Interpersonal factors in the valuation of statistical lives
By
Jon Strand
Department of Economics
University of Oslo
Box 1095, Blindern, 0317 Oslo, Norway
jon.strand@econ.uio.no
August 2003
1
Abstract
This paper discusses various interpersonal factors with implications for valuation of
statistical lives (VSL). We argue that such factors are important and that a valuation
principle whereby risk changes are elicited on a purely individualistic basis may
seriously bias VSL valuation. Risk-focussed altruism and purely selfish motivations
for the survival of others, in particular close family members, are likely to be
important sources of such bias. Financial and allocation effects associated with the
death of a spouse will also change VSL valuation, typically in a positive direction.
Externalities related to taxation and the financing of pension schemes tend to bias
individual-based VSL valuation, but only for particular groups and not on the average.
We also discuss individuals’ VSL valuation “on behalf of themselves” and “on behalf
of their households”, and argue that individuals are likely to represent their
households correctly on the average, even when interpersonal valuation factors such
as altruism are unimportant. We conclude that little precise quantitative information
exists about such factors, and that more research is warranted.
2
1. Introduction
In virtually all work to date dealing with valuation of changes in mortality risk (or
the corresponding valuation of statistical life, VSL), the object of valuation is
individuals’ own risk change, as it applies to himself or herself only. Two main
groups of methods, revealed preference (RP) and stated preference (SP) methods,
have both been widely applied in this context. RP studies are typically based on riskmoney or risk-time tradeoffs, in situations involving job or transportation mode
choice or other types of choices involving risk. This approach is individualistic in the
sense that it precludes valuation motives other than those arising directly from the
individual who is subject to valuation. In recent years stated preference (SP) studies,
whereby samples of individuals are surveyed about their value of (usually their
willingness to pay, WTP, for) particular risk changes, have however gained
predominance in the area of VSL valuation. A great advantage of SP studies over RP
studies is much greater flexibility in terms of objects to be valued, and motivations for
expressing value. The dominant approach is here the contingent valuation (CV)
method, where individuals are asked to state their WTP for particular risk changes
directly. Despite their much greater principal flexibility, SP studies of VSL are still
typically done by surveying individuals about their WTP for specified changes in risk
for themselves only, cf. e.g. Johannesson et.al. (1995), Beattie et. al. (1998), Corso,
Hammitt and Graham (2000), Alberini et al (2002a, 2002b). Note also that most
recent theoretical literature on principles behind VSL valuation uses an individualistic
approach, cf. Johansson (1994, 2001, 2002).
The purpose of this paper is to question this focus and present examples of cases
and situations where interpersonal factors are important or even decisive in VSL
valuation. I then also question the current focus in the empirical and theoretical VSL
3
literature, on several grounds. First, perhaps most obviously (and most recognized),
altruism is likely to be important for the value of those general mortality risk
reductions that follow from public projects to reduce overall risks in society. But other
reasons, less recognized in the literature, are also often important. This applies to both
motivations for valuation, and what or whom are the objects of valuation. When
considering interpersonal motivations apart from altruism, purely selfish preferences
may be attached to the survival of others whose survival probabilities are affected by
such projects, most noticeably ones children and spouse. On second thought (or
introspection) this is an obvious point, but it seems to have been lost in the academic
debate over how to treat altruism. Another, almost equally obvious, point is that the
survival of others (in particular ones close family) may affect ones future
consumption possibilities, negatively or positively, which in turn affects the
individual’s WTP for survival of other family members. A further related factor is that
externalities are often imposed on society as a whole (or what might here be denoted
“other individuals than those belonging to ones close family”), when the expected
lifetime of a given person is extended. This, I argue below, biases VSL when derived
from the individuals’ own statements about WTP for extending his or her lifetime.
Inter-personal issues also raise a separate set of issues for the valuation of public
projects affecting overall mortality rates in society. When an individual is surveyed
about his or her WTP for such a project, this individual may be required to answer
“on behalf of himself or herself”, or alternatively “on behalf of his or her household”.
It has then often been viewed as unclear whether valuation ought to be viewed as
conducted individually by one family member (spouse), or jointly by one member
valuing the relevant project “on behalf of” the household. In principle it may matter
greatly which of these alternatives is used. Still the theoretical and empirical
4
literatures are both virtually silent on the issue. I take the issue up below, when
discussing of two of my papers, Strand (2002b) and Strand (2003).
2. Altruism and VSL valuation
Among intra-personal issues and their implication for VSL valuation, altruism is
probably issue most studied and recognized in the literature, and several theoretical
papers (Bergstrom (1982), Johansson (1994), Jones-Lee (1991, 1992), Quiggin
(1998)) have dealt with the topic. The consensus is that altruism is an important basic
feature of VSL elicitation, but that its quantitative importance depends greatly on
what form altruism takes. The most important distinction is here between nonpaternalistic (or “pure”) altruism, and paternalistic altruism. Pure altruism implies that
any one individual “respects the preferences of others” in the sense that another
person’s utility level matters for a given respondent’s evaluation of the altruistic
effect. “Paternalistic” altruism is different and implies that a given surveyed
individual has preferences for some particular feature of the other person’s preference
structure. In the VSL context the most relevant such feature is survival over time
(equivalent to the consumption of some mortality-reducing public good). A main
result, derived by Bergstrom (1982) and discussed in a more concrete valuation
context by Milgrom (1993) and by Johansson (1994), is that altruism ought to have no
influence on average VSL valuation under pure altruism. This result was viewed as
surprising when first publicized (see e.g. the discussion in Jones-Lee (1992)). The
reason for the result is that pure altruism, essentially, leads to a proportional increase
in the value of all goods, as viewed by the valuing (and altruistic) individual. The
marginal rates of substitution between different goods (hereunder VSL) is left
unaltered by greater pure altruism, implying that VSL valuation is left unaltered.
5
Johansson (1994) considers a case where a set of respondents are surveyed about their
WTP for a project which reduces general mortality risk, where each respondent is
told that all other individuals except himself or herself are required to make monetary
payments equal to true WTP for the project, thus leaving these other individuals at
their initial utility levels. Under such circumstances the positive effects of the project
on other individuals are exactly eliminated. If respondents then exhibit “pure” (or
utility-focused) altruism, the altruistic motivation for WTP disappears and one is left
with only the individual’s own valuation of his own risk change.
The alternative case of paternalistic altruism usually implies that respondents are
concerned with the survival, and not the consumption, of other individuals. It can then
be shown (by Jones-Lee (1991, 1992) and others; see also Strand (2002a)) that
increased altruism leads to higher VSL valuation, i.e., life-prolonging projects are
given higher relative value when traded off against other goods. The reason is that
greater degree of altruism now alters respondents’ marginal rates of substitution
between the safety-focused good versus other goods, thus increasing their “true” WTP
for safety (in terms of other goods).
In most of the subsequent VSL literature, altruism has been assumed (in most
work, tacitly) to actually take a pure form, which in case implies that inter-personal
issues can be ignored. In my opinion this is a questionable approach, as altruism is
instead likely to take, at least partly, a paternalistic form of preference for higher
survival rates of others. This is admittedly a poorly researched area where more direct
knowledge is sorely needed. Preferences motivated by paternalistic altruism are also
easily confounded with egoistic preferences as motivation for VSL valuation
discussed below, which are also likely to be important.
6
To be more specific, in relationships between household members it seems clear
that paternalism typically plays a significant role. For one thing, many or most adults
exhibit paternalism by not automatically taking other household members’
preferences as given but instead attempt to affect them. For another, the very survival
(or the expected future lifetimes) of other family members is likely to be preeminently
important (more so, I will claim, than their particular consumption interests and
preferences). Thirdly, paternalism is of course a crucially important aspect of parents’
relationship with their children. The survival and future success and development of
ones children will typically have precedence over any consumption or consumption
pattern children themselves may desire. To this must be added that many of the things
that we as parents teach our children are just ways of improving their effective
survival (such as good eating habits, often at odds with childrens’ own immediate
desires, learning to master physical and social skills, and to avoid dangerous types of
activity). Altruism toward ones children is thus likely to take a strongly paternalistic
form whereby increased survival probability is strongly favored. But also in the
relationship with ones spouse one is likely to apply different types of pressure to
impose ones own values and preferences on the partner, implying that whatever
concern for the partner takes at least partly an altruistic form. This may apply to
friends as well, although in most cases in a less strong degree. Examples of
paternalistic concerns for ones spouse and close friends abound: one is e.g. likely to
argue in favor of quitting smoking, drinking or overeating, when faced with problem
smokers, drinkers or overeaters, and thus often clash with the immediate preferences
of partner and friends.
Note that the discussion here about the principal nature of altruism, is essentially
independent of the strength (or weakness) of the altruistic preference for others,
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relative to the direct (selfish) preference for oneself. Thus if, say, a particular
individual has paternalistically motivated altruistic WTP for a given increase in
survival probability of one particular other individual, which is equal to 1/10 of the
WTP for the same increase for himself or herself, this is paternalistic altruism,
although of a weaker form than that exhibited toward the self.
3. Egoistic inter-personal preferences and VSL valuation
Individuals may have purely selfish preferences for the survival of others,
something that is conceptually different from altruism. This point is obvious upon
introspection, but has played little role in the research on VSL valuation. The
overwhelming majority of individuals have a strong positive preference for their
spouse and children to survive over a given future period, as least as long as oneself is
alive. This may be related to altruism but can alternatively, and with equal
plausibility, be viewed as an individualistic value attached to the presence of others.1
A question is then whether such a distinction is interesting for the purpose of VSL
valuation. Observationally these two motivations are difficult to distinguish with the
use of WTP studies, or may even be conceptually indistinguishable for individuals
themselves. I know of no study to date that has attempted to make the distinction
empirically. It is probably also difficult to formulate CV questions that will contribute
toward this separation. In my opinion the distinction is still important, for principal
reasons. One such reason is that it may contribute toward a better understanding of the
more specific motivations behind VSL valuation, in a family context. Selfishly
motivated value attached to others’ survival is likely to take forms that directly benefit
1
Note in this regard that when individuals have positive preference for the survival of other family
members in states where oneself is dead, this preference must be motivated by altruism and cannot be
selfish; see Strand (2003) for more discussion.
8
the valuing person, in particular the company and presence of the other persons, and
less their consumption. Jones-Lee (1991) argues, albeit only heuristically, that
altruism exhibited toward ones nearest family is likely to be of a “pure” form and less
survival-specific. Since selfishly motivated valuation in this context is likely to take a
much more survival-specific form, more selfish and less altruistic concern for other
family members is likely to change the relative overall valuation attached to others (in
particular other family members) in a more survival-specific direction. Information on
the “degree of selfishness” in the expression of concern for others will then at the
same time help us to better understand whether such concern largely takes a “pure” or
a “paternalistic” form.
4. Pecuniary and real inter-personal effects
with implications for VSL valuation
An issue in VSL valuation that concerns interpersonal relationships but is unrelated
to either the altruistic or selfish motivations discussed so far, is that the survival or not
of a particular household member typically has (immediate or future) pecuniary and
real allocation effects for the remaining members, hereunder the member that
conducts the VSL valuation. These factors are likely to impact on the member’s
expressed VSL valuation. The effects can be either positive or negative, depending on
whether the value of the surviving member’s consumption increases or decreases in
the event that the other member dies. This in turn depends both on the nature of the
intra-family resource allocation mechanism, on the relative incomes of the two
spouses, and on the nature of possible life insurance or inheritance arrangements of
the household. To illustrate the issue, consider a case (as in Strand (2002b, 2003))
where the household consumes two types of goods, namely personal and joint
9
household goods, and where household members allocate their joint family resources
according to an efficient Nash bargaining solution (the plausibility of this model will
be discussed further in section 6 below). Assume then first that there exists no public
or market-based life insurance and that two spouses have equal bargaining powers
(and thus identical amounts of money disposable for purely personal consumption),
while the other spouse has higher (current and future expected) income relative to the
valuing member. Then the consumption of the valuing member will drop when the
other member dies, for two reasons. First, the overall consumption of the surviving
member must drop as that member’s budget is reduced. Secondly, the surviving
member will in effect experience an increase in the price of the joint household good,
as there is no longer anyone else with which to share the cost of this good. The intrahousehold allocation of resources as a result becomes less efficient, as only one
person instead of two enjoys the services from these goods. The reduced income and
increase in the relative price of the common good both tend to reduce the
consumption of the joint good, and reduce the overall value of consumption for the
surviving member, but not necessarily reduce this person’s consumption of the
individual good (as the relative price of this good is reduced). When the incomes of
the two spouses are identical at the outset, the welfare of the surviving member must
then also drop, due to less efficient consumption of the joint good. In all these cases,
such consumption effects increase the WTP for the survival of the other spouse, and
thus also the overall valuation of the public project.
Consider instead an opposite extreme case where the other spouse has no
independent income. Then the valuing family member will always enjoy an increase
in his or her overall consumption budget, and consumption, when the other member
dies (although it is still possible that the surviving member’s consumption of the joint
10
good will be reduced). The partial effect of this factor is then to lower the individual’s
valuation of the public project (since there will be a negative consumption effect from
the other person surviving instead of dying).
As shown in Strand (2003), the impact of this factor for each of the two spouses in
the event that the other dies, is positive on the average. This is due to the more
efficient intra-household allocation of resources when the two spouses live jointly in
one household, versus the case of single-person households. An increase in the
probability of survival for both household members then at the same time increases
the probability, for both of the spouses, of enjoying the economies of scale in the
consumption of common-household goods, due to a joint household.
Assume next that the family has life insurance that serves to maintain members’
overall consumption levels in the event of death of one of the spouses. Then such
pecuniary factors will have no negative effect on the individual’s VSL valuation. Note
however that life insurance schemes rarely have this property. An important point
here is, as shown in Strand (2003), that an efficient life insurance scheme generally
does not compensate fully for the value of lost income when that household members
consume both common-household and individual-specific goods, due to the reduced
efficiency in consumption of the common good resulting from the death of one spouse
(as discussed above). Thus there is likely to be an average pecuniary loss factor also
under efficient life insurance.
Such pecuniary effects can be quantitatively important, and more so the more
important joint household goods are in consumption, relative to purely personal
goods. I have no direct evidence on this distribution (and more research is needed on
this issue), but it seems obvious that joint goods are important.2. Note that the impact
2
To exemplify, the budget shares of average Norwegian households for typical joint goods such as
housing, house maintenance, furniture, appliances and household equipment exceed 35 %. Many other
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of this factor is reduced when there is a positive probability that the surviving spouse
will remarry after the death of the other spouse, as a remarriage (or cohabitation) is
likely to re-establish most of the economies of scale in joint consumption.
5. Externality effects of extended lifetimes
Positive or negative “pecuniary externalities” may result for the rest of society
(apart from the effect on other family members) when a person dies, with implications
for VSL valuation. The nature of these externalities can be illustrated by imagining a
case where all households consist of single persons, all of whom are purely selfish.
Assume then first that the object of VSL valuation is mortality risk over a future
retirement period where the individual who conducts the valuation relies on a fixed
per-period pension income. This is typical for individuals at or close to retirement
age, in countries that rely on pay-as-you-go public pension systems (as most
European countries have today). Under such systems pension payments will typically
be fixed and independent of (individual or aggregate) mortality risks. If the expected
lifetime of a given retiree then increases, this implies a greater expected pension
payment funded through higher taxes on those of working age.
This factor may create a positive difference between the individual’s WPT for
increased survival, and the value that society places on this survival. It is related to the
issue of VSL valuation under complete annuities markets with continuous
renegotiation of competitive life insurance contracts (over future periods where death
risks occur and may be affected); discussed by Breyer and Felder (2002) and by
Strand (2003). A public project leading to increased expected lifetime for a given
individual then invokes renegotiation of the initial life insurance contracts so as to
good may also be largely joint, including vehicles at common disposal, and common vacations and
12
make it more expensive for the individual. This in turn leads the individual to reduce
his or her WTP for this increase in lifetime by the same amount.3
This point is intuitively obvious upon reflection, and its public-finance
implications have recently been subject to considerable analysis, and worry, among
policy makers in Europe, regarding the ability of existing pension systems to support
the rates of future promised pension payments. To my knowledge it seems however
not to have been recognized in the recent VSL literature.4 It may here in a sense be
appropriate to say that the pendulum has swung back completely, from a singular
focus on labor market productivity effects as the basis for VSL valuation back in the
1970s, to an equally complete focus on individualistic value elicitation today.5 The
incorporation of this “externality effect” implies that one instead takes a, more
appropriate, middle ground on this issue.
Note that the possible biases resulting from the ignoring of such effects are very
different for different demographic population groups. For older persons and certain
disadvantaged groups, such as the disabled and individuals with long-term illness, the
externality effects are highly negative (as such groups have low work incomes relative
to pension benefits). The opposite extreme is found for young adult groups of working
entertainment.
3
A perhaps more straightforward way to view this effect is to assume that the individual in question
lives on fixed accumulated financial assets, and keeps running this asset down until death (and
assuming that death does not occur before the asset is exhausted). Increasing the individual’s lifetime
then implies that the bequest left for his or her heirs is reduced, thus creating a negative externality for
heirs. It is here of course possible that the heirs value the individual’s extended lifetime for its own
sake, which may even neutralize or turn around this negative externality. Such valuation by others
should however in any case be added to any valuation by the individual himself or herself, through the
altruistic motivation noted in section 2 above.
4
See e.g. Johansson (2003) who surveys recent VSL literature, hereunder VSL valuation under
complete annuities markets, without mentioning this effect. Note that Rosen (1988) derived
expressions for VSL under complete annuities markets, but also without discussing externalities caused
by pensions.
5
One possible reason for the lack of willingness to incorporate such factors in VSL estimates among
many economists, today, may be an objection to the notion that certain groups are “less valuable” than
others in society; e.g. that a disabled person is “less worthy” than an able-bodied and productive young
adult. This is a highly politicised and perhaps moral issue into which I will not deal further here. My
point is that given that individuals in such groups are “equally much worth” for their own sake or as
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age, where average net after-tax labor incomes are far lower than their productivities
over relevant future periods for mortality risk reduction envisioned in most CV
studies involving VSL. Individuals in this group are subject to often very high rates of
income taxation, and their current average labor productivities greatly exceed their
current labor incomes.6 An additional factor is that young persons are likely to face
increased tax burdens when mortality drops (as there will be more old people to pay
for), reducing their expressed WTP for such projects even further, below their true
VSL values (as the relevant increases in life expectancy for these are likely to come
too far into the future for the effect to be important).
Such factors may help to explain the (for some puzzling) finding in a number of
recent empirical studies, that VSL derived from interview surveys seems to be quite
stable across age groups (even for the very old; see e.g. Alberini et.al. (2002a,b)).7 We
also note that over-valuation of VSL by old individuals, and under-valuation by
young, ought to net out in the population as a whole, leaving average VSL largely
unaffected by such externality factors.
I here in effect call for a slight move back from the current, purely individualistic,
valuation approach, to make room also for labor-market and public-finance
considerations in VSL valuation. One likely implication is to move WTP-based VSL
valuation a few steps closer to the QALY-based currently currently favored within the
viewed by themselves, there are reasons to incorporate the externalities discussed here when arriving at
a correct VSL figure from the standpoint of society.
6
Two additional factors in the labor market draw in the same way. The first is the tendency toward
“front-end loading” of work incomes over workers’ lifetimes whereby wage profiles are upward
sloping relative to productivity profiles (due to a range of moral hazard, adverse selection and other
informational factors; see Lazear (1998) for discussions of various such factors). The second is the fact
that workers generally give rise to profits at the margin via bargaining relationships between firms on
one hand and workers on the other, individual or via unions. In such bargaining relations young
workers typically have lower bargaining power than old and thus give rise to greater profits. See e.g.
Pissarides (2000) for a presentation of the individual bargaining model, and Freeman and Medoff
(1982), for a standard and classical discussion of labor union behavior and implications.
7
Johansson (2003) correctly points out that in cases where individuals’ disposable incomes and
mortality rates are identical and constant, VSL as captured in CV surveys ought to be independent of
14
medical research community; see Hammitt (2002) for a recent comparison of the two
approaches. Under the QALY approach one typically assumes that the “one life year
lost” has a given value (although this value is often not directly quantified), and
embeds an assessment of the expected number of years lost when a person at a
specific age dies. The social value of saving lives at different ages is then directly
proportional to the expected remaining lifetime in the respective age group. As noted
above, under the standard WTP approach this value is typically more or less
independent of the person’s age. Under our modified approach, VSL is likely to
decrease substantially with the subject’s age, but less so than under the QALY
approach. While I do not endorse the QALY approach as such,8 it should serve to
remind us of the weaknesses embedded in the traditional WTP approach, and which
are noted here.
6. Individual versus household VSL valuation
with general mortality reductions
I will now address another type of issue involving interpersonal factors, namely
how to derive estimates of VSL from CV surveys designed to value public projects
with implications for general mortality. CV questions designed to elicit preferences
for general mortality reductions are typically phrased in the following two alternative
ways: 1. How much are you, personally, willing to pay for a (small) increase in the
quantity of a public good?” or 2. “How much are you willing to pay, on behalf of your
household, for an increase in the quantity of a public good?” Little has however been
age. What is here not fully recognized is that relying on pensions instead of work income reduces
“true” VSL for retirees.
8
One weakness of the QALY approach is that it typically gives no room for discounting. Another
weakness is that it relies overly much on “benefit transfer” principles and not on specific valuation in
the individual case. The value of a life year lost, whenever used at all, would typically be found not
15
done to explore the principal relationships between individual and household
payments in this context. Although not clearly stated, the underlying presumption in
the literature seems to be that when individuals are asked to state WTP “on behalf of
their household”, they may attempt to incorporate other household members’
preferences in their answers, in which case such inclusion is “altruistically”
motivated. The only previous paper to my knowledge that formalizes this issue is
Quiggin (1998), who considers a simple model with only one type of good purchased
directly by the household, namely a good consumed individually by each household
member. He shows that the individual then represents the household correctly if and
only if he or she has perfect and paternalistically altruistic preferences versus the
other family members (but is not altruistic versus other persons).
In two more recent papers (Strand 2002b and 2003) I have explored the
relationship between the answers to these two questions further, in the context of a
simple two-person household framework. Two fundamental assumptions, already
discussed in section 4 above, are common for both these papers. The first is that
households demand two types of goods, one good consumed individually by each
member, and one good consumed jointly by both. The second assumption is that the
household’s resources are allocated to common and individual-specific goods in an
efficient Nash bargain between the two spouses. I assume that when a person is asked
to express WTP on behalf of himself or herself, the payment is implicitly made in
terms of individually private goods foregone. In contrast, when asked to state WTP on
behalf of the household, I assume that payment is made in terms of the common
household good.
from a direct study of the implied population, but from some other independently established estimate
from outside of the population.
16
The most important result from this model is that an individual’s true WTP on
behalf of the household always in expectation equals the sum of household members’
individual WTP. This holds even with no altruism whatsoever. Individual and
household WTP are exactly equal in individual cases when the two household
members have the same marginal valuation of the pure public good in terms of the
household good, and both have the same bargaining powers in the Nash bargain.
When different family members value the public good differently, a given member
over- (under-) values the public good on behalf of the household when his or her
value is higher (lower) than that of the other member. On average these values are
however correct.
The key to these results lies in the nature of the intra-household resource allocation
assumed in this model. Given an efficient allocation within the household, the
marginal valuation of an individual good will exceed that of a common-household
good, when evaluated by any one of the household members. This leads a given
individual to be willing to give up fewer units of the individual good than of the
common good, in return for a given overall reduction in mortality. The empirical
implication of this is that WTP for a given overall mortality reduction, “on behalf of
oneself” (when the trade-off is with individual goods), is lower than the valuation of
the same mortality reduction “on behalf of the household” (when the trade-off is made
with the household good). As it turns out, the sum of true WTP levels “on behalf of
oneself” equals the average of individuals’ WTP levels“ on behalf of the household”
(these values exactly coincide in individual cases whenever the two individual have
equal bargaining power and equal valuations).
Provided that one accepts the underlying model, these results resolve a longstanding controversy in the valuation literature (generally and with application to VSL
17
valuation): Individuals are here shown to represent their households correctly on the
average in CV surveys, even when altruistic preferences play no role.
Note that this model provides a natural framework for incorporating a problematic
and very important, and so far neglected, aspect of VSL valuation, namely the value
of mortality reductions for children. Concern for ones children typically leads
households to purchase more common-household goods than otherwise, thus driving
the marginal utility of such goods (as viewed by the valuing individual) down further,
relative to personal goods. This will increase an individual’s WTP on behalf of the
household for a given mortality risk reduction, in the sense that he or she is personally
willing to give up more than otherwise of the common good, in return for this
reduction. This can be viewed as incorporating a concern for children in such
valuation. Such a “concern” is here independent of altruism in the normal sense;
paternalistic concern for children’s survival would come in addition to our measure.
In Strand (2002b) the same basic (but here static) model is applied to valuation of a
general public good (formally, survival probabilities are not affected in this model).
The main extension is to incorporate two types of altruism, namely “pure” and
“paternalistic” altruism as defined above. Under “pure” altruism among family
members (where the utility level of each member enters into the utility function of the
other) the average valuation is not increased by altruism. While this is well known
from the work of Bergstrom (1982) and others, one may still find it interesting that the
result reappears in this rather different model. “Pure” altruism however affects the
relative individual valuations on behalf of the household. I find that individual
valuations are closer to true aggregate household valuation (whenever these differ)
with stronger degrees of pure altruism. Under “paternalistic” altruism (where a given
household member cares about the other member’s consumption of the public good
18
but not about other goods) greater altruism by contrast implies that the expressed, and
true, overall valuation of the public good always increases.
The results obtained in these two papers hinge importantly on the assumptions
made about the intra-household allocation of resources. My assumption, that
household consume both individual and joint household goods, may here not be
controversial. In contrast, my assumption about the intra-household allocation
mechanism (efficient Nash bargaining) may be controversial to some. In the literature
there generally exist two different models, in addition to the Nash bargaining model,
for analysing intra-household allocations. These may be termed the “unitary” model
(where the household is viewed as one decision unit), the bargaining model (as
applied here), and the “conflict model” where the spouses are assumed to act noncooperatively. The unitary and bargaining models tend to yield similar results in our
context (in particular since the intra-household allocation will in both cases be
efficient). Under the conflict model results will however be different. Here the joint
good is typically underprovided, and we may even (in a case of no cooperation
whatsoever) have a situation where the marginal consumption values of the common
and private good are identical for any given household member. With no mutual
altruism between the family members (which appears reasonable for conflict
situations), WTP for a mortality-reducing public project for either of the family
members, on behalf of himself or herself, then tends to be the same as the person’s
WTP on behalf of the household. In such cases, obviously, individuals will not
express household WTP correctly on the average in CV surveys.
In my view the conflict model is however less relevant for the purpose of studying
individual behavior “on behalf of the household”, for two different reasons. First,
under the conflict model it is less reasonable to claim that individuals’ purchases of
19
common-household goods are made “on behalf of the household”. Thus a person
living in such a “conflict family”, who is asked about his or her WTP “on behalf of
his or her household”, will be unlikely to view this as equivalent to giving up units of
the common-household good, and will instead probably try to invoke some altruistic
feeling to motivate the answer (whatever such feeling may exist). Secondly and more
importantly, the high degree of interaction between most spouses on a daily basis
makes it quite plausible that a mutually advantageous solution will be chosen over a
conflict solution (even among spouses that are not very happy about each other).9 I
will argue so strongly that if there at all exists any social arena where efficient
bargaining solutions are likely to be reached, it must be within the family. This is not
to deny that family conflicts occur. When serious conflict occurs in some fraction of
households, stated WTP for public projects on behalf of such households should tend
to be too low for such households, with basis in our model framework.
7. The quantitative importance of inter-personal factors
in VSL valuation
I have so far said little about the quantitative and more practical importance of the
above factors for VSL valuation. It is for this purpose useful to restate the main interpersonal factors, from sections 2-5 above. These are:
1. Altruistically motivated valuation
2. Egoistically motivated valuation
3. Inter-personal pecuniary effects
4. Externality effects at the level of society.
9
A substantial amount of empirical evidence has recently been gathered in favor of the household
bargaining model, and in disfavor of the other models. See in particular Browning (2000), Browning
20
Possible distinction between factors 1 and 2 has been addressed at some length above
and will not be discussed further in the following. On the whole these likely to be
quantitatively decisive for the overall interpersonal valuation issue. The quantitative
impacts of factors 3 and 4 on the list above can be assessed by considering various
macro variables. We have argued that factor 4 ought to net out on average across the
population, since VSL is undervalued by the young and overvalued by the old,
arguably in similar degrees. Factor 3, we have argued, does not net out: This yields a
positive net effect due to economies of scale in multi-person households, which
implies that a surviving family member suffers a genuine loss when the spouse is lost
even when preferences are purely selfish. Altruistic or selfish motivations under
points 1-2 are here difficult to distinguish empirically and will be treated together.
Empirical information on the combined effect of factors 1-3 (which all involve
valuation motivated by changed mortality risk for others) may in principle be found
by asking individuals to state different motivations for assigning VSL value to public
projects that serve to reduce general mortality. This approach has been taken by
several researchers, notably Stevens et al (1991), Chilton and Hutchinson (1995),
Sælensminde and Hammer (1994), and in my own empirical study referred to above
(Strand 2002a). I will in the following present some results from my own study.
While we cannot here go through all features of this survey, one key aspect of it was
to ask respondents to split their valuation of a preferred public mortality-reducing
project up according to three different valuation motives: pure self motivation (or
motivation based only on the value of increased expected lifetime for oneself); value
attached to concern for ones own family; and value attached to “other motives”. Such
a splitting up may help to identify “purely self-motivated” and “inter-personally
and Crossley (2001), Chiappori (1988, 1992), Lundberg and Pollack (2001), Lundberg, Startz and
Stillman (2003).
21
motivated” parts of total VSL for the surveyed individuals. The main summary
figures from this question are presented in table 1 below. We here find that as an
overall average across respondents, about 30 % of total VSL was stated to be due to
concerns for ones own life, about 50 % for other family members’ lives, and about 20
% for other persons or motives. In the table there is a further splitting up according to
the cause of death that is affected by the relevant public project, where three possible
causes are specified, namely heart disease, traffic accidents, and environmental
causes. Each individual made the split for one of the causes (corresponding to the
preferred project as derived from a previous question).
From the table, the self-concern fraction was quite stable across death causes.
“Other family members” however have a higher than average share of total value in
the valuation of reduced traffic-accident risk (and lower for environmentally-caused
risk), while “other (altruistic) concerns” have a higher than average share for
environmentally-caused risk. It is unclear what is behind these differences, but one
factor may be that traffic accident risk is more immediately threatening to ones family
(and this factor scored high in particular for families with children), while
environmental factors may be viewed as somewhat more obscure and largely
affecting “others”.
In my opinion these figures strongly indicate a major role for inter-personal
concern in VSL valuation, both across family members and in relation to more distant
persons (we do not have further split ups e.g. by spouse versus children within the
household, or by friends and more distant family versus more anonymous individuals
in the “others” category; note however that even in families with two spouses but
without children the share to “rest of the family” is quite high, about one third on the
average).
22
Some authors (notably Carson et al (1999)) argue that such splitting up is
problematic for cognitive or strategic reasons. First, a splitting up is likely to be
unfamiliar and more so than most other questions in CV studies. Secondly,
respondents may tend to allocate too high shares to the “other than oneself” categories
simply to “appear nice” and thus satisfy an apparent expectation by the interviewer.
As a consequence our results must be considered suggestive. My claim is still that this
study at least points to the possibility that a substantial fraction of the overall value
expressed by individuals in VSL surveys, is due to inter-personal concerns. I also
want to mention that in the debriefing section of the survey respondents were asked
whether or not they felt comfortable with the questions and to what degree they were
easy to answer. Most respondents stated that the splitting-up question was among the
easier ones to answer (although this is by itself no proof that they were in fact easy to
answer). I also wish to point out that two different results, from different parts of our
survey, mutually support each other. While parts 1-2 found a public-good VSL value
of about 6 million USD, part 3 found a purely private-good value of about 1.8 million
USD, i.e., 30 % of the total value or the same as the expressed private share of total
valuation under part 2.
It is still not immediately obvious what these figures tell us about true VSL
valuation. Here a crucial issue is whether inter-person valuation motives are “pure” or
“paternalistic”, and our survey gives no direct information on this issue. If all such
value is of the “pure” type, we are left with only the self-motivated WTP as the true
representation of VSL (barring factors 3 on the list above). If all is paternalistically
motivated and attached to increased survival of others only, true average VSL is
closer to the total valuation expressed in the right-hand column of table 1.
23
Table 1. Relationships between preferred public projects for mortality reduction,
in terms of type of life saved, and payment according to different motivations, as
averages across respondents. Million USD per VSL (assuming an exchange rate
of 7 NOK per USD)..
Death cause
Other altruistic
concerns
Total
0.8 (14 %)
5.2
3.4 (37 %)
3.0 (33 %)
9.1
4.7 (62 %)
0.9 (12 %)
7.6
3.1 (53 %)
1.0 (18 %)
6.0
Concern for own Concern for
Life
other family
members
1.6 (31 %)
2.8 (54 %)
Heart disease
(612 respondents)
Environmental causes 2.7 (30 %)
(162 respondents)
Traffic accidents
2.0 (26 %)
(221 respondents)
Total average (995
1.7 (29 %)
respondents)
.
8. Conclusions
I have in this paper argued that interpersonal factors may be important, sometimes
decisively so, when attempting to derive VSL valuations for particular individuals and
as averages over a relevant population. This is due to several factors some of which
are already well recognized in the literature, and some which are not. It is well
recognized that altruism may play an important part, and that it then matters what
form altruism takes. It is less well recognized that selfish motivations may play
similar roles, although the distinction between selfishness and altruism is difficult to
make empirically. As argued above “selfish” motivations are here likely to be safetyfocussed (or “paternalistic”), while “altruistic” motivations may take more general
forms. When selfish factors are important, “paternalistic” motivations should be
important, implying that true VSL valuation is increased by inter-personal factors. We
have also pointed out that other issues play roles. One is financial and real gains and
losses sustained by a surviving individual when another family member dies, which
typically add positive amounts to individuals’ average VSL valuations. Taken
24
together these factors imply that a valuation principle, whereby individuals are
required to value only individual-specific risk changes, are bound to give too low
VSL values in most cases.
Two further important inter-personal issues are taken up in the current paper. The
first is related to externality effects resulting from differences between individuals’
future expected consumption, and their future labor market productivities, which are
not likely to be captured by individually-based VSL valuation principles. These
factors are likely not to bias average VSL valuation, but instead to bias the relative
valuations between individual groups, by giving too high VSL values to retired
persons, and too low to young working adults. The second issue deals with the
relation between individual and household WTP for particular mortality reductions. I
here argue that under a plausible model for household behavior and given truthful
answers to valuation questionnaires, one individual (spouse) will correctly represent
the entire household, even in the absence of altruism or other interpersonal valuation
motivations.
The bottom line is that a purely individualistic approach to VSL valuation is
inappropriate or at best incomplete, and that valuation studies eliciting WTP for
changes in mortality risk ought to make consideration for general and not personspecific risk changes. Another consequence is that most existing VSL studies likely
are biased, in terms of average VSL values and of VSL distributions across groups of
individuals, in particular by age. This principle applies to stated-preference as well as
to revealed-preference studies (hereunder hedonic wage studies); the latter are likely
to be biased downwards whenever work decisions are made without proper
consideration for the interpersonal preferences of other affected individuals (although
25
such incorporation of course may occur for the preferences of a spouse, in cooperating
households).
Too little is today known about the quantitative impacts of in particular altruistic
and selfish motivations for the survival of others, and more research is here clearly
warranted. In this research one ought to be much more careful than to date, in
designing tests whereby selfish and altruistic motivations for others’ survival are
distinguished.
26
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