The VSL Quandary
Even the simplest cost-benefit analysis suggests that the US government should be willing to spend up to $65 trillion and lock down the country to avoid extra deaths.
This is from Luigi Zingales, “Captured Western Governments Are Failing the Coronavirus Test,” published at promarket.org, March 13, 2020.
That $65 trillion is not a typo. Luigi (who blogged briefly on EconLog) is actually advocating that the U.S. government be willing to sacrifice 3 years of GDP to save what he estimates to be 7.2 million U.S. lives.
But here’s a good rule for reasoning about anything: if your model tells you that you should take measures to save 7.2 million people in a way that will likely cost the lives of over 30 million people, and if a large percent of those 7.2 million are in the pool of 30 million, there’s something seriously wrong with your model.
If the government were to shut down the economy in a way that cost 3 years of GDP, who would produce food, who would ship food, who would work at hospitals, who would produce electricity, and who would assure clean potable water? I think 30 million lives lost, just under 10 percent of the U.S. population, is probably a minimum estimate of the lives lost from the shutdown.
When I posted about this on Facebook, a commenter asked me if my problem was that Zingales estimated the value of a statistical life (VSL) at $14.5 million. I answered that although Zingales, strangely, argued for his $14.5 million number by citing a source that says the right number is $10 million in 2017 dollars, and we haven’t had cumulative inflation of 45 percent in 2.5 years, that wasn’t the main problem. (Later in the piece, Zingales uses a $9 million VSL because a disproportionate number of those who die would be elderly. He gets his $65 trillion by multiplying 7.2 million deaths saved by $9 million each.)
Still I couldn’t put my finger on the main problem. I still can’t.
In the cost-benefit analysis courses I taught at the Naval Postgraduate School over the years, I used the VSL analysis and I typically used a number between $4 million and $10 million for that value.
But even though this clearly was not Zingales’s intent, he has made me question whether I was right to do so.
This is a puzzle to which I don’t have the answer. But go to the paragraph early in my post about a good rule for reasoning about anything. Something is badly wrong with the VSL framework when we’re talking about millions of deaths.
Apr 12 2020 at 4:45pm
Very quick, very knee jerk reaction, but here’s one possible thought at what might be going wrong here with the VSL framework in this case – the opportunity cost is not being made explicit.
One of my rules for life is “always make the opportunity cost explicit.” Failing to do this is one reason why a lot of people fall short on personal goals and projects, I think. They decided “I’m going to do X” and just leave it at that. But all choice is choosing between alternatives – choose to do X means choosing to do X instead of some other thing. You can’t make a choice that’s just a pure addition to your life. So, make the opportunity cost explicit. I’m going to train to run a marathon, instead of remodeling the porch this summer. I’m going to learn to play acoustic guitar, instead of going to poker night with my friends on the weekends. I’m going to write a book, instead of spending my evenings sitting on the couch relaxing. Etc. If you can’t find an “instead of” that you’re willing to offer up, then you probably shouldn’t start the project. This rule of thumb has saved me a lot of frustration.
In this case, Luigi’s implicit proposal is “Let’s forgo $65 trillion worth of wealth to save 7.2 million people, instead of using that $65 trillion in wealth to support the lives of 300 million people.” Put that way, it’s not at all obvious that forgoing $65 trillion in economic activity is the right move. The “instead of” has real consequences here which also deserve consideration.
I’ve heard it said that economists are looking bad in this current environment because they want to “sacrifice human lives for the economy” or some such. I plead innocent to this charge. I think what economists are doing is simply taking a more expansive view of what saving and costing lives entails. Economic crashes and poverty are killers. I don’t know offhand what the math is on this – how big an economic decline would have to be before it costs more lives that the virus itself would have? What’s the right answer to that? Beats me, and I would be immediately suspicions of anyone who acted like the answer to that was easy. But we shouldn’t pretend this question simply doesn’t exist, or that over-correction doesn’t have consequences as big as under-correction, and we shouldn’t act as though people who raise this question simply don’t care about the lives of those who suffer from Covid-19. That’s a contemptible move – but, unfortunately, all too common.
Apr 12 2020 at 5:15pm
This is a question I’ve been wondering recently myself, so I’ll offer my “answer”: in the long term and the large scale, the (economic) value of a life has to be about the GDP generated; so if (in the USA) the average working life is 33 years and the average salary is $30k, then the average value has to be about $1M. Although that’s the new GDP generated; obvious as a child and as retired you’re a sink; and even as an adult you consume some, probably a lot, of that GDP you’re generating.
Apr 12 2020 at 6:05pm
There are two problems with Zingales’s analysis. The first one is general: the use of a gross utilitarian calculation that (among other problems) imposes costs on one set of persons for the benefit of another set of persons. That implies god-like judgments that economists (nor anyone else) should be making.
The second problem is inherent in VSL. It may be applicable to an individual or small group of persons, that is, to a marginal calculation. But it surely can’t be applicable to the populace as a whole. Shutting down the economy would reduce VSL drastically but cutting everyone’s output to zero for three years and then to something less than the pre-shutdown level for many years after that.
Apr 12 2020 at 6:44pm
Maybe the most important issue is that we need more marginal analysis here. Even if we might be willing to sacrifice 65 trillion in output to save ALL 7.2 million lives, the OPTIMAL reduction in output could very well be far smaller. E.g. if shutting the economy down for 3 months reduces the excess deaths extremely rapidly, (so maybe we have only 100k deaths, because we need to consider the shape of the curve), then maybe you shouldn’t bother keeping the entire economy shut down for an ADDITIONAL 2.75 years to save those remaining lives. You can’t just assume a linear sacrifice in output leads to a linear reduction in deaths.
It is critical to analyze the lowest cost way of reducing those deaths, until the marginal benefit equals the marginal cost. I would expect someone to look at total numbers and ignore marginal analysis only if they don’t understand econ 101…
Apr 12 2020 at 10:29pm
Yes, assuming linearity does most of the work here.
Not all GDP is made equally. The first few dollars of GDP lost will barely have an impact per capita. But the less that’s left, the more each dollar will hurt.
Perhaps an assumption of utility being proportional to log of GDP would give sensible answers? (And by utility, that would also somehow include David’s estimate of how many people would die from the lockdown.)
In general, we should probably also calculate in quality adjusted life years, not raw deaths. In the long run, we all die; but QALYs still differ.
Apr 13 2020 at 6:44am
I think if you want to take into account nonlinearities in GDP costs, you also have to take into account the nonlinearities in how people value their lives. Most VSL estimates come from labor market studies, looking at small changes in risk and then multiplying it out. What is the shape of the curve when you get the higher risk? I don’t know. I’m much more willing to accept compensation for small risk than for large risk. What happens if you used medical spending and medical debt analyses to measure VSL? You’d have to provide a discount for the presence of 3rd party payment, but would the amount of spending be less or more compared to labor market studies. Most of medical spending goes towards those at the end of their lives.
There is something wrong with the conclusion that we should be willing to shut the economy down for 3 years, but if you’re consistent on looking for non-linearities, looking only at VSL might not get you out of the problem.
Apr 13 2020 at 1:43pm
Well, Matthias I would say the GDP lost per capita depends on which workers stop working. If we eliminate minimum-wage service workers, those jobs reduce output far less than people earning 10x that much. In any case, it gets more complicated because their will be some synergies and/or inefficiencies with high and low wage workers. I believe he does try to adjust for a QALY by reducing the number, but it still seems a bit high to me. You have a $14M value for a 22 year old, and someone who has already lived 85% of their life is still worth $9M? I probably would have discounted significantly more. My point was that even assuming the VSL was accurate, it was a horrible argument because marginal analysis (basic economics!) is far more important. It’s disturbing that any alleged economist would so horribly fail basic econ 101.
And JFA, I would agree that people have a differing willingness to pay, or valuation, of their lives, but unless you are going to start differentiating between them (how do you determine which people have a higher value?) it doesn’t help you from a policy perspective compared to just knowing the average numbers. If anything, I think it would be fair to assume that higher earnings correlate strongly with a greater life valuation, so factoring in both the marginal benefit and cost to lost output will tend to not have massive deviations based simply on who we would expect values their life more or less than average, so just knowing the average is fine. Most important to the calculation would be the estimated risk of someone spreading or contracting the disease based on their job and/or lifestyle, because that affects the cost calculation more.
I agree there may be some increase in WTP to avoid higher rates of risk, but that just implies that the VSL being used is too low. And just because people spend more of their money on health care when they are old and near death doesn’t mean those lives become more valuable at that time. The timing of medical payments has nothing to do with it.
Perhaps I was not clear enough, but I never said that only the VSL was non-linear. Of course the lost output curve certainly won’t be a straight line either, as Matthias says, and I explain above. But the point is that you MUST do marginal analysis to get the right answer.
Apr 12 2020 at 7:48pm
By assigning a dollar value to a human life (better: to a year of human life), Zingales aims to put himself in a position to evaluate a possible governmental action, in the face of COVID-19, of “locking down the economy” in a way that will lose three years-worth of otherwise attainable GNP (“LDE3”).
As David Henderson notes, while LDE3 will save some people from dying from COVID-19, it will also produce many deaths from other causes (as well as many inconveniences not involving death, on which a monetary dis-value can be placed). If the deaths in the LDE3 scenario exceed the deaths in the “do-nothing” scenario, and the secondary costs are greater as well, we do not need to settle upon a precise dollar figure for a human life or life-year: doing nothing will dominate LDE3, emerging as the preferable alternative.
It seems to me that this result is not at all unacceptable–do-nothing really is better than LDE3, on the given assumptions–and so this thought-experiment in no way furthers the cause of those who object to putting a monetary value on human life. Henderson seems to think otherwise, but why?
Apr 13 2020 at 9:45am
You put it well, Philo, except for the last sentence. I don’t think otherwise. You’ve pointed precisely to the problem.
Apr 13 2020 at 10:18am
You wrote: “I used [to use] the VSL analysis . . . . Zingales . . . has made me question whether I was right to do so.” And again, in reply to Mark Z: “I much too glibly accepted VSL . . . .” I do not understand why Zingales’s piece has had this effect on you. He simply overlooked some relevant factors in his analysis; when they are taken into account, VSL seems to work fine here.
Apr 12 2020 at 8:03pm
There is also the very real possibility that all the epidemiological models we are working with are wrong and the case report mortality is much lower than we believe. Here is a very nice case study of a small German town that had a large cluster of SARS-CoV-2 cases: https://www.land.nrw/sites/default/files/asset/document/zwischenergebnis_covid19_case_study_gangelt_en.pdf
It’s a short paper and easy to read. They used serology to measure antibodies of a representative sample of citizens and also checked to see who was still actively infected. “The lethality (case fatality rate) based on the total number of infected individuals in the municipality of Gangelt is, with the preliminary data from this study, approx. 0.37%. The current lethality in Germany calculated by Johns Hopkins University is 1.98%, and is thus five times higher. The mortality based on the total population in Gangelt currently amounts to 0.06%.” Thus, what they are seeing in this small sample is pretty much the same mortality as the UK observed for the 1957-58 Hong Kong flu epidemic.
I’m not saying that these results will hold up for all places, but until we begin to do large scale serology testing (my favorite hobby horse), we cannot know the case fatality rate as those with mild symptoms are never picked up via current testing schemes.
Apr 13 2020 at 8:34am
Also my favorite hobby horse.
I didnt click the link so not sure if it is same article, but the article I saw on Gangelt compared to that one cruise ship. Gangelt had 15% infection, Ship had 17%. Death rate was higher on the cruise ship, but the demographic there was much older.
It looks like somewhere in the vicinity of 15% is the amount of people susceptible to the virus.
Apr 12 2020 at 8:51pm
I think the logic of concluding that, since I would spend $1 to save a 1-in-9 million chance of dying that I would spend $9m to save my life, is wrong. The curve doesn’t need to be linear like that.
I think this is similar to prospect theory. If the curve is nonlinear then we can’t extrapolate from small probabilities to large ones. Most people wouldn’t spend $9m (borrowing from their friends and family as necessary) to save their own life. They’d rather leave that money to their children.
Apr 13 2020 at 6:33am
If I were 75, I probably wouldn’t want to borrow 9 mil to save my life. If I were 22, I’d feel differently. Given the age structure of the mortality and morbidity (regardless of the discount Zingales applies to old people which is certainly cherry-picked), using a value of life year analysis would come in at certainly a lower estimate.
But let’s say that this only killed 10-30 year olds. Would it be worth doing it then? I think that where David’s issues come in.
Apr 12 2020 at 9:18pm
I think AMT and Josh is on to something. (A non-linear cost curve is the same as saying marginal cost is different from base cost). I don’t know much about VSL theory, but I figure the result must be a marginal value, not a base.
Here is a nice article on it on marginal thinking, from a smart economist I read recently. From the example in the article, the base cost of beer was $1.22 while the marginal cost was $0.33. Using just this difference between base and marginal cost would reduce the $65 trillion to $17 trillion. Of course, there is no comparison between beer and VSL, so this is purely as a thought experiment.
I wouldn’t know how to arrive at a base VSL from marginal VSL.
Apr 12 2020 at 10:00pm
Great commentary by everyone about the difference between marginal and inframarginal and, implicitly, diminishing marginal utility. At high consumption levels we value statistical life relative to other consumption goods more highly than at low consumption levels due to diminishing marginal utility of those other goods.
That might also explain an intuition that, right now, people don’t seem to mind stay-at-home orders as much as they might if those stay-at-home orders get extended beyond a few months. We have lots of months of “normal life” so giving up 1-2 of those months may not seem like such a big deal: diminishing marginal utility of months of “normal life”. The third and fourth months, however, will be more valuable than the first two, and the fifth and sixth months more valuable still. If a shutdown were extended to 36 months, that 36th month of forgone “normal life” will be a lot more valuable than the first one.
Apr 13 2020 at 3:42am
Right. One could think of prison terms as an analogy. The cost one would attribute to getting a 1 year prison sentence may be more than twice that of a six month sentence. It would be interesting to see what convicts would be willing to pay to get would of a sentence as a function of its length, to see what the curve looks like. I doubt that’s a study that would get IRB approval.
Apr 12 2020 at 10:10pm
I don’t get the sense that money is a useful concept in describing several years of complete reorganization of every resource in the US, any more than entropy is a useful concept when you’re simulating the 10^26 dimensions of every molecule’s state in a gas in a box.
Apr 12 2020 at 11:39pm
“…sacrifice 3 years of GDP to save what he estimates to be 7.2 million U.S. lives…I couldn’t put my finger on the main problem.”
Perhaps there isn’t one. I mean, there are plenty of problems with VSL. But I just don’t think that that figure, prima facie, sounds absurd. 7.2 million is a large city. What would the USA do to stop another country bombing New York out of existence? I think it would definitely be willing to engage in three years of total war, i.e. put the whole country on a war footing, like WWII.
Apr 13 2020 at 8:29am
I’m not sure this is a good comparison. The impact of three years of total war is much, much smaller than the impact of three years of total economic shutdown. Even in a state of total war, the majority of economic activity carries on as normal. During WWII, a large number of working age men were sent overseas, and a large amount of domestic production was allocated to building tanks and bombs. But the stores stayed open. Farmers continued to farm. Advertising executives tried to figure out how to pitch their products. And so on.
What Luigi Zingales is describing is the equivalent of three years of total shutdown. Every shop closed. Every order is canceled. Every job is lost. Nobody gets a paycheck, nobody builds a thing, nobody has work – for three years. Not so much as a single farmer grows a single bean. The impact of this would be much larger than three years of a total wartime economy, where output isn’t eliminated as much as it’s redirected to things like tanks and bombs. Three years of total war would be bad for a lot of reasons, as would New York getting razed to the ground, but it’s not at all clear that three years of total economic shutdown would be better in terms of things like lives lost and damage done – in fact, that seems highly unlikely to be the case.
Apr 14 2020 at 3:59am
OK… to be honest, in trying to answer you, I’m getting confused in all the hypotheticals going on.
Because the 65 trillion = 3 years’ GDP is a hypothetical, virtual notion; and my war was a hypothetical virtual notion; and the war was only there to be a way to think about the proportionate levels of response…
I dunno! You might be right that they’re different. But I still think the point holds. DH seems to find it prima facie absurd to spend 3 years’ out put on saving 5% of the population. I’m saying I don’t find it prima facie absurd. It could be wrong! I’m just saying that I don’t share instinct that DH had of what might be a reasonable level of action to take in pursuit of the preservation of 7.2 million lives.
Apr 13 2020 at 1:56am
Depends. Are we assuming the Yankees had already been eliminated from the pennant race?
Apr 13 2020 at 3:34am
Thinking about it at the individual level, that valuation sounds excessive. How many average people – not billionaire – if they could sell their house, their car, withdraw all of their kids’ college funds, take out millions of dollars in loans and subject oneself to decades of wage garnishment to buy medical care sufficient to save an 80- year old relative, even a parent, knowing that it would prolong their life by a few years?
I’m sure some would if they had the option; but I’m sure many wouldn’t and I would hope most people wouldn’t see it as callous to not do so. We spend less than that to extend the lives of comparably old people as is, and I don’t think many people believe that we aren’t spending enough on end of life care at the moment.
Apr 13 2020 at 9:47am
Really good point, Mark Z.
It reminds me, as did Zinagales’s article, that I much too glibly accepted VSL in all contexts.
Apr 14 2020 at 9:05am
Apr 16 2020 at 4:57am
VSL has a positive income elasticity. As you reduce GDP, VSL also goes down.
So there will be a point, with some but not all the economy having been closed down, where the benefits of avoiding more coronavirus deaths no longer justify the cost.
Apr 21 2020 at 12:54pm
He is using the value of a statistical life instead of QALY. His number is much too high because COVID disproportionately affects older people. So his number incorrectly assumes people’s entire lifetime is lost.
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