Reconciling the human capital and willingness-to-pay approaches to the value of a statistical life

There are various different approaches to measuring the value of a statistical life (VSL). As I discussed briefly in this 2019 post on the economics of landmine clearance, there are shortcomings associated with the human capital approach, which relies on estimating VSL based on the total value of output that an average person would produce over their lifetime. In my ECONS102 class, I teach that the willingness-to-pay approach, is better because it accounts for the life's worth beyond its value in labour or production. The willingness-to-pay approach essentially works out what people are willing to give up to avoid a small difference in the probability of death, and scales that up to work out what people would be willing to give up to avoid a 100 percent reduction in the probability of death.

Now, it turns out that my characterisation of these two approaches as different ways of measuring the same underlying concept (the VSL) needs some reconsideration. This new article by Julien Hugonnier (École Polytechnique Fédérale de Lausanne), Florian Pelgrin (EDHEC Business School), and Pascal St-Amour (University of Lausanne), published in The Economic Journal (ungated earlier version here) explains why. Much of the article is quite theoretical, so not for the faint of heart. However, Hugonnier et al. provide a great summary in the introduction (as well as thoroughly explaining throughout the article). Essentially, they look at three different valuations of life: the human capital value (HK), the VSL estimated using the willingness-to-pay approach, and the gunpoint value (GPV). They explain how these are related as:

An agent’s willingness to pay (WTP) or to accept (WTA) compensation for changes in death risk exposure is a key ingredient for life valuation. Indeed, a shadow price of a life can be deduced through the individual marginal rate of substitution (MRS) between mortality and wealth. In the same vein, a collective MRS between life and wealth relies on the value of a statistical life (VSL) literature to calculate the societal WTP to save an unidentified (i.e., statistical) life. The VSL’s domain of application relates to public health and safety decisions benefiting unidentified persons. In contrast, the human capital (HK) life value relies on asset pricing theory to compute the present value of an identified person’s cash flows corresponding to his... labour income, net of the measurable investment expenses. HK values are used for valuing a given life, such as in wrongful death litigation... or in measuring the economic costs of armed conflict... Finally, a gunpoint value of life (GPV) measures the maximal amount a person is willing to pay to avoid certain, instantaneous death. The GPV is theoretically relevant for end-of-life (e.g., terminal care) settings, yet, to the best of our knowledge, no empirical evaluation of the gunpoint life value exists...

So, it turns out that, while I have previously treated the VSL and HK measures as substitutes (and taught them as such):

...different life valuation methods are not substitutes, but rather complements to one another. Which of these four instruments should be relied on depends on the questions to be addressed.

It's clearly time for a bit of a re-think of how I approach the teaching of those concepts. Hugonnier et al. develop their theoretical model (which, I'm not going to lie, is heavy going), and then apply it to data on nearly 8000 people from the 2017 wave of the Panel Study of Income Dynamics (PSID). They develop a structural model (partially estimated econometrically, and partially calibrated) for people at different levels of health. They find that:

The HK value of life... [ranges] from $206,000 (poor health) to $358,000 (excellent health), with a mean value of $300,000...

The VSL mean value is $4.98 million, with valuations ranging between $1.13 million and $12.92 million...

The mean GPV is $251,000 and the estimates are increasing in both health and wealth and range between $57,000 and $651,000. The gunpoint is thus of similar magnitude to the HK value of life and both are much lower than the VSL.

Nothing unsurprising there. We know from past research (including my own, see here or here, or ungated here or here) that the HK value is much lower than the VSL value (to use Hugonnier et al.'s terms). The VSL measure is in line with the literature (as outlined in yesterday's post). The GPV is new, but people will be seriously constrained in what they can actually pay when facing certain, instantaneous death, which helps explain why it is so much lower than VSL. Now, as Hugonnier et al. noted, these different values are complementary and have different uses. They illustrate using the case of the coronavirus pandemic:

The first policy question is whether the substantial public resources allocated to vaccine development and distribution as well as in compensation for financial losses linked to shutdowns are economically justifiable on the basis of lives saved by the intervention. Our VSL estimate computes the societal willingness to pay for a mortality reduction of an unidentified person and is therefore appropriate for the relevance of public spending...

Consider next the case where an infected person j’s health deteriorates and is admitted to the intensive care unit (ICU). If access to life support in the ICU is constrained, our GPV measure calculates person j’s valuation of their own life and can be used to decide whether or not terminal care should be maintained or reallocated. If instead j dies as a result of COVID, both our HK and GPV values can be used by courts in litigation against the state, care provider, employer or other agents for insufficient intervention, malpractice or negligence.

So, in a policy context the VSL is the appropriate measure, but in the case of compensation for an identified life, the HK or GPV is more appropriate. This is where things get a little interesting though, because that implies that the value of statistical life is much higher than the value of an identified life. We know this to be untrue. The 2005 Nobel Prize winner Thomas Schelling observed a paradox wherein communities were willing to spend millions of dollars to save the life of a known victim (e.g. someone trapped in a mine), while at the same time being unwilling to spend a few hundred thousand dollars on highway improvements that would save on average one life each year. The value of an identified life is actually greater than the value of a statistical life. Hugonnier et al. don't engage with that paradox at all, so leave a serious policy problem unanswered. Nevertheless, this is an important article, and I will be changing my future teaching of the related concepts to highlight the different use cases of these measures better.