Friday, March 27, 2020

Value of a Statistical Life: Where Does It Come From?

One of the (many) questions that causes economists to pull their hair out takes the general form: "How can you economists even possibly try to weigh economic costs against the value of a life saved?" Even worse, the question is often delivered in a triumphalist tone of a deeper moral truth being unveiled.

But in the real world, people and governments actually weigh economic costs against the value of a life saved all the time. Certain jobs that pose a greater risk to life and limb also tend to pay more than jobs for similarly qualified workers without such risks. Those who take such jobs, or don't take them, are in part placing an economic value on a greater risk of losing their life. Many government regulations, from setting speed limits on the roads to health and safety standards for food, could be tightened in a way that would save more lives but impose greater costs, or loosened in a way that would save fewer lives but impose lesser costs. Deciding where to set such regulations will necessarily involve a decision about how much it's worth paying to reduce the risk of someone losing their life.

Thus, the relevant question is not "how" to put a monetary value on life or "why would anyone ever want" to put a monetary value on life. The discussion starts from the fact that people and governments are already putting a monetary value on life, albeit often implicitly, by the actual real-world decisions they make.  When economists say that the "value of a statistical life" is about $10 million, they are not just pulling a number out of the air. Instead, they are only pointing out the monetary values that people are already using.

Thomas J. Kniesner and W. Kip Viscusi offer a readable overview of the evidence behind such decisions in "The Value of a Statistical Life," which was published in June 2019 in the Oxford Research Encyclopedia, Economics and Finance. (If for some reason you don't have access, a version of the paper is available on SSRN.)

As Kneiser and Viscusi point out, evidence about the economic value that people place on a higher or lower risk of losing their life can come from several sources: "revealed preference" studies that look at choices people make about jobs or products with different risks, or "stated preference" studies that involve survey data. To understand the intuition here, it's important to recognize that they studies are not asking a question like: "How much money would we need to pay you before we kill you?" The "value of a statistical life" is about changes in risk. They write:
Suppose further that ... the typical worker in the labor market of interest, say manufacturing, needs to be paid $1,000 more per year to accept a job where there is one more death per 10,000 workers. This means that a group of 10,000 workers would collect $10,000,000 more as a group if one more member of their group were to be killed in the next year. Note that workers do not know who will be fatally injured but rather that there will be an additional (statistical) death among them. Economists call the $10,000,000 of additional wage payments by employers the value of a statistical life. It is also the amount that the same group of workers would be willing to pay via wage reductions to have safer jobs where one fewer of their group would be fatally injured or ill. In that sense the VSL measures the willingness of workers to implicitly pay for safer workplaces and can be used to calculate the benefits of life-saving projects by private sector managers and government policymakers.
Studies of specific jobs that compare risks of death and pay will come up with a range of numbers; after all, jobs differ in many ways other than just their mortality risk. Thus, in a 2018 study, Viscusi looked at 1,025 estimates of the value of a statistical life drawn from 68 publications. He looked both at the total group, and then also at a "best-set" subgroup of the estimates that used what he viewed as more reliable methods. He found: "The all-set mean VSL is $12.0 million and the best-set sample mean is $12.2 million, where all estimates are in $2015. The median values are somewhat lower—$9.7 million for the all- set sample and $10.1 million for the best-set sample."

Of course, not everyone will put the same value on reducing mortality risk, and those of different ages and income levels, for example, will prefer different values. But for evaluating a broad government regulation that affects a broad cross-section of the population, using an overall number makes sense.

Another branch of the literature looks at purchases of certain goods or services. For example, how much is the price of a house affected by being in a high-crime area or near a large source of air pollution? How does the price that people pay for bike helmets or smoke detectors compare to the reduction in risk from such purchases? Again, different studies have a range of answers: again, an estimate of $10 million as the value of a statistical life seems plausible.

Other studies have taken an approach that uses detailed scenario-setting surveys. For example, the questionnaire may lay out a starting scenario, which includes the health risk expressed in various ways, like the chance of living to 100 years of age or the annual risk of being killed in the next year by cancer or in a car accident. Then the follow-up question offers other scenarios, with a range of costs expressed in terms like expected changes in prices or taxes paid, and different health risks. Naturally, the construction and interpretation of such surveys can be controversial, and sometimes the answers seem crazy-high or crazy-low. But an OECD study a few years ago suggested, based on an overview of these studies, that using $3.6 million as the value of a statistical life was plausible.

When it comes to public policy, Kneiser and Viscusi note: "Most U.S. government agencies have now adopted VSL estimates in a similar range consistent with the economics literature." The point out that the  U.S. Department of Transportation (2016) uses $9.4 million as the value of a statistical life, compared with $9.7 million for Environmental Protection Agency and $9.6 million for the U.S. Department of Health and Human Services.

It's easy enough to come up with questions about the value of a statistical life. But again, it is simply a fact that people and governments make decisions all the time about weighing health and safety against costs. Blaming the economists for doing the calculations to figure out what values are actually being places on a statistical life is like blaming the bathroom scale, or perhaps the laws of gravity, when it tells you that you could stand to lose a few pounds.

In the midst of the coronavirus pandemic, an obvious question is what a value of $10 million for the value of a statistical life means about the ongoing strategy of causing a recession for the sake of protecting public health. The multiplication is straightforward. Imagine that the steps being taken to contain the virus save 500,000 US lives. With those lives valued at $10 million, a social cost of up to  $5 trillion in lost output would be justified. For comparison, US GDP is about $21 trillion. If steps taken to contain the virus save 50,000 lives, then a social cost of up to $500 billion in lost output would be justified. This calculation is so quick-and-dirty, and leaves out so much, that I hesitate even to include it  here. It does suggest to me that in these benefit-cost terms, it's plausibly worth a recession to contain the virus, even a deep-but-short recession. It also suggests that if looking at how health risks  have been valued by actual people and governments in the past, a long-term recession or depression would not be a price worth paying to contain the virus.

For some previous posts and articles on the value of a statistical life, and its cousin the "quality-adjusted life-year," see: