accept a positive income elasticity for VSL at that time due to opposition from other branches of the agency that regulated motor vehicles, things changed in 2008. Department of Transport's proposed adjustment of the VSL based on income levels is a very bold policy initiative to account for differences within population. The proper benefit measure must be grounded in the WTP of the beneficiaries of the policy.
Imposing limits on income adjustments or any other aspect of the benefit assessment process effectively overrides individual preferences and the central economic role of consumer sovereignty.
The Devaluation of Life Controversy
One of the main differences between the studies is that the Viscusi and Aldy study only used the single best estimate of the VSL from each study. Additionally, other branches of the EPA, such as the Office of Water, did not lower the VSL it used in its regulatory analyses. The public anger that accompanied the devaluation controversy did not delve into the rationale for the change in the VSL figure, only the direction of movement.
What is particularly remarkable about this incident is that it is the change in the VSL that has caused the controversy, not the level.
Adjustments for the Size of Risk
Risk Levels in Hedonic Wage Studies
A higher wage rate w1(p2) is required, where due to the curvature of EU1 this wage is necessarily higher than that implied by the hedonic wage analysis. However, as shown in Figure 12.1, EU1 lies above w(p) for risk levels less than p1, so that the WTP values (or the drop in wages that workers are willing to accept) for a significant reduction in the risk of death will be less than those that they are implied by the hedonic wage function. The levels of risk analyzed in hedonic wage studies have changed over time, in part because the workplace has become safer.1 Important risk measures are those that attempt to isolate the risk associated with a worker's particular job.2 The first such measures were those: based on early U.S.
While there are exceptions, for the most part the hedonic wage literature has focused on WTA amounts for job hazard levels averaging from 1/25,000 to 4/10,000.
A Calibration Example for Non-Incremental Risk Changes
That the discrepancy should be greater for WTA quantities is expected given the curvature of the constant expected utility locus. The WTP function shown in the diagram shows the estimated WTP function based on a meta-analysis of five studies. Linear extrapolation of the estimated VSL for large changes in risk will overestimate the WTP amounts for very large changes in risk since people have a positive but decreasing WTP for risk reduction.
How large the reduction in risk probability is depends on the nature of the risk exposure.
Latency and Cancer Benefit Issues
Some stated cancer preference studies simply refer to the disease as "cancer" with little description of the health consequences. If the respondent does not know the characteristics of the health risk being assessed and the consequences for personal well-being, the commodity being assessed may bear little relation to what is needed for benefit assessment. Two studies that obtained estimates of cancer risk after providing a detailed description of health consequences are Magat et al.
We would expect studies to generate different values due to different descriptions of health outcomes.
Dread and Contextual Sources of Variation in Valuing Life: Deaths from Attacks by Terrorists
Across the different categories of terrorism risk beliefs shown in Table 14.1, support for such assistance ranges from 72% to 85% of the population. The results of the series of paired comparisons based on questions such as those in Figure 14.1 are shown in Table 14.6. A key finding of the study is that, although the number of deaths is the same in each case, preventing 0.56 deaths from terrorism is equivalent to preventing deaths from natural disasters for people with an average risk assessment.
However, even taking into account differences in individual experiences of natural disasters in Viscusi (2009b), there remains a substantial gap in assessments of the risks of terrorism versus natural disasters.
Should the VSL Be Added to the Present Value of Economic Damages?
The second approach that Posner and Sunstein propose to determine VSL is to determine the victim's VSL. So if R is the compensation the person received for risk q, then the VSL amount that would be used is R/q. The fourth approach suggested by Posner and Sunstein for evaluating the VSL is to ask the jury to determine a “value of the pleasures of life that the victim has lost.” This concept is completely different from the VSL approach.
The value of life's pleasures is an entirely different concept than that enshrined in the VSL.
Conclusion
The estimates of heterogeneity of VSL and analyzes of the sources of heterogeneity are becoming more refined both for the labor market and for study populations. One challenge raised by this increased refinement in estimates of VSL heterogeneity is that new policy challenges are presented. The task for policymakers is to determine which estimates of VSL heterogeneity are meaningful reflections of differences in individual preferences and which are not.
But for policies that affect specific sub-populations, such as airline passengers, recognition of the heterogeneity of VSL is essential to the development of effective risk policies.
Schaur (2009), 'A quantile estimation approach to identify income and age variation in the value of a statistical life'. Viscusi (2007), 'Car Seat Belt Use and the Value of Statistical Life'. 2007), 'Valuing changes in mortality risk: lives saved versus years of life saved'. Viscusi (2010b), 'Saving lives through punitive damages'. 2005), 'The value of statistical life and the coefficient of relative risk aversion'.
Ziliak (2010), “Policy-relevant heterogeneity in the value of statistical life: new evidence from quantitative regressions of panel data.”
