L ife-CycleL earning, Earning, Incomeand
W ealth
D avid A ndolfatto
Simon FraserU niversity
ChristopherFerrall
Q ueen’s U niversity
P aulG omme
FederalR eserveB ankofCleveland
N ovember2000
1
Introduction
Individualswhoinvestheavilyinhumancapitaltendtoexperienceahigherlevel
ofearnings andincomethroughoutmostoftheirlife-cycle. M ostoftheirhigher
earnings arein theform ofhigherwages, butasigni…cantfraction is accounted
forby a greaterwork e¤ort. In addition, such individuals tend to consume
moreand accumulate…nancialassets atafasterrate. W hataccounts forthese
di¤erences? W hile one mightbe inclined to attribute such di¤erences largely
to luck, much ofthe heterogeneity we observe could also be due to personal
choices thataremadeonthebasis ofan intrinsicsetoftastes andabilities that
happen todi¤eracross people. O urpaperis aboutexploringtheplausibilityof
this latterhypothesis.
O neobvious measureofpasthuman capitalinvestments is thelevelofeducationalattainment. A mongadults in Canada and the U nited States, roughly
25% arehigh-schooldropouts, 50 % haveahigh-schooldiploma, and25% havea
collegedegree. U nlikedemographicvariables such as age, sex, and race, educationalattainment(orhumancapitalaccumulationingeneral) is largelyachoice
variable. Itseems reasonabletosuppose thatindividuals are from an early age
generally aware ofthe bene…ts associated with higherlevels ofhuman capital
investment;and yet, people clearly make di¤erentchoices. W hatdrives these
di¤erentdecisions?
O ne way tounderstand the human capitalchoice is in terms ofan optimal
investmentdecision;seeB en-P orath (19 67). In theB en-P orath model, individuals seektomaximize the presentvalueoftheirlifetime earnings by allocating
theirtime between work and learningactivities, and by choosingan appropriate expenditure path foreducationalgoods and services. A key parameterin
this modelis the‘abilitytolearn’, modelledas thetechnologicale¢ciencywith
1
which learninge¤ortand resources augmentthe value ofhuman capital.1 N ot
surprisingly, themodelpredicts thatmoreableindividuals choosetoundertake
greaterhumancapitalinvestments, especiallyearlyoninthelife-cycle, andthat
learninge¤ortdeclines overtime. D uring youth, less able individuals tend to
earn more (as they devote more time towork ratherthan learning), butmore
ableindividuals haverapidlyrisingearningpro…les thatsoon overtake thoseof
thelessable. Inaddition, dispersioninearningsacrosseducationalgroupstends
togrowovertime. T hese predictions are broadly consistentwith the evidence;
e.g., seeL illard(19 7 7 ).
W hilethebasicB en-P orath modelprovides aplausibleexplanation forwhy
earnings pro…les mightdi¤er, before one can be con…dentthat ability di¤erences are at the root of inequality it would be prudent to examine whether
the modelis consistentwith otherfacts, forexample, on laboursupply, consumption, and assetaccumulation behaviour. In orderto examine this issue,
thebasicmodelmustbe extended toincorporate alabour-leisurechoiceand a
consumption-savingdecision. Such an extension has been provided by B linder
and W eiss (19 7 6
), H eckman (19 7 6), and R yder, Sta¤ord and Stephan (19 7 6).
Judging by whatis reported in the recentsurvey by N ealand R osen (19 9 8 ),
these versions ofthe B en-P orath human capitalmodelrepresentthe extentto
which this theoreticalset-up has currently progressed.
B linderand W eiss (19 7 6) and R yder, Sta¤ord and Stephan (19 7 6
) are primarily concerned with exploringwhatsortoflife-cycledynamics mightemerge
in such an environmentfora ‘representative’individual.2 H eckman (19 7 6) reports theresults ofseveralcomparativedynamicsexercises, butdoes notalways
provide a fulldescription ofjointbehaviour. Forexample, he …nds thatindividuals with greaterlearningability have peaks in theirhours ofwork pro…les
atolderages, butwe are nottold howthese pro…les are positioned relative to
each other. A s well, he does notask howdi¤erences in ability a¤ect…nancial
assetaccumulation.
T hepurposeofourpaperis explorewhatthis environmenthas tosayabout
howlife-cyclepatternsofconsumption, learning, laboursupply, earnings, income
andassetaccumulationshouldbeshapedas afunctionofparameters describing
tastes and abilities. In this paper, we focus on three sources of parameter
heterogeneity: (1) theabilitytolearn;(2) thesubjectiverateoftime-preference;
and (3) thetasteforleisure. W ewish todiscover…rstofallwhetherany single
source ofparameterheterogeneity mightbe able toaccountforthe qualitative
di¤erences thatwe observe in the data. O urpreliminary …ndings suggestthat
no single source ofparameterheterogeneity can accountforthe facts. N ext,
we ask whetherthere are plausible combinations ofparameters thatmightbe
able to explain the data. O urpreliminary …ndings suggestthatthe modelis
broadly consistentwith the evidence ifwe assume thatpeople di¤erin their
rate oftime-preference and theirtaste forleisure; and ifthese parameters are
1A
notherwaytomodellearningability is in terms ofinitialendowments ofhuman capital.
a very rich and complex setofdynamics is possible.
2 Evidently,
2
positivelycorrelated amongindividuals.
1.1
Some Facts
In this section, we describe what‘typical’(median) life-cycle pro…les look like
across threeeducationalgroups: dropouts;highschool;andcollege. T hedatais
from theCanadian 19 9 2 FamilyExpenditureSurveyP ublicU seFile(FA M EX )
and is described in alittle more detailin A ppendix I. W e alsoreviewevidence
from A ttanasio (19 9 4) who reports similarmeasurements from the 19 9 0 ConsumerExpenditureSurveyfortheU nited States.
1.2
Income, ConsumptionandSaving
Figure 1 plots measures of after-tax income, consumption expenditures, and
savingforeacheducationalgroup overtenperiodsofalife-cyclebeginningatage
21 andendingatage7 0. N otsurprisingly, morehighlyeducatedindividualshave
signi…cantlymoreincomeateveryageexceptforveryearlyinthelife-cycle. T he
age-income pro…le fordropouts displays a modesthump-shaped pattern, with
incomepeakingage52 atalevelthatis 1 :65 times higherthan atage21. T he
age-incomepro…leforcollegegraduates, ontheotherhand, displaysasigni…cant
hump-shaped pattern, with income peaking atage 52 ata levelthatis 2:88
times higherthan atage21. A ccordingtothis data, collegegraduates generate
roughlytwicetheincomeofdropouts aroundthepeakincomeyears. A ttanasio
(19 9 4) reports similar …ndings for the U nited States. In particular, median
income peaks in the 51–55 year-old cohort, with college graduates generating
2.84 times more incomethan dropouts.
Q ualitatively, itappears thatconsumption tracks disposable income fairly
closelyinthesenseofsharingthesamehump-shapedpattern. T hisfactthathas
beenreferredtoasthe‘consumption-incomeparallel’(seeCarrollandSummers,
19 9 1) andis sometimes usedas anargumenttorejectthebasiclife-cyclemodel,
which predicts a ‡atage-consumption pro…le. A ttanasioand B rowning(19 9 5)
argue thatthe consumption-income parallellargely re‡ects family-size e¤ects.
U sing several years of U .K. FES data to follow cohorts through time, they
reproduce the …nding that consumption and income move togetherover the
life-cycle. H owever, de‡atingconsumption byan adult-equivalentscale renders
acompletely ‡atlife-cycle path foradjusted consumption. O n the otherhand,
G ourinchas and P arker(19 9 9 ) arguethatwith theiradjustments, consumption
continues todisplayahump-shape.
T he bottom panel of Figure 1 displays household saving, de…ned here as
thedi¤erencebetween householdafter-taxincomeandhouseholdconsumption.
A ccordingto this measure ofsaving, the median household ofeach education
group arenetsaversoverthelife-cycle(atleast, up toage7 0). H ighereducation
groupstendtosavemore, bothintotalandasaratiooftheirdisposableincome.
3
In fact, the propensity to save remains fairly constantfrom age 32 onward in
this data. O verthe entire life-cycle, saving rates average 8:8% fordropouts,
1 0 :6% forhighschoolgraduates, and 1 9:6% forcollegegraduates.
T he FA M EX data setprovides a series called ‘netchange in assets’ which
di¤ers (empirically, notconceptually) somewhat from the saving measure reported above. Q ualitatively, the net-change-in-assets series is similarin that
highereducation groups tend to save more overthe entire life-cycle. B utaccordingtothis measure, themedian savingfordropouts is pretty close tozero
overtheentire life-cycle and themedian savingforhighschoolgraduates is not
very much larger. In addition, the levelofsavingbycollegegraduates is about
halfofwhatis recorded by the earlierde…nition ofsaving.
T he savingbehaviourreported in Figure 1 is broadly consistentwith SCF
andP SID dataonwealthaccumulationpatterns across educationalgroups. A ccordingto Cagetti (19 9 9 ), median networth positions (includinghousingbut
abstractingfrom pensionentitlements) areverylowandsimilaracross individualsatage30. W hileallthreeeducationalgroupstendtosaveovertheentirelifecycle, therateofassetaccumulation is much higherforwell-educatedindividuals. B yage6
0, themedian dropouthas accumulatedroughlybetween $60,000–
9 0,000;themedianhigh-schoolgraduatehasbetween$125,000–18 0,000;andthe
median college graduate has between $250,000–300,000.3 In otherwords, to a
…rstapproximation, each levelofeducation is associatedwith adoublingofnet
worth in old age.
1.3 Earnings, L abourSupply and W ages
Figure 2 plots measures ofearnings, laboursupply, and wages foreach educationalgroup overtenperiodsofalife-cyclebeginningatage21 andendingatage
7 0. A gain, itis notsurprisingtodiscoverthatbettereducatedindividuals tend
tohave higherlife-cycle earnings. A ge-earningpro…les tend to display a more
pronounced hump-shaped pattern relative to income, partly because earnings
drop signi…cantly as peopleapproach old age.
T henexttwopanels inFigure2 revealthatbettereducatedindividuals have
higherearnings early on in the life-cycle because they allocate more time the
marketsector;i.e., notbecausethe pecuniary return tolabouris higher. W age
rates tendtogrowovertimeforalleducationgroups, butgrowmorequicklyfor
the bettereducated. L aboursupply pro…les rise early on in the life-cycle and
then ‡atten out, showinga modestdecline as the household ages;this pattern
holds forall education groups. T he main di¤erence in labour supply across
educationgroups is simplyinterms oflevels: collegegraduates workon average
abouttwiceas hard adropouts.
3T he …gures are in 19 9 2 dollars. T he lower bound is from the S CF; the upper bound is
from the P S ID .
4
1.3.1
T he R eturn on Education
T here is a large empiricalliterature concerned with measuringthe ‘return’ to
education;this literaturehas recentlybeensurveyedbyCard(19 9 8 ). T hestandard econometricmodeltaken tothe data is usually some variantofM incer’s
(19 7 4) ‘human capitalearnings function’thatrelates somemeasureoflogearnings(logy)tosomemeasuresofeducationalattainment(S )andworkexperience
(X );togetherwith astatisticalresidual(");e.g.,
logy = a+ bS + g(X )+ ":
(1)
A pparently, it is now conventional to refer to the estimated parameter b as
the ‘return to education’. T ypically, the return to education is found to vary
with certain characteristics ofindividuals, such as ‘ability’ and ‘family background’. Card argues thatthe empiricalspeci…cation above, with g modelled
as athird orfourth degreepolynomial, provides areasonably good…twith the
data, although, contrary to the speci…cation in (1), there does appearto be
someevidence ofan interaction between education and experience.
W hen log annualearnings are regressed on education and othercontrols,
the estimated return to education is the sum ofthe bcoe¢cients forparallel
models …ttothelogofwages (logw)andthelogofannualhours (logh):H ere,
we reproduce Card’s (19 9 8 ) T able 1, which reports the estimated returns to
education using(1) …ttothe19 9 4–9 6CP S.
D ependentV ariable
logw logh logy
M en
b
R2
0.100
0.328
W omen
b
0.109
R2
0.247
0.042
0.222
0.142
0.403
0.056 0.16
5
0.105 0.247
T hus, Card concludes thatin the U .S. labourmarketin the mid-19 9 0s, about
two-thirds ofthe measured return to education in annualearnings data is attributable to the e¤ectofeducation on the wage rate, with the remainderattributabletothee¤ecton annualhours worked.
1.4 D ataSummary
T hereadershouldkeep inmindthatthereareseveralpracticaland(unresolved)
conceptualissues relating to the measurementofthese variables; see B rowning and L usardi (19 9 6
) for details. B ut despite the quantitative di¤erences
thatemerge dependingon howvariables are de…ned ormeasured, anumberof
5
qualitative features appeartobe robustacross di¤erentdatasets and di¤erent
de…nitions/measurements. T heimportantqualitativedi¤erences areas follows:
1. Individuals ofa given age di¤erin terms ofaccumulated human capital
(e.g., as measured byeducationalattainment).
2. Individuals whoinvestheavilyin human capital(bettereducatedindividuals) tend tohave higherincomes, earnings, consumption, and savings;
(a) H igherearnings areattributabletobothhigherwagerates (2/3) and
greaterworke¤ort(1/3);
(b) H ighersavings attributabletohigherincomes and agreaterpropensity tosave.
3. T he dispersion in income, earnings, consumption, and savingacross educationalgroups peaks sometime in the middle ofthe life-cycle;the dispersioninlaboursupplyandsavingrates remains relativelyconstant;and
the dispersion in wagerates is (weakly) increasingwith age.
W e wish to focus on these qualitative features ofthe data and ask whethera
sensibly parameterized life-cycle model(that endogenizes human capital and
laboursupply) can accountforthesequalitativepatterns.
2
T he M odel
Consideran economy populated by overlappinggenerations ofindividuals who
liveforJperiods, indexedbyj = 1 ;2;:::;J:T hepopulation is assumedtogrow
ataconstantratenperperiod, andwedenotetheshareofage-j individuals in
thepopulation by ¹ j;which is time-invariantand satis…es ¹ j = (1 + n)¡1 ¹ j¡1
P
forj = 2;:::;Jand J
j=1 ¹ j = 1 :
T hereis an issueas towhetheridiosyncraticrisks playan importantrolein
the evolution oflife-cycle variables. O urfeeling on this matteris that, while
idiosyncratic risks may be important, they are not dominant. T his view is
supportedbytheempiricalworkofV enti andW ise(2000), whoinvestigatethe
question ofwhy the dispersion ofwealth atretirementages is sogreat. T hese
authors argue that90 % ofthe variation observed in retirementwealth is due
tothe di¤erentchoices thatpeople make and nottoidiosyncraticluck. In the
analysis below, we abstractfrom uncertainty.
Individuals have preferences de…ned overdeterministictime-pro…les ofconsumption cj, leisure lj, as wellas a …nalnetworth position aJ+ 1 (bequeathed
tothefuturegeneration);letpreferences berepresentedbytheutilityfunction:
XJ
±j¡1 [U (cj)+ ¸V (lj)]+ ÂB (aJ+ 1 ):
j=1
6
A ssumethatthefunctions U ;V andB areallstrictlyconcaveandthattheysatisfy standard Inadaconditions;wewilltreatthese functions as common across
individuals. P references are parameterized by the discountfactor±;the taste
forleisure¸;andthestrengthofthebequestmotiveÂ;individuals mayormay
notdi¤eralong these dimensions. N ote: in this version ofthe paper, we set
 =0 :
T here are three uses fortime: marketwork n;learninge¤orte;and leisure
l;where n+ e+ l= 1 (and theusualnon-negativityconstraints). L ethdenote
human capital. P eoplemightdi¤erin theirinitialendowmentofhuman capital
(onemeasureofdi¤erences in ability). A person’s human capitalis assumed to
augmenttime-usein workingand learning;measured in ‘e¢ciency units’, work
e¤ortequals hn and learninge¤ortequals he:
Following H eckman (19 7 6), the human capitalaccumulation technology is
given by:4
hj+ 1 = (1 ¡¾)hj + ®G (hjej);
whereG is strictlyincreasingandconcave, ¾ is thedepreciation rateon human
capital, and® isaparameterthatindexes‘learningability’. W ewillassumethat
G and ¾ are common across households; however, ® may di¤er. L etv denote
thevectorofparameters describingaparticularindividual;i.e. v = (®;±;¸):
T here are twoprices in the model. L et! denote the price ofan e¢ciency
unitoflaborand letR denotethe(gross) realrateofinterestpaid on …nancial
assets. B oth ofthese prices willbe determined by marketclearingconditions
in the generalequilibrium. N otethatlaborearnings are given by !hn;sothat
w= !hcan beinterpreted as therealwage.
Individuals can saveorborrowfreely atthegoinginterestrateR (thereare
no debtconstraints beyond the end-period restriction aJ+ 1 ¸ 0 ). T he asset
accumulation equation is given as follows:
aj+ 1 = R aj + wjnj ¡cj;
O ptimaldecision-making results in a desired pro…le fcj;nj;ej;lj;aj+ 1 ;hj+ 1 j
!;R ;vgJ
j=1 :
W hatremains nowis thedeterminationofprices. Inasteady-state, theper
capitacapitalstockis given by:
K = (1 + n)¡1
XJ
j=1
¹j
X
aj(v)¤(v);
v
4N otethatwearenotmodellingtheschoolingchoice perse. W hatwe are assumingis that
individuals in the data who attend schoollongerare likely to investmore heavily in human
capital atall stages ofthe life-cycle. T o the extentthat this is true, we can then associate
people in the model with higher levels of human capital with people in the data who have
highereducation.
7
where ¤(v)represents the fraction ofthe population with parametervectorv:
T he percapitalevelofhours (measured in e¢ciency units) is given by:
H=
XJ
¹j
X
hj(v)nj(v)¤(v)
v
j=1
O utputis produced by aconstantreturns toscale production technology Q =
F (K;H):Equilibrium prices aredetermined by theusualmarginalconditions:
! = F H(K;H)
R = F K(K;H)+ 1 ¡Á;
whereÁ is thedepreciationrateofphysicalcapital. Finally, goods-marketclearingrequires:
C + (n+ Á)K = Q ;
where,
C =
XJ
j=1
2.1
¹j
X
cj(v)¤(v):
v
P arameterization
Functionalforms arerequired forU ;V ;G and F :
U (c)
V (z)
G (x)
F (K;H)
=
=
=
=
(1 ¡° )¡1 [c1 ¡° ¡1 ]
(1 ¡´)¡1 [z1 ¡´ ¡1 ]
x³
KµH1 ¡µ:
3 Calibration
A tthis stage, we do nothave the time to calibrate orestimate the modelas
preciselyaswewouldlike. So, wewillcontentourselveswitharoughcalibration.
W ecalibrate…rsttoa‘representative’individual;theparameters arechosen as
follows.
3.1
D emographics
L etthenumberofperiodsbeJ= 1 1 ;thelengthofaperiodis…veyears(thinkof
peoplebeginningtheireconomiclifeatage20 andlivingto7 0). T hepopulation
growth rateis setton= 0 ;sothat¹ j = 1 =Jforallj:
8
3.2
P references
T he curvature parameteron U is chosen to be ° = 1 :5 (a standard choice).
T he curvature forV is also chosen to be ´ = 1 :5: T he weighting factor for
leisure is chosen tobe ¸ = 1 :752;this generates the resultthatroughly 1 =3 of
available time is devoted to the labourmarket. T he discountfactoris chosen
tobe ± = 0 :86;which implies an annualdiscountrate of3%:
3.3 Technology
T helearningabilityparameteris setto® = 0 :40 ;this implies thatyoungpeople
spend around 10% oftheiravailable time in learningactivities. T he curvature
ofthe learningtechnology is taken from H eckman (19 7 6);³ = 0 :70 :T he share
ofphysicalcapitalintotaloutputis settoµ = 0 :35:P hysicalcapitaldepreciates
atan annualrate of1 2%;setÁ = 0 :48: A ssume thathuman capitaldoes not
depreciate;¾ = 0 :
3.4 Endowments
T he human capitalendowmentis normalized toh1 = 1 :
4 R epresentative Individual
In Figure 3 we plot the life-cycle behaviourof the representative individual;
i.e., the equilibrium based on theparameterization above. A s Figure 3 reveals,
themodeldoes avery nicejob ofreplicating‘typical’life-cyclebehaviour, with
the possible exception ofthe very aged. In particular, the modelpredicts that
consumption continues torise throughoutthe life-cycle;the datasuggests otherwise. A s well, in themodel, individuals dissavein old agemuch morerapidly
than in the data (we only plotthe …rst10 periods ofthe 13 period life-cycle).
T his last feature could presumably be recti…ed by incorporating the bequest
motive.
5
Single Sources ofH eterogeneity
In this section, we shallconsiderthree separate sources ofheterogeneity and
evaluate howeach, in isolation, is predicted toa¤ectlife-cycle behaviour. T he
three parameters we considerare: (1) the ability tolearn, ®;(2) the discount
factor, ±;and (3) the taste forleisure, ¸: Foreach case, we willmodelthree
types, representinghigh, medium, and lowvalues, with 50 % ofthe population
takingon the medium value, and the other50 % evenly divided across the two
9
extreme values. In equilibrium, each type ofperson willchoose adi¤erentlifetime learning pro…le; we label the group with the greatest life-time learning
e¤ort‘collegegraduates’and thosewith thelowest‘dropouts’.
5.1
T he D i¤erent-A bility H ypothesis
Supposethatindividualsdi¤eronlyintheirabilitytolearn;e.g., ® = 0 :32;0 :40 ;0 :48:
T he results are plotted in Figure 4. N otsurprisingly, those with the highest
learningability become‘college graduates’.
O bservethattheearnings pro…les taketheexpectedshapein thesensethat
those with low learning ability have higherearnings when young (relative to
high learningability types), and relatively lowerearnings when old. T his basic
qualitativepatternisalsohighlightedinN ealandR osen(19 9 8, Figure4.2), who
remark thatthis U -shaped relationship between cohortearnings variance and
cohortageis an importantthemein theliteratureon human capital. H owever,
this U -shaped pattern is notpresentin ourdata, possibly because by age 21
(theyoungestageinoursample) wearealreadybeyondtheminimum dispersion
point. A bility di¤erences seem to generate the right type of life-cycle wage
patterns, butlaboursupplypro…les arequalitativelysimilaronlyafterperiod3
(age32).5
T hemostglaringde…ciencyin the“D i¤erent-A bilityH ypothesis” is whatit
implies forassetaccumulation behaviour. A ccordingtothe model, individuals
with low learning ability (dropouts) will accumulate …nancial assets rapidly,
while those with high learningability (college) are predicted to hold negative
net-worth positions formostoftheirlife.
T he model’s logicis perfectly clear. W ealth takes twoforms in this model:
human wealth and …nancialwealth. L owability individuals naturally wish to
substitute intotheaccumulation of…nancialwealth, whilehigh ability individuals allocate theirresources toward accumulatinghuman capital. L ateron in
thelife-cycle, thosewhoare rich in human capitalworkhardertoexploittheir
relativelyhighskilllevels, whilethosewhoarerichin…nancialwealthcana¤ord
toconsume moreleisure.
5.2
T he D i¤erent-D iscount-R ate H ypothesis
T he idea thatpeople di¤erin theirdegree of‘patience’, and thatthis might
explain much ofthe heterogeneity observed in economic behaviour, is an old
one (e.g., see R ae, 18 34). H ere, we consider three rates of time-preference
(annualized) equal to: 0 :0 275;0 :0 30 ; and 0 :0 325;the results are displayed in
Figure5.
5 M easured hours of work here is totalhours worked plus time spentlearning, exceptfor
those aged 21 and in college. T he idea here is thattraining is undertaken while on the job.
10
In a model without leisure, di¤erent discount rates would have no e¤ect
on the levelofhuman capitalinvestment(assuming perfectcapitalmarkets).
H owever, when leisure is endogenous and when personaltime is a necessary
inputtolearning, di¤erencesinthesubjectiverateoftime-preferencewillinduce
di¤erent levels of learning e¤ort. B ecause learning is a form of investment,
one might naturally expect that relatively patient individuals would end up
accumulatingmore human capital. Somewhatsurprisingly, the modelpredicts
thattheleastpatientindividuals willaccumulatethe mosthuman capital;i.e.,
impatience here is positively correlated with the levelofeducation, although
thedi¤erences in time devoted tolearningaresmall. O nepossible explanation
forthis resultmightlie in the factthathuman capitalcannotbe consumed or
sold as death approaches, unlike …nancialcapital. Consequently, more patient
individuals (whowhenyoungplaceagreaterweightonend-of-lifeconsumption)
mightpreferto accumulate wealth through a vehicle thatis bettersuited to
providingforoldageconsumption. Inaddition, themorepatientplaceagreater
weighton future leisure; and …nancialassetaccumulation ratherthan human
capitalcan betterprovide forfuture leisure.
In the model, patientindividuals (associated here with dropouts) preferto
postponeconsumptionandleisuretoalaterage;hence, theyconsumelittleand
workhardwhen young, sothatnetworth grows rapidly(although theyremain
relatively unskilled). A ccordingtothe model, the reason why laboursupply is
relatively lowfordropouts in latterstages ofthe life-cycle is because they are
sowealthy. N eedless tosay, themodel’s explanation hardlyseems plausible.
5.3 T he D i¤erent-Taste-for-L eisure H ypothesis
Suppose nowthatpeople di¤eronly in the relative weightthey place on consumptionandleisureatanypointin time;here, weconsiderthefollowingthree
values forthe leisure parameter: ¸ = 1 :54; 1 :74; and 1 :94: A ccording to the
model, those whoplace relatively lowweighton leisure arethe ones whoaccumulate morehuman capital.
O utofthe three hypotheses considered sofar, the taste-for-leisure hypothesis seems to hold the mostpromise. In particular, the pro…les forearnings,
hours worked and realwages are qualitativelysimilartoobservation. B utonce
again, themostglaringde…ciencyofthis hypothesis is whatitpredicts forasset
accumulationbehaviour: lowereducationgroups displayagreaterpropensityto
save. A pparently, thosewhodonot…ndworkorschoolinge¤ortsopainfulprefertoaccumulatewealth through human capital, ratherthan through …nancial
assets.
11
6 M ultiple Sources ofH eterogeneity
T he main source oftension in the modelis thatwhich seems toexistbetween
humancapitaland…nancialcapital;i.e., thesetwoforms ofcapitalrepresentalternativemechanisms bywhichtoaccumulatepurchasingpower. Consequently,
ifoneis relativelygoodataccumulatinghumancapital(whetheritis becauseof
higherability, less patience, oragreatertasteforconsumption), then onetends
tosubstituteintohumancapitalattheexpenseof…nancialcapital. Inthedata,
however, the propensity to accumulate human capitalis positively correlated
with thepropensity toaccumulate…nancialassets.
T heonlywaytogeneratethis positivecorrelationbetweenhumanand…nancialcapitalinvestmentis toconsidermultiple sources ofheterogeneity. In this
section, weconsidertwoeconomies: onein which peopledi¤erin theirlearning
ability and theirdiscountrate;and onein which peopledi¤erin theirtastefor
leisure and theirdiscountrate. Forsimplicity, we assume aperfectcorrelation
between thetwoparameters (sothattherewillcontinuetobeonlythree types
ofindividuals).
6
.1
L earningA bilityand D iscountR ate
A ssume thatpeople di¤erboth in theirability to learn and in theirdiscount
rate;and thatthe discountrate (discountfactor) is negatively (positively) related with learningability. T hethree types ofindividuals are described by the
followingparametercon…guration:
T ype1
T ype2
T ype3
®
0.30
0.40
0.50
±
0.84
0.86
0.88
In the model, individuals who have a high ability tolearn and a lowdiscount
rate(T ype3 individuals) end up accumulatinggreaterlevels ofhuman capital.
T hehopehereis thatthehigh learningabilitywillresultinhigh humancapital
investments and thatthe lowdiscountrate willresultin ahigh rate ofsaving.
T he results are displayed in Figure 7 . A s the …gure reveals, this hypothesis
holds some promise. H owever, high-ability people stilltend to be netdebtors
earlyoninthelife-cycle(theywishto…nancetheirhumancapitalinvestments).
Increasingthedispersion in the time-preferenceparametermay help alongthis
margin;however, doingsowouldexacerbatethetiltsintheconsumptionpro…les
(somethingwedonotsee in the data).
6
.2
Taste forL eisure and D iscountR ate
A ssume nowthatpeople di¤erin theirtaste forleisure and in theirdiscount
rate;andthatdiscountingispositivelyrelatedtothetasteforleisure. T hethree
12
types ofindividuals aredescribedby the followingparametercon…guration:
T ype1
T ype2
T ype3
¸
1.25
1.7 5
2.25
±
0.88
0.86
0.84
Inthemodel, individuals whohavealowtasteforleisureandalowdiscount
rate(highdiscountfactor) endup accumulatinggreaterlevels ofhumancapital.
A swiththeearlierexperiment, thehopehereisthatthelowtasteforleisurewill
resultin high levels ofhuman capitalinvestments while the lowdiscountrate
willresultin ahigh rateofsaving. Figure 8 demonstrates thatthis hypothesis
has a great deal of promise; this …gure …ts the data better than any of the
explanations proposed sofar.
T heimplications ofthis hypothesis arepotentiallyprofound. Itargues that,
while peoplemay appeartodi¤erin theirabilitytolearn, this di¤erencearises
notfrom intrinsicdi¤erencesinlearningability(®);butfrom thehumancapital
investments thatpeople have chosen tomake in the past(rememberthatitis
thee¢ciencyunitoflearninge¤orthethatenters intothelearningproduction
function). A bility here is to be interpreted as the manifestation ofhard work
and frugal(forward-looking) tendencies.
7
D iscussion
W ebelieve thatitis interestingtodiscoverwhatsortofintrinsicdi¤erences in
peoplemightcausethem tomakeverydi¤erenteconomicdecisions. Knowledge
oftheintrinsicstructureofheterogeneity(i.e., thedistribution ofdeep parametervalues) canplayanimportantroleinthedesignofsocialpolicy. Forexample,
ifheterogeneous discountingis found to be important, then any redistributive
policy should likely includeprovisions tomakeentitlements legally inalienable;
seeA ndolfatto(2000). Ifitis foundthatthetasteforleisurematters morethan
the ability to learn in explaining the data, then we can conclude thatpeople
di¤erin theirskills notbecause ofintrinsic ability di¤erences butbecause of
howtheychosetoallocatetheirtimein the past. Ifmitigatingskilldi¤erences
(earnings di¤erentials) is a policy goal, then such a resultmightpointtoeducation subsidies. O n the otherhand, ifobserved heterogeneity is attributable
to di¤erences in endowments (…nancialbequests orinitialhuman capitallevels), then lump-sum transfers may be the suitable instrumentto implementa
redistribution policy.
13
FIGURE 1
Canada 1992 FAMEX Data
Household After-Tax Income
70000
60000
50000
40000
30000
Dropouts
Highschool
College
20000
10000
1
2
3
4
5
6
7
8
9
10
8
9
10
Household Consumption
50000
40000
30000
20000
Dropouts
Highschool
College
10000
1
2
3
4
5
6
7
Household Saving
(After-Tax Income Minus Consumption Expenditure)
25000
Dropouts
Highschool
College
20000
15000
10000
5000
0
-5000
1
2
3
4
5
6
Age (21-70 Years)
14
7
8
9
10
FIGURE 2
Canada 1992 FAMEX Data
Earnings
80000
60000
40000
20000
Dropouts
Highschool
College
0
1
2
3
4
5
6
7
8
9
10
Full Time Equivalent Weeks Worked per Worker
60
50
40
30
20
Dropouts
High School
College
10
0
1
2
3
4
5
6
7
8
9
10
8
9
10
Wage Rate
(Earnings Divided by Hours)
40
30
20
10
Dropouts
Highschool
College
0
1
2
3
4
5
6
7
15
Age (21-70 Years)
FIGURE 3
Representative Agent
0.24
0.45
0.22
0.40
0.20
0.35
0.18
0.30
0.16
0.25
Income
Earnings
Consumption
0.14
0.12
Work
Work+Training
0.20
1
2
3
4
5
6
7
8
9
10
1
0.25
0.56
0.20
0.52
0.15
0.48
0.10
0.44
0.05
0.40
2
3
4
5
6
7
8
9
10
Wage Rate
Net Worth
0.00
0.36
1
2
3
4
5
6
7
8
9
10
1
16
2
3
4
5
6
7
8
9
10
FIGURE 4
Differences in Learning Ability
Earnings
Income
30
30
Dropouts
Highschool
College
25
Dropouts
Highschool
College
25
20
20
15
15
10
10
5
1
2
3
4
5
6
7
8
9
10
1
2
3
Consumption
4
5
6
7
8
9
10
7
8
9
10
7
8
9
10
Measured Hours of Work
28
0.50
Dropouts
Highschool
College
26
24
0.45
0.40
22
0.35
20
0.30
18
0.25
16
0.20
14
Dropouts
Highschool
College
0.15
1
2
3
4
5
6
7
8
9
10
1
2
3
4
Net Worth
5
6
Wage Rate
40
70
Dropouts
Highschool
College
30
Dropouts
Highschool
College
60
20
50
10
40
0
-10
30
1
2
3
4
5
6
7
8
9
10
1
17
2
3
4
5
6
FIGURE 5
Differences in Time-Preference
Income
Earnings
24
22
20
22
18
20
16
14
18
12
Dropouts
Highschool
College
16
Dropouts
Highschool
College
10
8
14
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
8
9
10
Measured Hours of Work
Consumption
26
0.50
24
0.45
0.40
22
0.35
20
0.30
18
0.25
Dropouts
Highschool
College
16
Dropouts
Highschool
College
0.20
14
0.15
1
2
3
4
5
6
7
8
9
10
1
2
3
4
Net Worth
5
6
7
Wage Rate
40
60
Dropouts
Highschool
College
30
55
20
50
10
45
0
40
-10
Dropouts
Highschool
College
35
1
2
3
4
5
6
7
8
9
10
1
18
2
3
4
5
6
7
8
9
10
FIGURE 7
Negative Correlation Between the Rate of Time-Preference
and the Ability to Learn
Earnings
Income
0.32
0.26
Dropouts
Highschool
College
0.28
Dropouts
Highschool
College
0.24
0.22
0.24
0.20
0.18
0.20
0.16
0.16
0.14
0.12
0.12
1
2
3
4
5
6
7
8
9
10
1
2
3
Consumption
4
5
6
7
8
9
10
7
8
9
10
7
8
9
10
Measured Hours of Work
0.32
0.50
Dropouts
Highschool
College
0.28
0.45
0.40
0.24
0.35
0.20
0.30
0.16
Dropouts
Highschool
College
0.25
0.12
0.20
1
2
3
4
5
6
7
8
9
10
1
2
3
4
Net Worth
5
6
Wage Rate
0.3
0.70
Dropouts
Highschool
College
0.2
Dropouts
Highschool
College
0.65
0.60
0.55
0.1
0.50
0.45
0.0
0.40
-0.1
0.35
1
2
3
4
5
6
7
8
9
10
1
19
2
3
4
5
6
FIGURE 6
Differences in the Taste for Leisure
Income
Earnings
28
26
26
24
24
22
22
20
20
18
18
16
16
14
Dropouts
Highschool
College
12
14
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
8
9
10
Dropouts
Highschool
College
Measured Hours of Work
Consumption
28
0.50
26
0.45
24
0.40
22
20
0.35
18
0.30
16
Dropouts
Highschool
College
14
Dropouts
Highschool
College
0.25
0.20
12
1
2
3
4
5
6
7
8
9
10
1
2
3
4
Net Worth
5
6
7
Wage Rate
40
65
Dropouts
Highschool
College
30
60
55
20
50
10
45
0
Dropouts
Highschool
College
40
-10
35
1
2
3
4
5
6
7
8
9
10
1
Figure 1:
20
2
3
4
5
6
7
8
9
10
FIGURE 8
Positive Correlation Between the Rate of Time-Preference
and the Taste for Leisure
Earnings
Income
0.35
0.28
Dropouts
Highschool
College
0.30
Dropouts
Highschool
College
0.26
0.24
0.22
0.25
0.20
0.20
0.18
0.16
0.15
0.14
0.10
0.12
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
8
9
10
Measured Hours of Work
Consumption
0.35
0.55
Dropouts
Highschool
College
0.30
0.50
0.45
0.25
0.40
0.35
0.20
0.30
0.15
Dropouts
Highschool
College
0.25
0.10
0.20
1
2
3
4
5
6
7
8
9
10
1
2
3
4
Net Worth
5
6
7
Wage Rate
0.4
0.60
Dropouts
Highschool
College
0.3
0.55
0.2
0.50
0.1
0.45
0.0
0.40
-0.1
Dropouts
Highschool
College
0.35
1
2
3
4
5
6
7
8
9
10
1
21
2
3
4
5
6
7
8
9
10
A ppendixI: D ataD escription
T he data come from the 19 9 2 Family Expenditure Survey P ublic U se File
(FA M EX ). W eselectedthosehouseholds withnomorethan 2 wageearners and
with thereferenceperson reportingsomeeducation. A llstatistics areweighted
by theFA M EX weightvariable.
H ouseholds were grouped into…ve-yearage categories and three education
categories. M arried households were grouped accordingto the greaterlevelof
education and age ofthe spouses. T hatis, the age category ofthe household
is the maximum ofthe two spouses ages, and the education category is the
maximum ofthe two spouses education levels. T he education categories, as
dictated in partby the publicuse …le, are less than a high-schooldegree, high
schooldegreeand somecollege oruniversity, and auniversitydegree ormore.
T heFA M EX contains avariableequaltothetotalnumberofperson-weeks
within the household takingintoaccountthe exitand entry ofpersons during
the year. Consumption and expenditure are converted to “perperson-week”
units usingthis variable.
T he documentation forthe Family Expenditure Survey 19 9 2 can be found
at: http://130.15.16
1.7 4/webdoc/ssdc/cdbksnew/famex/famex9 2guide.txt
22
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