The second problem with Wolfers’ estimate is his assumption of a $10 million value per life saved. This is the economists’ usual estimate of what we call the “Value of a Statistical Life.” A standard methodology for computing the VSL is to estimate the risk premium that workers earn for taking jobs in risky occupations. A typical number is an extra $1,000 annually for taking on an added 1-in-10,000 chance of dying in a year. If 10,000 workers are each paid to take on that added 1-in-10,000 risk, then the “expected” number of deaths (expected in a probabilistic sense, that is, the probability of death multiplied by the number at risk) is 1. So economists multiply that $1,000 by 10,000 workers to get the “Value of a Statistical Life.” The result: $10 million.
When I taught that concept in my cost/benefit analysis course, it was always in a context where a few lives were saved or lost. It breaks down when we’re talking about a million lives. I didn’t realize that until I read a post by economist Luigi Zingales of the University of Chicago. He estimated how much GDP we should be willing to give up to save 7.2 million people from dying of COVID-19. His 7.2 million lives lost is grossly overstated. But that’s not the point. What if it were true? He showed, using an apparently conservative $9 million per life saved, that we should be willing to give up $64.8 trillion, which is three years of GDP. The Zingales estimate amounts to an unintentional reductio ad absurdum. If we cut GDP to zero for three years we would do … what? Grow gardens and, in most of the country, live in very cold houses in the winter? In that case, over 100 million lives would be lost, which is 14 times his 7.2 million estimate. When your model tells you that because of the high value of life, you should be willing to give up 100 million lives to save 7.2 million lives, there’s something wrong with your model. Wolfers did not have an answer for that. The bottom line is that for a large number of lives like one million, a $10 million value of life is far too high.
This is from David R. Henderson, “End the Lockdowns Now,” Defining Ideas, May 7.
Justin’s discussion of least-cost avoider got me thinking further. Here’s that section:
When I made these points in the debate, Wolfers responded that he and his family should be able to go to a public park and not have to risk getting the disease from others. His is a valid point. But during the debate, he made another point that undercuts his response. He argued that employers who open up should be held liable if one worker gives the disease to another because, he said, the employer is the “least-cost avoider.”
The least-cost avoider is the entity that has the least cost of avoiding a harm from an externality. It’s often hard to tell how someone got the disease and it’s not at all clear that the employer should be liable. Wolfers responded that workers and customers don’t have deep pockets but employers do. The idea that there are millions of employers with deep pockets is absurd. Apple, Facebook, Microsoft, and Alphabet (owner of Google) do. But even in normal times a large percent of employers have shallow pockets and those are no doubt shallower after 6 to 7 weeks of lockdown.
Yet the Wolfers invocation of the least-cost avoider principle got me thinking. If you’re an older person with co-morbidities, who is the least-cost avoider: young people or you? It’s probably you.
Read the whole thing.
READER COMMENTS
Mark Friedman
May 8 2020 at 7:24pm
Prof. Henderson:
You say, “If we cut GDP to zero for three years we would do … what? Grow gardens and, in most of the country, live in very cold houses in the winter?” Indeed, this sounds worse than catastrophic, but why does this effect occur all at once over a three-year period? Why not incrementally over (say) a 20 year period, which has a less draconian effect and makes Zingales’s argument seem less insane. I’m probably missing something, so perhaps you could clarify. Thanks.
Kevin Dick
May 8 2020 at 11:02pm
The problem here is that VSL isn’t actually the optimal behavior. The optimal behavior is figuring out all the different ways you could save lives and then allocating the available dollars in order from lowest to highest cost until you run out of budget.
VSL is a much easier approximation of this for modest numbers of lives. It’s akin to a linear approximation in a small region of a logarithmic curve. A constant marginal benefit if you will. But when the number of lives gets large you have to take into account that the curve is really one of decreasing marginal returns.
Another way to look at it is, if the numbers are small, you can behave as if society’s “income” hasn’t really changed. But with very large numbers, there’s a substantial income effect that quickly bends its willingness to pay.
Mark Friedman
May 9 2020 at 12:08am
Thanks, but I’m still confused. Zingales apparently said that we should be willing–based on a VSL calculation–to give up $64.8 trillion to save 7.2 million (US, I believe) lives. I don’t understand him to say that we should immediately shutter all economic activity for three years, including the production of food. Prof. Henderson seems to read him this way, using the number of years of GDP required to pay off that $64.8 trillion “debt.” But, why should it come down to that? Why isn’t Zingales saying, for example, “save those 7.2 million lives by reducing GDP by $3.2 trillion per annum for 20 years.” This is a less dire outcome. I don’t see that you have answered my question, but then again I may be confused about this too.
Kevin Dick
May 9 2020 at 4:44pm
We could absolutely do what you say. It would just be an incredibly wasteful way to go about saving lives and isn’t actually consistent with societal risk preferences for the reasons I explained.
Mark Friedman
May 9 2020 at 7:05pm
Okay, thanks, I believe I understand your point. But, I didn’t say or recommend anything. I am attempting to understand whether Prof. Henderson correctly characterized Zingales’s argument, to the effect that what he is proposing would result in 100 million lost lives, reducing his proposal to absurdity.
Mark Bahner
May 9 2020 at 1:35am
Those statements are worth more than a trillion dollars. 🙂
And the lowest-cost ways would be:
A) Masks and gloves for everyone.
B) Everything else is not even close.
P.S. If one performs the analysis you properly recommend, one can see the absolute insanity of the focus in the U.S. and other countries on ventilators:
Ventilators are ridiculously expensive per patient treated
Ventilators are insanely expensive per life saved
John Alcorn
May 8 2020 at 7:32pm
Robin Hanson has drawn attention to an important wrinkle in “externality” mechanisms in the pandemic:
John Alcorn
May 8 2020 at 8:42pm
This (Hansonian) externality might be managed humanely if the population can be largely segmented into two groups: ‘the vulnerable’ (by age and comorbidity) and ‘the much less vulnerable.’
Then isolation of the vulnerable (e.g., shielding of eldercare facilities) thwarts most of the harms from the ‘standard’ externality discussed in the Henderson vs Wolfers debate.
Moreover, when the contrary externality (the Hansonian externality) is segmented and concentrated among ‘the much less vulnerable,’ it produces less harm than a medically arbitrary de facto segmentation (for example, self-isolation of healthy cognitive elites, who can work from home, whilst essential workers of all stripes brave the pandemic.)
Of course, all of this assumes that durable containment (suppression) is elusive, and that policies should focus on mitigation.
Michael
May 9 2020 at 7:23am
Steve Waldman argues here that this is the wrong way to think about herd immunity. There’s no magic impact of 70% of the population having immunity on the virus. The magic is that if an individual behaving “normally” would transmit the virus to 3 people he interacts with, he will only transmit it to 1 person if 2/3 of the people he interacts with are immune. That means that if our society has various subpopulation that tend to interact with others in their own group, each subgroup will need to develop its own herd immunity.
John Alcorn
May 9 2020 at 9:36am
That is why ‘the vulnerable’ should be segmented and shielded, or should self-isolate, perhaps until effective treatments or vaccines are discovered. Shine a bright light on eldercare facilities, and implement sharp protective protocols, with full resources. True, the recent infections of staff members at the White House remind us that perfect shielding is elusive; but we shouldn’t let the best be the enemy of the good.
Herd immunity among ‘the much less vulnerable’ greatly reduces the already low risk among the young and healthy. The devil is in the shades of gray (middle age, mild comorbidity).
See 3 new, model-based studies, listed below:
Paul M. McKeigue & Helen M. Colhoun (U. of Edinburgh), “Evaluation of ‘stratify and shield’ as a policy option for ending the COVID-19 lockdown in the UK,” (25 April 2020). Excerpt:
Xutong Wang (UT-Austin), “Cocooning is essential to relaxing social distancing,” [case study of Austin, TX] (3 May 2020). Excerpt:
Daron Acemoglu et al. (MIT), “A Multi-Risk SIR Model with Optimally Targeted Lockdown A Multi-Risk SIR Model with Optimally Targeted Lockdown,” NBER Working Paper No. 27102 (May 2020). Excerpt:
Of course, take all models with a large grain of salt. But the mechanisms and signs aren’t wrong.
John Alcorn
May 10 2020 at 9:22pm
See also a new study by Tom Britton (Stockholm U.) et al., “The disease-induced herd immunity level for Covid-19 is substantially lower than the classical herd immunity level” (6 May 2020). The authors make the standard epidemiological model more realistic by including social stratification by age and by sociability. They “divide the community into 6 age groups and fit contact rates from an empirical study of social contacts.” The age-stratified model then predicts herd immunity at prevalence = 43%, rather than the standard 60%. Here is the abstract:
J Cooper
May 9 2020 at 2:26am
This argument seems almost intentionally obtuse. The VSL calculation in the example doesn’t mean we should be willing to do absolutely anything that happens to cost $64 trillion, it implies we should be willing to spend that much on things that are actually effective at saving that many lives. It implies we should do things, starting with the most effective per dollar and ending with the least, until it would cost our chosen VSL to save the marginal life. That in no way implies cutting GDP to zero for any amount of time, which incidentally nobody in any position of power anywhere has done or plans to do, making that argument a straw man. The current “lockdowns” still allow a very large amount of GDP to be created, including and especially the creation of life-sustaining goods such as food and water. Your example wherein 100 million people die to save 7.2 million is possibly the most obtuse part, because the $64 trillion number was a given. In your scenario of cutting GDP to zero for three years, the total cost to society is that $64 trillion plus the value of all the lives lost, or 10 million x 100 million = 1 quadrillion. So your idea of shutting GDP to zero doesn’t actually cost $64 trillion, and therefore wouldn’t be one of the options available for those with a VSL of $9 million to do. If you want to make the argument that the current policies are costing more at the margin than whatever you think the appropriate VSL should be, then go ahead, but your argument that VSL shouldn’t be used at all doesn’t make any sense.
Jon Murphy
May 9 2020 at 3:33pm
That’s not the argument. What the argument is is that the $64 trillion has to come from somewhere (resources are scarce, after all) and if the resources are being used to do X, they cannot be used to do Y.
So, $64 trillion being devoted to stopping COVID necessarily means $64 trillion that cannot go to, say, education. Or feeding people. Or whatever else the tradeoff will be.
Michael
May 9 2020 at 8:30am
A couple of quibbles.
I don’t see any attempt in the article to make the case that this assumption (at least half of the GDP decline is caused by the lockdowns and not by voluntary measures taken by businesses and individuals). The framing here seems to imply that $241 billion is a conservative assumption of the cost of the lockdowns – I think it is an unreasonably aggressive one.
My underlying assumption is that voluntary social distancing measures have been widespread, effective, and costly, and David’s case comes across to me as downplaying the effectiveness and cost of these measures.
I’d make the same point here. Yes, the costs here are real and steep, both financially and otherwise. But, it is also true that the spread of infections in hospitals is a very well-established phenomenon, one that hospitals struggle to control in their normal course of operations to this day. During this pandemic “health care provider” is a risky occupation! Especially given the persistent shortages in personal protective equipment. I’d be shocked if, absent the prohibition of elective surgeries, these continued at any rate even remotely close to business as usual. So, yes, definitely a loss in health, but how much is related to the pandemic itself vs the shutdown measures is less clear.
I would have voted for Justin both before and after because I think the costs attributable to lockdowns in and of themselves are being greatly overstated while the costs due the pandemic are similarly understated. And because I am very skeptical of the “isolate high risk groups while everyone else conducts business as usual” strategy. (To me, the recent detection of multiple infected White House staffers highlights the limitations of this approach.)
Lawrence
May 9 2020 at 8:33am
Well I certainly know that MY life isn’t worth $10 million. Just ask my ex-wife!
Alan Goldhammer
May 9 2020 at 8:51am
Ending the lockdown is not a panacea that things are going to automatically rebound back to where they were. Interested participants might want to listen to Barry Ritholtz’s interview this week with Jim Bianco who looks at macroeconomics for a living. He rightfully notes that even if we return to 90% of the pre-lockdown economy it will still be a disaster. He also gets into a good discussion of MMT and that this is where the Fed has moved us to.
My observation is that a lot of us who are >65 years old and relatively high contributors to the economy in terms of travel, going out to eat, concerts, movies, etc. are going to change our near term habits. We have had dinner conversations of what we will be doing over the next 3-4 months and it pretty much does not involve any of the above until there is more confidence that things are being handled well from a public health perspective.
Most doctors offices in our area are doing remote appointments and this is going to continue for some time. How confident are any of you about going to the dentist today for a routine cleaning and check up?
David’s paper is fine as it stands but it’s not going to change the individual behaviors of a great many people who drive the economy through spending. I’m pretty much in line with what Jim Bianco said in the above cited interview. Stuff is going to be very ugly for a while longer. As one who has been looking across the medical/vaccine/pharma spectrum, not much is going to change for some time in terms of treatment for COVID-19. Continued infection outbreaks will be problematic in the absence of a containment plan and that is certainly not in place at the national level.
John P Palmer
May 9 2020 at 9:10am
Your last paragraph is pithy! “If you’re an older person with co-morbidities, who is the least-cost avoider: young people or you? It’s probably you.”
Ms. Eclectic and I take it to heart. We distance like mad (her, to the point of isolation nearly all the time) and we wear masks, even in open air settings, just in case, anytime we leave our condo building. It seems prudent. Besides, who would we sue if one (or more likely both of us) contracted it? Attaching liability would be next to impossible, and collecting would likely be even more difficult because, as you say, too many people who might otherwise be held liable are in fact judgement-proof.
robc
May 9 2020 at 11:21pm
$10MM is way too high. About $200k per year loss is about right (which is well more that $10MM for a full life). Based on age of deaths and ignoring comorbidities, 12 years per death is about right, so $2.4MM per death.
Both the $200k and the 12 years are a touch on the high side, so that estimate is high.
Vivian Darkbloom
May 10 2020 at 12:26pm
I don’t think the VSL anaylsis is appropriate to this situation for other reasons. Typically, when, for example, courts are asked to assess damages in wrongful death cases, a large percentage of the loss of value is attributable to loss of earnings. Pain and suffering, loss of consortium, etc., are also often considered. These calculations are inspired by economic reasoning.
As I understand it, the VSL calculation (being a “statistical life”) would include average lifetime earnings, etc., for that statistical life. The vast majority of the casualties of the virus are retired persons, quite often those with co-morbidities who live in nursing and retirement homes. They are not representative of the “statistical average” in that they rarely have earnings to lose, would have fewer statistical years of loss of consortium. It would be a much different calculation than, say, the loss of a statistical life in an actual war. Stated differently, the calculation is not statistically appropriate because the virus *does* heavily discriminate against the elderly.
As far as pain and suffering is concerned, and while death is never pleasant and the corona virus is not the normal influenza, pneumonia has been called by Dr William Osler (often referred to as the “father of modern medicine”) as “the old man’s friend”.
robc
May 10 2020 at 1:01pm
Agreed, so my post above yours where I “calculate” by years lost. Even in comparison with flu, covid skews old. I get 12 years lost for covid and 16 for flu. Ignoring comorbidities in both cases, so it is much lower than that really.
Vivian Darkbloom
May 10 2020 at 1:28pm
I don’t think so— if I understand your comment correctly, you make a somewhat different point. A “statistical life”, as I understand it, is a hypothetical life based on average life expectancy. Say, the average life expectancy is 80 years. If a person dies at age 78, the average life expectancy might be, say, 8 years (at that age of 78). Thus, it would take 10 persons aged 78 who die to make up a statistical life in this example. The value of each person who dies at age 78 would be 10 percent of the total VSL. Your point about age is therefore irrelevant because it is already actuarially taken into account; but, your point about co-moribidities is highly relevant because a person with a co-morbidity likely has a lower than average statistical life expectancy at the date of death than a person the same age without a (serious) co-morbidity.
My point is that regardless of co-morbidities, a person at age 78 is not statistically appropriate to the average due to lower loss of earnings, etc.
robc
May 11 2020 at 11:10am
Other than the comorbidities, there is one thing 1 agree on and 1 we disagree on. The statistical life is calculating the wrong value, because it is not adjusting for the skew in deaths due to COVID. COVID skews old, so the value is much less that the statistical life calculation.
I disagree on your point that value is relative to productivity…if anything retirement years are worth MORE than working years, or you would choose to work instead. The leisure time is worth more than the amount that could be made from working. I think that using a flat number per year works best, as opposed to trying to calculate the relative value of each person’s life.
Or better yet, don’t do the calculation at all and let each person decide for themselves. 350 million separate cost/benefit analyses vs 1 aggregated one.
John Alcorn
May 11 2020 at 1:14pm
Re: David Henderson’s critique of “Value of a Statistical Life” (VSL).
Robert S. Pindyck (MIT, NBER) offers a fresh critique of (VSL) in the context of pandemics. See his new paper, “COVID-19 and the Welfare Effects of Reducing Contagion” (11 May 2020). BTW, he has written a series of innovative papers in recent years about how to conceptualize and manage catastrophic risks (pandemics, catastrophic climate change, nuclear war, etc.). EconTalk interviewed Prof. Pindyck about these topics in 2013.
Here are excerpts from Prof. Pindyck’s critique of VSL in his new paper:
I have omitted Prof. Pindyck’s technical explanation, why we can’t calculate how much VSL overstates the benefit from lives saved (because “we cannot map out the indifference curves”). As the saying goes, read the whole thing.
John Alcorn
May 11 2020 at 1:37pm
I should mention that Prof. Pindyck’s new paper strikes a wise balance about how models help—and how they don’t. Accordingly, he acknowledges that his model neglects key dimensions of social heterogeneity. In recent weeks, numerous excellent cohort studies of patients have shown that differences in age, comorbidity, and sociability greatly shape the incidence of the pandemic. Therefore, these heterogeneities are crucial for policy. By neglecting these heterogeneities, the paper necessarily neglects policies that could reduce trade-offs between public health and the economy—policies that would segment and shield vulnerable demographics (for example, eldercare facilities). Now social scientists are starting to build more complex models that include social heterogeneity and targeted policies; for example, see the studies listed in one of my other comments in this blogpost’s thread.
robc
May 12 2020 at 9:03am
If we use $38k for the value of a year, then for COVID deaths, that would mean about $456k for the loss of average life, as COVID deaths skew old, and therefore have less years lost (12 by my calculation) than for a typical VSL.
$38k is too low, in my opinion, when I was looking info up on wikipedia a few weeks back (yeah, I know, but its the source I had), it suggested about $120k in 2008, so I have been using $200k…which is too high, but I figure erring on the high side is good.
Mark Bahner
May 12 2020 at 11:38pm
From the U.S. Environmental Protection Agency (EPA):
This simply makes no economic sense. It’s politically correct, but it’s economically insane. This can be seen from a simple mental experiment. Suppose you’re 85 years old, and you have $500,000 in your retirement account. You fall ill, and the doctors say that, for $400,000, they can keep you alive another two years. Otherwise, you’ll die in a month. Do you spend $400,000 of your $500,000 in your retirement account to stay alive the extra one year and eleven months? Or do you leave the full $500,000 to your heirs?
robc
May 13 2020 at 10:31am
That is exactly the question I have been posing. Well, close enough. And the answer is somewhere between yes and no, right? Some people would spend the $400k, some wouldn’t. I have proposed it as $40k per extra year, up to 10, how many years do you buy? Some people would buy 10, some 0. I think a lot would buy 1 or 2 years to say goodbye.
And increase the price to $200k per year, max 2, as you propose, and a lot less people would buy even the first year. But some still might buy 1.
Mark Bahner
May 13 2020 at 11:27am
I think only a very small percentage would spend the $400k. But I agree some might.
So I think we’re in total agreement on the basic point you and I are are both making: there’s no way in the world the $7.2 million is a valid figure for all lives, no matter how close the lives are to the end.
As Thomas Sowell constantly points out:
There’s simply no way it makes economic sense to spend millions of dollars to prolong the life of a very old person a few years. That money would be much better spent on alternative uses, such as making sure that many younger people live many more years.
Not to beat a dead horse, so to speak, but the situation can also be seen clearly by setting up a hypothetical “trolley car problem”, in which the trolley car can either kill a busload of high school students or an 80+ year-old couple. I can’t imagine anyone with that particular problem choosing to throw the switch such that the trolley car kills the busload of high school students, in order to spare the lives of the 80+ year-old couple.
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