In response to my ageless hypothetical, Jeremy Horpedahl raises some empirical doubts about the relative value of life for the young and the old:
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.
Here’s the relevant graph.
My main response: This result is more than merely “surprising.” It’s positively insane. If this graph is right, then the value of life from the age of 20 to the age of 50 is actually negative! You burn a year of life, and at the end of the year the total value of your life is somehow greater.
What then should we conclude? There are two main possibilities:
1. There’s something deeply wrong with the method used to calculate the value of life.
or;
2. People are very foolish indeed. So foolish, in fact, that their revealed preferences are a terrible measure of their actual well-being.
In the real world, both (1) and (2) are at work. To give just two examples:
On the methodological front, young people are usually liquidity constrained, so their measured value of life usually fails to account for most of their anticipated earnings.
On the folly front, young people are notoriously myopic, so they take bone-headed risks even though they have more to lose than the rest of us.
The severity of these problems would be even more obvious if we were talking about 10-year-olds rather than 20-year-olds. I wouldn’t be surprised if their measured VSL was under $100,000, or even $1000. Why? Because they have almost no money, and they’re immature enough to run into traffic to save Pokemon cards. Fortunately, their elders know better.
Jeremy continues:
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.
As an economist, I have a strong preference in favor of willingness-to-pay over our intuitions. Indeed, Caplan himself as defended the VSL approach quite forcefully!
For the record, the piece Jeremy links to rejects a bunch of bad but popular complaints about VSL. I leave open the possibility of good but unpopular complaints. Starting with: Slightly different methods of measuring VSL could easily yield radically different answers. Measuring the “overall value of life” probably implies very different results than measuring the “value of an hour of time” and multiplying it by expected time lost. Measuring VSL using compensating differentials for jobs probably implies very different results than measuring VSL using willingness to follow unpleasant medical regimens. And so on.
In any case, it’s a odd to describe my view that one 10-year-old life is worth 100 or 1000 80-year-old lives as merely “my intuitions.” I base my numerical answers on three virtually iron-clad reasons why the value of life has to decline sharply with age. To repeat:
1. When the young die, they lose far more years of life.
2. When the young die, they are far more likely to lose healthy years of life.
3. When the young die, the people who survive them miss them much more – and miss them for a much longer time.
(1) and (2) are beyond debate. Who would seriously deny that more years of life are better than fewer? Who would seriously deny that healthy years are better than unhealthy years?
(3) is slightly debatable, but Darwin should resolve any lingering doubt. The genes of animals that prefer their parents to their offspring soon perish – even in cultures that officially put the aged on a pedestal. Taken individually, each of these premises is stronger than any empirical paper I can recall. Taken together, these three premises are stronger than any empirical paper we’re ever going to see.
READER COMMENTS
Gabriel A Weil
Apr 19 2021 at 10:29am
Here’s how I think about the problem. There’s some combination of four things going on here.
Young, healthy people are irrationally undervaluing their remaining life years.
Young, healthy people are rationally discounting the value of far-future life-years, since they think they feel an attenuated sense of identity with successive future versions of themselves (see Parfit, Reasons and Persons).
Older people are willing to pay a lot to reduce mortality risks in part because they “can’t take the money with them” when they die.
Measurement issues mean the gap in per life-year willing to pay is smaller than existing studies suggest.
Importantly, ALL of these four explanations would sever the connection between measured WTP and social welfare. It’s easy to see why social policy shouldn’t defer to irrational preferences. But even if young people rationally discount the welfare of their future selves because they aren’t “them”, that doesn’t mean the welfare of those future people should have any less weight in a social welfare function. Likewise, maybe it’s rational for older people to be willing to pay more to extend their lives. since they can’t take their money/resources with them to grave, but society still does have many uses for those resources.
For the full argument, see my article in the Texas Environmental Law Review, Individual Preferences in Policy Analysis: A Normative Framework: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3424332
Matthew Lilley
Apr 21 2021 at 11:17am
This is an excellent comment, with several very nice insights. Thank you
Eric Rasmusen
Apr 19 2021 at 11:42am
Excellent topic! Gabriel Weil, you are on the right track and I ought to read your article. You’d be interested in mine below. It’s on-topic in that it talks about the inefficiency that arises because of a missing market between yourself at different ages. Your young self wants to smoke, but needs money even more; your old self has plenty of money, but wishes your young self hadn’t smoked. As you say, old peopel value money less– both because they ahve more, and because the sports car and pretty clothes can’t be used as effectively— so they value Life more, in dollar terms.
Eric B. Rasmusen, “Internalities and Paternalism: Applying Surplus Maximization to the Various Selves across Time.” Social Choice and Welfare, 38(4): 601-615 (2012). One reason to call an activity a vice and suppress it is that it reduces a person’s future happiness more than it increases his present happiness. Gruber & Koszegi (2001) show how a vice tax can increase a person’s welfare in a model of multiple selves with hyperbolic preferences across time. An interself analogy of the compensation criterion can justify a vice ban whether preferences are hyperbolic or exponential, but subject to the caveat that the person has a binding constraint on borrowing. http://www.rasmusen.org/published/2012-Rasmusen-SocChoi.Welfare-internality.pdf
Eric Rasmusen
Apr 19 2021 at 11:46am
The other thing you mention is discount rates. Young people are more impatient.
It must also be allowed, though, that we can’t push hard on the rationality assumption here, if by that we mean making unbiased decisions on average. You’re only young once. Thus, it’s quite possible for young people to systematically err in taking too much risk and spending too little on staying alive, in the sense that if they were perfectly informed they would agree their decisions were mistaken. It’s like Marriage and Crime and Buying a House: the first decision may well be wrong, but you’re stuck with it.
Of cousre, you’re also only old once. So it could be, and I suspect is, that it is the OLD people who are systematically mistaken— too nervous, too fearful, too risk averse. Plus, their brains don’t work as well in many respects. Old people fear death, but maybe it isn’t as bad as they think, nor Life as good.
Aaron Stewart
Apr 19 2021 at 11:48am
Not sure how the willingness-to-pay for risk reduction is measured, but it sounds like willingness-to-pay-out-of-one’s-own-pocket-for-risk-reduction-to-oneself. If that’s right, I’d be interested in seeing something like how much people are willing to pay for others’ (perhaps including non-immediate family) risk reduction
Eric Rasmusen
Apr 19 2021 at 11:49am
ps: “Old people fear death, but maybe it isn’t as bad as they think, nor Life as good.” Unless, that is, you’re going to Hell. Cf. Hamlet’s soliloquy, https://www.poetryfoundation.org/poems/56965/speech-to-be-or-not-to-be-that-is-the-question.
JFA
Apr 19 2021 at 11:49am
I think Caplan might be to dismissive (defensive, as well?) of these results.
“When the young die, the people who survive them miss them much more – and miss them for a much longer time.” This maybe so, but grief is not the only cost of death (nor is life years lost). And if a 10-year-old loses his parent, the grief of that actually lasts longer than the grief a parent might have (though, those 2 griefs are certainly of different quality). Is there not a sense of discounting in Caplan’s system? How negative is that value of grief in the 10th or 20th year? I know I would grieve for and miss my sons everyday for the rest of my life if they died, but I am not so clueless to think that the grief I feel 10 or 20 years hence would be the same as today.
A middle-aged man or woman (on average) provides for more people than a 10- or 20-year-old or an 80-year-old. Spouses, children, and parents depend heavily on these middle-aged individuals. The immediate effects always have higher weight than future effects. And there are many more immediate effects of the death of someone who has dependents rather than someone who does not.
What Caplan might be missing is the ceteris paribus assumption. All else being equal, the life of a 10-year-old is probably worth more than anyone older, but rarely is the ceteris actually paribus.
I don’t think Caplan is wrong, but I also don’t think the case is as clear cut as he makes it out to be from a pure calculation perspective.
Scott Sumner
Apr 19 2021 at 11:57am
You asked:
“Who would seriously deny that more years of life are better than fewer?”
Arthur Schopenauer?
Seriously, it may be rational for younger people to take greater risks. Suppose society reaches a certain steady state population. If population falls below that level, then housing becomes cheaper and birth rates rise, and vice versa. In that case, an individual death does not affect the aggregate flow of life years. Thus young people might want to take greater risks in order to enjoy a greater flow of utility. Maximizing aggregate utility for society is equivalent to maximizing the annual flow of utility for those who survive.
Philo
Apr 19 2021 at 7:10pm
You seem to be equating rationality with utilitarian thinking (that’s OK by me), and (implausibly, I think) stipulating static population; but how does that suggest that young people should take greater risks? Granted, young people may be able to get more enjoyment by taking big risks, so long as they survive; and although starting with death they get zero, they are promptly replaced by other (newborn) people (per your stipulation). But isn’t this true of old people, too?
Scott Sumner
Apr 20 2021 at 8:40pm
Young people get much more enjoyment out of risk-taking.
Fazal Majid
Apr 19 2021 at 12:10pm
You are discounting the effect of hedonic adaptation. Even if life sucks as you get older, you adapt to it and older people are not unhappier as a result.
zeke5123
Apr 19 2021 at 1:07pm
Isn’t part of this that when I am a parent I need to become more risk adverse because the cost of me dying isn’t just a cost to me but could be devastating to my kids (especially when the kids are younger). So it isn’t so much that I am valuing my life itself more, but that I am valuing my life more because a large amount of the value from my life is going to my kids.
Once I’ve adopted to that risk aversion, status quo bias largely remains.
RCooper
Apr 19 2021 at 1:18pm
I’d buy the chart that Horpedahl presents is accurate for simple life insurance estimates – i.e. covering productive responsibilities. A 40 year old has time-of-death financial responsibilities that may last for many decades. A 20 year-old generally has fewer responsibilities. For a 10 year-old, (outside of agrarian subsistence cultures, and situations with very sick parents), almost zero.
If you think of life as a string of dollar-based productivity values (including applying a value to things like grandparenting, and the sound of children happily playing), even discounted, a 10 year-old is much, much more valuable than an 80 year-old.
If you don’t think of life as pure productivity, but instead of happiness (however you want to measure it), 10 year-olds’ lifetime summed happiness (even discounted) is huge over 75 years vs 5 for an 80 year-old.
Ben Finn
Apr 19 2021 at 1:56pm
3 isn’t quite true. Evolutionary psychology research shows parental grief is at a maximum when their child dies as a young adult. (As predicted because that’s when their chances of producing children is highest, or something like that.)
Lawrence
Apr 19 2021 at 3:32pm
I generally agree with Bryan for humans on our society, but I don’t think the assumptions he sets out are as universal as he thinks.
Take for example sea turtles. We’ve all see the nature show where moma turtle comes out of the ocean, digs a hole on the beach, and lays dozens (or hundreds?) of eggs. Then we see the little guys flopping around towards the sea while the birds and fish gather for supper, and we are somberly informed by the narrator that only about 1 in 100 of them can expect to reach maturity. It seems pretty clear that moma, who has reached maturity and can be expected to keep coming back and laying eggs for many, many years to come (turtles live a long time, if they get to grow up) has a greater value than any randomly selected hatchling who, at 99% confidence, is just lunch for some other critter. As those turtles grow and achieve greater size, swimming ability, and any other protections that will keep them alive, their lives do in fact become ‘worth’ more, notwithstanding that the span of their lives is all the time elapsing.
MarkW
Apr 19 2021 at 3:54pm
Who would seriously deny that healthy years are better than unhealthy years?
Happiness research data indicates that a late-40s year is worth less than a late 60s year, since reported happiness levels are significantly higher for the older cohort (even though overall health is not as good).
Kunli
Apr 19 2021 at 4:11pm
It’s not that “burning” a years worth of your life increases its value. That year is spent developing the life, narrowing possible outcomes. If the outcome filtering increases probability of higher value living, then at the end of that one year the expected value increases. What this graph says is that young people have lower expected value because it includes the risk of somehow failing to develop in an economic sense. As they age they cut down this possibility to attain maximum expected value.
Basically the above comment with the sea turtle analogy is apt. Also, I think Kaplan is still correct about other factors like the fact that young people are less rational and that they have less ability to pay.
Actually this kind of proves my point right? If the graph is actually insane then you should be able to make a profit by lending money to young people who desperately need the liquidity. But it’s hard to argue that lenders aren’t lending enough in a functioning market, so we should conclude that there are economic risks to being young that lowers expected value.
DeservingPorcupine
Apr 19 2021 at 8:06pm
I read Horpedahl’s posts on this independently and indeed thought it was a crazy notion. Of course old people will pay more for a year of life. They have more money, and the fact that will die relatively soon regardless means they need to worry less about saving what resources they have.
If you’re about to die right now and have the option of spending all your assets to live an extra 24 hours, you’re very likely to spend it all. You don’t need it for the next day either way!
But for a 25yo to spend all of their assets on one more day of life at the end almost certainly makes no sense.
marc
Apr 20 2021 at 7:37am
As this is a BC text, I shall give in and go against the SD-Bias: Why would I suffer much more from the death of one of my 4 kids (I know of) than from the death of my 74 year old dad (He died, cancer – he might not have wanted to spend 100k on a year more; but for having him around in 2016, one year alone would have been worth it – even from my pocket.).
But my kids? I can make more, if need be. Does not make them disposable consumer goods, but hey: None of them is a Caplan twin either, obviously.
Human parents lost kids by the dozen before clean-water, soap, steady food supply et al. came in. Read James Stephens “The Crock of gold”(1912) or any good anthropologist. We (and other mammals) even evolved to cope with that pending loss – quote: Most new moms experience postpartum “baby blues” after childbirth, which commonly include mood swings, crying spells, anxiety and difficulty sleeping. Baby blues typically begin within the first two to three days after delivery, and may last for up to two weeks.
We all have only two parents. I was lucky to have one I loved. If my partners agreed, I would have 80+ kids (even without Bryan’s book). Would Ziona Chana grieve that much about one of his 96 kids? If, he would grieve more if one died at 24 then at 0.5 .
Disclosure: I am male. When I read about a woman suffering from having had an abortion of a down-fetus – I nod sadly. And think: why then not have some kids more? Distraction guaranteed! – Fully agree on point 1 and 2. I would even in hindsight not put much value on my years 12-18, though. Years as a school slave.
Eric Hammer
Apr 20 2021 at 12:47pm
A few things occur to me:
1: Risks for young people are not the same as risks for old. When I was younger I didn’t care about e.g. breaking bones because they healed. When you get older, that sort of thing stops happening so well. Further, injuries are not linear in their effect, but arguably exponential. Two broken arms is more than twice as bad as one. Combined with a reduction in speed of correction, that makes any given risk of injury much worse for an older person than younger.
2: People seem to pay a lot of money towards remaining or becoming more youthful. People searched for the fountain of youth, not the fountain of aged. Perhaps that’s because they were likely to get aged in any case, but still, people seem a lot more interested in being younger and having more life, especially when they are older. Related…
3: Young people presumably don’t know how good they have it. I seem to recall a saying that youth is wasted on the young.
4: Young people almost certainly way over discount the value of a year of life. Young people as a group seem entirely certain they will live forever for all practical purposes. A class mate dying really throws them for a loop, whereas people in their 40’s and 50’s start seeing that as normal.
Further, if young people understood the scarcity of years the same way older people do, how many would really be willing to spend time in high school and college classes?
David Henderson
Apr 20 2021 at 3:36pm
You wrote:
It’s a line in the movie It’s a Wonderful Life.
andy
Apr 21 2021 at 11:58am
Isn’t this just a corollary on ‘impossibility of interpersonal value comparison’? What is the question anyway, value of life for whom? It’s how I value your life? How you value your life? How an insurance company values your life? Is it your discounted tax payments? How parents value their life vs. the life of their children?
How do we compare how much a poor person values their life vs. a rich person? A person with dependent children is likely to be more risk averse than a same childlress person. Does it say anything about he value of their life?
It seems to me that there are no good answers. Yet there are places where these decisions must be made. Maybe we should stop worrying about ‘value of life’ and use different terms and arguments to support such decisions.
Malcolm Kirkpatrick
Apr 21 2021 at 12:29pm
Somewhat related: when did human children, on average, start to outlive their parents? The average feral hen outlives the average chick.
Peter Gerdes
May 11 2021 at 7:06pm
Seems like you are blurring together the value of a life for society and the value of the life for the individual.
In particular, it’s far from clear that the government should care about how many years of life I have left in itself. Supposing you are morally indifferent about population increase then you are saying that on average the resources used by an extra member of society about equal the value of their lifelong happiness plus net econ prod.
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