I’ve written about the social benefits (in terms of the value of lives saved) of COVID mitigation measures, such as wearing face masks, before. But at this juncture in the pandemic (and really for the past 12 months), the key mitigation measure has been vaccines. How much does it cost to save one life through increased vaccination?
Robert Barro has a new rough estimate: about $5,000. In other words, he finds that it takes about 250 additionally vaccinated people in a state to save one life, and the vaccines cost about $20 to produce (marginal cost). So, about $5,000.
Barro gets this number (specifically, that 250 new vaccinated people saves one life) by using cross-state regressions on COVID vaccination rates and COVID death rates. Of course, there are plenty of potential issues with cross-state regressions. It’s not a randomized control trial! But Barro does a reasonable job of trying to control for most of these problems.
Another way to restate these numbers: if we assume that the VSL of an elderly life is somewhere around $5 million, then the social benefit from each person getting vaccinated is around $20,000. In other words from a public policy perspective, it would have made sense to pay each person up to $20,000 to get vaccinated!
Or thought of one more way: each $20 vaccine is worth about $20,000 to society. That’s an astonishing rate of return. And we’re not even including the value of opening up the economy earlier (from both a political and behavioral perspective) than an alternative world without the vaccines.
Bryan Caplan has kindly responded to my latest blog post, which was in turn a response to his blog post on the relative value of human lives by age. Caplan has always been kind in his responses, even when responding to pesky graduate students — kind in both his approach and the time he dedicates to responding thoughtfully. So I appreciate his taking the time to respond to me, and I will offer a few more thoughts on the matter.
To briefly summarize: Caplan believes that young lives (10 year olds) are worth 100-1,000 as much as old lives (80 year olds). I contend that they are closer to roughly equally valued. My disagreement with Caplan can be broken down into two categories:
A. Caplan’s three reasons why young lives are worth more (a lot more!) than old lives. I didn’t respond to that directly, but I will do so here. I think Caplan is narrowing the goalposts.
B. A disagreement over the shape of the VSL curve over the lifetime, specifically whether an inverted-U-shaped curve makes sense. I’ll say more about this too, but Caplan doesn’t just have a beef with me, but with almost everyone in the VSL literature!
Let’s start with Caplan’s three reasons, which he calls “iron-clad”: young people have more years to live, those years are generally healthier, and young people will be missed more when they are gone. The first in undeniably true on average, the second is probably true almost all the time, and I’m not sure on the third, but I’m willing to admit it’s not a slam dunk either way.
So how can I disagree? These are only three things. There are many other considerations, and we can imagine other reasons that old lives are valued as much or more than younger lives! I’ll call mine 4-6 to go with Caplan’s 1-3:
Old age spending is the largest component of public budgets in developed countries (and this is unlikely mostly due to rent seeking or the self interest of younger generations).
The elderly possess wisdom which is highly valuable and that the young benefit from.
The last years of your life are, on average, worth a lot more — you are usually very wealthy, have no employment obligations, you have grandchildren you love (without the responsibilities of parenting), and are (until the very end) generally healthy too.
Taken as a whole, I think these three reasons present a strong counterargument to Caplan’s three reasons. And I think we could certainly come up with more! My point being that Caplan has picked three areas where clearly young lives have the advantage, but ignored all the good reasons why old lives are more valuable. These is what I mean by we shouldn’t rely on our intuitions. Neither of our lists are exhaustive, but let me elaborate on a few of these.
Bryan Caplan argues that the life of a 10-year-old is worth 100-1,000 times that of an 80-year-old. But he suggests the modal answer people would give is that the two lives are equally valued.
I’m not sure if he is right about what the modal answer would be that they are exactly equal (though see below for an attempt to answer this question). Surprisingly, though, roughly equally valuing all lives is actually the answer that a normal economic calculation, willingness-to-pay for risk reduction, would give you! Or at least roughly. I haven’t seen an estimate for a 10-year-old, but estimates of the Value of a Statistical Life for 20-year-old is roughly equal to an 80-year-old. I’ve written about this before, and here’s a summary of a working paper by Aldy and Smyth that I am drawing on. Middle age lives are worth more, using this method, though perhaps just 2-3 times more.
Caplan doesn’t directly connect his hypothetical to the COVID pandemic, but in the comments Don Boudreaux does make that connection and says that “surely the correct level of precaution to take against a disease that kills X number of old people is lower [than a disease that kills the same number of young people].” I find this a very interesting statement because Don Boudreaux, and many others, have been against just about any precaution (other than asking the elderly to isolate) in the current pandemic. Would he and others support more caution if they believed the VSL estimate to be true?
So who is right? Caplan’s intuition? Or the modeled VSL calculations? For surely these are miles apart, and they can not both be correct.
How do we conduct cost-benefit analysis when different policies might harm some in order to help others? This question has become increasingly important in the Year of COVID.
In particular, it is possible that some interventions to prevent the spread of COVID may save the lives of the vulnerable elderly, but have the unfortunate effect of causing other harms and potentially deaths. For example, increased social isolation could lead to increased suicides among the young (we don’t quite have good data on this yet, but it’s at least a possibility).
If you don’t think any public policies will reduce COVID deaths, then the post isn’t for you. It’s all cost, no benefit!
But for those that do recognize the trade-offs, a common way to do the cost-benefit analysis is to look at “years of life lost” or YLL. This is a common approach on Twitter and blogs, but I’ve seen it in academic papers too. In this approach, you look at the age of those that died from COVID, and use an actuarial life table to see how long they would have been expected to live. For example, an 80-year-old male is expected to live about 8 more years. Conversely, a 20-year-old males is expected to live another 56 years.
So, here’s the crude (and possibly morbid) YLL calculus: if a policy saves six 80-year-olds, but causes the death of one 20-year-old, it’s a bad policy. Too much YLL! (Net loss of 8 years of life.) However, if the policy saves eight elderly and kills just one young person, it’s a good policy. A net gain8 years of life. (Of course, we can never know these numbers with precision, but that’s the basic idea.)
But I think this approach is fundamentally flawed. Not because I oppose such a calculation (though maybe you do, especially if you are not an economist!), but because it’s using the wrong numbers. Briefly: we shouldn’t value every year of life equally.
The superior approach for this calculation is to use an approach called the “value of a statistical life” (VSL). In this approach, we assign a value to human life (the non-economists are really cringing now) based on revealed preferences of various sorts. Timothy Taylor has a nice blog post summarizing how this value can be estimated, which is much better than how I would explain it.
In short, the average VSL in the US is around $10-12 million, depending on how you calculate it. You might be skeptical of this figure (I was at first too!), but what really convinced me is that you get roughly this number when you do the calculation using very different approaches. It just keeps coming up.
So how does VSL apply to our COVID calculation? What’s really interesting about VSL is that it varies with age. And not perhaps as you might expect, as a constantly declining number. It’s actually an inverted-U shape, with the highest values in the middle of the age distribution. Young and old lives are roughly equally valued! Once we realize this, I think we can see how the YLL approach to analyzing COVID trade-offs is flawed.
Kip Viscusi has been the pioneer in establishing the VSL calculation. If you’ve heard that “a life is worth about $10 million” and scratched your head, Viscusi is the man to blame. Over the weekend, Viscusi gave his Presidential Address to the Southern Economic Association (he actually delivered it in-person at the conference in New Orleans, but to a very small crowd since the conference was over 90% virtual).
As you might have guessed given his area of research, Viscusi used this address to estimate the costs of COVID, both mortality and morbidity (the talk is partially based on this paper). He didn’t talk much about the policy trade-offs, but we can use his framework to talk about them. Here’s a very relevant slide from the presentation.
Notice here we see the inverted-U shaped VSL curve. You may not be able to read it very well, but Viscusi helps us with a bullet point: VSL at age 62 is greater than at age 20. Joseph Aldy, a frequent co-author of Viscusi, has extended the curve even further up to age 100 which you can see in this column. Aldy and Smyth use a slightly different approach, but the short version is that the VSL for a 62-year-old is much greater than a 20-year-old (roughly double). The 20-year-old VSL is roughly equal to that of an 80-year-old.
So let’s go back to the above YLL calculation, which told us that if a policy intervention only saves six 80-year-olds but results in the death of one 20-year-old, it’s bad policy. Too many YLL!
However, using the VSL calculation, this policy is actually good, since 20- and 80-year-olds have roughly equally valued lives. The policy only becomes bad if it kills more 20-year-olds than elderly folks. This may seem strange, given the short life left for the 80-year-old, but it is where the VSL calculus leads us.
I will admit, this calculations are morbid in some sense. But we live in morbid times. Death is all around us, and we need to some clear method for assessing trade-offs. YLL seems like the wrong approach to me. VSL seems better, but if we take a third approach, something like All Lives Matter (and matter equally), we end up with the same calculation when comparing a 20- and 80-year-old.
In the end, we should also be looking for policy interventions that have low costs and don’t result in additional deaths. For example, I think there is now good evidence that wearing masks slows the spread of viruses, which will lower deaths without any major costs. But if we are going to talk about trade-offs, let’s do it right.
(Final technical note: there is an approach that combines YLL and VSL, called “value of a statistical life year” [VSLY]. Viscusi discusses VSLY in the paper that I linked to above. I won’t get into the technicalities here, but suffice it to say VSLY involves more than simply adding up the years of life lost.)
Economist Writing Every Day 