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On Balance: COVID-19 Benefit-Cost Analysis and the Value of Statistical Lives
07/01/2020

July 1, 2020
By: Lisa A. Robinson 

Reducing COVID-19 risks requires making extraordinarily difficult decisions that trade-off saving lives and economic damages. Benefit-cost analysis is well-suited for investigating these trade-offs and informing these decisions. However, interpreting and using the results requires understanding the framework and addressing its limitations, including the uncertainties in the value of mortality risk reductions and the distribution of impacts across those who are advantaged and disadvantaged. 
 
For related information, view JBCA Editor Tom Kniesner's conversation with W. Kip Viscusi.

The COVID-19 crisis has focused unprecedented attention on the use of benefit-cost analysis and approaches for valuing mortality risk reductions, commonly referred to as the value per statistical life (VSL). The pace at which new studies are being completed is extraordinary as is the significant attention they are receiving in the media. While emphasizing the important role that benefit-cost analysis plays in promoting systematic investigation of policy impacts, this attention has also highlighted the need to clearly communicate: (1) the scenarios considered and the policy implications; (2) the meaning of the value per statistical life terminology; and (3) the uncertainties in the VSL estimates and their effects on the analytic results.
 
Clarifying the scenarios considered and the policy implications. As conventionally conducted, benefit-cost analysis is a comparative exercise. It predicts future conditions without and with a change in policy and estimates the costs and benefits that result. Regardless of whether the context is COVID-19 or another problem, analysts at times are unclear about the comparisons being made and the underlying assumptions, which can make it difficult to interpret the implications for decision-making.
 
The COVID-19 analyses conducted to-date vary in the extent to which they consider realistic scenarios. Analyses that compare conditions without and with COVID-19, or that compare COVID-19 with no policy response to a widespread and fully-effective policy (such as national social distancing with 100 percent compliance), provide important insights into the scope of the crisis and the difficulty of the choices. Analyses that predict future conditions without and with an incremental change in policy over a defined time period provide a more useful guide to action, however, particularly if they incorporate reasonably realistic assumptions about behavioral responses. For example, some people will adhere to social distancing recommendations regardless of government requirements while others will ignore these recommendations even if social distancing is mandated. These responses in turn have potentially important ramifications for the costs and benefits of the policy.
 
Many of the initial, highly publicized COVID-19 benefit-cost analyses emphasized the central trade-off between severe economic damages and high death rates, relying on relatively simplistic policy scenarios to draw attention to key issues. Researchers are now addressing a broader range of policies and a wider array of impacts using more realistic assumptions, which will aid decision-makers in selecting the most effective set of options.
 
Understanding the value per statistical life concept. Consistent with the underlying conceptual framework, these benefit-cost analyses often apply VSL estimates to value reductions in COVID-19 mortality risks. The VSL terminology is easily misinterpreted and widely misunderstood. VSL is not the value that the government, or anyone else, places on saving someone’s life. Rather, it reflects our willingness to exchange our own money for a small change in our own risk. Examples include our willingness to pay more for a car with additional safety features or for other types of protective measures.
 
Many organizations have developed recommended values based on substantial review of the literature. The U.S. Department of Health and Human Services (HHS), the U.S. Environmental Protection Agency, and the U.S. Department of Transportation have issued widely used guidance. Globally, many other countries have developed their own guidance; values for low- and middle-income countries are discussed in a recent article in the Journal of Benefit-Cost Analysis.
 
When adjusted to 2019 dollars and income levels, the U.S. population-average values recommended by the three Federal agencies are all about $10 million, which is consistent with recent work by W. Kip Viscusi that addresses publication selection bias. This $10 million VSL means a typical individual is willing to pay $1,000 to reduce his or her chance of dying within a year by 1 in 10,000; VSL is calculated by dividing willingness to pay by the risk change ($10 million = $1,000 divided by 1/10,000).
 
Individual willingness to pay is the fundamental measure – the $1,000 in this case. The conversion to a $10 million VSL is simply for convenience.
 
Willingness to pay can also be summed across those affected to estimate the total value of a risk reduction. For example, if a policy would reduce the risk of dying by 1 in 10,000 for each of 100,000 people over the next year, the economic value would be $100 million ($1,000 x 100,000) and 10 fewer people would die that year (1/10,000 x 100,000). Using VSL to value the mortality risk reductions associated with COVID-19 or other policies is equivalent to estimating how much money each affected individual would be willing to exchange for the risk reduction he or she would receive, respecting individual preferences.
 
Exploring uncertainties in COVID-19 VSL estimates. The value of mortality risk reductions dominates the benefits estimates in many COVID-19 analyses. Hence understanding uncertainties in these estimates is essential to interpreting the results. For the United States, some researchers rely on a population-average VSL estimate while others adjust for the age distribution of those affected. The sources referenced above suggest that a population-average estimate of about $10 million is well-established, however, the appropriate adjustment for age is uncertain. In addition, this approach ignores many factors other than age that influence these estimates.
 
Explicitly assessing how uncertainty in the VSL affects the analytic conclusions seems essential. Reporting the “breakeven” VSL (the value at which benefits would equal costs) in addition to best estimates can provide useful insights. In some cases, uncertainty in the VSL may not affect the desirability of the policy options; in others the effect may be more consequential.
 
The value of reducing mortality risks depends on the characteristics of the risks and of the individuals affected, as does the amount we are each willing to pay for most goods or services. In the United States, VSL estimates are often derived from studies of the change in wages associated with changes in occupational risks among working adults, excluding children and the elderly and others not participating in the labor force. Federal agencies generally do not adjust VSL for the age of those affected, although the HHS guidance recommends adjustments in sensitivity analysis when the risk changes disproportionately accrue to the very old or the very young.
 
This lack of adjustment in part reflects uncertainty about the relationship between VSL and age. It also reflects public opposition to these adjustments. Because VSL is often misinterpreted as the value the government places on saving an individual’s life, rather than the value that individuals themselves place on small changes in their own risks, it is easy to see why people might oppose any approach that appears to give greater or lesser weight to individuals with different characteristics. In addition, even if these values are correctly interpreted, such adjustments raise equity concerns, emphasizing the need to consider the distribution of the impacts across those who are advantaged and disadvantaged as well as the total net benefits.
 
Alternative approaches to adjusting for age can lead to substantially different results. Because older individuals have fewer expected life years remaining than the average member of the population, intuition suggests that lower VSL estimates may be applicable. This intuition is behind a commonly used approach for age adjustments, which applies a constant value per statistical life year (VSLY). Under this approach, per-case values are lower for older individuals than for younger individuals because they have a shorter life expectancy. However, neither theory nor empirical research supports this approach.
 
Some instead argue that the relationship between VSL and age should follow the pattern of consumption over the lifecycle, which is typically an inverse-U distribution. One challenge in applying this approach is uncertainty about the shape of the curve (the rate of increase and decrease) and the age at which VSL peaks. In addition, much of the empirical work is based on occupational risks; it is unclear whether this pattern extends to younger or older individuals. Research on values for children suggests that they likely exceed values for middle-aged adults, perhaps by as much as a factor of two. Research on values held by the elderly leads to inconsistent results; it is unclear whether these values increase, decrease, or remain constant above age 65.
 
More importantly, factors other than age influence the value of reducing COVID-19 mortality risks, but often do not receive much, if any, attention. It is challenging to determine the appropriate population-average VSL for COVID-19 risks without more work on understanding the influence of these other attributes. It is also difficult to ascertain the extent to which these attributes interact with age; they may increase or decrease the VSL by the same proportion over the lifecycle or may dampen or amplify the effects of age on the VSL.
 
One example is the effect of income. There is substantial evidence that individual WTP per unit of risk reduction, and hence VSL, increases with income. In the COVID-19 context, income is important in several respects. First, responses to the COVID-19 epidemic are reducing earnings, which means individuals have less money to spend on risk reductions as well as other things, potentially reducing the VSL. Second, even if income remains unchanged, it constrains individuals’ ability to pay more for larger risk reductions. For example, while a typical individual may be willing to pay $1,000 for a 1 in 10,000 risk change, it would be difficult for many to pay $10,000 for a 1 in 1,000 risk change, and impossible for most to pay $100,000 for a 1 in 100 risk change. As a result, VSL will decrease. The relevance of this second concern depends on the without and with policy scenarios considered. A study that compares an uncontrolled scenario to a scenario with fully effective controls will yield a larger risk reduction than a study that considers an incremental change.
 
A third concern relates to the distribution of the risks within the population. Increasing evidence suggests that lower income individuals are more significantly affected by COVID-19 risks, in part because it is more difficult for them to undertake protective measures. For example, they may live in more crowded conditions and may have a stronger need to continue working regardless of the safety of their commute and work environment. However, analysts generally do not adjust VSL for within-population income differences due to the equity and other concerns discussed earlier in the age context. Whether this approach is in fact equitable is debatable. A core strength of the benefit-cost analysis framework is that it respects individual preferences. If the costs of a policy fall primarily on the poor, but a population-average VSL is used to value benefits, the policy may appear cost-beneficial even though the costs may exceed the value those affected place on the benefits they receive.
 
The impacts of other population and risk characteristics are more difficult to estimate. For example, there is increasing evidence that COVID-19 deaths occur disproportionately among those with impaired health. However, the impact of poor health on VSL is ambiguous and more research would be needed to determine whether and how to adjust the values.
 
Other characteristics may increase VSL by an unknown amount. The occupational risks that underlie many estimates lead to relatively immediate death from injury. In contrast, COVID-19 deaths may be preceded by substantial pain and suffering, including severe breathing difficulties and ventilator use. While such morbidity will likely increase the value of reducing the risk, the size of the increase is uncertain. In addition, the characteristics and magnitudes of many risks addressed in the VSL literature are relatively well understood. COVID-19 risks are not. Research suggests risks perceived as more dreaded and ambiguous, and less controllable and voluntary, likely increase VSL.
 
The attention being paid to benefit-cost analyses in addressing the COVID-19 crisis demonstrates the important role it plays in encouraging careful investigation of policy impacts. However, communicating the underlying concepts, their advantages and limitations, and the implications of uncertainty is essential to promoting evidence-based decisions. The relationship between individual willingness to pay and personal characteristics such as income also emphasizes the need to consider the distribution of the impacts. As noted in the government guidance documents cited above, it is crucial to accompany benefit-cost analysis with distributional analysis, including estimates of the net benefits that accrue to individuals in different income, racial, and other groups. Location also matters; policies that are cost-beneficial in densely populated urban areas may be less desirable in rural areas. Many people care deeply about extent to which those who are disadvantaged are disproportionately affected by COVID-19 risks and by the economic consequences of policy actions. These factors are important policy considerations.
 
Lisa A. Robinson is SBCA past President, member of the Journal of Benefit-Cost Analysis Editorial Board, and recipient of its Richard O. Zerbe Distinguished Service Award. She is a Senior Research Scientist at the Center for Health Decision Science and Center for Risk Analysis, Harvard T.H. Chan School of Public Health. This article is based on several reviews of the VSL research that can be accessed here.
Comments
07/16/2020 5:11pm
Your article is appreciated.
07/17/2020 3:20pm
Excellent piece. My only comment is that I have never understood why the term Value of a Statistical Life is used. It is a term only an economist could love, and leads to enormous controversy and confusion. As you explain (and everyone who reads this blog probably already knows), VSL is just WTP for a 1 in 10,000 reduction in risk, multiplied by 10,000. I have never understood why this multiplication is necessary. If VSL is just the value of risk reduction, why not skip the multiplication and just compute what could be called "The Value of Mortality Risk Reduction" (VMRR). End of confusion. End of controversy.
07/18/2020 2:09pm
Thanks very much for your comments! I am very pleased you liked the essay.

On the value per statistical life terminology, it really is unfortunate that it is so widely misunderstood. Although there have been many attempts to replace it over the years, each has advantages and limitations, and none have caught on at least so far, unfortunately. Plus people tend to think that the difference in terminology refers to a different concept, so don't connect it to what is now a large VSL literature.

Its a challenging problem that I am not certain how to solve. My approach has been to reference, and attempt to explain, the VSL terminology, while also using the value of mortality risk reductions terminology to the extent possible.

If you are interested, we briefly discuss some of the alternatives in a JBCA article (https://doi.org/10.1017/bca.2018.26). These include the VMRR terminology recommended by Simon et al. (2019) (https://doi.org/10.1093/reep/rey022) based on their focus group work, and the “value per standardized mortality unit” (VSMU) terminology at times used in global health. In the United Kingdom, the term "value per prevented fatality" (VPF) is often used; a few researchers use the term “micro-mort.”

BTW, one issue is that to the extent that these terms drop the reference to “statistical life,” the size of the risk reduction to which the value applies must also be defined. VSL is not necessarily tied to WTP for a 1 in 10,000 risk reduction; that is just an example. While we expect that VSL will not vary as long as the risk change is small (at least in theory), it will decrease as the risk change becomes large and WTP is increasingly bounded by income.
07/22/2020 11:27am
Thank you for this important essay: it provides helpful and much needed context and synthesis. It uplifts me for showing what economic analysis has to offer but also frustrates me for how our principles and techniques, even best practices such as including distributional analysis, still fall short of arriving at satisfactory analytical conclusions. Shortcomings of welfare economics remain that troubled me since getting my Ph.D. at Wisconsin in the 1980s. In my view it is regrettable that the literature on VSL emphasizes individual preferences toward risk reduction rather than the potential of revealed preference in public budgeting and cost-effectiveness comparisons between programs that reduce mortality and morbidity. In learning this concept from Burton Weisbrod forty years ago, my perspective remains that this "public revealed preference" approach would be more fruitful long-term and more useful to policy makers. But perhaps its pitfalls would be worse than the pitfalls of relying on individual preferences that your essay explains. I find that the historic challenges of today have me reflecting on the progress and remaining limitations of our profession. Having Dan Bromley as a professor also focuses my thoughts on the conundrum that remains in the inseparability of our willingness to pay estimates from ability to pay of the individuals. The inequities of the patterns of COVID-19 damages brings me back to a troubling question I posed to my students: Does the fact that kidnappers see greater potential for high ransom from rich families rather than poor families indicate that poor families value their children less?
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