By James Kwak
“Bush stopped weighing the costs and benefits of deregulation and issued an executive order allowing OIRA to intercede before agencies made their initial proposals, thereby providing industry lobbyists with a back door to block regulations. OIRA also instructed agencies to discount the value of future lives in constructing cost-benefit analyses by 7 percent a year, so that 100 lives in 50 years would only be worth 3.39 current lives. (Such logic can be used by conservatives to argue that the present cost of regulating greenhouse gases outweighs the future benefits of stopping climate change.)”
There is a normative argument against valuing lives in cost-benefit analysis; some people think it’s just wrong. I don’t agree with that; I think that in practice, you either value lives implicitly or you do it explicitly, and so you might as well do it explicitly. And for what it’s worth, the practice of valuing lives is firmly entrenched in our legal system; the amount you pay in damages if you kill someone negligently depends primarily on that person’s future earning potential, and also on the monetary value of the benefits that other people gained from his or her life.
There is another argument against discounting future lives, however. The basic premise of discounting is that money in the future is worth less than money today. This has two components. One is the time value of money: $100 with certainty one year from now is worth about $99 today, because you can invest $99 in an FDIC-insured account at about 1% and get back $100 in a year. The second is risk: Future events are not certain, and the less certain they are to occurthe less valuable they are to you.
Does this apply to lives, however? If a regulatory agency says, this rule will cost industry $1 billion in present-value terms, but it will save 1,000 lives twenty years from now, is that any different from saying it will save 1,000 lives today? That seems wrong to me; you can’t take, say, 900 lives now, put them in the bank, and get back 1,000 lives in twenty years. I can see the counterargument, though: once you’ve agreed to value lives in monetary terms, you can translate those 1,000 lives twenty years in the future into some amount of money twenty years in the future, and you can discount that back to today.
But if we’re going to do that, let’s at least do it right. A discount rate of 7 percent?
I assume that’s a real discount rate, not a nominal one, since anyone doing this kind of spreadsheet over decades would use real terms to avoid inflation uncertainties.* A discount rate of 7 percent means that 100 lives in ten years are worth roughly 50 lives today. Is that justified?
By the time value of money theory, the government (or industry) could put aside money in an account today and use it to pay benefits to the survivors of dead people at some point in the future when the deaths occur. But if we’re going to use that logic, we need to look at the risk-free rate of return. Over the last five years, the ten-year Treasury yield has generally been between 4 and 5 percent. Call that 4.5 percent. Inflation has been in the low 2 percent range, so at best this is a risk-free return of 2.5 percent.
But it gets worse than that, because the real value of lives is continually increasing. This is because GDP grows faster than inflation, and faster than inflation plus population growth. The rest of GDP growth is productivity growth, which means that people produce more and, on average, they earn more (even if the median workers doesn’t). Since the legal value of a life is primarily based on future income, this means that the real value of a life increases roughly with productivity. Productivity growth runs at about 2% per year. So if you are getting 2.5 percent on your risk-free investment, 2 percentage points of that just goes to make up for the fact that the people your policy is killing are getting more expensive, which means your discount rate should be 0.5 percent. (The numbers don’t quite add up here, since I think population growth is actually around 1% per year. So let’s say your discount rate should be 1 percent — still a lot less than 7 percent.)
But that’s just the time value of money — shouldn’t we also be discounting for risk? But I think that’s wrong. In the corporate finance model, you look at the volatility of the expected cash flows. Let’s say you have an investment that has an expected return of $1 million in ten years with some probability distribution around $1 million. The textbook says you should adjust your discount rate based on that probability distribution — the wider the distribution (the riskier the investment), the higher the discount rate. This makes sense because of basic risk aversion. In the financial context, the more risky the project, the higher the expected return has to be to justify it.
Now let’s translate this into lives. Say you have a policy that is likely to kill 1,000 people in ten years, but it might kill more or it might kill fewer. Should that be counted as fewer lives than a policy that is certain to kill 1,000 people in ten years? In other words, does risk aversion mean that we should prefer policies that kill variable numbers of people to policies that kill certain numbers of people? That doesn’t make sense to me, and hence discounting for risk doesn’t make sense to me in the lives context.
That leaves us with a discount rate of 1 percent, not 7 percent. And instead of 3.39 lives today, you get 60.80 lives today. That’s a big difference.
(If the 7 percent is nominal instead of real, you don’t deduct inflation from the 10-year Treasury yield; however, then the value of lives grows because of both productivity and inflation, so you end up roughly in the same place.)
* It might make sense to use nominal terms if some of your future values were fixed in nominal terms. But in a situation like this, where all of your future values are fixed in nominal terms, I can’t see any reason to do the calculations in nominal terms.