Thursday, July 17, 2003

Your Money and Your Life

Julian has an excellent article on the valuation of life up at Reason, with some further ruminations on the subject posted on his personal blog. I have just a couple of comments.

First, as a political matter, I wonder if the EPA’s short-lived plan to discount the value of life for the elderly (for purposes of doing cost-benefit calculations) would have met less opposition if it hadn’t adopted such a sharply discontinuous value of life function. According to Julian, the EPA placed a value of $2.3 on the life of someone over 70, versus a value of $3.7 on the life of someone younger. Well, it’s not like something magical happens at the age of 70. They could just as well have adopted a “years of life saved” metric, without even having to refer to particular lives. The value of your total remaining years of life would consequently decline as you got older, simply because you have fewer of potential years remaining. I wonder why they chose to look at two arbitrarily defined blocks (over 70 and under 70) instead?

Second, in the discussion on his personal blog, Julian takes on the notion of valuing a life by finding out how much money one would accept to avoid a risk. In his example, if someone would take $5K to accept a one in 1000 chance of death, you might think we could just multiply $5K by 1000 to find that the value of life is $5 million. Julian argues that this approach is mistaken because “the function is non-linear, and … asymptotic to infinity as probability approaches one and time-to-demise approaches zero. (In other words, there's no amount you'd take to be killed with certainty five seconds from now.)”

This is all perfectly correct, and it explains why we wouldn’t let a potential murderer just pay a fee of $5 million for the privilege of killing his lover. But it seems to me that, when we’re talking about environmental regulations, product liability, and so on, that the logic works just fine, because we aren’t talking about a certainty of death for any particular individual. We cannot identify in advance the specific person killed by a certain increment of pollution, or saved by the EPA regulation (or liability rule) that prevents that pollution. We only know the specific person after the fact, and sometimes not even then (because we don’t know which death was the marginal death). So in cases like these, it seems perfectly appropriate to value lives in the manner described, because for each individual we are talking about a small risk of death rather than a certainty. One odd implication of this approach, though, is that there may be many different values of life depending on the size and context of the risk. The value of life would presumably be much, much larger for a one in 100 chance of death than for a one in 1000 chance of death. Perhaps it is misleading to call this a “value of life” at all, and we should call it a risk premium instead. But at the aggregrate level, it comes out in the wash: counting $5K one thousand times is functionally equivalent to count $5 million just once.

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