An Ageless Hypothetical: Horpedahl’s Critique

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.