## YLL or VSL? Cost-Benefit Analysis in the Year of COVID

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 gain 8 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.)

### 5 thoughts on “YLL or VSL? Cost-Benefit Analysis in the Year of COVID”

1. wazza1234567 November 26, 2020 / 2:34 pm

VSL is not a good representation of value – it represents value at age datum. What you are looking for is area under the curve

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