Happiness and altruism within the extended family

19 Pages·2011·0.3 MB·English

JPopulEcon(2011)24:1033–1051
DOI10.1007/s00148-010-0326-8
ORIGINAL PAPER
Happiness and altruism within the extended family
JohannesSchwarze·RainerWinkelmann
Received:2September2008/Accepted:21May2010/
Publishedonline:29June2010
©Springer-Verlag2010
Abstract Weproposeadirectmeasureofaltruismbetweenparentsandadult
children, using survey data on happiness from the German Socio-Economic
Panel for the years 2000–2004. The question of altruism within families has
policy relevance, for example, to understand whether public transfers crowd
out private ones. Previous empirical evidence, based on observed transfer
behavior,hasfailedtoestablishaclearconsensus.Usingvariouscrosssection,
paneldata,andinstrumentalvariableestimators,wefindarobustassociation
betweenthehappinessofparentsandthatoftheiradultchildren.A1standard
deviationincreaseinachild’shappinessisassociatedwiththesameincreasein
ownhappinessasthatofa20–45%increaseinhouseholdincome,depending
onspecification.
Keywords Utilityinterdependence·Sympathy·Paneldata
JELClassification D64·C25·J10
“How selfish soever man may be supposed, there are evidently some
principles in his nature, which interest him in the fortune of others, and
Responsibleeditor:ChristianDustmann
AnearlierversionofthepaperwaspresentedatseminarsinBerlin,Gottlieben,Lausanne,
Philadelphia,andatthe2005populationeconomicsmeetingoftheGermanEconomic
AssociationinBasel.
J.Schwarze
FakultätfürSozial-undWirtschaftswissenschaften,Otto-Friedrich-UniversitätBamberg,
96045Bamberg,Germany
R.Winkelmann(B)
DepartmentofEconomics,UniversityofZurich,Zürichbergstr.14,8032Zurich,Switzerland
e-mail:[email protected]
1034 J.Schwarze,R.Winkelmann
rendertheirhappinessnecessarytohim,thoughhederivesnothingfrom
itexceptthepleasureofseeingit.”
AdamSmith(1790)
“...we might suppose that the object which X (whose own utility is P)
tends—inacalm,effectivemoment—tomaximise,isnot Pbut P+λ(cid:3);
whereλisacoefficientofeffectivesympathy.”
FrancisYsidroEdgeworth(1881,p.53)
1Introduction
Altruism denotes the willingness to make voluntary transfers of resources to
another person or other persons, disregarding of own benefit. The empirical
importance of altruism for economics has been debated for several decades,
yetnoclearconsensushasemergedsofar.Aninitialliteraturewasconcerned
with the way resources are distributed within the extended family and its
consequences for optimal public transfer policies (Becker 1981; Altonji et al.
1992). More recently, evidence on widespread pro-social behavior in labo-
ratory experiments has led to renewed interest in altruism and challenged
theviewthateconomicagentsmostlybehaveselfishly(FehrandFischbacher
2003).Importantly,altruisticbehaviorisfoundnotonlyamongrelatedfamily
membersbutalsoamongstrangersinone-shotinteractions.
Behavior-based research of altruism faces the obstacle that such transfers
canalmostalwaysbeattributedtoanumberofdifferentmotives.Ifthemotive
foratransferis“nothingexceptthepleasureofseeingthehappinessofothers”,
as Adam Smith puts it, then we have indeed an instance of genuine altruism.
But other motives reflect plain selfishness because they give the donor a
personal benefit. Among the possible benefits are “joy-of-giving” or “warm
glow”effects(Andreoni1990),wherebytheactofgivingprovidesasourceof
satisfactionperse,forexample,byaccordingprestigeorrespecttothedonor,a
benefitthatisindependentofhowthebeneficiaryvaluesthetransfer.Another
potentialbenefitisreciprocity,i.e.,theexpectationthatafavorisreturnedin
thefuture.Also,pro-socialbehaviorcanleadtopositivereputationeffectsthat
eventuallyprovidematerialbenefits.
While the literature has proposed a number of tests between these alter-
native explanations, some based on observational data, others on laboratory
experiments (e.g., Altonji et al. 1992; Ribar and Wilhelm 2002; Fehr and
Fischbacher2003),wesuggestinthispaperanalternativerouteforuncovering
genuine altruism, namely by exploiting information on measured utility of
people.Suchinformationcanrevealtheextenttowhichpreferencesareother
regardingorinterdependent.Interdependentpreferences,inturn,canbeseen
astheproximatemechanismbywhichgenuinelyaltruisticbehaviorisinduced
in humans. In other words, without interdependent preferences, all observed
behaviorsofapparentlyaltruistictransferswouldneedtobeascribedtoselfish
motives.
Happinessandaltruismwithintheextendedfamily 1035
Inthissense,interdependentpreferencesaremorefundamentaltoaltruism
than actual transfers: the absence of transfers (or altruistic behavior more
broadly defined) in a specific period and environment does not rule out
altruismingeneral,whiletheabsenceofinterdependentpreferencesdoes.For
theformer,considerthesituationofparentsandtheirchildren:Ifincomeflows
areverysimilar,altruisticparentswillnotmaketransfersalthoughtheywould
dosoifasufficientlylargeincomegapweretodevelop.
Theapproachweproposeisbasedonself-reportedhappinessasaproxyfor
utility.Weanalyzetheextentofinterdependentpreferencesinthecontextof
parents and their adult children who have moved out and live on their own.
Theobjectiveofthepaperisthustotestwhetherandtowhatextentparents’
happinessisrelatedtothatoftheirchildren.Forthatpurpose,auniquelinked
parent–child dataset has been extracted from the German Socio-Economic
Panel(GSOEP)fortheyears2000to2004.
Our primary finding is that of a strong association between the utility
proxies, i.e., evidence for interdependent preferences. We explore a number
of potential explanations, including shared environment, inherited predispo-
sition toward happiness, paternalistic preferences, and reversed causation.
Thepositiveassociationpersistsaftercontrollingforahostofsocioeconomic
background variables and, exploiting the longitudinal structure of the data,
individualspecifictimeinvariantfixedeffects.Wealsoperformedinstrumental
variable estimation, although it is difficult to find credible instruments in the
data,andtherequiredexclusionrestrictionsmaynotholdfortheinstruments
we used. While this leaves some uncertainty as to the magnitude of the
association, we can reject the null hypothesis of no preference independence
inallspecifications.Thisrobustnesssupportstheviewthatparents’andchild’s
happinessareindeedrelatedandthatthisrelationcanbemeasuredinsurvey
data.Dependingonspecification,a1.5point(1standarddeviation)increasein
child’shappinessisassociatedwithanincreaseinparents’reportedhappiness
thatequalsthatofa20–45%increaseinownincome.
2Happinessandaltruism
Measures of happiness have been developed and tested extensively in psy-
chological research (Diener 1984). In the simplest case, there is a single
item question on life satisfaction or happiness. According to Veenhoven,
“happinessisthedegreetowhichapersonevaluatestheoverallqualityofhis
present life-as-a-whole positively” (Veenhoven 1988, p.3.) There is a general
consensusthatsubjectivewell-beingtapsprimarilyintocognitivedimensions,
toalargeextentindependentlyofaffect(Dieneretal.1985).
These happiness data are increasingly used to tackle important questions
in economics, as reviewed in Frey and Stutzer (2002), Layard (2005), and Di
Tella and MacCulloch (2006). Indeed, the recent surge in interest is quite
dramatic, as pointed out by Clark et al. (2008a), who counted 417 happiness
related articles between 1960 and 2005 in Econlit. Of these, 76% had been
1036 J.Schwarze,R.Winkelmann
publishedsince1995and30%since2003.Mostofthesepapersuse,inoneway
or another, answer to current happiness or life satisfaction questions in cross
section and panel survey data to study the factors that determine well-being,
among them economic policies and institutions. Some of them test whether
happinesspredictsbehavior.Clarketal.(1998)showthatlowjobsatisfaction
predicts quits; Clark et al. (2008b) show that low happiness among married
peoplepredictsdivorce.
Themajorityofpapershastakenanindividualisticapproachtohappiness:
One person’s happiness is not directly affected by how happy others are.
Instead,there has beena substantialamountof work onindirect interdepen-
dence, such as status interdependence or other kinds of externalities (e.g.,
Clark and Oswald 1996). Where direct interdependence has been studied, it
has been limited to happiness interdependence among individuals within the
samehousehold(e.g.,ShieldsandPrice2005;Winkelmann2005;Powdthavee
2009).
Inthispaper,webroadenthescopeofanalysisandinvestigateinterdepen-
denceamongindividualslivinginseparatehouseholds.Clearly,itismeaning-
lesstosearchforinterdependencebetweenrandomlyselectedhouseholds.The
households must be somehow related, know each other, communicate, and
interact. In our case, the relationship is that of kinship, as we consider par-
ent households and child households. Alternative relationships are possible.
FowlerandChristakis(2008),forinstance,analyzehappinessinterdependence
amongfriends.
Our focus on the relationships between parents and children ties in with
the economic literature on altruism within extended family. Becker (1981,
1991), taking seriously the Edgeworth (1881) proposal, formalized altruism
withinaframeworkofutilitymaximizationunderinterdependentpreferences.
Formally,supposethat
V =U +ηU
p p k
wherethetotalutilityofaparent V isadditivelyrelatedtothechild’sutility
p
U . In this very simple model, η is the “coefficient of effective sympathy”, to
k
followEdgeworth’sdefinition,or,inourcontext,thealtruismparameter.Ifηis
0,wehaveasituationofnon-interdependentpreferences,or“selfishness”.For
positiveη,anincreaseinthechild’sutilityleadstoanincreaseintheparent’s
utility.Wecallthissituationoneof“altruisticpreferences”.Anegativeηwould
reflectenvy.
Becker (1981) showed that utility function 1 implies altruistic behavior:
Undercertaincircumstances,parentswilltransferresourcestotheirchildren.
But the inverse conclusion does not hold: Transfers can have many motives,
and knowing whether they are driven by altruism, exchange, or joy of giving
is relevant for many policy questions, including efficient reform of old age
security, long-term care, and social assistance. It can be shown, e.g., that
attempts by governments to redistribute income between generations can be
neutralized if families are altruistic since if the income of a beneficiary of an
Happinessandaltruismwithintheextendedfamily 1037
altruistictransferisincreased,thattransferwillbereducedbyanequalamount
(seeLaferréreandWolff2006,forarecentsurveyoftheliterature).
The majority of empirical papers estimate inter-household transfer equa-
tions where the amount of transfers from parents to children is regressed on
the parents’ income and income of the child together with other variables.
Subsequently, tests can be set up to verify predictions from the model of
altruistic families. However, this approach requires specific data on transfer
paymentsbetweenfamilymembers.AsindicatedbyAltonjietal.(1992),the
timingoftransfersisarbitrary,sothatstudiesthatarenotabletocoveralong
periodmayleadtoincorrectconclusions.Inaddition,non-monetarytransfers,
suchasservicesorhouseholdproducedgoods,aredifficulttoobserve.
3Data
Our empirical analysis is based on the 2000–2004 waves of the GSOEP. This
panel household survey was started in 1984 with a random sample of 5,624
householdsinWestGermany(Wagneretal.1993).In1990,itwasaugmented
by a sample of East German households. From the outset, an attempt was
made to trace and interview adult children who moved from their parents’
household to live in an own household alone or together with a partner and
own children. If the tracing was successful, the GSOEP allows to link the
originalhouseholdwithitsspin-off(s).Itisthereforepossibletomergedataon
parentswiththoseontheirchildrenwhohavemovedout.Initially,suchcases
wererarebutinrecentyearsthenumberoflinkableparent–childobservations
became quite large, enabling the kind of analysis we want to conduct. We
therefore selected the year 2000 as our first year of analysis. For that year,
wecouldidentify930parenthouseholdswithlinkablespin-offs.By2004,that
numberhadincreasedto1,118parenthouseholds.
Thebasicunitofobservationisaparent–childpair.Westartedbyextracting
all parents. If we could find for any of these fathers or mothers in any year
information on at least one child living in a spin-off household, this parent–
childpairconstitutesoneobservation.Eachadditionalyearforagivenchild,
oreachadditionalchildinagivenyear,generatesoneadditionalobservation.
The cross-sectional structure of the dataset from the parents’ point of view,
for the year 2002, is depicted in Table 1. There were 1,750 parents for
whom information on up to five children not living in the same household
was available. Information for exactly one adult child not living in the same
household was present for 1,317 parents. Three hundred sixty-three parents
canbematchedtotwochildrenandsoon.Alltogether,the2002datacomprise
2,264observations(=parent/childpairs).Fromthetotalof1,750parents,1,454
or83%arecoupleswhereastheremaining296casesrefertosingleparents.
Inthe2000–2004timedimension,thedataformanunbalancedpanel.The
numberofparents(countingmothersandfathersseparately)withatleastone
entryinanyofthe5yearsis2,562;26.4%ofparentsareobservedatmostthree
times,19.6%areincludedfourtimes,andtheremaining54.0%isobservedin
1038 J.Schwarze,R.Winkelmann
Table1 Structureofthedataset2002
Childrennotlivingin Numberofparents Mothers Fathers Numberof
parents’household observations
Frequency % Frequency Frequency Frequency %
1 1,317 75.3 708 609 1,317 58.0
2 363 20.7 199 164 726 32.2
3 61 3.5 33 28 183 8.1
4 7 0.4 4 3 28 1.2
5 2 0.1 1 1 10 0.4
Total 1,750 100 945 805 2,264 100
Parentsin2-parent 1,454 83.1 – – – –
households
Source:GSOEP2002
all 5 years, adding up to 8,630 separate parent-year observations. The total
number of adult and independently living children contributing at least one
observationis2,009.Again,manychildrenareobservedrepeatedlyovertime,
sothatthereisatotalof6,520child-yearobservations.
The particular structure of the dataset deserves some comment, as it de-
viates from the standard random sampling assumption in a number of ways,
necessitating corresponding adjustments to the econometric analysis. First,
therearemultipleobservationsforthesameparent–childpairovertime.Time
invarianteffectscanbeaccountedforbyusingfixedeffects,randomeffects,or
byadjustingthestandarderrorsforclustering.
Second, at any point in time, there can be either one or two parent–child
observations in the same household. Two observations occur if both mothers
and fathers respond in the survey. Household effects can be either period
specific or time invariant. In the latter case, since parents are nested within
households,householdfixedeffectsdonotcontributeanythingoverandabove
parent fixed effects mentioned previously. In the former case, it is not an
optiontoconditiononperiodspecifichouseholdeffectssincethemainvariable
ofinterest,childhappiness,doesnotvarybetweenfathersandmothersatone
point in time. Instead, standard errors can be adjusted for clustering at the
householdlevel.
Third, instances where the same parent is matched to several children
constitute a problem in a regression context. The stochastic error capturing
the unobserved determinants of a parents happiness is essentially the same,
regardless of whether we condition on the happiness of a first or that of a
second child, and hence, these observations cannot be independent. While
this does not make running a regression technically impossible, one would
need to account for the near perfect correlation when computing standard
errors. Alternatively, one can average over the children’s observations and
run the regression using such synthetic parent–child pairs. This approach is
choseninthispaper.Italsoensuresthatparentswithmultiplechildrendonot
get stronger weights in the regression than parents with a single child. The
sensitivity of the results to taking averages was explored by using alternative
Happinessandaltruismwithintheextendedfamily 1039
sampleslimitedtoparentswithonechildortheoldestchildonly,butnoneof
thesubstantiveconclusionswasaffected.
For each parent and child, we extracted a wide range of household and
person specific socioeconomic variables. Happiness is measured using the
following question: “How satisfied are you with your life, all things consid-
ered? Please answer according to the following scale: “0” means completely
dissatisfied,“10”meanscompletelysatisfied”.Lifesatisfactionandhappiness
are treated here as synonymous. Potential determinants of happiness include
age,agesquared,health,gender,nationality,yearsofeducation,maritalstatus,
whetherwidowed,whetherdivorced,householdsize,numberofchildren,place
ofabode,employmentstatus,andincome.Healthismeasuredbyaself-rating
of the respondents on a five-point scale and converted to a “good-health”
indicator for the values 4 and 5. Income is measured as disposable monthly
post-government income of the household. Instead of applying an arbitrary
equivalence scale, all models adopt a flexible specification of economies of
scalebyincludingthelogofhouseholdsize,inadditiontothelogofhousehold
income.
The following variables are extracted for adult children not living in the
parent’shousehold:age,gender,maritalstatus,health,education,employment
status, and household income. They are computed in the same way as they
wereforparents.InTable2,weseethatthearithmeticmeanofthehappiness
Table2 Descriptivestatistics
Parents Children
Variable Mean Standarddeviation Mean Standarddeviation
Happiness 6.57 1.80 7.06 1.59
Female 0.54 0.50 0.51 0.50
Age 57.4 8.7 30.7 6.1
Goodhealth 0.31 0.46 0.70 0.46
Married 0.82 0.38 0.46 0.50
Yearsofschooling 11.2 2.4 12.3 2.5
Unemployed 0.08 0.28 0.07 0.25
Retired 0.33 0.47
Houseownership 0.56 0.50 0.26 0.44
Loghouseholdincome 8.29 0.52 8.16 0.56
Loghouseholdsize 0.80 0.39 0.77 0.54
Distance(inkm) 49.3 112.1
Samedistrict 0.64 0.48
Numberofchildren 1.97 1.19
Ageatleavinghome 23.3 4.4
Year2000 0.18 0.39 0.18 0.39
Year2001 0.19 0.39 0.19 0.39
Year2002 0.20 0.40 0.20 0.40
Year2003 0.21 0.41 0.21 0.41
Year2004 0.22 0.41 0.22 0.41
Observations 8,630a 6,520b
Source:GSOEP2000–2004
aExcludesmultipleperson-yearobservationsforparentswithseveralchildren
bExcludesmultipleperson-yearobservationsforchildrenwithtwoparents
1040 J.Schwarze,R.Winkelmann
responseisa6.6forparentsanda7.1forchildren.Parentsareonaverageabout
26.7yearsolderthantheiradultchildren.Childrenreportasubstantiallybetter
healththanparents(70%asopposedto31%with“goodhealth”).Ontheother
hand,themaritalrateismuchloweramongadultchildrenthanamongparents
(46%asopposedto82%).Feweradultchildrenownahouse,andtheiraverage
logincomeisabout13logpointsbelowthatoftheirparents.
We also observe when children left their parental home and how far they
moved.Theaverageageatmovingoutis23.3years.Sincetheaverageageat
thetimeofsurveyis30.7,itmeansthatthesechildrenhavelivedontheirown
foranaverageofabout7years.Thereissubstantialvariationinthetimeaway.
About 20% of all children have moved within the last 2 years; about 25% of
all children have moved out more than 10 years earlier. One might suspect
that the elapsed time since moving out can affect the strength of measured
preferenceinterdependence,aninteractionthatwillbetested.
A similar moderation might result from the distance between parent and
child. For example, any happiness interdependence effectively requires that
parents know about their children’s momentary happiness, and distance can
serve as a measure of the quality of that information. For example, the
greaterthedistancebetweenthehouseholds,thelessaccuratelymightparents
be informed about the living conditions and well-being of their children. In
addition,ofcourse,distanceitselfmightdirectlyinfluenceaparent’shappiness.
We employ two measures for geographical distance (this part of research
using regional information was carried out at the DIW Berlin. We thank the
staff for making the information available). The first is a simple indicator
whether or not the child lives in the same district as the parents—this is the
case for 65% of all children. The second is the distance in kilometers, using
thegeographicalcoordinateofthecountyofresidence’smidpoint(European
Terrestrial Reference System, ETRS89). The average distance between a
parent’shouseholdandachild’shouseholdamountsto49km.
4Results
Whatprimafacieevidenceisthereforinterdependenthappinessinourdata?
In particular, is it the case that happier parents also have happier children?
Table3showsasimplecross-tabulationofhappinessforparentsandchildren.
Observationsarepooledover5years.Theoriginal11-pointscaleiscollapsed
into a trichotomy: 0–5, 6–7, and 8–10 corresponding to the notions of below,
average,andaboveaveragehappiness,respectively.Thetablerevealsastrong
positiveassociationbetweenthehappinessofadultchildrenandthehappiness
oftheirparents.Forexample,only23%ofparentsofadultchildrenwithbelow
average happiness report an above average happiness themselves, compared
to 44% of those parents with above average happy adult children. A formal
Pearson chi-squared test rejects the independence hypothesis with p value
of zero. A similar result is obtained when the original 11-point scale is used
insteadofthegroupedcategories.
Happinessandaltruismwithintheextendedfamily 1041
Table3 Happinessresponses
Happiness Happinessofchild
ofparentsandchildren
(inpercent,n=8,630) ofparent 0–5 6–7 8–10 Total
0–5 40.0 27.9 20.1 26.6
6–7 36.9 40.7 36.3 38.3
8–10 23.1 31.4 43.6 35.1
Total 100.0 100.0 100.0 100.0
Source:GSOEP2000–2004
As mentioned before, the association in happiness of parents and children
can reflect genetic and environmental factors as well as a true causal inter-
dependence due to altruistic preferences. If happiness between parents and
children were causally related, then one would expect to find that changes in
happiness of parents are related to changes in happiness of children. Such an
association is more convincing evidence for a causal relation, as it eliminates
anypotentialconfoundinginterferenceoftime-invariantgeneticandenviron-
mental factors. In Table 4, we show the distribution of year-to-year changes
inaparent’shappiness(decline/increase)conditionalonyear-to-yearchanges
inthereportedchildhappiness.Thefirsttwocolumnsareforanydecreaseor
increase,respectively,whereasthesecondtwocolumnsrefertolargechanges
in a child’s happiness, a decline or increase by a minimum of three points on
the11-pointresponsescale.
Indeed, we find an association in first differences as well. For example,
the relative frequency of an increase in happiness for parents is lowered by
7.1 percentage points if the child’s happiness decreased by a minimum of 3,
comparedtothecasewherethechild’shappinessincreasedbyaminimumof3.
Inthe“allchanges”comparison,thecorrespondingassociationisreducedtoa
4.6percentagepointsdifference.APearsonchi-squaredtestindicatesrejection
oftheindependenceassumption.
To summarize, the evidence is compatible with the notion that part of the
associationinhappinessresponsesofparentsandadultchildrenisduetodirect
utility interdependence, or altruism. However, such a descriptive analysis
cannot rule out that there are alternative explanations for interdependence.
Foracloserunderstandingofwhattheseresultstellusaboutaltruism,weturn
nowtoamoreformalmodelingapproach.
Table4 Changesin
Changeinhappiness Changeinhappinessofchild
happinessresponsesof
parentsbetweent−1andt, ofparent Anychange Largechange
conditionalonchangesfor ≤−1 ≥+1 ≤−3 ≥+3
children(inpercent) Decrease 55.5 50.9 59.6 52.5
Increase 45.5 49.1 40.4 47.5
Total 100.0 100.0 100.0 100.0
Observations 1,173 954 166 143
pvaluechi-squared 0.036 0.204
Source:GSOEP2000–2004
1042 J.Schwarze,R.Winkelmann
4.1Regressionmodelsofparentalwell-being
Astochasticversionofalinearizedutilityfunctionofparentscanbewrittenas
V =U +ηU +u (1)
p p k
where V istheoverallutilityfunction,U =U(x )istheutilitythatparents
p p p
derive from things other than their child’s well-being, U =U(x ) is the
k k
child’s utility, u is a stochastic error term, and η is the altruism parameter of
interest.x andx includeallfactorsthathavebeenidentifiedbytheprevious
p k
happiness literature as determinants of individual well-being. In traditional
microeconomicutilitymodels,asexemplifiedbyBecker(1981),thiswouldbe
primarily own consumption. The subjective well-being approach is broader,
however, and x therefore includes many other factors, such as marital status,
health,andemployment,besidesincomeandconsumption.
The important assumption captured by Eq. 1, apart from linearity, is the
absence of paternalistic preferences. By this, we mean that x enters the
k
parents’ overall utility not directly but only by way of mediation through the
child’s utility U(x ). This assumption may not be very plausible, depending
k
on the variable x we have in mind. We can easily think of some factors that
k
makethechildhappybuttheparentunhappy(suchasperhapsanextramarital
affairofthesonordaughter).Forothervariables(suchasage),theexclusion
restrictionofnodirecteffectmaybemorereasonable.Ofcourse,thepresence
ofpaternalisticpreferencesdoesnotmeanthataparentcannothavealtruistic
preferencesatthesametime.Itonlymakesitsmeasurementfromsurveydata
harder, as it generates endogeneity in model 1, through correlation between
U andu.Wereturntothisissuelater.
k
Finally, the model does not say anything about more complex patterns of
happinessinterdependence,suchasaltruismofchildrentowardtheirparents,
or altruism between spouses. With altruism among spouses, a third term,
V , should be included. An increase in child happiness increases V directly,
s p
throughη,andindirectly,throughitseffecton V .Equation1shouldthenbe
s
interpretedasapartialreducedform,measuringtheoveralleffect.
4.2Pooleddataregressions
Happiness equations are often estimated using the ordered probit or the
ordered logit model. However, as pointed out by Van Praag and Ferrer-i-
Carbonell(2004),suchmodelsimplyanimplicitcardinalizationaswell.While
linear regression models do not allow to draw inference on single outcome
probabilities (such as the probability of scoring an 8 or above on a 0–10
response scale), trade-off ratios can be computed, and there is widespread
evidence(exploredamongothersinFerrer-i-CarbonellandFrijters,2004)that
these are quite robust to the choice of model. We use here the linear model
approachsinceitmakestherequiredextensionstopaneldataandinstrumental
variablemethodsmuchmoretransparent.