The Value of a Statistical Life and Coronavirus, with Alan Krupnick

Notable Quotes

• The origins of the “value of a statistical life” (VSL) concept: “[Thomas Schelling] made the crucial distinction between valuing a life and valuing a reduction in the risk of dying. That’s where [VSL] started … It’s not the value of saving a life; it’s the value of reducing your risk of death by a little bit. How much are you willing to pay for those slight reductions to your risk of dying prematurely?” (7:39)
• One of many moral dilemmas associated with VSL: “You want to be clear with people that if they do pay this amount that they're telling you, that they're going to have less money to spend on other things. So you will get lower willingness-to-pay values in developing countries than developed. That's a fact. So the question is, in your cost-benefit analyses where you're comparing interventions in various countries, do you use a lower value of statistical life in those countries and in those developing countries?” (21:55)
• Why VSL might not be appropriate for today’s pandemic: “My overarching feeling on this is the cost-benefit analysis at this particular time of this particular choice is inappropriate, and that means that the VSL is inappropriate to even use. The reason for that is because there's not a trade-off. Economics is the science of trade-offs in society ... Until we get into that flattening of the curve that everyone's talking about, the economy just cannot get started again. Even if all these restrictions were lifted, no one would go back to work. So it's not a trade-off.” (24:27)

Top of the Stack

• Mengele: Unmasking the "Angel of Death" by David G. Marwell

The Full Transcript

Daniel Raimi: Hello, and welcome to Resources Radio, a weekly podcast from Resources for the Future. I'm your host, Daniel Raimi. This week, we talk with RFF senior fellow, Alan Krupnick, about the value of a statistical life or “VSL.” As we all try to stay safe during the coronavirus pandemic—and I hope you, your family members and your loved ones are staying safe—some analysts have started to ask the question, how much economic pain is appropriate to withstand in order to protect public health? That question is studded with ethical and moral landmines, but it points us directly to understanding the value of a statistical life. In today's episode, Alan will help us understand the history of the VSL concept, different methods for calculating it, and how VSL might be applied or not applied in today's rapidly changing world. Stay with us. Okay, Alan Krupnick, my colleague and friend from Resources for the Future. Thank you so much for joining us today on Resources Radio.

Alan Krupnick: Well, it's my pleasure, Daniel. I consider you my friends as well, so it's great to be talking to you.

Daniel Raimi: Absolutely. And we talk probably multiple times per week, so it's nice to feel at home talking to you partly because I am literally at home talking to you, and I imagine you are as well.

Alan Krupnick: I am.

Daniel Raimi: So Alan, today, we're going to talk about the value of a statistical life, which is a tool used in regulatory analysis and cost-benefit analysis whereby we approximate the value of preventing deaths through regulatory policy. I may have butchered that definition a little bit, but you're going to help us understand what the correct definition is.

Alan Krupnick: Yeah, hopefully.

Daniel Raimi: Yeah, hopefully, of a VSL. But before we actually talk about the definition of the term, can you give us a little bit of background on why we need a concept such as the value of statistical life when we think about benefit-cost analysis and regulatory analysis?

Alan Krupnick: Well, for benefit cost analysis, let's say of regulations like you mentioned, let's think about a regulation that would reduce pollution. And we want to compare the cost of that regulation, let's say to business, to the benefits of that regulation. Now, the benefits of reducing pollution include all sorts of things, but certainly, a big chunk of it is the benefits of better health. And as the epidemiology literature tells us, one of the big benefits to health of reducing pollution is to lower the risk of dying prematurely. So when we want to tally up all the benefits of pollution, we want to include the benefits to reduce mortality, and we want to compare the benefits to the costs in the same numeraire. We want to use money as a way to compare the benefits to the cost, so we need to monetize the lives that are saved by these regulations and that's where the VSL comes in.

Daniel Raimi: Got it. This might go without saying, I should have said it at the outset of our conversation. But we're talking about VSL today because the concept has been used quite a bit by people in the last couple of weeks when thinking about the coronavirus and what types of efforts should be made to protect people from the epidemic, and how much economic pain is it "worth" to protect the lives of certain people. That's what's just motivating this entire conversation today. We're going to come back to the coronavirus specifically in a few minutes, but let's talk a little bit more about the origins of VSL. Can you talk a little bit about where the value of a statistical life, this concept that we use today, where it comes from?

Alan Krupnick: Sure. Well, there's a great paper by a former colleague of mine, Spencer Banzhaf, who is now at the Georgia State University. He wrote a paper called “The Cold War Origins of the VSL” where he goes in all this history. And I actually knew where the VSL term itself came from, but I didn't know where the analytical cost-benefit use of the values of reducing mortality started. And where that started is actually with the US Air Force in the late 1940s where the Air Force was interested in figuring out what the best configuration and design of bombing runs would be for bombing the Soviet Union if they needed to do that. They really wanted to do a cost-benefit of that, that included all the damages that would occur in the Soviet Union and include the costs of all the flights and the bombs. And so the RAND Corporation did this analysis, but they forgot one thing which really angered the Air Force, which was the lives of the pilots that would be killed in these bombing runs. So they came back to RAND and said, "This is unacceptable."

So RAND comes back to them and says, "Well, if a pilot dies, then you have to train another pilot. The cost of a training is maybe $10,000, $15,000. So we'll use that." And the Air Force of course was not very happy about that answer either. But fast forward, over the next couple of decades, this concept morphed into what we call the human capital approach. And what that means is that life itself is worth the productivity that it provides to society. So if someone dies prematurely from whatever reason, then the loss of that productivity that they would have to society is that you would otherwise have had, that's the benefit of preventing that premature death.

Daniel Raimi: Would that be measured by something like future earnings or something like that?

Alan Krupnick: Yes, it would measure by future earnings and medical costs that might otherwise go into that as well. So of course that wasn't very popular either because old people, people who were unemployed, homemakers who were not in the formal workforce, were not very happy about that being excluded from these calculations. Gradually, the idea was that, "Well, we need something that really gets at how people feel about reducing their risk of death, what their preferences are to reduce those risks." And this is where Tom Schelling came on. In 1968, this Nobel laureate wrote a paper where he coined the term "the value of statistical life." He made the crucial distinction between valuing a life and valuing a reduction in the risk of dying. And that's where it started. So this VSL, the S is the key word. It's not the value of saving a life as it was with the human capital approach, it's the value of reducing your risk of death by a little bit and how much are you willing to pay for those slight reductions to your risk of dying prematurely?

This is the distinction Schelling made and that was in '68. So here we are 50 plus years later and we're still using that that term. I should say that this term causes an enormous amount of controversy because people go value, and something in the middle, and life. And they ignore the S. So there've been attempts periodically to redefine a term for this that doesn't involve valuing life. But the VSL is a very sticky concept.

Daniel Raimi: Right. We are where we are certainly at the moment with this term.

Alan Krupnick: We are where we are.

Daniel Raimi: That's a really helpful definition. Or maybe not a definition, but a description of the history of the term. Can we move now into a little bit about how VSL is calculated today? And I imagine there are different approaches that people take, but can you walk us through the general framework for how people calculate VSL?

Alan Krupnick: Yeah. Well, the first thing is to understand exactly what this concept is from an arithmetic point of view. So suppose that there's a million people in a city and you can have some regulation that's going to reduce the probability of death by one in a million. What that really means is for a million people, somebody in that city is going to not die that would have otherwise died by cleaning up the pollution, let's say. So we're saving one life. Nobody knows whose life it will be, but we're saving one life. And then we ask people or we find out however we do that, which is the next thing I'll say. We find out that each person on average is willing to pay $10 to know that the risk of them dying prematurely is going to go down by one in a million. And so then we add up those $10 for each person in the city. So that's $10 million. So the value of a statistical life is 10 million. And what it is formally, it's the willingness to pay to reduce your risk of death divided by what that risk change actually is.

And in this case, it's one in a million. So it's 10 divided by one in a million, and that's 10 million. That's how it works. Now, where does this $10 come from? Basically there are two techniques. One is called “revealed preference,” and the other is called “stated preference.” The revealed preference techniques are observations and statistical analyses of how people in their everyday lives trade-off small changes in risk of death for money. The most popular approach for getting this estimate about people's preferences for trading risk for money is called the “hedonic wage approach.” What we know is that people in riskier jobs than other people, all other things equal, get paid a wage premium for taking that added risk. So if you know what those wage premiums are and you know what the added risk is, that's the numerator and denominator of this VSL calculation. Those studies yield this estimate actually of about $10 million per statistical life.

Daniel Raimi: So if we're looking at people working risky jobs, let's say people working on an oil and gas rig or people working on dangerous fishing vessels, we observe the change in their risk of dying and then we observe how much additional money they're paid for that job compared to some other similar job that doesn't have that risk of death. Is that right?

Alan Krupnick: Yeah, exactly. We noticed that people on oil rigs have a higher risk of dying than people sitting in an office on the job, so that's the difference in risk. And then we know the wage premium that people on that oil rig get paid, so then we have the pieces to calculate the VSL. Now, remember: people on that oil rig, they probably don't have PhDs. So when you do the statistical analysis, you need to correct for differences in education, or gender, or race, or other factors that actually do affect wage differentials across the industry. But once you do that—and you can do it in pretty sophisticated ways—that yields the wage premium that's associated with this higher risk of death. The other approach is the “stated preference approach.” This approach involves using sophisticated surveys to elicit people's preferences for reducing their risk of death, and this is actually an area where my research specializes. I do these studies where I asked people in certain contexts, situations, how much they're willing to pay to reduce their risk of death by a little bit.

We could go on and on about all the details of these surveys and all the checks and credibility issues. So how one can really believe the results you get from a survey, that's hypothetical. It's not their observed behavior as it is in revealed preference approaches. It's their stated behavior within these surveys. Those surveys tend to yield a number that's actually lower than the 10 million that you get from the wage hedonics in the range of $3-$5 million.

Daniel Raimi: Great. So we've got these two approaches, the stated preference approach that you just described and then the revealed preference approach, which you described earlier. I imagine as our listeners were listening to your very nice descriptions of those two approaches, they are maybe thinking about some of the pitfalls of either approach. Maybe some moral landmines lurking within these methodologies that could affect your calculation for a VSL. One that came to mind when you were describing the revealed preference approach: It seems to me that looking at people's wage premium associated with more risky jobs, that assumes that those individuals in those jobs have full information. They have a perfect understanding about the additional risk that they are taking on. And I imagine in some cases that that might not be the case. But there are probably some other ethical and moral complexities here, so can you talk us through what some of those landmines might be?

Alan Krupnick: Sure. Well, the hedonic wage studies echo the human capital approach actually, because they're only looking at the preferences of people who actually work. These people tend to be healthier than people who don't work ... who are disabled, let's say, or don't work very much. And of course, they're younger. We're not picking up the elderly where most of the deaths that would be avoided, certainly by pollution, that's the group that's at risk.

Daniel Raimi: Right. And in the context of coronavirus too, right? Of course, that's where we see the greatest risk as well.

Alan Krupnick: Exactly. So those groups are not polled, if you will, doing that kind of analysis. Now, in the stated preference approach, you get to choose who takes the survey, and you can have ... What we usually try to do is a random sample of adults. So we get the elderly people, we get infirm people, we get healthy, working adults. We get the full range of people if the sample is large enough. But of course, the problem with the stated preference approach is that it's hypothetical. It's within a survey context. So as I noted, you have to take great pains to prove that what people are saying has internal validity, that it makes sense on its face as best as you can. With a wage premium as you rightly say, Daniel, workers don't necessarily know what their risks really are. These added risks. They have an anecdotal handle on it, I would imagine, but they don't know precisely and so that leads to problems as well. But again, there are tests that can be used to check the validity of these responses.

Daniel Raimi: That makes sense. I know you said we could do a whole podcast episode or probably seven or ten podcast episodes on your surveys looking at VSL. But I just want to ask one follow up question on that, which is when you do look at the survey data, are there any kind of general trends that you find when it comes to different age groups stating a different willingness to pay to protect themselves?

Alan Krupnick: Well, so this is where one of the moral landmines or ethical landmines come into play. Your listeners may remember something called a senior discount or a senior death discount.

Daniel Raimi: Oh, I was thinking about a senior discount at a diner or a restaurant, but I guess there's something different here.

Alan Krupnick: This is something different. The EPA at one point floated the idea of using a lower value of statistical life for elderly people than normal healthy people because they have fewer years left. You could go into the literature, the state of preference literature, and look at what the preferences are for older people reducing their risk of death by a given amount versus a younger person reducing their risk of death by the same amount. So you can draw a curve with age on the horizontal axis, and willingness to pay on the vertical axis, and you can see what that curve looks like. For some studies that curve has a hump in it, or the relevant part of it is ... let's say the 40 year old down to the older and older you get, it's sloping downwards. So the willingness to pay is lower. But there are other studies that don't show that, and it's hard to know what the motivation is underlying these willingness to pay answers that you get on surveys. But you can imagine two factors are going on.

One is an older person is saying, "Well, I do have fewer years of life left,"if they thought about this at all. They're just saying, "Well, I don't have that many years of life left, so I'm not willing to pay that much." But on the other side, they're saying, "Well, every year of life I've got left is really, really precious to me." So it can go either way. There's not a theoretical reason to expect that line to be going down with age, and of course it's an ethical dilemma. Are you willing as a society to value the lives of elderly people or risk reductions to elderly people lower than the value of risk reductions you apply to, let's say, people in the middle of their life, in the 40s or 50? The EPA looked at that one long and hard and said, "Nah. Nah. We'll use the same VSL no matter what the age."

This also came up in the World Bank, a similar ethical dilemma where in developing countries where incomes are very low, you can imagine that willingness to pay would likely be lower there for a given risk reduction than in a place like the United States or other developed countries.

Daniel Raimi: Right. It would be like ability to pay more than willingness to pay, or you know both would be factored in.

Alan Krupnick: Well, both are actually always factored in because your ability to pay affects how much you are willing to pay. You want to be clear with people that if they do pay this amount that they're telling you, that they're going to have less money to spend on other things. So you will get lower willingness to pay values in developing countries than developed. That's a fact. So the question is, in your cost-benefit analyses where you're comparing interventions in various countries, do you use a lower value of statistical life in those countries and in those developing countries? Larry Summers was as the head of the World Bank back many years ago and was the one that got involved in this controversy. The answer at that time was absolutely not, use the same VSL. But now, it's actually routine to use a lower VSL in developing countries. One reason is that when we do these studies there we find lower values, so that's an easy call. And in fact, if we don't have a study, it's usually thought that the VSL is proportionally lower to their income difference.

Daniel Raimi: Very interesting, and certainly poses all sorts of difficult ethical and moral questions.

Alan Krupnick: Always.

Daniel Raimi: Yeah. Well, probably we'll get it to some of them maybe now. Let's move on from talking about the VSL in theory to the VSL in the real world. You've mentioned a couple of air pollution contexts where the VSL might be used, but I'd love to ask you how you're thinking about the VSL now in the context of the coronavirus epidemic and how people are talking about it? What do you think is appropriate or what might not be appropriate? Can you just give us your take on applying VSL in today's context?

Alan Krupnick: Yeah, sure. And I have been thinking about this as a variety of cost-benefit analyses have come out that apply the VSL to value the benefits of social distancing relative to a model where you don't have social distancing and what that benefit is against the cost to the economy. So if you have social distancing, there's going to be bigger economic effects than if you don't have social distancing. I guess my overarching feeling on this is the cost-benefit analysis at this particular time of this particular choice is inappropriate, and that means that the VSL is inappropriate to even use. The reason for that is because there's not a trade-off. Economics is the science of trade-offs in society and until the health problems are over that hump ... That is, until we get into that flattening of the curve that everyone's talking about, the economy just cannot get started again. Even if all these restrictions were lifted, no one would go back to work. So it's not a trade-off.

Now, after we've moved beyond that hump and the curve starts going down ... and maybe we're pretty sure it's going lower and lower in terms of death rates and confirmed cases, then it would be appropriate to use cost-benefit analysis to help decide how fast you try to get back to normal, how fast you limit restrictions on social distancing, and then the VSL would be appropriate.

Daniel Raimi: Can you, Alan, elaborate a little bit more on why there's no trade-off right now whereas there would be a trade-off in the future? I mean, some people certainly have voiced the possibility that there could be a trade-off. I mean, famously the Lieutenant governor of Texas suggested that he and other grandparents would be willing to sacrifice themselves for their grandchildren's economic benefit. So it seems like some people are thinking about those trade-offs. Do you think that's just too morally fraught to consider? Or is there a technical reason?

Alan Krupnick: No, this is more of a personal observation from reading and watching the news, and querying myself and my friends and family and that I don't see that trade-off happening society-wide. Of course, we all feel this trade-off is potentially out there. But I think until we get on the way down on that death curve, that as a society, we can't do that. But that's not a professional opinion, that's my own opinion. But eventually, as I said, the VSL and cost-benefit analysis can be useful. So then the question is, what VSL would you use when you're doing the benefits of a faster or slower removal of social distancing restrictions? So here there's a bunch of issues that come up, and there's some on both sides of whether you would want to use a higher or a lower VSL. There've been a bunch of studies that show that when the cause of a death is more dreaded, the willingness to pay to avoid that death is higher.

So imagine comparing the willingness to pay for avoiding a cancer death, or avoiding a reduction in the risk of dying from cancer. That would be the more technical way of saying it, to avoid the reduction in the risk of dying from cancer versus the willingness to pay for the same risk reduction of dying in an automobile accident. The latter is really quite familiar. This happens every day. People feel they're in control even though a lot of times they're not, and the death comes often quite swiftly. Compare that to cancer where you often feel you have utterly no control, and it can be a terrible death, and it affects a lot of people around you ... I guess both kinds of deaths would affect a lot of people around you, but it's definitely a dreaded way of going, relative to dying in an automobile accident. So those value of statistical lives tend to be higher for cancer than they are for dying in an automobile accident. Now, let's compare cancer to a coronavirus.

No one's done the study yet, but I would venture that if you did that study right now, the dread for coronavirus would be totally off the scale, off the charts. So that would tend to push the VSL up. One of the reasons would be that there's no cure, or there's not even medicine to help you not die. There are ventilators, but that's about it. In cancer, we have a lot of treatments. Survival rates are lengthening, so there's hope. But coronavirus, once you get to a certain point, there's really nothing that can be done. So that's really dreaded, that would lead to a higher VSL. On the other side ... This is a little technical, but the fact that the death rates are so high ... let's say there are about 2 percent that is in the population. Once you're a confirmed case, your chance of dying is about 2 percent. But in the general population, I haven't seen a statistic on what that risk is.

If it's in the pollution range, if you have a pollution rule, that reduces the risk of death, generally setting a tighter ambient air quality standard is in the range of 1 in 10,000.

Daniel Raimi: Right. So a much lower percent.

Alan Krupnick: So much lower potentially, but maybe not. It really depends on how many people not only are asymptomatic, but how many people don't actually even get it. So you'd want to take the number of deaths divided by the entire population is the test. And we don't know where that is going to ultimately be, but that's the kind of statistic that you would want to use here. I would venture that those death rates are probably pretty low and in the range of the pollution rates, that would mean that the VSL on that score alone would be appropriate to use, the $10 million or something even larger. But on the other side, there is this distinction that we talked about earlier that, between the revealed preference wage hedonic studies which get you in the 10 million range, and the stated preference studies that gets you in the 3 million, 4 or 5 million range, which have the elderly people in them, and the disabled, and infirm people in them, which may be more appropriate. And if that's the case, then maybe you want to use a lower VSL that appropriately captures those groups.

But as I say, these decisions are fraught with ethical and moral dilemmas. So my guess would be you would end up using about $10, or maybe doubling it for the dread to $20 million. I don't know. But that's the kind of calculus one would have to go through as an analyst trying to do these benefit-cost analyses.

Daniel Raimi: Right. That's so interesting. We're pretty much out of time. I think one of the key takeaways for me is going to be as the months go on and we start to think about trade-offs and we start to see people producing these types of analyses, which we already have ... At least I already have, and I expect we'll see more of them. Just we'll need to keep a very critical eye on understanding the assumptions that underpin the VSLs that people are using and treat them with the range and caution that at least, to me, they seem to deserve.

Alan Krupnick: I agree with that. And in fact my guess would be that most analysts would want to punt on this question and just use the standard VSL that EPA and other agencies use, which is $10 million per statistical life. And then what you might see being done ... and I've seen this in one analysis already by another colleague of ours at University of Wyoming, Jay Sjogren and his team, is to use a breakeven analysis. So they actually find using the $10 million number that the benefits of social distancing outweigh the costs by about five times. And then they say, "Well, what VSL would equate benefits and costs?" So they get a much lower VSL. If the VSL is lower than $1 million or something like that, then in that case the costs would outweigh the benefits. So you might see analyses like that of breakeven analyses that would tell you, "Well, if you really think the VSL is kind of small, then you should get rid of this social distancing faster."

Daniel Raimi: Interesting. Well, Alan Krupnick, again from RFF, thank you so much for talking us through this complex and morally fraught issue. It's not an easy task and you've done a great job. We really appreciate it. Normally on the show we have a question at the end of each episode called Top of the Stack where we ask you what you're reading, and listening to, and enjoying lately. I don't actually have one prepared for today because we organized this podcast at the last minute. But Alan, I'm wondering, do you have any books or movies or anything you've been watching and enjoying lately?

Alan Krupnick: Well, I have one that I've been reading that's appropriate. I have a book I've been reading that's appropriate to this discussion and it's a book that my neighbor David Marwell, has written and just came out just before the outbreak. It's about Mengele, commonly termed “the angel of death.” And within that book, it very carefully lays out the Nazi strategy and underlying rationale for killing people in concentration camps. The idea was that the benefit to the group outweighs the benefit to individuals. So the Hippocratic Oath says your duty as a physician, as a medical person is to make that individual better. And the Nazis turned that around and said, your duty as a physician is to make the society better, particularly the German society better. So the focus on society overwhelmed the focus on the individual and was the rationale underlying the medical profession. And people like Mengele who was a physician justify this killing of Jews and other groups, undesirable groups in concentration camps. David's book goes through this in a very compelling, highly readable manner, so I would recommend it to anyone.

Daniel Raimi: Great. Yeah, that sounds fascinating. Although I have to say after a long day of childcare and work and watching the news, I'm not sure if I have the appetite to read about the Nazis. But maybe some of us do.

Alan Krupnick: Maybe they do, and you can read it after things are all better.

Daniel Raimi: Yes, absolutely. Great. Well, one more time, Alan, thank you so much for joining us, talking us through VSL, and giving us your Nazi book recommendations. We really appreciate it.

Alan Krupnick: You're welcome, Dan, it was a pleasure.

Daniel Raimi: You've been listening to Resources Radio. Thanks for tuning in. If you have a minute, we'd really appreciate you leaving us a rating or a comment on your podcast platform of choice. Also, feel free to send us your suggestions for future episodes. Resources Radio is a podcast from Resources for the Future. RFF is an independent, nonprofit research institution in Washington DC. Our mission is to improve environmental energy and natural resource decisions through impartial economic research and policy engagement. Learn more about us at rff.org.

The views expressed on this podcast are solely those of the participants. They do not necessarily represent the views of Resources for the Future, which does not take institutional positions on public policies. Resources Radio is produced by Elizabeth Wason with music by me, Daniel Raimi. Join us next week for another episode.