Altruism, Fertility, and the Value of Children

34 Pages·2007·0.33 MB·English

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IZA DP No. 2783
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Altruism, Fertility, and the Value of Children:
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A Health Policy Evaluation and Intergenerational Welfare
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O Javier A. Birchenall
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Rodrigo R. Soares
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D May 2007
Forschungsinstitut
zur Zukunft der Arbeit
Institute for the Study
of Labor
Altruism, Fertility, and the Value of
Children: Health Policy Evaluation and
Intergenerational Welfare

Javier A. Birchenall
University of California, Santa Barbara

Rodrigo R. Soares
University of Maryland, Catholic University of Rio de Janeiro,
NBER and IZA

Discussion Paper No. 2783
May 2007

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IZA Discussion Paper No. 2783
May 2007

ABSTRACT

Altruism, Fertility, and the Value of Children:
*
Health Policy Evaluation and Intergenerational Welfare

This paper accounts for the value of children and future generations in the evaluation of
health policies. This is achieved through the incorporation of altruism and fertility in a “value
of life” type of framework. We are able to express adults’ willingness to pay for changes in
child mortality and also to incorporate the welfare of future generations in the evaluation of
current policies. Our model clarifies a series of puzzles from the literature on the “value of
life” and on intergenerational welfare comparisons. We show that, by incorporating altruism
and fertility into the analysis, the estimated welfare gain from recent reductions in mortality in
the U.S. easily doubles.

JEL Classification: J17, J13, I10

Keywords: value of life, mortality, fertility, altruism, intergenerational welfare,
willingness to pay

Corresponding author:

Rodrigo R. Soares
Department of Economics
University of Maryland
3105 Tydings Hall
College Park, MD 20742
USA
E-mail: [email protected]

* Previous versions of this paper circulated under the title “Fertility and the Value of Life.” We owe
special thanks to Maureen Cropper for important suggestions. We also benefited from comments from
Ted Bergstrom, Roger Betancourt, Trudy Ann Cameron, Kevin Frick, Robin Jenkins, Michael Manove,
Esteban Rossi-Hansberg, Seth Sanders, and seminar participants at EPGE-FGV, PUC-Rio, SUNY
Buffalo, Universidad Nacional (Bogotá), University of Maryland, University of Oregon, USP, the 2006
Latin American Meeting of the Econometric Society (Mexico City), and the 2007 NBER Health
Economics Program Meeting (Cambridge). Soares gratefully acknowledges financial support from the
Conselho Nacional de Pesquisa e Desenvolvimento Tecnológico (CNPq), Brazil.
1 Introduction
This paper accounts for the value of children and future generations in the evaluation of health
policies. This is achieved through the incorporation of altruism and fertility in a “value of life”
type of framework. We argue that altruism and fertility are natural ways to model the value that
parentsattachtochildren,whichisintrinsicallyrelatedtothevaluethatpresentgenerationsattach
to the welfare of future generations. By bringing these new dimensions into the analysis, we are
abletoexpressadults’willingnesstopayforchangesinchildmortalityandalsotoincorporatethe
welfare of future generations in the evaluation of current policies. This is done in a setting where
fertility, and therefore the size of future generations itself, is endogenous to current generations’
decisions. Our model clarifies a series of puzzles from the literature on the “value of life” and
on intergenerational welfare comparisons, ranging from the profile of the “value of a statistical
life” over the life-cycle to the specific way in which future generations whose existence itself may
−
depend on current actions could be incorporated in cost-benefit analyses.
−
Anincreasingbodyofliteraturehasappliedthe“valueoflife”methodologytoanalyzedifferent
aspects of welfare gains from changes in mortality rates.1 These studies made important contri-
butions to the understanding and measurement of non-monetary aspects of human welfare. Yet
they suffer from an important methodological drawback: they do not incorporate in the analysis
altruism, fertility decisions, and their consequences in terms of welfare evaluation. Two interre-
lated dimensions of fertility choice are essential in evaluating life expectancy and health-related
welfare gains. First, child mortality rates which would be irrelevant for the welfare of an adult
−
individual in an egoistic setup can be very important in determining welfare in a context in
−
whichindividualschoosethenumberofchildrentheyhave. Second,ifaltruismmotivatesfertility,
life expectancy gains have a twofold effect: they directly increase utility via increased survival
probabilities, and they increase utility via the increased welfare of the offspring.2
1 The main contributions to the theoretical literature were made by Schelling (1968), Usher (1973), Arthur
(1981), and Rosen (1988, 1994), among others. Nordhaus (2003), Murphy and Topel (2003), and Garrett (2001)
appliedthismethodologytoanalyzedifferentaspectsofhealth-relatedgainsinwelfareintheUnitedStatesthrough-
outthetwentiethcentury. PhilipsonandSoares(2005)usedthismethodologytoestimatetheincomevalueofthe
welfarelossduetoAIDSinsub-SaharanAfrica,whileSoares(2006)appliedthismethodologytoestimatethewel-
farecostofviolenceacrossdifferentregionsoftheworld. Becker,Philipson,andSoares(2005)applied anadapted
versionofthesametechniquetoevaluatetheevolutionofwelfareinequalityacrosscountries,onceimprovementsin
lifeexpectancyareaccountedfor. BeckerandElías(2006)useestimatesfromthe“valueoflife”toinferhowmuch
it would cost to increase sufficiently the supply of organs for live transplants in order to eliminate any significant
waiting time.
2 Cropper and Sussman (1988) and Rosen (1994) consider the problem of marginal willingness to pay for
reductionsinmortalityrateswhenindividualsleavebequeststoasingledescendant. Undercertaincircumstances,
thismaycorrespondtotheincorporationofaltruism. Someoftherecentliteraturecitedabovetriestoincorporate
futurepopulationsbyextendingdiscountorinterestratesacrossdifferentgenerations. Ingeneral,intergenerational
discount is different from time discount, so these should not be treated as being the same concept. One cannot
extrapolate what one individual does over the lifetime to different individuals. In any case, none of these papers
1
In this paper, we evaluate the welfare implications of mortality reductions in a setup in which
individuals choose the number of children they have and are altruistic toward their children. We
showthat,underthesecircumstances,thevalueofadultmortalitychangescanbedecomposedinto
threefactors: theconsumptionfactorfromthetraditional“valueoflife”specification,discussedin
Rosen(1988); afertilityfactor,whichaccountsforthewelfareimprovementsrelatedtothehigher
probability of having children; and an altruism factor, which accounts for the fact that mortality
reductions will also be enjoyed by all future generations. In addition, our approach allows us
to calculate an adult’s willingness to pay for reductions in child mortality. This willingness to
pay generally depends on the effect of child mortality on the final costs of child production,
the uncertainty regarding the number of surviving children, and the emotional loss associated
with the death of a child. As in the case of adult mortality, child mortality reductions are also
valued because future generations will benefit from it. In fact, we show that, when parents
care for their children through altruistic links, any marginal willingness to pay approach that
adequately accounts for parents’ preferences will also account for the value of welfare gains to
future generations.
In ordertoillustrate therelevanceof thenewdimensions introduced byour theoretical frame-
work, we calibrate our model to U.S. data and calculate the value that the population alive in
1965 would attribute to the mortality reductions observed between 1965 and 1995. Our results
imply that the welfare gain for an 18-year-old individual is between 79% and 200% higher than
what would have been estimated if the welfare that young adults derive from their children was
ignored. The aggregate social value is between 27% and 80% higher. These differences are due to
benefitsfromchildmortalityreductionsthatareenjoyedbyyoungadultsandthatcouldnothave
been estimated had we not incorporated altruism and fertility in the analysis. In addition, our
calibrated model generates as by-products some curious numbers, never before estimated in the
literature. Forexample,afunctionofparametersthatcanberoughlyunderstoodasthemonetary
value of the emotional loss from the death of a child is estimated to be between $1.2 million and
$3.9 million.
Though applied to the analysis of changes in health, the paper touches on the more general
question of how to deal with children and future generations in the evaluation of policy interven-
tions. Since mortality risk at any age is a completely forward-looking measure, if no economic
benefit from children is assumed, egoistic adults who survive childhood place zero value on mor-
tality changes at earlier ages. As a consequence, in the standard framework, the contribution
of changes in child mortality to the welfare of an adult is null, since altruistic behavior toward
include the choice of number of children together with the value that parents attach to children, and therefore
cannotbeextended to adequately accountforfuturegenerations.
2
offspring is not taken into account. In reality, however, future generations cannot voice their con-
cernsorrevealtheirpreferencesviamarketbehavior,andchildren,becauseoflackofmaturityand
dependence on parental care, are incapable of legally deciding. For these same reasons, contrac-
tualarrangementsinvolvingchildren orpossiblyunbornindividuals cannotdirectlyincorporate
− −
future benefits in current evaluations of policy interventions (see the discussion in Becker and
Murphy, 1988). As analternative, our modelallowsfor endogenous fertilityandaltruismin order
to transfer the benefits of certain policies across different generations. In our theory, as in reality,
parents are the ones who decide and are liable for their children.
Altruisminhumansocietiesiscertainlynotrestrictedtotheimmediatefamilyoreventodirect
descendants. Nevertheless, the case for incorporating parents’ altruism toward children in public
policy evaluation seems far stronger than any other.3 Not only does this approach incorporate
the preferences of a significant share of the population that is not allowed to decide (children),
but it also establishes an intergenerational link that ultimately accounts for the benefits accrued
byall futuregenerations. Inaddition, thetaskof assigningvaluestowelfaregains experiencedby
childrenistransferredtothosewhoarethechildren’s legalguardiansandalreadydecideforthem
in all relevant dimensions of life, namely, the parents.
The literature on theeconomic valuation of child mortalityriskis not as developed as that re-
gardingadults. Whilesomeempiricalstudieshaveexaminedpossibledifferencesofvaluesbetween
adultsandchildren,theroleoffactorslikefamilysizeandthetimingoffertilitydecisionshavenot
been incorporated in theoretical models, since most empirical estimates assume exogenous popu-
lation and egoistic agents (see Dickie and Gerking, 2006, for a review of the literature).4 Family
composition and the timing of fertility however are important determinants of the willingness to
pay for changes in mortality risk. Parents’ willingness to pay for adult and child mortality risk
reductionsvarysystematicallywiththepresenceandtheageofchildren(Cameron,DeShazo,and
Johnson, 2007, and Dickey and Ulery, 2001).
3 Bergstrom (1982,2006) and Jones-Lee (1992)study altruism within the family and its effects on the value of
life,butwithnoconsiderationsforcostlyfertilitydecisions. Bergstrom(1982)showsthat“purealtruism”produces
no additional value for changes in health risks if altruistic concerns are dealt with in the first order condition.
Jones-Lee (1992) provides several extensions and generalizations. The case of fertility poses different problems
because, in a marriage, as studied for example in Bergstrom (2006), the utility functions of husband and wife are
well-defined and the formation of a marriage is voluntary. Not only are children self-produced by parents, but
children do nothave preferencesrelevantforvaluation ofmortality risk.
4 Examplesofvaluationswherenon-fatalityrisksarethemainconcernincludeAgeeandCrocker(1996),Dickie
and Messman (2004), Joyce, Grossman, and Goldman (1989), Lui et al. (2000), and Viscusi, Magat, and Huber
(1987). Ageneraloverviewofthemainempiricalfindingsandmethodologicaldifficultiesintheeconomicvaluation
associatedwithreducedriskstochildrenisavailableinScapecchi(2006). AsindicatedinScapecchi(2006,14)the
valueofchildren’shealthbenefitsisoftenhigherthanthoseofadultsalthoughthisisnotalwaysthecase. Interms
of the “value of a statistical life,” or valuations for reductions in child mortality risk, studies are often based on
the purchase or use of safety-related goods (see Blomquist, Miller, and Levy, 1996, Carlin and Sandy, 1991, and
Jenkins,Owens,andWiggins,2001). Wewillconsiderindetailcurrentestimatesofthe“valueofastatisticallife”
in ourquantitative section.
3
Several of these applications have stressed that the evaluation of policies affecting children
requires knowledge of parental preferences, since children are not the actual decision-makers in
most legal and economic contexts (see, for example, Scapecchi, 2006, Carlin and Sandy, 1991,
Mountetal.,2000,DickieandUlery,2001,andJenkins,Owens,andWiggins,2001). Endogenous
fertility decisions have also been suggested as a way to deal with evaluations of welfare involving
future generations, since exogenous fertility implies a series of puzzling considerations. Under
exogenous fertility, an unrestricted number of births is always advocated because it increases the
aggregate number of years lived in society and, hence, social welfare. Also, changes in mortality
immediately before or after birth cannot be adequately taken into account, since there are almost
noexpendituresundertakenbyparentsuptothatpoint,eventhoughparentsdoseemtobewilling
to pay for reductions in child mortality risk. As a consequence, there is no theoretical basis to
account for the change in births that would be generated as a by-product of health programs,
or to determine how future generations should be treated (see Preston, 1993, Deaton, 2004, and
Viscusi, 2005).5
Our framework shows that these puzzling considerations arise because altruism and fertility
decisions are absent from traditional models. Once altruism and fertility are incorporated in
the analysis and an endogenous link between parents and children is established the problems
− −
disappear.6 Generally, the same principle explored here can be extended to any other policy
contextinwhichgovernmentinterventionshavetheircostsorbenefitsspreadoutthroughdifferent
generations.
The structure of the remainder of the paper is outlined as follows. Section 2 presents a simple
model illustrating the main implications of the incorporation of fertility and altruism into “value
oflife”calculations. Section3developsthegeneralversionofthemodel,andderivesaformulafor
thesocialvalueofchangesinsurvivalfunctions. Section4illustratestheempiricalrelevanceofour
approach by calculating the value of the mortality reductions experienced by the U.S. population
between 1965 and 1995. Section 5 concludes the paper with some general remarks.
5 Valuationsmadebynineteenth-centurycourtsafterwrongfuldeathsofchildrenweregivenintermsofreplace-
mentofchildren’slostwagesbutbecameunfounded whenchild laborwasabolished (Zelizer,1994). Valuationsin
termsofparentalinvestmentsintheupbringingofachildarealsocontradictory,especiallyforveryyoungchildren,
because, as Zelizer (1994, p.135) notes, they “would lead to the awkward conclusion that the average child had a
negativeworth and itsdeath was abenefitforparents.”
6 Weconsider,asinBeckerandBarro(1988)andGolosov,Jones,andTertilt(2007),intergenerationallinksasa
directconnection between potentialpeople. Golosov,Jones,and Tertilt(2007)areconcerned with efficiency when
population is endogenous, so they assume preferences and costs defined over survivors alone. As a consequence,
parents would not be willing to pay for changes in child mortality risk. Our model is complimentary to theirs.
An alternative to the parentalperspective described in the paper is the adults-as-children valuation, where adults
wouldassessthevalueofriskreductionsthatwouldhaveoccurredwhentheywerechildrenThisapproach,however,
lacks an underlyingtheoreticalstructure (see the discussion in Scapecchi,2006).
4
2 A Simple Model of Fertility and the Value of Life
This section illustrates the consequences of altruism and endogenous fertility for the valuation of
life expectancy changes, and shows that they are intrinsically related to the value that parents
attach to children and future generations. We construct a simplified example, as close as possible
to the simplest model presented in Rosen (1988), in order to highlight the dimensions added to
the problem and to compare our results to the previous literature.
Consider individuals who live for three periods: childhood, young adulthood, and mature
adulthood. Individualsfaceaprobabilityp ofsurvivingbirth. Iftheysurvivebirth,theybecome
c
young adults and face a probability p of survival into mature adulthood. Decisions are made
a
at this stage, after individuals survive child mortality, and just before their adult mortality is
realized.7 If individuals surviveintomatureadulthood, theirconsumptionandfertilityplansare
carried out, and then their offspring face the child mortality risk.
At time t, young adults receive an endowment w . Young adults decide on consumption and
t
number of births before the event with probability p is realized. Actuarially fair insurance is
a
available for every good consumed by parents, so that the budget constraint can be written as
w =p [c +n b+(p n )e], (1)
t a t t c t
wherebisthegoodscostofhavingachildandeisthegoodscostofraisingasurvivingchild. The
costsofhavingandraisingchildrenareassumedtobefixed. Tokeepthingssimpleandcomparable
tothepreviousliterature, weassumenomarginin whichparentscaninvest ortransferadditional
resources to their children.8
Adults value consumption, the number of surviving children they have, and the utility that
each child will enjoy as an adult. Adults are responsible for all decisions in the economy. Figure
1 summarizes the sequence of events in this simple version of the model.
As in Rosen (1988), utility is assumed to be state-dependent in dimensions involving life and
7 Though this sequence of events may seem excessively artificial, it keeps things as simple as possible. The
interpretation ofthedifferentstagesbecomesmorenaturalin thegeneralizedversionofthemodel. Forsimplicity,
we also ignore general equilibrium effects of changes in mortality and analyze an economy without production.
With the exception of Arthur (1981), all papers in this literature have ignored general equilibrium implications.
In Arthur (1981), however, all fertility decisions are exogenous. In our model, we address the economic value of
changesinhealththatareoutsidethecontrolofanyparticularindividual(asrelatedtoscientificandtechnological
developments in medical and biological sciences, for example). If households have control over some aspects of
mortality,endogenousmortalitychangeswillhavenoeffectonwelfareinadditiontothatreflectedonexpenditures.
8 Notethatourassumptionseliminatethetraditionalquantity-qualitytrade-offintermsoftheanalyticalresults
ofthemodel. Parentscouldstillvaluechildqualityashumancapitalifwemakethevaluefunctiondependonhuman
capital. We also ignore alternative motives for fertility such as old-age security. In modern societies, children’s
costsarehigherthanthereturnstheyprovide. Nevertheless,whenthemodelisappliedtodatatoevaluatedifferent
situations, a quantity-quality trade-off and additional fertility motives will be reflected in different values of the
parameters band e,since in equilibrium these reflectthemarginalvalue thatparentsattach to children.
5
Figure 1: Sequence of events in the simple model

Individual becomes a young Consumption and fertility
Individual adult and makes consumption plans are realized and next Individual
is born and fertility plans generation is born dies
Child mortality realized Adult mortality realized
(survival prob. p) (survival prob. p )
c a
time
deathevents. Weassumethatsurvivingindividualsderiveutilityfromconsumptionandchildren,
but that utilityincaseof deathis equaltoaconstantM . Similarly, weassumethateventhough
a
parentsderiveutilityonlyfromsurvivingchildren,thereisastate-dependentutilitylossassociated
with the death of a child. Therefore, the expected utility for a young adult satisfies the following
value function
Vt =max pa u(ct)+E[v(nt,Nt,Vt+1)] +(1 pa)Ma ,
ct,nt { } −
n o
subject to the consteraint (1), wheere ct is ceonsumptieon by adults at time t, nt is the number
of children born, N is the number of surviving children, and V is the future utility that
t t+1
the surviving children will enjoy as they become adults. The function u(c ) denotes the utility
t
e
derived from consumption, and v(n ,N ,V ) denotes the overall utility derived from children,
t t t+1
e
including the enjoyment from the surviving children and their welfare, and the emotional loss
e
associated with children who are born but do not survive childhood (n N ). Since there is an
t t
−
additional dimension of uncertainty related to the survival of children (probability p ), parents
c
try to maximize u(c ) plus the expected value of v(n ,N ,V ), conditional on survival into
t t t t+1
adulthood.
e e
In addition, we assume that the utility derived from surviving children follows the usual for-
mulation from the fertility literature (as, for example, in Becker and Barro, 1988), so that the
utility derived from N surviving children is given by αNφV , with 0 φ 1. As mentioned
t t t+1 ≤ ≤
before, we also consider a state-dependent utility loss of αM for each child born who does not
c
survive childhood. The utility loss associated with the death of (n N ) children is given by
t t
−
α(n N )M . In our setting, M will have the connotation of the utility value associated with
t t c c
−
the loss of one child (regardless of family characteristics). This is a state-dependent formulation
in the event of death of a child, analogous to the approach adopted by Rosen (1988) in relation
6
to adult deaths. Finally, in order to simplify the analysis, we assume that there is no uncertainty
about child quality or, in other words, that the series w is known. Therefore, there is no
{ i}∞i=t
uncertainty regarding the value of V itself.
t+1
In this context, we can normalize adult utility in the death state to zero by defining the
instantaneous utility function u(c ) = u˜(c ) M . By defining the value function V = V M ,
t t a t t a
− −
we can specify a young adult’s objective function as
e
Vt =mct,anxt pa{u(ct)+αE[NtφVt+1−(nt−Nt)Mc]} .
n o
Note that there are two different dimensions of uncertainty in the problem. One is related to
whether the individual will die before being able to realize the consumption and fertility plans,
while the other is related to the number of children who survive (N ) out of the total number of
t
childrenborn(n ). Sincethevaluefunctionisdefinedastheexpectedutilityofanadultindividual,
t
theonlyremainingdimensionofuncertaintyaftertheindividualsurvivesadultmortalityisrelated
to the number N of children who will survive out of n births.
t t
ThisproblemisascloseaspossibletotheonediscussedinRosen(1988,Section1),oncefertility
and altruism are incorporated in the analysis. Nevertheless, altruism and fertility introduce new,
nontrivial dimensions of uncertainty in the discussion. Since one of our main motivations is
to explore child mortality in a context of value of life calculations, we deal explicitly with the
uncertaintyrelatedtop . FollowingSah(1991),withconstantp ,thenumberofsurvivingchildren
c c
N follows a binomial distribution with density function
t
n
f(Nt,nt)=⎛ Nt ⎞pNct(1−pc)nt−Nt, for Nt =0,1,2,...,nt. (2)
t
⎝ ⎠
Therefore,
nt
E[NtφVt+1−(nt−Nt)Mc]=E[NtφVt+1]−E[(nt−Nt)Mc]=Vt+1 Ntφf(Nt,nt)−(1−pc)ntMc,
NXt=0
since E(nt Nt)=(1 pc)nt and Vt+1 is known to parents.
− −
As inKalemli-Ozcan(2002), weapproximatethefunctionE[Ntφ]aroundtheexpectednumber
of survivors E[Nt] using the delta method. This strategy allows us to deal with fertility as a
continuous variable and still account for theeffects associated with the risk regarding the number
of surviving children via the explicit consideration of the second moment of the distribution. A
second order approximation to E[Ntφ] leads to
7