EUROPEANCENTRALBANK

EUROSYSTEM

RichardAudoly,RoryMcGee,SergioOcampo,GonzaloPaz-Pardo

WorkingPaperSeries

Thelife-cycledynamicsofwealthmobility

No2976

Disclaimer:ThispapershouldnotbereportedasrepresentingtheviewsoftheEuropeanCentralBank(ECB).TheviewsexpressedarethoseoftheauthorsanddonotnecessarilyreflectthoseoftheECB.

ECBWorkingPaperSeriesNo29761

Abstract

Weuse25yearsoftaxrecordsfortheNorwegianpopulationtostudythemobilityofwealthoverpeople’slifetimes.Wefindconsiderablewealthmobilityoverthelifecycle.Tounderstandtheunderlyingmobilitypatterns,wegroupindividualswithsimilarwealthrankhistoriesusingagglomerativehierarchicalclustering,atoolfromstatisticallearning.Themobilitypatternsweelicitprovideevidenceofsegmentedmobility.Over60percentofthepopulationremainsatthetoporbottomofthewealthdistributionthroughouttheirlives.Mobilityisdrivenbytheremaining40percent,whomoveonlywithinthemiddleofthedistribution.Movementsaretiedtodifferentialincometrajectoriesandbusinessactivitiesacrossgroups.Weshowparentalwealthisthekeypredictorofwhoispersistentlyrichorpoor,whilehumancapitalisthemainpredictorofthosewhoriseandfallthroughthemiddleofthedistribution.

JEL:D31,E21,C23,C38,C55

Keywords:wealthdynamics,agglomerativehierarchicalclustering,lifecycle,equalityofopportunity,intergenerationallinks

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Non-technicalsummary

Individualsmoveupordownthewealthdistributionduringtheirlives.Thesemovementsarerelatedtotheeventsandchoicesthatpeopleface,includingtheireducationdecisions,theirlabourmarketincomeandthebusinessactivitiestheyengagein.Althoughanextensiveliteraturehasstudiedthedistributionofwealthandwealthinequality,muchlessisknownabouthowpeopletransitionacrossthewealthdistributionduringtheirlives,i.e.,wealthmobility.

ThispaperstudieswealthmobilityoverthelifecyclebyusingNorwegianadministrativedataoriginatingfromthetaxregistry(1993-2017).Thisdataisexceptionalinaninternationalcontext.NorwayisoneofthefewcountriesinEuropetohaveawealthtax,andasaresultNorwegiantaxauthoritiesmustcollectinformationabouttheassetsandliabilitiesofNorwegianindividuals.Theinformationisparticularlyhighqualitybecause,unlikemostsurveydatasets,itisnotselfreported,butratherobtaineddirectlyfromthirdpartiessuchasfinancialinstitutions.OurdatasetcontainstheuniverseofNorwegianindividuals,theirincomeandwealth,andalsootherdemographicinformation,suchastheireducation,age,andmaritalstatus.

Weusethisdatatoestablishthatmobilityoverthelifecycleissubstantial,butthatitisrarethatindividualsmakeverylargemovementsacrossthewealthdistributionduringtheirlives.Instead,householdsthatarebornwithinthetopofthewealthdistribution(therichest20%)andthebottomofthewealthdistribution(thebottom40%)tendtostaywithinthatrange,withsomerelativelysmallfluctuations.Ontheotherhand,weidentifytwogroupsofindividualsthatarepartofthemiddleclassandsufferreversalsoffortuneduringtheirlifetimes.Oneofthemtendstoriseoverthewealthdistributionastheyage,reflectingrapidwealthaccumulation,whiletheothertendstofalloverthewealthdistribution,reflectingstagnantorevenfallingwealthlevels.Weidentifythesegroupsusingagglomerativehierarchicalclustering,atoolfromstatisticallearning.

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Westudyhowthesedifferentgroupsdifferintermsoftheirhomeownershiprates,portfolios,sourcesofincomeandinheritances.Wefindthatthetopandfallinggroupsaremorelikelytoownbusinessesandtobeself-employed,whiletherisersaremorelikelytobeemployeeswithastarklyrisingincomeprofile.Individualsatthebottomofthedistributionaredifferentfromtherest:theirincomesarepersistentlylower,theyrarelybecomehomeownersanddonotownbusinesses.

Werelatethesefourdistinctgroupswiththeirparentalbackground,educationandothercharacteristicswhicharedeterminedatthestartoftheirworkinglives.Wefindthatindividualsborntoveryrichparentsarealmost30percentagepointsmorelikelytobepartofthegroupthatispersistentlyatthetopoftheirowngeneration’sdistribution,comparedtothoseborntothepoorestparents.Incontrast,thoseborntoparentsatthebottomofthedistributionaremorelikelytobepersistentlypoorthroughouttheirlives.

Forindividualswhoexperienceariseorfallthroughthedistribution,educationisastrongerpredictoroftheirevolutionthanparentalwealth.Highlyeducatedindividualsaremarkedlymorelikelytorisethroughthewealthdistributionastheyage.Bycontrast,evenaftercontrollingfortheirparentalbackground,thosewithoutpost-secondaryeducationarebetween5and10percentagepointsmorelikelytobepartofthefallinggroupthanthosewithatleastundergraduatedegrees.

Ourresultshighlightthatthepositionofanindividualoverthewealthdistributionvariessubstantiallyoverhisorherlifetime,butthatcertaingroups,suchastherichestandpoorest,tendtohaverelativelystablepatterns.Theseresultsarerelevanttounderstandthedistributionalimplicationsofpoliciessuchasthewealthtaxorgovernmentinsurance,butalsohowshocksordevelopmentssuchaschangesintheneutralrateofinterestwillultimatelyaffectthewealthdistributionandhouseholdwelfareinthelongrun.

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1.Introduction

Dorichandpoorpeopleremainthatwaythroughouttheirlives?Isittypicalforpeopletoexperiencereversalsoffortunemovingupordownthewealthdistribution?Ifso,howlargearethereversals,andwhendotheyhappen?Thesemovementsacrossthewealthdistributionreflecttheoutcomesofcriticaleventsandchoicesinpeople’slives,includingtheirhumancapitalaccumulation,earnings,andbusinessactivities.Wealthmobilitythusspeakstotheopportunitiesthatpeopleface.

1

However,despitegrowingevidenceonthedynamicsofwealthconcentrationforthewealthiest,

2

weknowlittleaboutthelife-cycledynamicsofwealthmobilityforthepopulationasawhole.

Ourmaincontributionliesindocumentingwealthmobilityoverthelifecycle.Weconductacomprehensivestudyofthecompletedistributionoflifetimeindividualwealthtrajectories,whichweconstructusing25yearsofadministrativedatafromtheNorwegiantaxregistry(1993–2017).Wefindincreasingwealthmobilityoverthelifecycle,sothatanindividual’sinitialpositioninthewealthdistributionmatterslessastheyage.Onlyone-fourthofindividualsareinthesamequintileofthedistributionafter25years.However,thispopulationtrenddoesnot,byitself,tellusmuchabouttheunderlyinglife-cyclepatternsthatdriveit.Whoisactuallymoving?Andhow?

Toanswerthesequestions,weelicittypicallife-cyclewealthtrajectoriesfromthedistributionofwealthhistoriesusingagglomerativehierarchicalclustering,atoolfromstatisticallearningthatgroupsindividualsbasedontheirfullrealizedtrajectories.Wegroupindividualsintofourmaingroups,whosetypicaltrajectoriesexplainmorethanone-halfofthevariationinwealthhistories.Wealsostudytheheterogeneitywithin

1Lowwealthmobilitycanbeasymptomoflimitedequalityofopportunityandcanexacerbatetheeffectsofhighinequality.Inthecontextofincomeinequality,AlanKrueger,thenChairmanoftheCouncilofEconomicAdvisorsunderPresidentObama,remarkedthat“ifwehadahighdegreeofincomemobilitywewouldbelessconcernedaboutthedegreeofinequalityinanygivenyear”(

Krueger

2012,pg.3)

.

2See

Gomez

(2023)forevidencefromthe

Forbes400listand

Ozkan,Hubmer,Salgado,andHalvorsen

(2023)forevidenceonthetop0.1percentofNorwegianwealthholders

.Quantitativeanalysisoftheoriginsofthewealthiestindividualsdatesbacktoatleastto

Wedgwood

(1929)

.

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thesegroupsbyexploitingthehierarchicalnatureofourclusteringmethodology.

Themobilitypatternsweuncovershowthatincreasingwealthmobilityoverthelifecycleisnotbroad-basedandisnotdrivenbymovementsspanningthewholedistribution.Instead,itcomesfromacombinationoftwolargelyimmobilegroups(60percentofthepopulation)thatstayrelativelyrichandpoor,andtwogroupsthatundergolargetransitionsthatareneverthelesscontainedtothemiddleofthewealthdistribution

.3

Thetwogroupsdrivingincreasingmobilityalongthelifecycleexperienceareversaloffortunesastheyage,withonerisingthroughthedistributionandtheotherfalling.Weinterpretthesepatternsasevidenceofsegmentedwealthmobility:mobilitytakesplaceonlyforsomegroupsofindividualsandwithinasectionofthedistribution.

Further,weestablishhowdifferenteconomicfactors—suchasportfoliocomposition,sourcesofincome,familystructure,andinheritances—relatetothelargegapsinwealthaccumulationbetweengroups.Wefindthat,whilepropertyistheprimaryassetforallgroups,thereareimportantdifferencesinbusinessassetsandprivateequity.Theseassetsareconcentratedinthetopandfallinggroups,whichalignswiththeirhigherratesofself-employment.Notably,risersengageinlessbusinessactivityandinsteadrelyonemploymentincomeastheymoveupthedistribution.Theirlaborincomeishigherthanthatofthefallers,andtheirhouseholdincomesmatchthoseofthetopgroup(thathasalargershareofcapitalincome).Bycontrast,fallershavesimilar,butultimatelylesssuccessful,entrepreneurialactivitiescomparedtothoseatthetop.Theindividualsatthebottomofthedistributionareverydifferentfromtheothers:theirincomesarepersistentlylower,theystayrentersthroughouttheirlives,andtheyrarelyownbusinesses.

Turningtothecompositionofourmaingroups,welookintotheirmost

3DifferencesinrealizedwealthranktrajectoriescorrespondtomeaningfuldifferencesinlevelsreflectingthehighdegreeofwealthinequalityinNorway.Forinstance,thegapatage55betweenthetwogroupsinthemiddleofthedistributionrepresentsadifferenceintheirnetworthofalmost600,000USdollars.

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representativesubgroupsexploitingthehierarchicalnatureofourclusteringalgorithm.Thoserisingmostlydifferinthetimingoftheirmovements,withsubgroupsexperiencingsimilargainsinrelativewealthpositionsbutatdifferentages,apatternwerelatetotheireducationalattainment.Onaverage,therisersareinthe40thpercentileofthewealthdistributionaroundage30andclimbtothe70thpercentilebyage55.Thereissubstantiallymoreheterogeneityintheinternalpatternsofthosefallingthroughthedistribution.Twosubgroupsarecontinuouslyfalling;theoneexperiencingthelargestfallgoesfromthe75thtothe38thpercentilebetweenages30and55,apatternwetietodecliningbusinessperformance.Athirdgroupexperiencesarapidrisebyage45butlaterfallsbackdown;thesemovementscoincidewithhighearlymarriageratesandlatedivorcerates.WeexploretheheterogeneitywithinallmajorgroupsinSection

6

.

Finally,wecontrasttheroleofindividuals’circumstances,includingparentalwealthandeducation,inpredictingfullwealthrankhistories

.4

Wefindanimportantandnonlinearroleforfamilybackground.Individualsborntoparentsatthetopofthewealthdistributionarealmost30percentagepointsmorelikelytobepartofthegroupthatispersistentlyatornearthetopoftheirowngeneration’sdistribution,comparedtothoseborntoparentsatthebottomofthedistribution.Incontrast,thoseborntoparentsatthebottomofthedistributionarenotonlylikelytobepooreratagivenage;theyarealsomorelikelytobepersistentlypoorthroughouttheirlives.

However,parentalwealthplaysamorelimitedroleforindividualswhoexperienceariseorfallthroughthedistribution.Fortheseindividuals,educationisthemainpredictoroftheirevolution.Highlyeducatedindividualsaremarkedlymorelikelyto

risethroughthewealthdistributionastheyage.Bycontrast,evenaftercontrollingfor

4Ourexercisemovesbeyondstandardmeasuresofintergenerationalmobilitythatcomparetherankofdifferentgenerationsatasimilarpointintheirlifecycle,thus,relyingonasnapshotoftheirwealthtrajectorytoinfermobility(see,forexample,

Chettyetal.

2014;

Fagereng,Mogstad,andR?nning

2021)

.Weinsteadaskwhetherindividualcharacteristicscanpredictcompletelife-cyclehistories.

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theirparentalbackground,thosewithoutpost-secondaryeducationarebetween5and10percentagepointsmorelikelytobefallersthanthosewithatleastundergraduatedegrees.Overall,parentalwealthandhumancapitaleachaccountfor40percentoftheexplainedvariationingroupmembership—highlightingtheimportanceofhereditaryadvantageinwealthdynamics(

BeckerandTomes

1979

)

.5

Theseresultsprovideanovelapproachtostudyingintergenerationalmobilityintermsofentirelife-cyclehistories.Wefinddecliningintergenerationalmobilityalongthelifecycle,sothatthewealthranksofindividualsmoveclosertotheirparent’sranksastheyage.Notonlydoesthismirrortheintragenerationalmobilitytrendwedocument,butwefindthatthesameindividualsdrivebothpopulationtrends.Asrisersriseandfallersfall,theirreversalsoffortunedriveincreasingintragenerationalanddecreasingintergenerationalmobility.

Themainmethodologicalcontributionofthepaperistoproposeadata-drivenapproachtosummarizingheterogeneousmobilityinlarge-scaledatasets.Theagglomerativehierarchicalclusteringalgorithmweemployworksbyrecursivelygroupingindividualswithsimilarwealth-rankhistories

.6

Thisprocessresultsinaglobalhierarchyofclustersthatminimizesthedistancebetweenthepathstakenbyindividualsineachgroup,makinguseofthewholevectorofrealizedwealthranks.Crucially,ourmethodologyallowsustocharacterizemobilitypatternswithoutresortingtoasinglesummarystatistic;italsodoesnotrequireustospecifywhichobservablecharacteristicsdeterminethegroupsortorelyonaspecificparametricmodelfortheevolutionofwealth.Tothebestofourknowledge,thisapproachhasnotbeenappliedtothestudyofmobilitypriortothispaper.

5Ourresultsalsocomplementthosein

Huggett,Ventura,andYaron

(2011),whostudylifetime

inequalityusingamodel-drivenapproach.Althoughwefocusonmobility,webothfindimportantrolesforhumancapitalandinitialconditionsincludingtheinitialwealthlevelofindividuals.

6See

Hastie,Tibshirani,andFriedman

(2009,

ch.14)foranintroductiontoclustering;

Borysov,Hannig,

andMarron

(2014),and

Egashira,Yata,andAoshima

(2024)deriveasymptoticpropertiesofhierarchical

clustering.

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Relatedliterature.Weprovidenewevidenceonwealthmobilityalongthelifecycle,notonlymeasuringthedegreeofpersistenceinindividuals’positionsinthewealthdistributionbutalsothewaysinwhichindividualsmovebycharacterizingtheirtypicaltrajectories.Indoingso,wecomplementanextensiveliteratureonthedynamicsofearningsoverthelifecycle(see,forinstance,

Arellano,Blundell,andBonhomme

2017;

DeNardi,Fella,andPaz-Pardo

2020;

Guvenen,Karahan,Ozkan,andSong

2021;and

Guvenen,Kaplan,Song,andWeidner

2022)andacrossgenerations(see,forinstance,

Solon

1992;

Chetty,Hendren,Kline,Saez,andTurner

2014;

Chetty,Grusky,Hell,

Hendren,Manduca,andNarang

2017;and

Halvorsen,Ozkan,andSalgado

2022)

.

Relatedly,

Hurst,Luoh,Stafford,andGale

(1998)studyhowsavingbehaviourdiffers

overadecadebyrace,education,householddemographics,andinitialwealthusingthePanelStudyofIncomeDynamics.We,instead,studymobilitywithwealthtrajectoriesover25yearswithoutconditioningonspecificvariables.

Wealsocontributetotheliteratureonintergenerationalmobilityinwealth(see,forinstance,

CharlesandHurst

2003;

Boserup,Kopczuk,andKreiner

2017;

Adermon,

Lindahl,andWaldenstr?m

2018;and

Fagereng,Mogstad,andR?nning

2021)

.Ourmethodologyallowsustogobeyondcomparingacrossgenerationsatagivenpointintheirlifecyclebyconsideringthefullwealthhistoriesofindividuals.Weshowthatbothparentalbackgroundandtheindividuals’positionsinthewealthdistributionnearthebeginningoftheirwork-lifehavelong-lastingimpactsonthewealthtrajectoriesofindividuals.Intergenerationalmobilitydeclinesoverthelifecycleaschildren’srelativepositionsintheirowngenerationconvergetowardthoseoftheirparents.

Ouranalysisismadepossiblebylongitudinaldatacharacterizingthedistributionof

wealthhistoriescompiledbyStatisticsNorway.Observingindividualsoverlongperiodsoftimeiscrucialforstudyingthenatureofwealthaccumulationandpriorcontributionshaveusedthisdatatoinvestigatetheroleofreturnheterogeneity(

Fagereng,Guiso,

Malacrino,andPistaferri

2020),differencesinsavingbehaviors(

Fagereng,Holm,Moll,

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andNatvik

2019),theimportanceofgiftsandinheritancesforlifetimeresources(

Black,

Devereux,Landaud,andSalvanes

2022),andtherelationshipbetweenwealthand

lifetimeincome(

Black,Devereux,Landaud,andSalvanes

2023).Inrelatedwork,

Ozkan,

Hubmer,Salgado,andHalvorsen

(2023)focusonthedriversofwealthaccumulation

amongthewealthiest0.1percentatage50lookingbackwardattheirlifetimetrajectories.Wecomplementthesepapersbycharacterizingthelife-cyclepathsofindividualsacrosstheentirewealthdistribution,includingthosewithrising,falling,andstablepaths.Ourfindings,therefore,contributetoourunderstandingofwealthinequalityandmobilitybeyondthedynamicsofwealthaccumulationattheverytop.

Theclusteringmethodweemployconstitutesafeasiblewaytostudytrajectoriesoflongitudinaloutcomes,suchasmobility,inlargepaneldatasets.Italsoallowsustodecomposecommonlyusedsummarymeasuresofmobility,suchastheOLScoefficientinarank-rankregression.Similarapproacheshavebeenusedinsociologytosummarizemobilitybetweendiscretestates(

DijkstraandTaris

1995;

McVicarandAnyadike-Danes

2002;

DlouhyandBiemann

2015)

.

Ineconomics,clusteringhasbeenusedtoanalyzesortingandtransitionsinthelabormarket(see,amongothers,

Bonhomme,Lamadon,andManresa

2019;

Gregory,

Menzio,andWiczer

2021;

Humphries

2022;and

Ahn,Hobijn,and?ahin

2023)andto

identifylatentheterogeneity,asin

Lewis,Melcangi,andPilossoph

(2021)

.ManyoftheseapplicationsusevariantsofK-meansclustering,whoseasymptoticpropertiesarederivedin

BonhommeandManresa

(2015)and

Bonhomme,Lamadon,andManresa

(2022)

.Relativetothesemethods,ourapproachprovidesaglobalhierarchyofpartitionsthatfacilitatesstudyingwithinclusterheterogeneitywithoutimposingcomputationalburdensintheanalysisoflargedatasets.Althoughhierarchicalclusteringisourpreferredapproach,weshowinSection

8

thatourmainresultsholdwithK-meansclustering.

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2.Data:apanelofwealthhistoriesfortheNorwegianpopulation

WeemploydatafromtheNorwegiantaxregistrybetween1993and2017anditsassociatedpopulationcharacteristicsfiles.Weareabletolinkthesevariousdatasetsattheindividualandhouseholdlevelsusingunique(anonymized)identifiers.Theresultingdatacontainsinformationonwealth(networth),assets,debt,income,andavarietyofindividualcharacteristics

.7

Wereportmonetaryvaluesin2019USdollars.

ThecoverageandpropertiesoftheNorwegianadministrativedatasetsitapartfromsurveyandadministrativedataavailableinothercountriesandmakesituniquelysuitedtothestudyofwealthmobilityoverthelifecycle.Westartbyhighlightingthekeystrengthsofourdata.

First,Norwayhasrecordedwealthinitstaxreturnssince1993,providinguswithalongpanelwithtwenty-fiveyearsofobservations.Thislongpanelallowsustotrackindividualsoverimportantphasesoftheirlifecycles.Trackingindividualsiscrucialtounderstandmobilityoverlonghorizonsandtodifferentiatethelife-cycletrajectoriesexperiencedbyindividuals,aswedowhenwedocumentthetrajectoriesofwealthmobilityusingourclusteringprocedure.

Second,theNorwegianincomeandwealthtaxrecordscovertheentirepopulation.Wethereforeconstructaccuratemeasuresofanindividual’srankinthewealthdistribution,withincohortsandthepopulationatlarge.Furthermore,thedatacovers

individualsattheverybottomandtopofthedistribution,whoaretypicallydifficultto

7Thequalityanddetailofthisdatahaveprovenusefulinavarietyofstudies.MoreinformationontheNorwegianadministrativewealthdatacanbefoundin

Fagereng,Guiso,Malacrino,andPistaferri

(2020),

Fagereng,Mogstad,andR?nning

(2021),and

Fagereng,Holm,andNatvik

(2021).Additionally,

Blundell,

Graber,andMogstad

(2015)provideadetaileddiscussionofincometaxrecords

.

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captureinsurveydata

.8

Moreover,mostofthecomponentsofincomeandwealtharethird-partyreportedandarenottop-orbottom-coded,eliminatingconcernsaboutmeasurementerrorfromself-reportingandcensoringthatarecommoninsurveydata.

Third,weareabletolinkindividualswithinhouseholdsandacrossgenerations,aswellastotheirdemographicandeducationalinformation.Thiswealthofinformationletsuslinktrajectoriesofwealthmobilitytotheindividualcircumstancesthathelpdeterminethem,suchasparentalbackgroundandeducationalattainment.

2.1.Wealthandassetdata

Weobserveeachindividual’sassets,debt,andnetworth,asreportedintheirwealthtax

return.Theseareindividualreturns,wherethevalueofassetsjointlyownedbyacoupleissplitequallybetweeneachpartner.Wefocusouranalysisonwealthattheindividuallevel,butwealsoreportrobustnessresultsforwealthatthehouseholdlevel.Usingindividualleveldataallowsustoconsiderhowmobilityvarieswithsexaswellastotrackindividualsthroughhouseholdformationanddissolution.InSection

6.4

,weshowthatthesedynamicsarerelatedtothemobilitypatternsofsubgroupsofindividuals.

Wealsoobservethevalueofvariousassetclassesincludedinindividuals’wealthtax

returns.However,thereturnsdonotincludetransactionswithinclasses.Thesinglelargestassetformostindividualsishousing.Weadjusthousingvaluesusingthereportedvaluesin

Fagereng,Holm,andTorstensen

(2020)treatingcondominiumsandother

propertiesseparately.

9

Weaggregateprimaryresidences,secondaryresidencesandleisureproperties,andforeignresidencesintoaproperty-assetclass.Finally,wedefine

8Thisproblemhasledtomethodsthatoversamplethetailsofthedistribution.Thesemethodsareill-suitedtothefocusofourstudy.Forexample,theU.S.PanelStudyofIncomeDynamicsoversampleslowerincomehouseholds(theSurveyofEconomicOpportunityhouseholds),whiletheSurveyofConsumerFinancesoversampleswealthierhouseholds.Researchersoftenresorttoadhocmethodstobuildmoreaccuratemeasuresoftheuppertailofthewealthdistribution,forexample,byaugmentingtheSurveyofConsumerFinanceswiththeForbes400listofthe400richestAmericansorestatetaxdata(see,forexample,

Vermeulen

2016

).

DaviesandShorrocks

(2000)provideanextensivereviewofthesemethods

.

9Wethank

Fagereng,Holm,andTorstensen

forprovidinguswithupdatedadjustmentvaluescoveringoursampleperiod.

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ahomeownershipindicatorexcludingsecondaryandforeignproperties.

Theotherassetclassesincludedinthetaxreturnsarevehicles,public