H. Spencer Banzhaf, The Cold-War Origins of the Value of Statistical Life (VSL), Part III
Thomas Schelling (b. 1921) is a Nobel-prize winning economist famous for his work on cold war
strategy and conflict.[14] Schelling received his BA from Berkeley in 1944 and his PhD from
Harvard in 1951. During the last years of the war he served in the fiscal division at the Bureau
of the Budget under Harvard economist Arthur Smithies, an advisor to many second-generation
architects of applied welfare economics. Schelling joined RAND as an adjunct fellow in 1956,
spent the summer of 1957 there followed by a whole year during 1958-59 with Hitch as his host,
a year which he recalled as the most productive in his career (Breit and Hirsch 2007). He also
had direct connections to the Pentagon, working with it in the early 1960s to construct war
games and advising on the Vietnam conflict (Sent 2007). In other words, Schelling joined
RAND a few years after the debacle of the strategic bombing analysis, and visited with Hitch
during years when Hitch continued to reflect on the criterion problem and continued to illustrate
it with the formative example of valuing the lives of airplane crews.
Jack Carlson (1933 - 1992) was a former Air Force fighter pilot who completed his dissertation,
entitled "The Value of Life Saving," in 1963 under Schelling and Smithies. After first
beginning his academic career at the Air Force Academy, Carlson went on to a career in government--
in the Council for Economic Advisors, the Office of Management and Budget, and as
an assistant secretary of the interior--then as head of the National Association of Realtors.
Whether the idea to address the question of valuing life saving first came to Carlson and Schelling
via RAND or via Carlson's experience in the Air Force is not clear, though to the best of
Schelling's recollection the idea for the dissertation topic was Carlson's.[15] What is clear is that
the issue had been one of considerable policy relevance to the USAF for some time.
At the time Carlson and Schelling were turning their attention to the problem, seemingly
the only approach to valuation of life was the human capital approach, in which a person's life
was valued by either his gross earnings or his net earnings after subtracting personal consumption.
The approach was used by the courts and some economists (e.g. Weisbrod 1961), but on
the whole economists in the 1960s seemed to feel it was inappropriate for valuing a life. Human
capital might reflect the material contribution of a person to the market economy, but evidently
ignored his non-market contributions, not to mention his own valuation of his life. (Is a retiree
of no value to society? Or a homemaker? Do their own feelings count?) How to overcome this
problem was not clear however.
Nevertheless, economic elements were recognized. Most importantly, both public and
private investments in life-saving have associated opportunity costs. Consequently, there are
trade-offs to be made, and therefore economic choices (Fromm 1965, Spengler 1968, Weisbrod
1961).
But if economists were clear on the idea that there were choices to be made, they were
less so on what the precise nature of that choice was and who was making it. A number of
economists recognized that individuals make tradeoffs between risks and money (e.g. Fromm
1965, Mushkin 1962).16 Reading back in light of Schelling (1968) and the subsequent literature,
it is tempting to view that work as a proto-VSL literature. Until Schelling's essay, however,
there was no clear connection between those individual's tradeoffs over risks and the apparent
policy-relevant question of the value of lives. To illustrate the point, consider an applied problem
like measuring the benefits of a highway safety improvement. It is entirely natural to approach
that problem by asking what the effect would be of the policy, and to proceed by answering
that it would save x lives, perhaps with some confidence interval around x. The next logical
question would be, what is the value of those lives? How individual values for risks came into it
was by no means obvious.
The issue was also tied up with evolving views during the period about the relative roles
of consumer sovereignty and political or social sovereignty (Banzhaf 2009, 2011). Though
economists could agree that there were tradeoffs to be made, they were not of one mind about
who was making those tradeoffs. For private goods, it was clear that it was the individual. For
public questions about national defense, public safety, clean air and water, or the distribution of
income, that was not so clear. Some economists felt consumers should be sovereign and that
their values for these things should be aggregated up to a social value. From this perspective,
benefit-cost analysis could be used to judge or evaluate public policies.
Others felt these were inherently social questions that only the political process could answer.
Consequently, political representatives were sovereign and it was their willingness to trade
off among these goods that counted for benefit-cost analysis. From this perspective, benefit-cost
analysis could be used to inform decision making. First, economists could present the political
authorities with an efficient frontier. Once those authorities revealed their willingness to trade
off lives for other goods, in later phases those "exchange ratios," as Alchian et al. had put it,
could be built into the design.[17] This latter view seemed especially compelling in the case of
human lives. No individual would be willing to trade his own life for other social goods. But
because that was the relevant policy choice, apparently society had to make the choice as a moral
matter. Wrestling with this dilemma, the literature in the 1950s and 60s was quite vague about
whose values were at stake (e.g. Fromm 1965, Mushkin 1962, Valavanis 1958, Weisbrod 1961).
All these issues can be seen in Carlson's dissertation (1963). Life saving, he said, is an
economic activity because it uses scarce resources. For example, he noted that the construction
of certain dams resulted in a net loss of lives (more than ever were expected to be saved from
flood control), but apparently, in proceeding with the projects, the public authorities revealed that
they viewed those costs as justified by the benefit of increased hydroelectric power and irrigated
land. There are choices to be made, and those choices do not necessarily maximize safety, but a
broader objective. In considering how to evaluate those tradeoffs in formal benefit-cost analysis,
Carlson considered the human capital approach to be "usable as a first approximation" (86) but
as falling short of the full contributions of a person to society. A better approach was to find
people making actual choices that revealed their willingness to trade lives for other social goods.
Not surprisingly given his own career and Schelling's RAND connections, Carlson considered
choices about life-saving entirely within the context of USAF applications. Taking the
approach Hirshleifer had outlined ten years earlier, Carlson considered the USAF's willingness to
trade off costs and machines to save men. He considered two specific applications. One was a
study of the USAF's recommended emergency procedures when pilots lost control of the artificial
"feel" in their flight control systems. The USAF manual provided guidance on when to eject
and when to attempt to land the aircraft, procedures which were expected to save the lives of
some pilots at the cost of increasing the number of aircraft that would be lost. This approach
yielded a lower bound on the value of life of $270k, which Carlson concluded was easily justified
by the human capital cost of training pilots. (Note this is an estimate of the lower bound, as
the USAF revealed, in making the investment, that lives were worth at least that much.) Similarly,
Carlson's other approach was a study of the B-58 capsule ejection system. The USAF had
initially estimated that it would cost $80m to design an ejection system for the bomber. Assuming
a range of typical cost over-runs and annual costs for maintenance and depreciation, and
assuming 1-3 lives would be saved by the system annually, Carlson estimated that in making the
investment the USAF revealed its "money valuation of pilots' lives" to be at least $1.17m to
$9.0m (92). (Though this was much higher than the other estimate, as two lower bounds they
were not inconsistent.)
Why were these values seemingly so high? One reason (among others) was that "valuation
placed on a pilot's life must be more closely tied to the decision-makers involved," which
here were the commanders of the USAF, "and must include their criteria and preferences" (105).
Carlson pointed out that in the USAF important decision makers like General Lemay were often
former pilots, who identified with the individuals affected. Additionally, he noted that some of
the value might not have been for the lives per se, but for the implicit message the investments
sent to air crews that they were highly valued, a message that might boost morale.
Importantly, in both applications just considered, Carlson took the public perspective: it
was a matter of either the government generally, or the USAF specifically, to make tradeoffs
between lives and equipment.18 Recall this was the perspective also taken by Hirshleifer and
Alchian et al. at RAND a decade earlier. This perspective is particularly natural for military
applications. Somebody like General Lemay would certainly factor casualty rates into his decision
making, but he would hardly weight those casualties by the preferences of his men. It
would be his decision to make based on his own willingness to trade off damage to the enemy for
lives. Again, I emphasize "lives" here because from the standpoint of the public agency, the
outcome is the number of lives saved in the aggregate population, not risks. Consequently, it
was perfectly natural for Carlson to call these estimates the value of "life saving" or the "value of
human life" (89, 96) and even the "costs and benefits…of preserving a particular life or lives"
(1).
Interestingly, however, Carlson had earlier in his dissertation briefly considered the case
of hazardous duty pay, in which an individual reveals information about his willingness to accept
added on-the-job risk for a compensating increment to income. Here, the decision maker was
not a public agency, but an individual choosing a job. Carlson gave examples from the private
sector as well as volunteer positions in the military. For example, he figured that a pilot willingly
increases his annual risk of dying (during peace time) by 0.00232 to 0.00464 percentage
points, for some $2,280 of increased pay. [19] If he followed the methodology he had used when
considering the public choice applications, he might have divided $2,280 by those risks to estimate
a per-life value of $491k to $983k. Tellingly, Carlson did not do so in this case: he left it
as $2,280 as the willingness to accept for that range of risks. The crucial (albeit implicit) distinction
here appears to be the individual perspective versus the social perspective. For the individual
as a decision maker it was a matter of evaluating risk—and only risk, so there was no point in
aggregating up to per-life values. In contrast, when the public agency was the decision maker, it
was a matter of the realizations of the individuals' risks aggregated over the group (expected
lives), hence it made sense to convert the values to dollars per life.
Taking up the subject himself five years after his student, Schelling's crucial move was to
finesse this distinction. At the outset of his essay, Schelling wanted to make clear that he was by
no means tackling the question of the "worth of human life" itself. That question, he suggested,
was rightfully tied up in moral questions and was too "awesome" for the economist to even begin
to address. Rather, Schelling made clear that his more modest objective was to value the postponement
of deaths; and not the death of a particular, known person, but "statistical death."
"What is it worth," he asked, to reduce the frequency of death—the statistical probability of
death?" (127).
After defining the question in these terms, Schelling next asks, "Worth to whom?" Now,
Schelling was clearly addressing the problem of evaluating public investments (indeed, his was
part of a conference and book volume dedicated to this topic). Although writing solely about
public investments, he took the view that those public investments should be evaluated in terms
of the private worth they had to the individuals who would be affected: "Worth to whom? …I
shall propose that it is to the people who may die" (127).
Elaborating on this point, Schelling addressed the oft-articulated view that life and death are moral—or at least intangible—matters that cannot be priced:
"For a variety of reasons it is beyond the competence of the economist to assign objective values to the losses suffered under [pain, fear, and suffering]."[20] The same is true of cola and Novocain…. If they were not for sale it would be beyond our competence, as economists, to put an objective value on them, at least until we took the trouble to ask people. Death is indeed different from most consumer events, and its avoidance different from most commodities….. But people have been dying for as long as they have been living; and where life and death are concerned we are all consumers. We nearly all want our lives extended and are probably willing to pay for it. It is worth while to remind ourselves that the people whose lives may be saved should have something to say about the value of the enterprise and that we analysts, however detached, are not immortal ourselves. (128-129)
In other words, consumers' sovereignty must reign when evaluating public investments: it is
their preferences which count, not the preferences of public officials. [21] Because it was recognized
that individuals do make choices over risk, once consumer sovereignty was embraced it
became possible to look to choices over risk as the basis of social values. These exchange ratios
can be observed, Schelling suggested, from either the price system itself or through surveys
(142-143), both methods that were followed up on in the coming years (e.g. Thaler and Rosen
1976, Jones-Lee 1976). While public policies would still have the effect of costing or saving
lives in the population, from the individual's perspective, these effects were measured as risks,
and that was what mattered for valuation.
