Value of statistical life Jim

Value of statistical life

Jim Holt (The Human Factor (New York Times, March 28); a copy of the article can be found here) doesn't think anyone "should be knowingly sacrificed for a sum of money." He apparently thinks this is implicitly what happens when a cost-benefit analysis places a value on a "statistical life."

"How much is your life worth to you? On the face of it, that's an idiotic question. No amount of money could compensate you for the loss of your life, for the simple reason that the money would be no good to you if you were dead. And you might feel, for different reasons, that the dollar value of the lives of your spouse or children -- or even a stranger living on the other side of the country -- is also infinite. No one should be knowingly sacrificed for a sum of money: that's what we mean when we say that human life is priceless."

Economists don't know what the value of a human life is. Fortunately, there are very few public policy decisions that require information on the value of a human life.

There are, however, a lot of decisions that can change the risks of dying, and information on the value people place on these changes can be very helpful. Widening or straightening a road may reduce each driver's risk of an accident and death; forward positioning a rescue helicopter near a risky fishery can reduce each fisherman's risk of death if there is an accident; eliminating leaded gasoline can reduce each adult male's risk of death from cardiopulmonary disease.

While these individual risks may translate into a certain number of deaths in a given population, individuals themselves tend to face a relatively small risk, that will only be changed a small amount by the policy.

EPA guidelines on cost-benefit analysis define statistical lives:

"This measure is the aggregation of many small risks over an exposed population. Suppose, for example, that a policy affects 100,000 people and reduces the risk of premature mortality by one in 10,000 for each individual. Summing these individual risk reductions across the entire affected population results in the policy saving 10 statistical lives. It is unknown who these ten people might be - everyone faces some risk of being affected - but the policy can be expected to prevent premature fatality for 10 individuals in the population." (Page 68)

Now, if you have information on the value each person places on a 1/10,000 reduction in the risk of their death, you can estimate the value the entire population places on the overall reduction in risk:

"If 10,000 individuals are each willing to pay, for example, $500 for a reduction in risk of 1/10,000, then the value of saving one statistical life equals $500 times 10,0000 - or $5 million." (Page 87)

This "statistical life" isn't the value of a human life, it is a convenient tool for summarizing information on the value the people in a population place on a reduction in risk. However, Holt appears to mistake what statistical life is, for what it isn't.

Do you think human life is priceless? That's not the generally the issue. We are valuing risks of death. One difference: just because there is a risk of death doesn't mean that anyone is going to die. A policy change that reduces the risk of death to the individuals in a population has a value, even if no one would have died in the absence of the change.

So, where do these values come from? Holt's introduction suggests that the values are arbitrary, foisted on us by faceless government bureaucrats:

"But the government set a price for it four years ago: $6.1 million. That's the figure the Environmental Protection Agency came up with when it was trying to decide how far to go in removing arsenic from drinking water. Arsenic can cause diseases, like bladder cancer, that will predictably kill a certain number of people. But reducing the arsenic in water gets more and more expensive as the poison levels approach zero. How many dollars should be spent to save one ''statistical life''? The answer, reasoned the people at the E.P.A., depends on how much that life is worth..."

Well, the "government" didn't just arbitrarily set that value - as Holt's remarks actually make clear a little later. Cost benefit analysts make inferences about how people themselves value these risks. After all, people are constantly making decisions about these risks. They make these decisions when they choose occupations, when they change the speed with which they drive, when they choose neighborhoods to live in, when they invest in safety features in their houses, when they behave more circumspectly in the dark. In each instance they balance the greater or lesser risk with the benefit or cost the change confers or imposes.

It seems reasonable to see if you can make inferences about how people value risks, and apply these values to policy decisions. The values people place on the risks they face can be inferred in a lot of ways. - inferences can be made from the wages people need to induce them to take additional risks, from the investments people make in additional safety (smoke or carbon monoxide detectors in homes), or from asking people how much they would have to be paid to take on additional risks or how much they would pay to avoid additional risks.

But in every case, there is an attempt to find the value people themselves place on more or less risk. Government or economists aren't inventing numbers they think should be appropriate - they're trying to find out what it is worth to people themselves to reduce the risks they face. There's something democratic about that.

There are lots of good questions about the use of the value of statistical life methodology. The technique is evolving. There's still a lot to learn. Estimates of the values people place on changes in risk are changing. Value of life-years may be more important than value of life. There are all sorts of issues raised by extrapolating values from one context to another or from one population to another. And no one I know, certainly no economist I know, thinks that an excess of aggregate benefits over aggregate costs is the only criterion relevant to policy decisions.

But, while VSL is a flawed tool, nevertheless, it is valuable.

There's some other commentary on Holt's essay here (scroll down) and here. In fairness, Holt alludes to additional problems - some I think are mistaken, some I think may have some merit. I've dealt here with with the two fundamental problems I have with his essay: mistaking the value of statistical life for the value of life, and what I see as his rhetorical device of misdirecting attention (at least early on) from the source of the valuation in inferences about the valuations of actual people.