VSL is BS?

Gabriel wants to talk about SVL or “statistical value of life” (aka VSL). Where would we be without acronyms.

First, why should we have such a thing? Isn’t putting money value on human life too icky to contemplate? If we have such a value, wouldn’t it suggest Bill Gates could buy our lives? Would it be condoning slavery?

Answers: because we have to, yes but someone’s got to do it, no and really no. Simply put: there’s no way to know how much money to spend on life preserving/extending goods and services if we don’t have a sense of how much its worth to us to preserve that life. “Life is priceless” is a nice sentiment, but taking it literally, and via a sufficiently snarky reductio ad absurdum, this refrain would suggest we spend infinite resources making sure people don’t get the slightest owies. See how absurdum that reductio would be?

Anyway, how much I spend on air bags for my bicycle or how much time I spend indoors instead of braving the mean streets of Davis ((Bikers don’t think they need to follow road rules.)) reflects the value I give to my life. If I value my life more, I’ll spend more time in bed. Usually, I don’t spend all my time in bed so I can’t have an infinite value for my life. If I value my life less, I’ll spend more time sky-diving. Because I’m not spending all my time jumping out of perfectly good airplanes, the value I give to my life can’t be zero. Somewhere between zero and infinity, then, you’ll find the value of my life. The things between zero and infinity are called numbers and that’s all economists are doing when they assign a money value to life; they’re assigning a number to that subjective value we all have in our heads anyway.

There’s a couple of things we’d expect to be true about that number:

  1. It shouldn’t vary too much between different types of people
  2. To the extent it does vary, it should do so primarily because of the underlying difference in risk preferences of individuals
  3. It shouldn’t vary too much by age except in the last moments of life
  4. It should be big in any case. It would be really disappointing (and unbelievable) if economists said lives were worth pocket change (even, or especially, for the infirm) .

With my limited imagination, I can think of two ways to put a dollar value on a human life. The first is to use lifetime income or the slight variant, the income yet to be earned. In other words, just add up pay checks. This breaks a bunch of the rules listed above, but mostly it violates #2 and #3.

Another way to come up with a dollar figure is to look at how much money people spend on safety equipment (willingness to pay) or how much extra money they earn doing dangerous jobs (compensating differentials) relative to mortality rates. The fancy folks down the hall that specialize in Public economics call this the value of a statistical life (emphasis on the “statistical”).

There’s lots of estimates of this value, but most put it between $4m and $9m ((see Viscusi and Aldy. They find safety is a normal good, unions are associated with higher hazard pay and VSL declines with age.)). This method does an OK job not breaking any of the above rules. Take for example the estimates showing a 10% increase in income leads to a 5% increase in VSL. This may seem disturbing at first, but assuming I’ve done my marginal effects calculations right, this values Americans at the poverty line at $2.5m or so ((and Bill Gates at $1.5B, but he may be slightly out of sample)).

9 thoughts on “VSL is BS?”

  1. I don’t see why your 1-4 points should be true. Best counterexample would be seeing what people are willing to do in Thailand or India for a hot meal.

    Anyway, it’s a bit of a straw man to say, if not VSL then “life is priceless”. — Since you don’t get to observe my willingness-to-pay, nor my subjective probabilities, any number you come up with is on shaky grounds, and then never mind that different choices might reveal widely different numbers (on a strictly individual level).

    By the same theory, there exist a sum such as you are indifferent between nothing happening and someone paying you that sum so that he can cut your leg off and beat you over the head with it. If that person would offer you 1 cent more, you would strictly prefer to get clobbered.

    All I’m saying is that expected utility is an imperfect theory and the strong, normative consequences of the SVL concept are overreaching.

  2. Ok. I’ll buy the VSL number is too low. By how much should it be increased? Why?

    Is there a finite sum of money for which I’d be willing to clobbered with my own leg? Yes. But whatever my answer, this has nothing, that I can see, to do with the failings of expected utility. The existence of money values doesn’t require Eu-type preferences.

  3. No, that’s not it. It’s not a matter of too small/too large/just right…

    But I don’t know how to say it, so I’m quiting for now. If I find a way to put my disagreement in perspective, I’ll try again.

    Thanks for indulging me!

  4. “someone paying you that sum so that he can cut your leg off and beat you over the head with it. ”

    I bid two bits. Cash up front.

    Income seems suspect unless you want to calculate things like the cash value of parenting.

    Why would risk preferences be the strong driver of value? We’re not all clones. Maybe you could play a game to work out the market value of a human life. Let’s say we’re members of a conquering alien species who have enslaved all of humanity, and we’re trading humans among ourselves. Would you bid more quatloos for a one armed beggar from Calcutta, or the twenty-six year old Cambridge-educated chemical engineer? How many? The units don’t matter too much if you’re just trying to work out the bounds.

  5. “Why would risk preferences be the strong driver of value?”

    Well, you’re fisherman example works to demonstrate this. Those crab boat guys just value their lives less.

  6. Or their perception of the risk is disproportionate, despite abundant evidence to the contrary.

    These are dissimilar assessments, though. A rational individual will always place a higher value on their own life than others will assign to it. VSL seems to seek an objective, unbiased value.

    I guess I see what you’re implying – a fisherman with a low self-assessment demands lower wages for dangerous work, lowering their market value in exchange for the opportunity to work. Why are preferences the only strong driver of value, though? Surely a healthy, productive fisherman is eminently more valuable than a coma victim, right?

  7. I think fishermen know the risks of their profession more intimately than the couch potatoes watching them on TV.

    “Surely a healthy, productive fisherman is eminently more valuable than a coma victim, right?” I don’t think this is obvious, but if you believed in this sense of “value” you’d use lifetime income as your measure I’d think. That measure is bad because we tend to think there’s more value to life than money income. The best measure would take all the non-money measures of that value into account.

    This makes me think, though, that maybe the problem people have with VSL is that its a measured in dollars. Maybe if we measured it in gallons of water or calories or some other “essential” good it would make people feel better about it.

    If you’re interested the VSL is between 4 to 9 million gallons of water (about 1 to 3 seconds of flow from the Mississippi river) or 3.5 to 8 billion calories of corn meal (about the yield of 250 acres of corn fields).

  8. On said TV show, they usually list the pay. The wages look comparable to what a decent attorney can make, at much, much higher risk. Surely they would be better off going to law school, unless the job compensates them in other ways.

    I’m not sure how a fisherman isn’t more valuable than someone in a coma using any metric. Dollars, euros, gold, liquor, waffles, quatloos, rollover minutes, whatever. One pulls tasty meat out of the ocean. The other *is* meat. Projected lifetime income: $0. Cultural output: 0. That doesn’t even account for any of the resources spent keeping them watered and fed.

    I think the dollar figure worries people because it implies that a decision maker might choose property over human life. I don’t think this tends to be a problem, in the West.

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