Endogenous Altruism

59 Pages·2013·0.3 MB·English

Endogenous Altruism:
∗
Theory and Evidence from Chinese Twins
Junjian Yi†
November 18, 2013
Abstract
In this paper, I investigate the endogenous formation of inter-sibling altruism and its impli-
cations for intra-household investment in children’s human capital. The theoretical analysis
shows that parental fostering of inter-sibling altruism during childhood serves as a device to
amelioratecommitmentconstraintswithinfamilies. Theincreaseininter-siblingaltruismen-
hancestotalreturnsfromintra-householdinvestmentinchildren’shumancapitalbyallocating
moreresourcestobetter-endowedchildren,anddecreasesinequalityinthedistributionofcon-
sumptionamongchildrenviainter-siblingtransfers. Theoreticalpredictionsaresupportedby
the empirical results that are based on the Chinese longitudinal child twin survey. I find that
parentsaremorelikelytoeducatetheirchildrentobealtruistictowardoneanotherwhengaps
inchildren’sprenatalendowmentsarelarger. Givengapsinprenatalendowments,parentsin-
vest more in better-endowed children’s human capital when they educate their children to be
more altruistic. When parents have more children, they educate children to be more altruis-
tic. Hence, parental investment becomes more likely to reinforce gaps in children’s prenatal
endowments in larger families. The empirical results suggest that the literature understates
the degree of parental aversion to inequality among their children because of the omission of
inter-siblingaltruism.
JELclassification: D10,D13,J24
Keywords: Altruism,intra-householdhumancapitalinvestment,inter-siblingtransfers
∗I am grateful to my supervisors, James Heckman, Gary Becker, and Junsen Zhang, who provided support, en-
couragement, guidance, and extremely helpful suggestions. I am also thankful for the essential feedback provided
by Richard Blundell, Ted Bergstrom, Pierre-Andre` Chiappori, Steve Durlauf, Michael Keane, Robert Pollak, Mark
Rosenzweig, ZhengMichaelSong, AlessandraVoena, aswellasparticipantsintheseminaroffamilyeconomicsat
the University of Chicago. The collection of survey data sets used in this paper was financially supported by the
ResearchGrantCouncilofHongKongandtheChineseUniversityofHongKong,andhasbeencarefullyguidedby
Junsen Zhang, Mark Rosenzweig, and James Heckman. The idea of this paper is inspired by my early experience
when I lived with my parents and brother in a small village in rural China. Comments are welcomed. The usual
disclaimerapplies.
†DepartmentofEconomics, UniversityofChicago, 1126East59thStreetChicago, IL60637, USA;Email: jun-
[email protected].
1 Introduction
This paper investigates the endogenous formation of inter-sibling altruism and its implications for
intra-household investment in children’s human capital. Although economists rely heavily on the
assumptionthatpreferencesarefixedandimmutable,manywouldconcedethatpreferencescanbe
influenced by examples and persuasion. It is increasingly recognized that families play a crucial
role not only in developing children’s human capital but also in fostering children’s preferences.
Le´vy-Garbouaetal.(2006)reviewthesocial,biological,andpsychologicalliteratureaboutfamily
influenceontheformationofchildren’ssocialpreferencessuchasaltruism. Furthermore,children
aremostmalleableattheirveryearlystageswhenlivingwiththeirparents(Heckman,2007). Thus,
parentscansignificantlyinfluencechildren’spreferenceformation. However,theliteratureseldom
explores why parents have incentives to influence children’s preferences. This paper shows that
parents’ desire to influence children’s inter-sibling altruism is closely related to their decisions on
intra-householdinvestmentinchildren’shumancapital.
We consider a conflict between efficiency and equality in intra-household investment in chil-
dren’s human capital (Becker & Tomes, 1976; Behrman et al., 1982; Sheshinski & Weiss, 1982).
Efficiency is defined as that total returns from intra-household investment in children’s human
capital are maximized, and inequality refers to the distribution of or gaps in consumption among
children throughout the paper. If parents invest more in better-endowed children’s human capital
trying to equalize marginal productivity of investment among children, on one hand, total returns
from investment in children’s human capital are maximized. In this case, efficiency increases
whereas equality deteriorates. On the other hand, if parents invest more in less-endowed children,
equalityimproveswhereasefficiencydecreases.1
The literature suggests parents invest more on better-endowed children’s human capital, and
then use inter-vivos transfers or bequests to compensate less-endowed children. Through this
scheme, both objectives of efficiency and equality can be achieved. However, the literature has
1Parentalhumancapitalinvestmentandchildren’sprenatalendowmentsareassumedtobecomplementaryinputs
inthehumancapitalproductionfunction. Ifurtherassumethatthecreditmarketisimperfect.
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not found empirical evidence on compensatory inter-vivos transfers or bequests from parents to
children(Behrman,1997).
If parents and children can make a binding commitment, there exists another mechanism
through which parents can improve efficiency and equality simultaneously. Specifically, parents,
who act as social planners, invest more in better-endowed children to equalize marginal produc-
tivity of family investment. When children become adults, these better-endowed children, who
have higher earnings because of better endowment and heavier human capital investment, make
transfers to their siblings. By doing so, total returns from investment in children’s human capital
aremaximized. Atthesametime,theinequalityinthedistributionofconsumptionamongchildren
decreasesviainter-siblingtransfers.
However, it is difficult to enforce such an agreement with intertemporal choices. The return
from investment in children’s human capital is received after the investment period. The children
withhigherearningsmaynotmakeasmuchinter-siblingtransfersasparentsrequested. Therefore,
acommitmentproblemarises. Thispaperproposesthatparentalfosteringofinter-siblingaltruism
during childhood serves as a device to ameliorate the commitment problem within families. In
particular,theincreaseininter-siblingaltruismenhancestotalreturnsfromintra-householdinvest-
ment in children’s human capital by allocating more resources to better-endowed children, and
decreases inequality in the distribution of consumption among children via inter-sibling transfers.
Therefore,parentaldesiretofosterchildren’sinter-siblingaltruismisdrivenbybothefficiencyand
equalityconsiderations.
Fivetestablepredictionsarederivedfromthetheoreticalanalysisontheendogenousformation
of altruism and intra-household investment in children’s human capital. First, parents invest more
in educating children to be altruistic toward one another when gaps in children’s prenatal endow-
ments are bigger. This prediction is intuitively appealing because the marginal gain to parental
investment in fostering children’s altruism is larger when gaps in children’s prenatal endowments
are bigger. Second, given gaps in children’s prenatal endowments, parents invest more in better-
endowed children’s human capital when they educate children to be more altruistic. Therefore,
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parental investment in children’s altruism enhances total returns from intra-household investment
in children’s human capital. The third prediction is derived by combining first two predictions.
That is, the degree of parental aversion to inequality among children is understated if parental in-
vestment in fostering children’s altruism is omitted from the commonly adopted regression equa-
tion of intra-household resource allocation. Two more predictions are derived when family size
is introduced into the analysis. Fourth, family size increases marginal gains from parental invest-
ment in fostering children’s altruism. Therefore, parents invest more in educating children to be
altruisticinlargerfamilies. Fifth,moreparentalinvestmentinchildren’saltruisminlargerfamilies
causes larger gaps in intra-household investment in children’s human capital, reinforcing gaps in
children’sprenatalendowmentsmore.
Thesefivetheoreticalpredictionsareempiricallytestedbyusingdataderivedfromthelongitu-
dinal Chinese child twin survey (LCCTS). The LCCTS is probably the first longitudinally socioe-
conomicsurveyontwinhouseholdsaroundtheworld. Thefirstwavewasconductedin2002with
childrenaged9onaverage. Thesecondwavewasconductedin2013. TheLCCTScoversdetailed
informationonintra-householdinvestmentinchildren’shumancapitalinthefirstwave,inaddition
to an extensive array of variables on child-, parent-, and household-specific characteristics in both
waves.
The LCCTS is ideal for the present study for several reasons. First, we carefully design the
LCCTSquestionnairetosolicitinformationaboutpracticesoffamilyeducationonchildren’sinter-
siblingaltruism,whichiscalledasfamilyaltruisticeducationinthepaper. Inparticular,weinclude
twoquestionsaboutfamilyaltruisticeducationinthequestionnaire. Oneisthefrequencyinwhich
parents brought children together to worship ancestors during the Qingming festival. The other is
the frequency in which parents told children that having fraternal love among siblings is a virtue,
such as telling children the story of “Kong Rong giving up pears.” The construction and validity
of these two measures of family altruistic education are discussed in a more detailed manner in
the data section below, in which I show that both measures are good proxy variables for family
altruisticeducation.
3
To directly examine the validity of these two measures of family altruistic education, second,
we further design an experiment to measure inter-sibling transfers in the LCCTS.2 Empirical re-
sults indicate that family altruistic education measured by either variable increases an individual’s
transfers to twin siblings, suggesting that these two variables are effective in predicting children’s
inter-siblingtransfers.
Third, the LCCTS provides two natural experiments brought about by twinning. These exper-
iments facilitate identification in the empirical analysis. The first experiment is the within-twin
variation in birth weight which is used as a proxy variable for prenatal endowment. The second
is the variation in family size induced by twinning. These two types of variations are crucial in
empiricallytestingthetheoreticalpredictions.
The empirical results are consistent with the theoretical predictions. First, the empirical ev-
idence shows that parents are more likely to educate their children to be altruistic when gaps in
children’s birth weight are larger. Given gaps in children’s birth weight, I find that parents invest
more on better-endowed children’s human capital when parents educate children to be more al-
truistic. If the variable of family altruistic education is omitted from the regression equation of
intra-household resource allocation, parental human capital investment is more likely to reinforce
gaps in children’s prenatal endowments. The result suggests that the degree of parental aversion
toinequalityisunderestimatediffamilyaltruisticeducationisomitted. Whenfamilysizeislarger
which is exclusively induced by twinning in the estimation sample, parents educate their children
tobemorealtruistic. Finally,intra-householdinvestmentinchildren’shumancapitalismorelikely
toreinforcegapsinchildren’sprenatalendowmentsinlargerfamilies.
This paper conceptually links to four strands of economics literature. The first one is about
altruism, commitment problems, and resource allocation. Becker (1974) concludes that altruism
enhances resource allocation efficiency by internalizing externality. This conclusion is challenged
by later studies (Hirshleifer, 1977; Bernheim & Stark, 1988; Lindbeck & Weibull, 1988). For in-
stance,Hirshleifer(1977)noticesthattheeffectofaltruismonresourceallocationcruciallyhinges
2We are not able to directly measure inter-sibling transfers in the LCCTS because most of the children are in
schoolin2013.
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on whether parents who are altruistic have the last word or not. If parents cannot control the last
action in temporal sequence, a commitment problem arises. In this case, altruism does not nec-
essarily improve resource allocation efficiency. In this regard, the literature focuses on how the
presenceofcommitmentproblemslimitstheeffectofaltruismonresourceallocation. Thecurrent
paper approaches the relationship between altruism and commitment problems from the opposite
direction. That is, children’s inter-sibling altruism can be endogenously fostered by parents in
response to commitment constraints within families, enhancing total returns from intra-household
investmentinchildren’shumancapital.
Second, this paper links to the literature of the endogenous formation of preferences. Stable
preferences, maximizingbehavior, andmarket equilibrium haveonce beenregarded asa trinityof
fundamentalassumptionsineconomics. Theliteraturelateradmitsindividualdifferencesinprefer-
encesandthenexploreseconomicrationalesofendogenouslyforminganindividual’spreferences
(Becker&Mulligan,1997;Stark&Falk,1998). Parentsarefoundtoexertsignificantinfluenceon
childrenhumancapitaldevelopmentandpreferenceformation(Heckman,2008). Recently,Becker
et al. (2013) investigate incentives for parents to “manipulate” preferences of children to induce
them to support their parents in old age. The current paper contributes to this strand of literature
byinvestigatingparentalincentivestoeducatechildrentoformadifferenttypeofpreferences,that
is,theinter-siblingaltruism.
Intra-household resource allocation is the third strand of economics literature to which the
current paper contributes to. Parental investment strategy of reinforcement versus compensation
has been an important research topic (Becker & Tomes, 1976; Griliches, 1979; Rosenzweig &
Wolpin,1980;Behrmanetal.,1982). However,theliteraturedoesnotconsiderinter-siblingtrans-
fers in studying parental investment decisions. The current paper suggests that parents consider
children’s inter-sibling transfers in adulthood by fostering children’s inter-sibling altruism when
they make investment decisions. Considering the endogenous formation of inter-sibling altruism,
inferencesdrawnfromtheobservedintra-householdresourceallocationintheliteratureshouldbe
re-evaluated. Specifically,becauseoftheomissionoftheendogenousformationofinter-siblingal-
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truism,thisstrandofeconomicsliteratureunderstatesthedegreeofparentalaversiontoinequality
amongchildren.
Fourth, this paper is closely related to the literature of inter-household transfers. Altruism and
inter-household transfers have been extensively studied by economists (Cox, 1987, 1990; Altonji
et al., 1992; Laferre`re & Wolff, 2006). The literature focuses on parent-child transfers. However,
inter-sibling transfers are important for families, in particular for those living in developing coun-
trieswhereextendedfamiliesareprevalent(Zhang,2013). Theresultsofthispaperhaveimportant
implications for future studies on inter-sibling transfers. That is, both the degree of altruism and
earnings of adult children are endogenous, which are determined by parental decisions simultane-
ously.
Empirically,thispaperhastwomajorcontributions. Tothebestofmyknowledge,ononehand,
thisstudyisthefirstoneempiricallyexaminingeconomicincentivesfortheendogenousformation
of inter-sibling altruism. On the other hand, this is also the first empirical study examining the
effectofchildren’sinter-siblingaltruismonparentalresourceallocation. Theempiricalevidenceof
thispapershowsthatinter-siblingaltruismenhancestotalreturnsfromintra-householdinvestment
inchildren’shumancapital.3
Theremainderofthepaper isorganizedasfollows. Section2buildsthe theoreticalmodeland
derives testable predictions. Section 3 describes the data. Section 4 tests the predictions. Section
5discussestherobustnessoftheempiricalresults. Section6concludes.
2 Theory
This section explores theoretically parental decisions about intra-household investment in chil-
dren’shumancapital,takingchildren’sinter-siblingtransfersinadulthoodintoaccount. Moreover,
parents can influence children’s altruism toward one another, and thus, children’s altruism is en-
dogenously formed. I first characterize incentives for parents to influence children’s altruism, and
3Although economists are interested in altruism, few studies empirically examine altruism and intra-household
resource allocation. Foster & Rosenzweig (2001) may be exceptional by showing evidence that altruism increases
gainsfromincomepoolinginthepresenceofrisk. Buttheydonotconsidertheendogeneityofaltruism.
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then analyze implications of the endogenous formation of children’s altruism for intra-household
humancapitalinvestment. Themodelshowsthatparentalfosteringofchildren’saltruismservesas
a device to ameliorate commitment constraints within families. I demonstrate that fostering inter-
sibling altruism by parents may not only enhance total returns from intra-household investment
but also decrease gaps in children’s consumption. Finally, I introduce family size into the analy-
sis, and study family size, the endogenous formation of children’s altruism, and intra-household
human capital investment. Several theoretical predictions are derived from the model, which are
testedinfollowingsections.
2.1 Model Set-up
Parents are assumed to be altruistic toward their children. They care about not only their own
consumption c , but also children’s consumption c , where τ indexes the τth child (τ = 1,...,n).
p τ
Therefore, parents have a utility function such that U = U(c ,c ,...,c ). The parental utility
p 1 n
functionhasthefollowingproperty:
U (cid:83) U ifc (cid:84) c , (1)
ci cj i j
where i, j = 1,...,n. Property (1) indicates that the ratio of marginal utilities derived from child
i(cid:48)s consumption over that of child j is independent of or separable from parental consumption.
With this separability property, the intra-household resource allocation between parents and chil-
dren does not qualitatively affect the resource allocation among children. To focus on resource
allocation among children only, parental consumption is omitted from the utility function below.
Furthermore, Property (1) implies that, in addition to children’s total consumption, parents care
about the distribution of children’s consumption. That is, parents are averse to inequality in the
distribution of consumption among their children because parents derive higher marginal utility
fromthechildwhoconsumeslessthantheotherone. Tocapturethedegreeofparentalaversionto
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inequality,Ispecifythefollowingparentalutilityfunction:
U = (cρ +cρ)ρ1, (2)
i j
where ρ ≤ 1. With this specific function form, the parameter ρ can effectively capture the degree
of parental aversion toward inequality among children. For example, if ρ = 1, parents exhibit
no inequality aversion, and then U = c + c . When ρ = −∞, parents exhibit infinite inequality
i j
aversion. ThelatteristheRawlsiancase,thatis,U = min(c,c ). Forsimplicity,eachhouseholdis
i j
assumed to have two children only (τ = i, j).4 Furthermore, children are assumed to be symmet-
rically treated. The relaxation of this assumption does not affect the comparative static analysis
belowasdiscussedinAppendixA.
Children’sconsumptiondependsonlabormarketearningEplusorminusinter-siblingtransfers
T. That is, c = E ± T. If child τ makes transfers to the sibling −τ, his or her consumption is
τ τ
E − T; otherwise, it is E + T. The labor market earning is determined by the wage rate ω and
τ τ
children’s human capital h. The latter is a function of children’s prenatal endowment e and family
humancapitalinvestment I. Therefore,
E = ωh(e ,I ).
τ τ τ
To simplify the analysis, I assume a Cobb-Douglas human capital production function form, such
thath = φeβeIβI,where0 < β ,β < 1.
τ τ τ e I
The inter-sibling transfers T are determined in equilibrium which is a function of children’s
earnings and the degree of inter-sibling altruism a, such that T = T(E ,E ,a), where 0 ≤ a ≤ 1.
i j
The household budget constraint is that p (I + I ) = Y, where p is the price of intra-household
I i j I
investmentinchildren’shumancapitalandY isfamilyincome,whichisassumedtobeexogenous
intheanalysis. Withoutlossofgenerality,Iassumethate > e throughoutthepaper.
i j
4Thecasewiththreeormorechildrenisanalyzedbelow.
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2.2 Intra-household Investment in Children’s Human Capital
I first analyze intra-household investment in children’s human capital without considering inter-
sibling transfers, which sets up a benchmark for future analysis. In this case, the degree of inter-
sibling altruism a is assumed to be zero. Children’s consumption depends solely on labor market
earning E. The optimal intra-household investment in children’s human capital is determined by
thefollowingequilibriumcondition:
(cid:32) (cid:33)
I ρβ e
Inequalityaversion: ln i = e ln i (3)
I 1−ρβ e
j ρ<1,a=0 I j
If ρ = 1, parents are not averse to inequality. The optimal intra-household human capital invest-
mentinthisspecialcaseisdeterminedby
(cid:32) (cid:33)
I β e
Efficient: ln i = e ln i (4)
I 1−β e
j ρ=1,a=0 I j
Equation (4) sets the equilibrium condition that total returns from intra-household investment in
children’s human capital are maximized. Therefore, the equilibrium condition of Equation (4) is
defined as the efficient condition in intra-household human capital investment in the paper. In this
specialcase,children’stotalearningsorconsumptionarealsomaximized.
Comparing Equation (3) with Equation (4), parents allocate fewer resources to the better-
endowed child when ρ < 1 than that in the case ρ = 1. Furthermore, when ρ is smaller, parents
invest less in the better-endowed children. Thus, total returns from intra-household human capital
investmentdecreases,andthegapinchildren’searningsshrinks. Thisobservationleadstomyfirst
proposition:
Proposition1 An efficiency versus equality trade-off exists in the intra-household investment in
children’s human capital when parens are averse to inequality in the distribution of earnings
amongchildren.
Thisisastandardresultinfamilyeconomics.
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