What is the value of a life, and can it be estimated by finding a wage premium for risk?
Regressions of wage as a function of risk
This paper by Dora Costa and Matthew Kahn says yes, and they use historical data across industries to estimate the value of risk–the increase in pay for riskier jobs. This article by W. Kip Viscusi and Joseph Aldy offers a comprehensive review of studies estimating the dollar value that people implicitly assign to risk, based on estimated wage premiums.
Skepticism about regressions of wage as a function of risk
On the other hand, Peter Dorman and Paul A. Hagstrom argue that there is no evidence that risky jobs pay more. Dorman also wrote a book on this topic that I found convincing. If you’re not careful, you can get negative coefficients in these wage/risk models.
In its general form, the question of risk compensation must have multiple answers depending on context. It is well known that people are generally not good at understanding risks, even of an essentially monetary nature. (For example, my dad persists in buying car insurance that reimburses him for the car value if it is destroyed in a crash, even though he could easily afford to replace it. That is, I think he’d be better off “self-insuring” the value of the car. But, nooooo…., he wants the “peace of mind.”) When you start bringing in life and death, well, of course people will be inconsistent. Perhaps having risk premiums in some industries and not others. And, as Dorman points out, a lot will depend on the forms of collective bargaining available.
I care about this for (at least) two reasons. First, the value of a life is a wonderful example when teaching decision analysis. Math and stat students who have not previously thought about the topic will commonly refuse to assign a dollar value to even the smallest risk (for example, I had a student who would not accept $1 for a 1-in-a-trillion chance of death).
The second reason for caring about the value of a life is that it is relevant for decsions such as whether to measure your house for radon or larger policy questions. It’s frustrating that we can’t just use wage regressions to estimate how much people value their lives, but to be realistic I have to recognize that the cost of a risk depends on its context. Statistical decision analysis can still be useful, however, in ensuring that decision recommendations are consistent across different conditions and localities.
P.S. See here for much more on this.
Isn't this inability to accept even infintesimal risks endemic in our politics?
Standards for allowances of known pollutants are set at ridiculously low levels; standards for 'potentially cancer-causing' substances are set very, very high.
As you point out, Andy, individuals have inconsistent attitude towards risk. The same is true at the group or societal level. For example, CAFE fuel economy standards are urged higher even at the obvious, significant increase in human life and limb (lighter cars ceterus paribus are more fuel efficient, and simultaneously less safe for their passengers due to immutable laws of physics).
And, of course, our car-loving culture is blase about the risks of driving while being terrified about plane travel, one of least risky forms of transportation.
Boris, you are correct, ceteris paribus, but imposing standards does not just change a single vehicle: in a 2 vehicle collision, increasing the weight of the vehicles is an arms race–almost certainly a negative sum game. Making both vehicles lighter benefits both drivers.