L ife-CycleL earning, Earning, IncomeandW ealth

D avidA ndolfattoSimonFraserU niversity

ChristopherFerrallQ ueen’sU niversity

PaulG ommeFederalR eserveBankofCleveland

N ovember2000

1 Introduction

Individualswhoinvestheavilyinhumancapitaltendtoexperienceahigherlevelofearningsandincomethroughoutmostoftheirlife-cycle. M ostoftheirhigherearningsareintheformofhigherwages, butasigni…cantfractionisaccountedforby agreaterworke¤ort. In addition, such individuals tend toconsumemoreandaccumulate…nancialassetsatafasterrate. W hataccountsforthesedi¤erences? W hileonemightbeinclinedtoattributesuchdi¤erences largelytoluck, muchoftheheterogeneityweobservecouldalsobeduetopersonalchoicesthataremadeonthebasisofanintrinsicsetoftastesandabilitiesthathappentodi¤eracrosspeople. O urpaperisaboutexploringtheplausibilityofthislatterhypothesis.

O neobviousmeasureofpasthumancapitalinvestments isthelevelofedu-cationalattainment. A mongadults inCanadaandtheU nitedStates, roughly25% arehigh-schooldropouts, 50 % haveahigh-schooldiploma, and25% haveacollegedegree. U nlikedemographicvariablessuchasage, sex, andrace, educa-tionalattainment(orhumancapitalaccumulationingeneral) islargelyachoicevariable. Itseemsreasonabletosupposethatindividualsarefromanearlyagegenerallyawareofthebene…ts associatedwithhigherlevels ofhumancapitalinvestment;andyet, peopleclearlymakedi¤erentchoices. W hatdrives thesedi¤erentdecisions?

O newaytounderstandthehumancapitalchoiceis intermsofanoptimalinvestmentdecision;seeB en-Porath(1967 ). IntheBen-Porathmodel, individ-ualsseektomaximizethepresentvalueoftheirlifetimeearningsbyallocatingtheirtimebetweenworkandlearningactivities, andbychoosinganappropri-ateexpenditurepathforeducationalgoods andservices. A keyparameterinthismodelisthe‘abilitytolearn’, modelledasthetechnologicale¢ciencywith

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whichlearninge¤ortandresourcesaugmentthevalueofhumancapital.1 N otsurprisingly, themodelpredictsthatmoreableindividualschoosetoundertakegreaterhumancapitalinvestments, especiallyearlyoninthelife-cycle, andthatlearninge¤ortdeclinesovertime. D uringyouth, less ableindividuals tendtoearnmore(as theydevotemoretimetoworkratherthanlearning), butmoreableindividualshaverapidlyrisingearningpro…lesthatsoonovertakethoseofthelessable. Inaddition, dispersioninearningsacrosseducationalgroupstendstogrowovertime. T hesepredictionsarebroadlyconsistentwiththeevidence;e.g., seeL illard(19 7 7 ).

W hilethebasicB en-Porathmodelprovidesaplausibleexplanationforwhyearnings pro…les mightdi¤er, beforeonecan becon…dentthatabilitydi¤er-ences are atthe rootofinequality itwould be prudenttoexaminewhetherthemodelis consistentwith otherfacts, forexample, on laboursupply, con-sumption, andassetaccumulation behaviour. Inordertoexaminethis issue,thebasicmodelmustbeextendedtoincorporatealabour-leisurechoiceandaconsumption-savingdecision. Suchanextensionhas beenprovidedbyB linderand W eiss (19 7 6), H eckman(19 7 6), and R yder, Sta¤ordandStephan (19 7 6).Judgingbywhatis reported intherecentsurveyby N ealand R osen (19 9 8),theseversionsoftheBen-Porathhumancapitalmodelrepresenttheextenttowhichthistheoreticalset-uphascurrentlyprogressed.

B linderandW eiss (19 7 6) andR yder, Sta¤ordandStephan(19 7 6) arepri-marilyconcernedwithexploringwhatsortoflife-cycledynamicsmightemergeinsuchanenvironmentfora‘representative’individual.2 H eckman(19 7 6) re-portstheresultsofseveralcomparativedynamicsexercises, butdoesnotalwaysprovideafulldescriptionofjointbehaviour. Forexample, he…nds thatindi-vidualswithgreaterlearningabilityhavepeaks intheirhoursofworkpro…lesatolderages, butwearenottoldhowthesepro…les arepositionedrelativetoeachother. A swell, hedoesnotaskhowdi¤erences inabilitya¤ect…nancialassetaccumulation.

T hepurposeofourpaperisexplorewhatthisenvironmenthastosayabouthowlife-cyclepatternsofconsumption, learning, laboursupply, earnings, incomeandassetaccumulationshouldbeshapedasafunctionofparametersdescribingtastes and abilities. In this paper, we focus on three sources ofparameterheterogeneity: (1)theabilitytolearn;(2)thesubjectiverateoftime-preference;and(3) thetasteforleisure. W ewishtodiscover…rstofallwhetheranysinglesourceofparameterheterogeneitymightbeabletoaccountforthequalitativedi¤erences thatweobserveinthedata. O urpreliminary…ndings suggestthatnosingle sourceofparameterheterogeneitycan accountforthefacts. N ext,weaskwhetherthereareplausiblecombinationsofparameters thatmightbeabletoexplainthedata. O urpreliminary…ndings suggestthatthemodelisbroadlyconsistentwith theevidence ifweassumethatpeopledi¤erin theirrateoftime-preferenceandtheirtasteforleisure;and iftheseparametersare

1 A notherwaytomodellearningabilityis intermsofinitialendowmentsofhumancapital.2Evidently, averyrichandcomplexsetofdynamics is possible.

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positivelycorrelatedamongindividuals.

1.1 SomeFacts

Inthis section, wedescribewhat‘typical’(median) life-cyclepro…les looklikeacrossthreeeducationalgroups: dropouts;highschool;andcollege. T hedataisfromtheCanadian19 9 2 FamilyExpenditureSurveyPublicU seFile(FA M EX )andisdescribedinalittlemoredetailin A ppendixI. W ealsoreviewevidencefrom A ttanasio(19 9 4) whoreports similarmeasurements from the19 9 0 Con-sumerExpenditureSurveyfortheU nitedStates.

1.2 Income, ConsumptionandSaving

Figure 1 plots measures ofafter-tax income, consumption expenditures, andsavingforeacheducationalgroupovertenperiodsofalife-cyclebeginningatage21 andendingatage7 0. N otsurprisingly, morehighlyeducatedindividualshavesigni…cantlymoreincomeateveryageexceptforveryearlyinthelife-cycle. T heage-incomepro…lefordropouts displaysamodesthump-shapedpattern, withincomepeakingage52 atalevelthatis 1 :65 timeshigherthanatage21. T heage-incomepro…leforcollegegraduates, ontheotherhand, displaysasigni…canthump-shaped pattern, with incomepeakingatage 52 atalevelthatis 2:88timeshigherthanatage21. A ccordingtothisdata, collegegraduatesgenerateroughlytwicetheincomeofdropoutsaroundthepeakincomeyears. A ttanasio(19 9 4) reports similar…ndings forthe U nited States. In particular, medianincomepeaks inthe51–55 year-oldcohort, withcollegegraduates generating2.84timesmoreincomethandropouts.

Q ualitatively, itappears thatconsumptiontracks disposableincomefairlycloselyinthesenseofsharingthesamehump-shapedpattern. T hisfactthathasbeenreferredtoasthe‘consumption-incomeparallel’(seeCarrollandSummers,19 9 1)andissometimesusedasanargumenttorejectthebasiclife-cyclemodel,whichpredicts a‡atage-consumptionpro…le. A ttanasioandBrowning(19 9 5)arguethattheconsumption-incomeparallellargelyre‡ects family-sizee¤ects.U sing severalyears ofU .K. FES data tofollowcohorts through time, theyreproduce the …ndingthatconsumption and incomemove togetheroverthelife-cycle. H owever, de‡atingconsumptionbyanadult-equivalentscalerendersacompletely‡atlife-cyclepathforadjustedconsumption. O ntheotherhand,G ourinchasandParker(19 9 9 ) arguethatwiththeiradjustments, consumptioncontinuestodisplayahump-shape.

T hebottom panelofFigure 1 displays household saving, de…nedhereasthedi¤erencebetweenhouseholdafter-taxincomeandhouseholdconsumption.A ccordingtothis measureofsaving, themedianhouseholdofeacheducationgrouparenetsaversoverthelife-cycle(atleast, uptoage7 0). H ighereducationgroupstendtosavemore, bothintotalandasaratiooftheirdisposableincome.

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In fact, thepropensitytosaveremains fairlyconstantfrom age32 onwardinthis data. O vertheentirelife-cycle, savingrates average 8:8% fordropouts,1 0 :6% forhighschoolgraduates, and 1 9:6% forcollegegraduates.

T heFA M EX datasetprovides aseries called‘netchangeinassets’whichdi¤ers (empirically, notconceptually) somewhatfrom the savingmeasurere-portedabove. Q ualitatively, thenet-change-in-assets series is similarin thathighereducationgroups tendtosavemoreovertheentirelife-cycle. Butac-cordingtothismeasure, themediansavingfordropouts is prettyclosetozeroovertheentirelife-cycleandthemediansavingforhighschoolgraduates isnotverymuchlarger. Inaddition, thelevelofsavingbycollegegraduates isabouthalfofwhatisrecordedbytheearlierde…nitionofsaving.

T hesavingbehaviourreported inFigure1 is broadlyconsistentwithSCFandPSID dataonwealthaccumulationpatternsacrosseducationalgroups. A c-cordingtoCagetti (19 9 9 ), mediannetworthpositions (includinghousingbutabstractingfrompensionentitlements)areverylowandsimilaracrossindividu-alsatage30. W hileallthreeeducationalgroupstendtosaveovertheentirelife-cycle, therateofassetaccumulationismuchhigherforwell-educatedindividu-als. B yage60, themediandropouthasaccumulatedroughlybetween$60,000–9 0,000;themedianhigh-schoolgraduatehasbetween$125,000–180,000;andthemediancollegegraduatehas between$250,000–300,000.3 Inotherwords, toa…rstapproximation, eachlevelofeducationisassociatedwithadoublingofnetworthinoldage.

1.3 Earnings, L abourSupplyandW ages

Figure2 plotsmeasuresofearnings, laboursupply, andwages foreacheduca-tionalgroupovertenperiodsofalife-cyclebeginningatage21 andendingatage7 0. A gain, itisnotsurprisingtodiscoverthatbettereducatedindividualstendtohavehigherlife-cycleearnings. A ge-earningpro…les tendtodisplayamorepronouncedhump-shapedpatternrelativetoincome, partlybecauseearningsdrop signi…cantlyaspeopleapproacholdage.

T henexttwopanelsinFigure2 revealthatbettereducatedindividualshavehigherearnings earlyon inthelife-cyclebecausetheyallocatemoretimethemarketsector;i.e., notbecausethepecuniaryreturntolabourishigher. W ageratestendtogrowovertimeforalleducationgroups, butgrowmorequicklyforthebettereducated. L aboursupplypro…les riseearlyon inthelife-cycleandthen‡attenout, showingamodestdeclineasthehouseholdages;this patternholds foralleducation groups. T hemain di¤erence in laboursupply acrosseducationgroupsissimplyintermsoflevels: collegegraduatesworkonaverageabouttwiceashardadropouts.

3T he …gures are in 19 9 2 dollars. T he lowerbound is from the SCF;the upperbound isfrom theP SID .

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1.3.1 TheR eturnonEducation

T hereis alargeempiricalliteratureconcernedwithmeasuringthe‘return’toeducation;thisliteraturehasrecentlybeensurveyedbyCard(19 9 8). T hestan-dardeconometricmodeltakentothedatais usuallysomevariantofM incer’s(19 7 4) ‘humancapitalearningsfunction’thatrelatessomemeasureoflogearn-ings(logy)tosomemeasuresofeducationalattainment(S)andworkexperience(X );togetherwithastatisticalresidual(");e.g.,

logy=a+ bS + g(X )+ ": (1)

A pparently, itis nowconventionaltorefertothe estimated parameterbasthe‘returntoeducation’. T ypically, thereturntoeducation is foundtovarywith certain characteristics ofindividuals, such as ‘ability’and ‘familyback-ground’. Cardargues thattheempiricalspeci…cationabove, withgmodelledasathirdorfourthdegreepolynomial, providesareasonablygood…twiththedata, although, contrarytothe speci…cation in (1), theredoes appeartobesomeevidenceofaninteractionbetweeneducationandexperience.

W hen logannualearnings areregressed on education and othercontrols,theestimatedreturn toeducation is thesum ofthebcoe¢cients forparallelmodels…ttothelogofwages(logw)andthelogofannualhours(logh):H ere,wereproduceCard’s (19 9 8) Table 1, which reports theestimatedreturns toeducationusing(1) …ttothe19 9 4–9 6CPS.

D ependentVariablelogw logh logy

M enb 0.100 0.042 0.142R 2 0.328 0.222 0.403

W omenb 0.109 0.056 0.165R 2 0.247 0.105 0.247

T hus, Cardconcludes thatintheU .S. labourmarketinthemid-19 9 0s, abouttwo-thirdsofthemeasuredreturntoeducation inannualearnings datais at-tributabletothee¤ectofeducationonthewagerate, withtheremainderat-tributabletothee¤ectonannualhoursworked.

1.4 D ataSummary

T hereadershouldkeepinmindthatthereareseveralpracticaland(unresolved)conceptualissues relatingtothemeasurementofthesevariables; see B rown-ingand L usardi (19 9 6) fordetails. B utdespite the quantitative di¤erencesthatemergedependingonhowvariablesarede…nedormeasured, anumberof

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qualitativefeaturesappeartoberobustacrossdi¤erentdatasetsanddi¤erentde…nitions/measurements. T heimportantqualitativedi¤erencesareasfollows:

1. Individuals ofagivenagedi¤erinterms ofaccumulatedhumancapital(e.g., asmeasuredbyeducationalattainment).

2. Individualswhoinvestheavilyinhumancapital(bettereducatedindivid-uals) tendtohavehigherincomes, earnings, consumption, andsavings;

(a) H igherearningsareattributabletobothhigherwagerates(2/3)andgreaterworke¤ort(1/3);

(b) H ighersavingsattributabletohigherincomesandagreaterpropen-sitytosave.

3. T hedispersion in income, earnings, consumption, andsavingacross ed-ucationalgroups peaks sometimeinthemiddleofthelife-cycle;thedis-persioninlaboursupplyandsavingratesremainsrelativelyconstant;andthedispersioninwagerates is (weakly) increasingwithage.

W ewishtofocus onthesequalitativefeaturesofthedataandaskwhetherasensiblyparameterized life-cyclemodel(thatendogenizes human capitalandlaboursupply) canaccountforthesequalitativepatterns.

2 TheM odel

ConsideraneconomypopulatedbyoverlappinggenerationsofindividualswholiveforJperiods, indexedbyj=1 ;2;:::;J:T hepopulationisassumedtogrowataconstantratenperperiod, andwedenotetheshareofage-j individualsinthepopulationby¹j;whichistime-invariantandsatis…es ¹j =(1 + n)¡1 ¹j¡1forj=2;:::;Jand

PJj=1 ¹j=1 :

T hereisanissueastowhetheridiosyncraticrisksplayanimportantroleintheevolutionoflife-cyclevariables. O urfeelingonthis matteris that, whileidiosyncraticrisks may be important, they are notdominant. T his viewissupportedbytheempiricalworkofVenti andW ise(2000), whoinvestigatethequestionofwhythedispersionofwealthatretirementages is sogreat. T heseauthors arguethat90 % ofthevariationobserved inretirementwealth is duetothedi¤erentchoicesthatpeoplemakeandnottoidiosyncraticluck. Intheanalysisbelow, weabstractfrom uncertainty.

Individualshavepreferencesde…nedoverdeterministictime-pro…lesofcon-sumptioncj, leisurelj, aswellasa…nalnetworthpositionaJ+ 1 (bequeathedtothefuturegeneration);letpreferencesberepresentedbytheutilityfunction:

JX

j=1

±j¡1 [U (cj)+ ¸V (lj)]+ ÂB (aJ+ 1):

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A ssumethatthefunctionsU ;V andB areallstrictlyconcaveandthattheysat-isfystandardInadaconditions;wewilltreatthesefunctionsascommonacrossindividuals. Preferences areparameterizedbythediscountfactor±;thetasteforleisure¸;andthestrengthofthebequestmotiveÂ;individualsmayormaynotdi¤eralongthesedimensions. N ote: in this version ofthepaper, weset =0 :

T herearethreeusesfortime: marketworkn;learninge¤orte;andleisurel;wheren+ e+ l=1 (andtheusualnon-negativityconstraints). L ethdenotehumancapital. Peoplemightdi¤erintheirinitialendowmentofhumancapital(onemeasureofdi¤erences inability). A person’shumancapitalisassumedtoaugmenttime-useinworkingandlearning;measuredin‘e¢ciencyunits’, worke¤ortequalshnandlearninge¤ortequalshe:

FollowingH eckman (19 7 6), thehumancapitalaccumulationtechnology isgivenby:4

hj+ 1 =(1 ¡¾)hj + ®G(hjej);

whereG isstrictlyincreasingandconcave, ¾ isthedepreciationrateonhumancapital, and® isaparameterthatindexes‘learningability’. W ewillassumethatG and ¾ arecommonacross households;however, ® maydi¤er. L etv denotethevectorofparametersdescribingaparticularindividual;i.e. v=(®;±;̧ ):

T herearetwoprices inthemodel. L et!denotethepriceofane¢ciencyunitoflaborandletR denotethe(gross) realrateofinterestpaidon…nancialassets. Bothofthesepriceswillbedeterminedbymarketclearingconditionsinthegeneralequilibrium. N otethatlaborearningsaregivenby!hn;sothatw=!hcanbeinterpretedastherealwage.

IndividualscansaveorborrowfreelyatthegoinginterestrateR (therearenodebtconstraints beyondtheend-periodrestrictionaJ+ 1 ¸ 0 ). T heassetaccumulationequationisgivenasfollows:

aj+ 1 =R aj + wjnj¡cj;

O ptimaldecision-makingresults in adesired pro…lefcj;nj;ej;lj;aj+ 1 ;hj+ 1 j!;R ;vgJj=1 :

W hatremainsnowisthedeterminationofprices. Inasteady-state, thepercapitacapitalstockisgivenby:

K=(1 + n)¡1JX

j=1

¹jX

v

aj(v)¤(v);

4N otethatwearenotmodellingtheschoolingchoiceperse. W hatweareassumingisthatindividuals in thedatawhoattend schoollongerarelikelytoinvestmoreheavily in humancapitalatallstages ofthelife-cycle. T otheextentthatthis is true, we can then associatepeople in themodelwith higherlevels ofhuman capitalwith people in the datawhohavehighereducation.

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where¤(v)represents thefractionofthepopulationwithparametervectorv:T hepercapitalevelofhours(measuredine¢ciencyunits) isgivenby:

H=JX

j=1

¹jX

v

hj(v)nj(v)¤(v)

O utputisproducedbyaconstantreturnstoscaleproductiontechnologyQ =F (K;H):Equilibrium pricesaredeterminedbytheusualmarginalconditions:

! = F H(K;H)R = F K(K;H)+ 1 ¡Á;

whereÁ isthedepreciationrateofphysicalcapital. Finally, goods-marketclear-ingrequires:

C + (n+ Á)K=Q ;

where,

C =JX

j=1

¹jX

v

cj(v)¤(v):

2.1 Parameterization

FunctionalformsarerequiredforU ;V;G and F :

U (c) = (1 ¡° )¡1 [c1¡° ¡1 ]V (z) = (1 ¡´)¡1 [z1 ¡́ ¡1 ]G(x) = x³

F (K;H) = KµH1¡µ:

3 Calibration

A tthis stage, wedonothavethetimetocalibrateorestimatethemodelaspreciselyaswewouldlike. So, wewillcontentourselveswitharoughcalibration.W ecalibrate…rsttoa‘representative’individual;theparametersarechosenasfollows.

3.1 D emographics

L etthenumberofperiodsbeJ=1 1 ;thelengthofaperiodis…veyears(thinkofpeoplebeginningtheireconomiclifeatage20 andlivingto7 0). T hepopulationgrowthrateissetton=0 ;sothat¹j=1 =Jforallj:

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3.2 Preferences

T hecurvatureparameteron U is chosen tobe ° = 1 :5 (a standardchoice).T he curvatureforV is alsochosen tobe ´ = 1 :5: T heweightingfactorforleisureischosentobe¸ = 1 :752;this generates theresultthatroughly 1 =3 ofavailabletimeis devotedtothelabourmarket. T hediscountfactoris chosentobe±=0 :86;whichimpliesanannualdiscountrateof3%:

3.3 Technology

T helearningabilityparameterissetto® =0 :40 ;thisimpliesthatyoungpeoplespendaround10% oftheiravailabletimeinlearningactivities. T hecurvatureofthelearningtechnologyistakenfrom H eckman(19 7 6);³= 0 :70 :T heshareofphysicalcapitalintotaloutputissettoµ=0 :35:Physicalcapitaldepreciatesatanannualrateof1 2%;setÁ = 0 :48: A ssumethathumancapitaldoes notdepreciate;¾ =0 :

3.4 Endowments

T hehumancapitalendowmentisnormalizedtoh1 =1 :

4 R epresentativeIndividual

In Figure3 weplotthe life-cycle behaviouroftherepresentative individual;i.e., theequilibrium basedontheparameterizationabove. A sFigure3reveals,themodeldoesaverynicejobofreplicating‘typical’life-cyclebehaviour, withthepossibleexceptionoftheveryaged. Inparticular, themodelpredictsthatconsumptioncontinuestorisethroughoutthelife-cycle;thedatasuggestsoth-erwise. A swell, inthemodel, individualsdissaveinoldagemuchmorerapidlythan inthedata(weonlyplotthe…rst10 periodsofthe13periodlife-cycle).T his lastfeaturecould presumablyberecti…ed by incorporatingthebequestmotive.

5 SingleSourcesofH eterogeneity

In this section, we shallconsiderthree separate sources ofheterogeneityandevaluatehoweach, in isolation, is predictedtoa¤ectlife-cyclebehaviour. T hethreeparametersweconsiderare: (1) theabilitytolearn, ®;(2) thediscountfactor, ±;and (3) thetasteforleisure, ¸:Foreach case, wewillmodelthreetypes, representinghigh, medium, andlowvalues, with 50 % ofthepopulationtakingonthemedium value, andtheother50 % evenlydividedacrossthetwo

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extremevalues. Inequilibrium, eachtypeofpersonwillchooseadi¤erentlife-time learningpro…le;welabelthegroup with thegreatestlife-time learninge¤ort‘collegegraduates’andthosewiththelowest‘dropouts’.

5.1 TheD i¤erent-A bility H ypothesis

Supposethatindividualsdi¤eronlyintheirabilitytolearn;e.g., ® =0 :32;0 :40 ;0 :48:T heresults areplotted in Figure4. N otsurprisingly, thosewith thehighestlearningabilitybecome‘collegegraduates’.

O bservethattheearningspro…lestaketheexpectedshapeinthesensethatthosewith lowlearningabilityhavehigherearnings when young(relativetohighlearningabilitytypes), andrelativelylowerearningswhenold. T hisbasicqualitativepatternisalsohighlightedinN ealandR osen(19 9 8, Figure4.2), whoremarkthatthis U -shapedrelationship betweencohortearnings varianceandcohortageisanimportantthemeintheliteratureonhumancapital. H owever,this U -shaped pattern is notpresentin ourdata, possiblybecausebyage21(theyoungestageinoursample)wearealreadybeyondtheminimumdispersionpoint. A bility di¤erences seem togenerate the righttype oflife-cyclewagepatterns, butlaboursupplypro…lesarequalitativelysimilaronlyafterperiod3(age32).5

T hemostglaringde…ciencyinthe“D i¤erent-A bilityH ypothesis” iswhatitimpliesforassetaccumulationbehaviour. A ccordingtothemodel, individualswith lowlearningability (dropouts) willaccumulate …nancialassets rapidly,whilethosewithhigh learningability (college) arepredictedtoholdnegativenet-worthpositionsformostoftheirlife.

T hemodel’s logicis perfectlyclear. W ealthtakestwoforms inthismodel:humanwealthand…nancialwealth. L owabilityindividuals naturallywishtosubstituteintotheaccumulationof…nancialwealth, whilehighabilityindivid-uals allocatetheirresources towardaccumulatinghumancapital. L ateron inthelife-cycle, thosewhoarerichinhumancapitalworkhardertoexploittheirrelativelyhighskilllevels, whilethosewhoarerichin…nancialwealthcana¤ordtoconsumemoreleisure.

5.2 TheD i¤erent-D iscount-Rate H ypothesis

T he ideathatpeopledi¤erin theirdegreeof‘patience’, andthatthis mightexplainmuchoftheheterogeneityobserved in economicbehaviour, is an oldone (e.g., see R ae, 1834). H ere, we considerthree rates oftime-preference(annualized) equalto: 0 :0 275;0 :0 30 ;and 0 :0 325;the results are displayed inFigure5.

5 M easured hours ofworkhere is totalhours worked plus time spentlearning, exceptforthoseaged21 and in college. T he ideahere is thattrainingis undertakenwhileon thejob.

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In amodelwithoutleisure, di¤erentdiscountrates would havenoe¤ecton thelevelofhuman capitalinvestment(assumingperfectcapitalmarkets).H owever, when leisure is endogenous andwhen personaltime is anecessaryinputtolearning, di¤erencesinthesubjectiverateoftime-preferencewillinducedi¤erentlevels oflearninge¤ort. B ecause learningis a form ofinvestment,onemightnaturally expectthatrelatively patientindividuals would end upaccumulatingmorehumancapital. Somewhatsurprisingly, themodelpredictsthattheleastpatientindividualswillaccumulatethemosthumancapital;i.e.,impatiencehere is positivelycorrelatedwith the levelofeducation, althoughthedi¤erences intimedevotedtolearningaresmall. O nepossibleexplanationforthis resultmightlieinthefactthathumancapitalcannotbeconsumedorsoldasdeathapproaches, unlike…nancialcapital. Consequently, morepatientindividuals(whowhenyoungplaceagreaterweightonend-of-lifeconsumption)mightprefertoaccumulatewealth throughavehiclethatis bettersuited toprovidingforoldageconsumption. Inaddition, themorepatientplaceagreaterweightonfutureleisure;and…nancialassetaccumulationratherthanhumancapitalcanbetterprovideforfutureleisure.

Inthemodel, patientindividuals (associatedherewithdropouts) prefertopostponeconsumptionandleisuretoalaterage;hence, theyconsumelittleandworkhardwhenyoung, sothatnetworthgrowsrapidly(althoughtheyremainrelativelyunskilled). A ccordingtothemodel, thereasonwhylaboursupplyisrelativelylowfordropouts inlatterstagesofthelife-cycleis becausetheyaresowealthy. N eedlesstosay, themodel’sexplanationhardlyseemsplausible.

5.3 TheD i¤erent-Taste-for-L eisure H ypothesis

Supposenowthatpeopledi¤eronlyintherelativeweighttheyplaceoncon-sumptionandleisureatanypointintime;here, weconsiderthefollowingthreevalues forthe leisureparameter: ¸ = 1 :54; 1 :74;and 1 :94: A ccordingtothemodel, thosewhoplacerelativelylowweightonleisurearetheoneswhoaccu-mulatemorehumancapital.

O utofthethreehypotheses consideredsofar, thetaste-for-leisurehypoth-esis seems toholdthemostpromise. In particular, thepro…les forearnings,hoursworkedandrealwagesarequalitativelysimilartoobservation. B utonceagain, themostglaringde…ciencyofthishypothesis iswhatitpredictsforassetaccumulationbehaviour: lowereducationgroupsdisplayagreaterpropensitytosave. A pparently, thosewhodonot…ndworkorschoolinge¤ortsopainfulpre-fertoaccumulatewealththroughhumancapital, ratherthanthrough…nancialassets.

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6 M ultipleSourcesofH eterogeneity

T hemainsourceoftension inthemodelis thatwhichseemstoexistbetweenhumancapitaland…nancialcapital;i.e., thesetwoformsofcapitalrepresental-ternativemechanismsbywhichtoaccumulatepurchasingpower. Consequently,ifoneisrelativelygoodataccumulatinghumancapital(whetheritisbecauseofhigherability, lesspatience, oragreatertasteforconsumption), thenonetendstosubstituteintohumancapitalattheexpenseof…nancialcapital. Inthedata,however, thepropensitytoaccumulatehumancapitalis positivelycorrelatedwiththepropensitytoaccumulate…nancialassets.

T heonlywaytogeneratethispositivecorrelationbetweenhumanand…nan-cialcapitalinvestmentis toconsidermultiplesourcesofheterogeneity. Inthissection, weconsidertwoeconomies: oneinwhichpeopledi¤erintheirlearningabilityandtheirdiscountrate;andoneinwhichpeopledi¤erintheirtasteforleisureandtheirdiscountrate. Forsimplicity, weassumeaperfectcorrelationbetweenthetwoparameters(sothattherewillcontinuetobeonlythreetypesofindividuals).

6.1 L earningA bilityandD iscountR ate

A ssumethatpeopledi¤erboth intheirabilitytolearnand intheirdiscountrate;andthatthediscountrate(discountfactor) is negatively(positively) re-latedwithlearningability. T hethreetypesofindividualsaredescribedbythefollowingparametercon…guration:

® ±T ype1 0.30 0.84Type2 0.40 0.86Type3 0.50 0.88

Inthemodel, individualswhohaveahighabilitytolearnandalowdiscountrate(Type3individuals) endupaccumulatinggreaterlevelsofhumancapital.T hehopehereisthatthehighlearningabilitywillresultinhighhumancapitalinvestmentsandthatthelowdiscountratewillresultinahighrateofsaving.T heresults aredisplayed in Figure 7 . A s the …gurereveals, this hypothesisholds somepromise. H owever, high-abilitypeoplestilltendtobenetdebtorsearlyoninthelife-cycle(theywishto…nancetheirhumancapitalinvestments).Increasingthedispersioninthetime-preferenceparametermayhelpalongthismargin;however, doingsowouldexacerbatethetiltsintheconsumptionpro…les(somethingwedonotseeinthedata).

6.2 TasteforL eisureandD iscountR ate

A ssumenowthatpeopledi¤erintheirtasteforleisureand intheirdiscountrate;andthatdiscountingispositivelyrelatedtothetasteforleisure. T hethree

12

typesofindividualsaredescribedbythefollowingparametercon…guration:

¸ ±T ype1 1.25 0.88T ype2 1.7 5 0.86Type3 2.25 0.84

Inthemodel, individualswhohavealowtasteforleisureandalowdiscountrate(highdiscountfactor)endupaccumulatinggreaterlevelsofhumancapital.A swiththeearlierexperiment, thehopehereisthatthelowtasteforleisurewillresultinhighlevelsofhumancapitalinvestmentswhilethelowdiscountratewillresultinahighrateofsaving. Figure8 demonstratesthatthishypothesishas agreatdealofpromise; this …gure …ts thedatabetterthan anyoftheexplanationsproposedsofar.

T heimplicationsofthishypothesisarepotentiallyprofound. Itarguesthat,whilepeoplemayappeartodi¤erintheirabilitytolearn, thisdi¤erencearisesnotfrom intrinsicdi¤erencesinlearningability(®);butfromthehumancapitalinvestmentsthatpeoplehavechosentomakeinthepast(rememberthatitisthee¢ciencyunitoflearninge¤orthethatenters intothelearningproductionfunction). A bilityhereis tobeinterpretedas themanifestationofhardworkandfrugal(forward-looking) tendencies.

7 D iscussion

W ebelievethatitis interestingtodiscoverwhatsortofintrinsicdi¤erences inpeoplemightcausethemtomakeverydi¤erenteconomicdecisions. Knowledgeoftheintrinsicstructureofheterogeneity(i.e., thedistributionofdeepparame-tervalues)canplayanimportantroleinthedesignofsocialpolicy. Forexample,ifheterogeneousdiscountingis foundtobeimportant, thenanyredistributivepolicyshouldlikelyincludeprovisionstomakeentitlementslegallyinalienable;seeA ndolfatto(2000). Ifitisfoundthatthetasteforleisuremattersmorethantheabilitytolearn in explainingthedata, thenwecanconcludethatpeopledi¤erin theirskills notbecauseofintrinsicabilitydi¤erences butbecauseofhowtheychosetoallocatetheirtimeinthepast. Ifmitigatingskilldi¤erences(earningsdi¤erentials) is apolicygoal, thensucharesultmightpointtoedu-cationsubsidies. O ntheotherhand, ifobservedheterogeneityis attributabletodi¤erences in endowments (…nancialbequests orinitialhumancapitallev-els), thenlump-sum transfersmaybethesuitableinstrumenttoimplementaredistributionpolicy.

13

10000

20000

30000

40000

50000

60000

70000

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Household After-Tax Income

10000

20000

30000

40000

50000

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Household Consumption

-5000

0

5000

10000

15000

20000

25000

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Age (21-70 Years)

Household Saving(After-Tax Income Minus Consumption Expenditure)

FIGURE 1Canada 1992 FAMEX Data

14

0

20000

40000

60000

80000

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Earnings

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10

DropoutsHigh SchoolCollege

Full Time Equivalent Weeks Worked per Worker

0

10

20

30

40

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Age (21-70 Years)

Wage Rate(Earnings Divided by Hours)

FIGURE 2Canada 1992 FAMEX Data

15

0.12

0.14

0.16

0.18

0.20

0.22

0.24

1 2 3 4 5 6 7 8 9 10

IncomeEarningsConsumption

0.20

0.25

0.30

0.35

0.40

0.45

1 2 3 4 5 6 7 8 9 10

WorkWork+Training

0.00

0.05

0.10

0.15

0.20

0.25

1 2 3 4 5 6 7 8 9 10

Net Worth0.36

0.40

0.44

0.48

0.52

0.56

1 2 3 4 5 6 7 8 9 10

Wage Rate

FIGURE 3Representative Agent

16

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Income

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Earnings

14

16

18

20

22

24

26

28

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Consumption

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Measured Hours of Work

-10

0

10

20

30

40

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Net Worth

30

40

50

60

70

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Wage Rate

FIGURE 4Differences in Learning Ability

17

14

16

18

20

22

24

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Income

8

10

12

14

16

18

20

22

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Earnings

14

16

18

20

22

24

26

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Consumption

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Measured Hours of Work

-10

0

10

20

30

40

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Net Worth

35

40

45

50

55

60

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Wage Rate

FIGURE 5Differences in Time-Preference

18

0.12

0.16

0.20

0.24

0.28

0.32

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Income

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Earnings

0.12

0.16

0.20

0.24

0.28

0.32

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Consumption

0.20

0.25

0.30

0.35

0.40

0.45

0.50

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Measured Hours of Work

-0.1

0.0

0.1

0.2

0.3

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Net Worth

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Wage Rate

FIGURE 7Negative Correlation Between the Rate of Time-Preference

and the Ability to Learn

19

14

16

18

20

22

24

26

28

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Income

12

14

16

18

20

22

24

26

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Earnings

12

14

16

18

20

22

24

26

28

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Consumption

0.20

0.25

0.30

0.35

0.40

0.45

0.50

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Measured Hours of Work

-10

0

10

20

30

40

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Net Worth

35

40

45

50

55

60

65

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Wage Rate

FIGURE 6Differences in the Taste for Leisure

Figure1:

20

0.10

0.15

0.20

0.25

0.30

0.35

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Income

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Earnings

0.10

0.15

0.20

0.25

0.30

0.35

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Consumption

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Measured Hours of Work

-0.1

0.0

0.1

0.2

0.3

0.4

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Net Worth

0.35

0.40

0.45

0.50

0.55

0.60

1 2 3 4 5 6 7 8 9 10

DropoutsHighschoolCollege

Wage Rate

FIGURE 8Positive Correlation Between the Rate of Time-Preference

and the Taste for Leisure

21

A ppendixI: D ataD escription

T hedatacomefrom the19 9 2 FamilyExpenditureSurveyPublicU seFile(FA M EX ).W eselectedthosehouseholdswithnomorethan2 wageearnersandwiththereferencepersonreportingsomeeducation. A llstatisticsareweightedbytheFA M EX weightvariable.

H ouseholdsweregrouped into…ve-yearagecategories andthreeeducationcategories. M arriedhouseholdsweregroupedaccordingtothegreaterlevelofeducationandageofthespouses. T hatis, theagecategoryofthehouseholdis themaximum ofthetwospouses ages, and theeducation category is themaximum ofthe twospouses education levels. T he education categories, asdictatedinpartbythepublicuse…le, areless thanahigh-schooldegree, highschooldegreeandsomecollegeoruniversity, andauniversitydegreeormore.

T heFA M EX containsavariableequaltothetotalnumberofperson-weekswithinthehouseholdtakingintoaccounttheexitandentryofpersonsduringtheyear. Consumption andexpenditureareconverted to“perperson-week”unitsusingthisvariable.

T hedocumentationfortheFamilyExpenditureSurvey19 9 2 canbefoundat: http://130.15.161.7 4/webdoc/ssdc/cdbksnew/famex/famex9 2guide.txt

22

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2. A ttanasio, O razio P. (19 9 4). “PersonalSaving in the U nited States,”in InternationalComparisons ofH ouseholdSaving, editedbyJames M .Poterba, N ationalB ureauofEconomicR esearch, T heU niversityofChicagoPress.

3. A ttanasio, O razioP. and M artin Browning(19 9 5). “ConsumptionovertheL ifeCycleandovertheBusinessCycle,” A mericanEconomicReview,85(5): 118 7 –1237 .

4. B lackorby, CharlesandD avidD onaldson(19 88). “CashVersusKind, Self-Selection, and E¢cientTransfers,” A merican Economic Review, 7 8(4):69 1–7 00.

5. B linder, A lanS.(19 7 4). TowardanEconomicT heoryofIncomeD istrib-ution, T heM IT Press.

6. B linder, A lan S. and Yoram W eiss (19 7 6). “H umanCapitaland L aborSupply: A Synthesis,” JournalofPoliticalEconomy, 84(3): 449 –47 2.

7 . B rowning, M artin and A nnamaria L usardi (19 9 6). “H ousehold Saving:M icroT heoriesandM icroFacts, JournalofEconomicL iterature, X X X IV (4):17 9 7 –1855.

8. Cagetti, M arco(19 9 9 ). “W ealth A ccumulationO verthe L ifeCycleandPrecautionarySavings,” M anuscriptpresentedatthe19 9 9 N B ER SummerInstitute.

9 . Card, D avid(19 9 8). “T heCausalE¤ectofEducationonEarnings,” forth-comingintheH andbookofL aborEconomics.

10. Carroll, ChristopherD . and L awrence H . Summers (19 9 1). “Consump-tionG rowthParallelsIncomeG rowth: SomeN ewEvidence,” in N ationalSavingandEconomicPerformance, editedbyB . D ouglas B ernheim andJohnB . Shoven, N ationalBureauofEconomicR esearch, T heU niversityofChicagoPress.

11. G ourinchas, P ierre-O livierandJonathanA .Parker(19 9 9 ). “ConsumptionO vertheL ifeCycle,” M anuscriptpresentedatthe19 9 9 N B ER SummerInstitute.

12. H eckman, James J. (19 7 6). “A L ife-Cycle M odelofEarnings, L earning,andConsumption, JournalofPoliticalEconomy, 84(4) Part2: S11–S39 .

13. L illard, L eeA .(19 7 7 ). “Inequality: Earningsvs. H umanW ealth,” A mer-icanEconomicReview, 67 : 42–53.

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14. M incer, Jacob (19 7 4). Schooling, Experience and Earnings, ColumbiaU niversityPress.

15. N eal, D erekandSherwinR osen(19 9 8). “T heoriesoftheD istributionofL aborEarnings,” N BER workingpaper637 8: www.nber.org/papers/w637 8.

16. R ae, John(1834). StatementofSomeN ewPrinciplesontheSubjectontheSubjectofPoliticalEconomy, B oston: H illiard, G rayandCo., reprintedbyA ugustus M .Kelley, Bookseller, N ewYork(1964).

17 . R yder, H arlE., Sta¤ord, FrankP. and PaulaE. Stephan (19 7 6). “L a-bor, L eisureandTrainingO verthe L ifeCycle,” InternationalEconomicReview, 17 (3): 651–67 4.

18. Venti, StevenF.andD avidA .W ise(2000). “Choice, Chance, andW ealthD ispersionatR etirement,” N BER workingpaperno. 7 521.

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