## Tuesday, October 22, 2013

### Value of a Statistical Life? \$9.1 Million

The costs of regulations can be measured by the money that must be spent for compliance. But many of the benefits of regulation are measured by lives saved or injuries avoided. Thus, comparing costs and benefits requires putting some kind of a monetary value on the reduction of risks to life and limb. For example, the US Department of Transportation estimates the "value of a statistical life" at \$9.1 million in 2012. In a memo called "Guidance on Treatment of the Economic Value of a Statistical Life in the U.S. Department of Transportation Analyses," it explains how this number was reached. I'll run through the DoT estimates, and then raise some of the broader issues as discussed in a recent paper by Cass Sunstein called "The value of a statistical life: some clarifications and puzzles," which appeared in a recent issue of the Journal of Benefit Cost Analysis (4:2, pp. 237-261).

There are essentially two ways to estimate what value people place on a reduction in risk. Revealed preference studies look at how people react to different combinations of risk and price. For example, one can look at what workers are paid in jobs that involve a greater risk of death or injury, or at what people are willing to pay for safety equipment that reduces risks.  As DoT explains: "Most regulatory actions involve the reduction of risks of low probability (as in, for example, a one-in-10,000 annual chance of dying in an automobile crash).  For these low-probability risks, we shall assume that the willingness to pay to avoid the risk of a fatal injury increases proportionately with growing risk.  That is, when an individual is willing to pay \$1,000 to reduce the annual risk of death by one in 10,000, she is said to have a VSL of \$10 million.  The assumption of a linear relationship between risk and willingness to pay therefore implies that she would be willing to pay \$2,000 to reduce risk by two in 10,000 or \$5,000 to reduce risk by five in 10,000.   The assumption of a linear relationship between risk and willingness to pay (WTP) breaks down when the annual WTP becomes a substantial portion of annual income, so the assumption of a constant VSL is not appropriate for substantially larger risks."

As the report also points out, while the result of this calculation is called the "value of a statistical life," it's not actually putting value on a life, but on a reduction in risk. "What is involved is not the valuation of life as such, but the valuation of reductions in risks."

The alternative method is called a "stated preference" approach, in which people work their way through a sophisticated survey tool that informs them about various combinations of risks and costs, and seeks to elicit their preferences. This method is sometimes called "contingent valuation," and it's a controversial subject as to whether the values that are inferred from surveys can capture "real" preferences. (For a three-paper symposium on the use of contingent valuation techniques in estimating environmental damages, see the Fall 2012 issue of the Journal of Economic Perspectives.) When it comes to estimating value of reductions in risk, the DoT dismisses this method, on these grounds: "Despite procedural safeguards, however, SP [stated preference] studies have not proven consistently successful in estimating measures of WTP [willingness-to-pay] that increase proportionally with greater risks."

The DoT gets its value of \$9.1 million with a literature review: specifically, it looks at nine recent studies that consider risk and pay in various occupations and that seem methodologically sound, and takes the average value from those studies. DoT also looks at costs of health or injury, as measured by research on what are called "quality-adjusted life years," which sets up criteria for categorizing the severity of an injury. They set up a scale with six levels of severity of injury: minor, which is worth .003 of the value of a statistical life, moderate, .047 of a VSL; serious, .105; severe, .266; critical, .593, and unsurvivable, 1.0.

The DoT memo lays out where its numbers come from, but quite appropriately, it doesn't venture into a broader discussion of using the value of a statistical life in the first place. Cass Sunstein was for several years
Administrator of the Office of Information and Regulatory Affairs in the Obama White House, so his views are of more than ordinary interest. While he supports using the value of a statistical life, he is also clear and thoughtful about a number of the tricky issues involved. Here are some of the tough questions raised by his article.

1) If the benefits of a regulation outweigh the costs, why is the regulation even necessary? Presumably, the answer is that there is some reason that buyers and sellers in the market cannot coordinate on an appropriate safety outcome. Potential reasons might include that people lack information or a range of choice between safety and price options.

2) Should the value of a statistical life be different across people? For example, perhaps reducing the risks faced by a child who lacks capacity to weigh and measure risk should be weight more heavily than risks faced by an adult. Or perhaps reducing the risks for a young adult, with a long life expectancy, should carry a higher value than reducing the risks faced by an elderly person. This point seems logically sound, but administratively and politically difficult.

3) If the reduction in risk is based on willingness to pay, then don't those with low incomes end up with less protection than those with higher incomes? Sunstein faces up to this point and accepts it. As he writes: "The reason is not that poor people are less valuable than rich people. It is that no one, rich or poor, should be forced to pay more than she is willing to pay for the reduction of risks." Guaranteeing low-income people a level of safety where the costs are higher than what they wish to pay ultimately doesn't make sense. "Government does not require people to buy Volvos, even if Volvos would reduce statistical risks. If government required everyone to buy Volvos, it would not be producing desirable redistribution. A uniform VSL has some of the same characteristics as a policy that requires people to buy Volvos. In principle, the government should force exchanges only on terms that people find acceptable, at least if it is genuinely
concerned with their welfare."

4) What if the costs of risk reduction are carried by one group, but the benefits are received by another? Sunstein points out that in some cases, like regulation of drinking water, much of the cost of safer water is passed along in the form of higher water prices, and thus paid by everyone. Similarly, the cost of the worers' compensation program basically means that the benefits received by (nonunionized) workers are essentially offset by lower take-home pay.  However, in regulation of air pollution, it's quite possible that the costs are spread across companies that pollute and their shareholders, while the benefits are realized by people regardless of income. Here, Sunstein points to the classic and controversial argument that if overall benefits for society exceed overall costs to society, even if there are some individual winners and losers, the policy can be justified. But he argues that redistribution is not the right goal for regulatory policy:  "It is important to see that the best response to unjustified inequality is a redistributive income tax, not regulation – which is a crude and potentially counterproductive redistributive tool ..."

5) people aren't knowledgeable or rational their thinking about costs and benefits of risk reduction? Maybe they place a high value on avoiding some risks, but not on avoiding others, even though the objective level of risk seems much the same. Sunstein takes the technocratic view here: "Regulators should use preferences
that are informed and rational, and that extend over people’s life-histories."

6) Instead of thinking about willingness to pay to reduce risk, the problem instead should be formulated as one of rights: that is, people have a right not to have certain risks imposed on them. Sunstein argues that this idea of rights applies in situations where the risk is extremely high, but doesn't apply well to issues of changes in statistically small risks. He further argues that if the issue is one of rights, then the cost-benefit calculation no longer applies  (as implied in the DoT quotation above). Sunstein notes that in issues involving, say race and gender discrimination or sexual harassment, we quite rightly don't apply a cost-benefit calculation. But a regulatory issue like what kinds of bumpers should be put on cars to reduce risks during a crash is not a "right" in this sense, and so a cost-benefit calculation becomes appropriate.

Ultimately, Sunstein is a supporter of using the value of a statistical life in setting regulatory policy. As he notes, there are easier and harder cases for applying this principle. What he doesn't emphasize in this article is that if we can figure out which regulations have greater benefits for their cost, and which regulations have lower benefits for their cost, we should then be able to tighten up the very cost-effective regulations and loosen up the cost-ineffective regulations, and end up helping more people at the same or even lower cost.