From: cave@cis.rand.org (Jonathan Cave)
Newsgroups: sci.econ
Subject: Re: Value of Life
Date: 1 Sep 92 17:35:07 GMT
Reply-To: cave@cis.rand.org (Jonathan Cave)
Organization: RAND, Santa Monica CA


The neoclassical approach bases valuation on lifetime consumption
optimization.  The "value of life" is largely meaningless (cf e.g. Broome).
Valuing risk increases or reductions is not only useful but, as several
posters have pointed out, inevitable.

There are many technical issues confounding the process, but essentially it
works like this:

For a reduction in "objective risk" -- climber's term for stuff that one
cannot control, the procedure is as follows:

let V(L,I) = PDV of maximized lifetime utility with life-table
(age-specific conditional survival rates) L and income I.

The willingness-to-pay for a change from L to L' is defined implicitly by

	V(L,I) = V(L',I-WTP)

The willingness-to-accept (money in lieu of the change) is defined by:

	V(L,I+WTA) = V(L',I)

Among the issues:

WTP generally differs from WTA - just like the compensating and equivalent
variations or varieties of price indices, there is no good sense of a
"true" measure.

The change from L to L' may be complex: increases in risk at some ages,
decreases at others.  To pass from WTP or WTA for a specific change to a
"value of life" or even "value of 1% decrease in probability of death"
measure is impossible or potentially inconsistent.

Most studies show that WTA/P is not linear in probabilities, even
*subjective* risk.

WTA/P is far different from "ability to pay" - cf this morning's NPR
discussion of "free-market environmentalism."

Empirical studies show a wide range of values, reflecting differences
between perceived and real probabilities, "dread" and quality-of-life
factors, state-dependant utilities and violations of the independance or
betweenness axioms, etc. etc.

Even when risks are really objective and expected utility follows von
Neumann- Morgenstern, there may be problems with the lifetime utility
optimization.  For one thing, the optimization depends on reallocations of
resources over time.  This depends on markets, and (implicitly) on
market's evaluation of the risks.  So probabilities must also be common
knowledge (which they *never* are).

More seriously, the dynamic optimization problem depends on the rate at
which the future is discounted.  While the "normal", "psychological" or
"financial" discounting may occur at a constant exponential rate, the
"mortality discounting" almost certainly does not.  Since even conditional
survival probabilities vary with age, the standard solution to the lifetime
optimization problem is almost surely *not* time-consistent.  This means
that there are reallocations away from the "optimal" plan that can make the
individual better off at *all* ages.  Thus the WTA/P of the individual
today has no normative significance as a measure of the WTA/P of his
"future selves."  But usually it is the future selves who are affected by
the change!

Of course, there is a time-consistent solution to the optimization problem,
computed by backwards induction.  But if individuals do not follow this
solution, it is of limited utility for policy making.

There are similar problems with probabilities.  If the multiple-decrement
mortality process has a complex structure, it may be hard to understand the
implcations of change.  For instance, while heart attacks (broadly defined)
account for more than half of the deaths in middle-aged males, eliminating
them entirely would only extend life expectatncies by 1-2 years.

This approach only takes account of consumption decisions.  If risks are
affected by individual actions, the difficulties increase.  Without
constant exponential discounting *and* strong independance assumptions, the
Gittens-Jones theorem on the existence of optimal strategies that can be
computed locally (via the so-called Gittens index, which is a
generalization of the dynamic-programming "value" function given above)
cannot be used, and optimal strategies may be *very* hard to compute or
may even (under admittedly weird conditions) fail to exist.

It also ignores WTA/P for risks to others, and the distinction between
different risk distributions.  For example, there is a big difference
between a 10% chance of death for a group of 100 people that may entail:

a) certain death for 10 named individuals;
b) certain death for precisely 10 individuals chosen at random;
c) an independant and identically-distributed 10% chance of death for
*each* individual;

and so on.

There are other approaches as well.  One can look at data on individual
choices and infer WTA/P from them.  If you look at wage premia, you get
very small numbers (like the "human capital" approach which values an
individual's life to his employers, or workman's comp figures).  In part,
this reflects adverse selection: individuals choosing such jobs may have
abnormally high risk tolerance, may be systematically deluded, may discount
the future quite steeply, etc.  Alternatively, they may be attracted by the
risk, as studies of crack dealers consistently indicate.  On the other
hand, if one infers WTA/P from consumption decisions (e.g. price
differentials between commercial and organic produce, controlled for
appearance, taste, nutritional value, etc.) one gets much bigger numbers;
like 4 orders of magnitude bigger.

The other major approach is contingent valuation, that uses individual (or
sometimes collective - cf "Delphi methods") surveys to elicit risk
valuations.  They have lots of pitfalls as well -- but bandwidth forbids a
discussion here.

A few other comments:

The ability to act, even ineffectively, greatly increases risk tolerance.
A few years back, there was a big TCE spill in East LA groundwater.  After
several false starts (notifying people in English, or in writing, when
those media were ineffective), the affected residents of the affected
(poor, hispanic-speaking, largely illiterate) neighbourhoods were notified
of the problem.  Well, so what?  For the most part, they could not afford
bottled water to drink, let alone to bathe in (skin and inhalation
absorbtion of short-chain hydrocarbons and their halogenated cousins being
a major route of contamination).  Thus, at the individual level, the
information simply lowered people's utility, and in a neoclassical world
they would have been willing (though unable) to pay *not* to be informed.
Collectively, it might be a different matter; the information might
mobilize them politically to seek a (gasp) non-market solution.  But the
odds are heavily against it.  Well, who is going to decide what information
to provide, and to whom?

Back to the original point for one last comment.  The "apples and oranges"
nature of money-risk comparisons is pervasive.  If individuals do not
behave as single "rational" decisionmakers (see above time-consistency
point), there is no certainty that those who decide on behalf of others
either can or should maximize a "virtual" utility function -- anyway, this
is only defined if optimality prevails.  This is precisely like standard
general equilibrium stuff: unless commodity distribution is optimal, the
"collective" or "virtual" MRS is undefined -- and WTA/P is just another
measure of the MRS - in fact, the demand curve is (absent income effects)
the marginal WTP curve.

Personally, I don't think it matters much whether the person who chooses on
behalf of others is a government official (boo, right libertarians?) or an
official of a for-profit corporation (like the Ford folks conducting
cost-benefit studies of the consequences of fixing Pinto fuel tanks).  The
same principles/difficulties apply.  The bottom line; valuations will be
made, and will be made badly.  The best we can do is to make those who
decide aware of the limitations of what they do, and experiment with
"better" (not optimal) ways of doing it.  One can see big differences in
national styles in this respect.  In Britain, both the science and the the
utilities are largely left to government.  In Germany, the science is left
to scientists, but the social aspects are the subject of public debate.  In
the US, we debate both the utility and the probabilities (the science).
This may build or destroy concensus, and individual reactions to
information or collective policy decisions may be good or bad.  The one
thing we can say is that leaving things alone is probably a bad idea- if
some aspects of a decision are easily quantifiable (like costs or profits)
and others are not (risks to life & health, risks to one person vs another,
etc.), guess which factors will control the decision?