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ContentslistsavailableatScienceDirect

Journal

of

Economic

Behavior

&

Organization

jo u r n al ho me p ag e :ww w . e l s e v i e r . c o m / l o c a t e / j e b o

Entrepreneurship

and

income

inequality

Daniel

Halvarsson

a

,

Martin

Korpi

b,∗

,

Karl

Wennberg

c

aRatioInstitute,P.O.Box3203,10364,Stockholm,Sweden bRatioInstitute,Stockholm,Sweden

cInstituteforAnalyticalSociology(IAS),LinköpingUniversity,60174Norrköping,Sweden

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received14March2017

Receivedinrevisedform3November2017 Accepted9November2017

Availableonline21November2017 JELclassification: J31 J24 L26 015 Keywords: Inequality Entrepreneurship Incomedecomposition

a

b

s

t

r

a

c

t

Entrepreneurship research highlights entrepreneurship as a simultaneous source of enhancedincomemobilityforsomebutapotentialsourceofpovertyforothers.Research oninequalityhasfurtherednewtypesofmodelstodecomposeandproblematizevarious sourcesofincomeinequality,butattentiontoentrepreneurshipasanincreasingly preva-lentoccupationalchoiceinthesemodelsremainsscant.Thispaperseekstobridgethese twoliteraturesusingregression-basedincomedecompositionamongentrepreneursand paidworkersdistinguishingbetweenself-employed(SE)andincorporatedself-employed (ISE)individualsinSweden.Wefindthattheproportionofself-employedinthe work-forceincreasesincomedispersionbywayofwideningthebottomendofthedistribution, whereastheproportionofincorporatedself-employedcontributestoincomedispersionat thetopendofthedistribution.Implicationsforresearcharediscussed.

©2017TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCC BY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Thelastfewdecadeshavewitnessedanotableriseinbothself-employmentandsmallbusinessownershipinmost devel-opedeconomies,andmuchpublicpolicyinthiscontexthasbeendirectedtowardincreasingthesupplyofentrepreneurs (Blanchflower,2000;SteinmetzandWright,1989).Atthesametime,manycountrieshaveexperiencedincreasingincome inequalityandstratifiedunemployment(Atkinson,2003;Autor,2014;Goldthorpe,2010).Despitethesetwoparallel eco-nomictrends,studiesthatprobethedirectrelationshipbetweenentrepreneurshipandoverallworkforceinequalityremain scantinthestilllargelyseparateliteraturesonentrepreneurshipandinequality(VanandVersloot,2007;WrightandZahra, 2011).Intheentrepreneurshipliterature,manystudieshavedocumentedatwo-prongedeffectofentrepreneurshipon individualincome,arguingthatentrepreneurshipisasourceofenhancedincomemobilityforsomebutresultsin lower-than-averageincomesforthelargefractionoftheself-employedworkforce(e.g.,Hamilton,2000;Åstebroetal.,2011). However,attentiontothepotentialimplicationsofthesepatternsformacro-levelincomedistributionhasbeenscantinthe entrepreneurshipliterature.Intheinequalityliterature,recentstudieshavedevelopednewtypesofmodelstodecompose andproblematizedifferentsourcesofincomeinequality(e.g.,CowellandFiorio,2011;CreedyandHérault,2011;Thewissen etal.,2013),butthesestudieshavetendedtooverlookentrepreneurshipasoneofthesepotentialsources.Thisoversightis problematicsinceentrepreneurshipisanincreasinglyprevalentoccupationalchoiceinmanyeconomies(Audretsch,2009).

∗ Correspondingauthor.

E-mailaddresses:daniel.halvarsson@ratio.se(D.Halvarsson),martin.korpi@ratio.se(M.Korpi),karl.wennberg@liu.se(K.Wennberg).

https://doi.org/10.1016/j.jebo.2017.11.003

0167-2681/©2017TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/ licenses/by-nc-nd/4.0/).

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Inthispaper,weseektoaddressthisgapintheliterature,whichalsoformsthebasisofouroverallresearchquestions: (1)Doesentrepreneurshipaffectoverallworkforceincomeinequality?(2)Whichaspectsoftheincomedistributionaffect overallinequalityandtowhatextent?(3)Whatindividualcharacteristicsamongentrepreneurs(comparedtoemployed workers)mayaccountfortheeffectsobservedinQuestions1and2?

Toaccountforthefactthatself-employedentrepreneursareover-representedinbothtailsoftheearningsdistribution (Åstebroetal.,2011),weallowfortwotypesofentrepreneurs—thosewhoareself-employedinsoleproprietorships(SE)and thosewhoareself-employedinincorporatedbusinesses(ISE)—andwecomparethesetwogroupswithsalariedworkers(W). Whileentrepreneursarefoundtoearnlessthansalariedworkersonaverage,recentstudies,suchasLevineandRubinstein (2017),ÅstebroandTåg(2017),andÖzcan(2011),havesuggestedthateventhoughthisistrueforSE-entrepreneurs, ISE-entrepreneurstendtoearnrelativelymoreevenwhencomparedtoemployeeswithcomparabletraitsandskills.Thus,in distinguishingbetweenSEandISE,weallowforthepossibilitythatdifferenttypesofentrepreneurship,ordifferenttypes ofentrepreneurs,maydifferintheireffectsontotalincomedistribution.1

UsinghighlydetaileddataonthefullSwedishworkforceandcapitalizingonrecentinequalityresearch(e.g.,Cowelland CowellandFiorio,2011;CreedyandHérault,2011;Thewissenetal.,2013),wedevelopanovelempiricalapproachtoanswer theseresearchquestions.Centraltoouranalysisisourchoicetouseaflexibleinequalitymeasure—thegeneralizedentropy (GE)index—tofinetuneourdecompositionanalysistodifferentsegmentsoftheincomedistribution.Usingthismeasure, webegintheanalysisbystudyingwhetherchangesinaggregateinequalityaresystematicallyrelatedtoSE,ISE,andWand whichpartsofthedistributionareaffected.Next,wepresentanintegratedfactor-sourcedecompositionanalysisinwhich weconsideranumberofmicro-levelsourcestoaccountfortheinequalityamongSE,ISE,andW.Specifically,thisapproach allowsustotesthowdifferentexplanatoryvariablesrelatetowithin-groupinequalityaswellastheextenttowhichthe samegroup-specificexplanatoryvariablesrelatetoaggregateinequalityinthetotalworkforce(CowellandFiorio,2011; Fields,2003).

Basedonthisanalysis,wefindthatonaverage,SE-entrepreneurshavelowerincomesthanworkers(W),whereas ISE-entrepreneurstendtoearnrelativelymorethanboththesetwogroups.Whenconsideringthetotalincomedistribution intheworkforce,wefindthatSE-andISE-entrepreneurscontributesubstantiallytoincomeinequality,butusingdifferent GEindices,wefindthatthisrelationshipisU-shaped.WhiletheprevalenceofSE-entrepreneursincreasesinequalityby wideningthebottomendofthedistribution,ISE-entrepreneursaugmentinequalityfromthetopofthedistributionby enhancingthetotalnumberofhigh-incomeearnersintheworkforce.Inparticular,whentuningtheGEindextolowerparts oftheincomedistribution,SEaccountsforabout30%oftotalinequalityandISEcontributesonlyafraction,buttheopposite istruefortheupperendoftheincomedistribution.WhentuningtheGEindextothetopofthedistribution,weinstead findthatISEaccountsforabout10%oftotalinequalityandSEaccountsforonlyafraction.Bothtypesofentrepreneurship, however,captureverylittlevariationinthemiddleoftheincomedistribution.

Theseresultshighlighttheimportanceofconsideringentrepreneurshipinstudiesofincomeinequalityanddemonstrate thatinequalitymeasuresemphasizingmiddle-rangeincome,suchasthecommonlyusedGinicoefficient,maynotcapture theseeffectswell.Inregardtoourfactor-sourcedecompositionanalysis,akeyfindingisthatindividuals’educationand genderdifferenceseachaccountforabout4%oftotalincomeinequality.Whilethevariableyearsofeducationexplains inequalityamongworkersandamongISE-entrepreneurs,thisisnotsoamongSE-entrepreneurs,suggestinglowreturnsto educationamongSE-entrepreneurs(VanderSluisetal.,2005).2Further,genderdifferencesinearningscontributemoreto inequalityamongworkersthanamongeitherSEorISE.

Tothebestofourknowledge,thispaperisthefirsttoassesstheeffectsofentrepreneurshiponincomeinequalityusing state-of-the-artdecompositiontechniques.Italsorepresentsafirstattempttoaddressthejointtheoreticalconcerninthe literaturesonentrepreneurshipandeconomicinequalityregardinghowchangesintherelativenumberofentrepreneurs andtheirwithin-groupincomedispersionaffectaggregateincomedynamicsinmoderneconomies.Whileahostofstudies haveshownthatentrepreneursgenerallyhaveamuchwiderdistributionofearningscomparedtoworkers,asfaraswe know,noonehasactuallyexaminedtheimplicationsofthisforthewiderdistributionofincomeintheeconomyasawhole. Ourresultssuggestthatentrepreneurship,atleastatthetailsofthedistribution,affectstheeconomy-widedistributionof earningsinasimilarmagnitudeasmoreconventionalfactorsincludedinmostmodelsandstudiesgauginginequality.

OurmethodologyleansheavilyontheworkofCowellandFiorio(2011),whichdecomposesinequalityindicesusing severalsub-groupsembeddedinaregressionframework.Thisapproachhelpsexplaineachgroup’scontributiontooverall inequality,providingaclearerpictureofthegroupdynamicsthatdriveinequalityatthepopulationlevel.Further,weare abletopinpointthesignificanceofanumberofexplanatoryvariablescommonlyusedinincomeregressionswhilealso assessingtheirindividualcontributiontosub-groupandaggregateinequality.

1 Wealsochosethisdivisionbecauseinmostcountries,includingSweden,thesetwoformsofentrepreneurshiparesubjecttodifferenttaxlaws(Edmark

andGordon,2013).AsshowninTablesA7andA8intheappendix,thetypeoffirmsstartedbySE-andISE-entrepreneursalsodiffersystematicallyinterms ofentrepreneurialteamsize(TableA7),firmsize(TableA7),andindustryclassification(TableA8).Recentstudieshavealsosuggesteddifferencesinterms ofinnateabilityamongSE-andISE-entrepreneurs(LevineandRubinstein,2017,Åstebroetal.,2011),apointwereturntolater.Foralengthydiscussion andanoutlineofdifferencesalongsimilarlinesusingUSdata,seeHerranzetal.(2009)andDeNardietal.(2007).

2 Robustnesstestsforasub-groupofthe2005cohortpresentedinFootnote17suggestthatincomeinequalityamongSE-entrepreneursmaybeexplained

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Ourpaperisstructuredasfollows:Inthenextsection,weoutlinethetheoreticalbackgroundandpreviousliterature. Section3outlinesourempiricalstrategyandtheregression-baseddecompositionmethodusedtoanalyzethelinkbetween entrepreneurshipandincomeinequality.Section4detailsthedatausedintheanalysis,whichisfollowedbytheresultsin Section5.Thepaperconcludeswithadiscussionabouttheimplicationsforpublicpolicy.

2. Entrepreneurship,incomedynamics,andinequality

Theempiricalliteraturehasnotedthatentrepreneurshipinmoderneconomiesdoesnottaketheformofgrowing pro-ductivefirmsbutratherofincreasingratesofself-employment(SanandajiandLeeson,2013;Stam,2013;Steinmetzand Wright,1989).However,researchhasbeenscantonthepossibleconsequencesofthisdevelopmentintermsofincome inequality.

Asubstantialnumberofstudieshaveinvestigatedincomedifferentialsbetweenemployeesandtheself-employed.Byand large,thisliteraturehasconcludedthatentrepreneurshipgenerallyresultsinearningslowerthancomparablesalariedwork. Forexample,thewell-citedpapersbyBlau(1987),BorjasandBronars(1989),andEvansandLeighton(1989)estimatethat theearningsofself-employedindividualsarebelowthoseofworkersand—forthelattertwostudies—thatthedistributionof theseearningsisconsiderablyskeweddownward(i.e.,skewedtowardlow-incomeearners).Similarly,inapapercomparing thereturnoninvestmentforUSnon-publiclytradedequitywiththatofpublicequity,MoskowitzandVissing-Jorgensen (2002)identifyalargepublicequityinvestmentpremiumandsimilarlyarguethatentrepreneurshiphaspoorreturnsoverall. Morerecentstudieshavefurtheredthesefindings,confirmingthatentrepreneurialearningsarebelowthoseof compa-rablesalariedworkersonaveragebutaddingthattheoveralldistributionofentrepreneurialearningsalsocomeswitha substantially“fat”upwardtail.UsingdatafromtheCanadianSurveyofLaborandIncomeDynamics(SLID)1993–1994,Lin etal.(2000)addressearningsdifferencesatdifferentquantilesoftheearningsdistributionandtheextentandcyclicalityof entryandexitintoandoutofentrepreneurship.Theirstudyshowsthatthemeanincomeofself-employedindividualsis about20%lowerthanamongcomparableworkersacrossthefirstfourquantilesoftheearningsdistributionbutmorethan doublethatofemployedworkersinthetopfifthquantile.

Similarly,usingmonthlypaneldataonUSmalenon-farmworkersfrom1983to1986,awell-citedstudybyHamilton (2000)findsthatmostentrepreneurspersistinsmallbusinesseseventhoughtheyhavebothlowerinitialearningsand lowerearningsgrowthrelativetoemployees.Estimatingamedianworker-entrepreneurearningsdifferentialofaround 35%acrossindustriesandrulingoutthepossibilitythatentrepreneurshavelowerabilitiesonaverage,thestudysuggests thatnon-pecuniarybenefitslikelyexplainbothentrepreneurialentryandpersistence.Hamiltonalsofindssupportforthe “superstarhypothesis”—namely,thatentrepreneurialincomeattheverytopoftheearningsdistributionishighlyskewed upwardbecauseofarelativelysmallnumberverysuccessfulhigh-productivityindividuals—andcautionsthatthispattern isnotcapturedinhisestimatesofmedianincomedifferentials.

OtherrecentstudieshavevindicatedandextendedthestylizedpatternprovidedbyHamilton(2000).Åstebroetal. (2011)usedatafromtheKoreanLaborandIncomePanelStudy1998–2004totestamodelofoccupationalchoice,finding thatentrantsintoself-employmentaredrawndisproportionatelyfrombothtailsoftheearningsdistribution.However,in contrasttotheHamiltonstudy,Åstebroetal.alsofindthattheskewedincomedistributionreflectsthedistributionofability intheworkforce,withworkerswithbothabove-averageandbelow-averageunobservedabilitybeingmorelikelytoengage inentrepreneurship.AnotherrecentstudybyLevineandRubinstein(2016)usesUSdatafromtheCurrentPopulationSurvey 1994–2010toseparatesalariedworkersandentrepreneursintheformofSEandISE,pinpointingboththedeterminants behindthesortingofpeopleintothesedifferenttypesofemploymentandtheirsubsequentearnings.LevineandRubinstein arguethatearlierfindingssuggestingthatentrepreneursearnbelowthemedianincomeofsalariedworkersessentially reflectthefactsthattherearesignificantlyfewerincorporatedentrepreneursthanself-employedentrepreneursandthat thislattergroup—whichindeedtendstoexhibitlowerincomes—tendstodominateestimatesof“averageoutcomes”in earningequationscomparingentrepreneurstoworkers.Incontrast,theirresultssuggestthatincorporatedentrepreneurs’ earningsareinthemagnitudeof30%abovesalariedworkerswithcomparabletraitsandskills,whointurnearnmore thantheirself-employedcounterparts.AssuggestedbyÅstebroetal.(2011),LevineandRubinstein(2017)findthatthese outcomesreflectinnateability(i.e.,non-cognitivetraitsandcognitiveskills)toasignificantdegree.Whereassometraits arecommonofbothtypesofentrepreneurs(e.g.,engaginginillicitactivitiesasteenagersandriskybehavior),incorporated entrepreneursscorehigherinlearningaptitudeteststhanself-employedindividuals.3

Turning to studies that focus specifically onentrepreneurship and income inequality, we note a thinner empiri-cal literature that emphasizes the association between inequality within organizationsand employees’ transition to entrepreneurship.Ratherthanexploringpossiblelinkstoworkforceincomedispersionperse,thesestudieshavemostly focusedontheconditionsinwhichincomedispersionwithinfirmsmayrepresentasourceofupwardearningsmobility

3Theseresultsareinlinewithworkfocusingon“necessityentrepreneurship.”Necessityentrepreneursaredefinedasthosewhohavestartedtheirown

firm“becausetheycannotfindasuitableroleintheworldofwork,[so]creatinganewbusinessistheirbestavailableoption”(Reynoldsetal.,2005).The GlobalEntrepreneurshipMonitorsuggeststhatbetween3%and30%ofallentrepreneursinOECDcountriesfitthiscategorywithhighfluctuationsover time(Singeretal.,2014).Thesenecessityentrepreneurshavebeenshowntoexhibitlimitedincomemobilityaswellaslowgainsinindividualproductivity (BlockandWagner,2010;Poschke,2013).

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amongindividualschoosingtoleavethesefirmsforentrepreneurship(Carnahanetal.,2012;KacperczykandBalachandran, 2017;SørensenandSharkey,2014).However,afewmacro-orientedstudieshaveindicatedthatthegreaterthenumberof smallfirmsinaneconomy,themoreunequaltheearningsdistributioninthateconomyis(Davis,2013;CobbandLin,2017; FieldsandYoo,2000).Intermsofexplainingthispattern,theliteraturehasmostlyprovidedverybroadstructural explana-tions.Forexample,Lippmannetal.(2005)providecross-countryevidenceontherelationshipbetweenworkforceincome inequalityandtherateofentrepreneurshipusingGlobalEntrepreneurshipMonitor(GEM)data.Theyfindthat entrepreneur-shipratesarehigherincountrieswithsignificantincomeinequalityanddiscusssevenstructuralfactorsbroadlyassociated withthispattern:levelofeconomicdevelopment,governmentpolicies,foreigndirectinvestment,servicesectorgrowth, increasinglabormarketflexibility,wealth-transferprograms,andvariationinworkerunionization.

Tosummarize,theliteratureonearningsdifferentialsbetweensalariedworkersandentrepreneurshasarguedthat risinglevelsofentrepreneurshipmayincreaseinequalitybyexpandingtheshareofeithertoporbottomincomeearners—or both—intheworkforce.However,thispossibilityisindirectlyinferredfromequationsofearningsdifferentialsbetween entrepreneursandworkers,andwedonotknowhowentrepreneurshipaffectstotalinequalitywithintheworkforceasa whole.Studiesexplicatingapotentialrelationshipbetweenentrepreneurshipandincomeinequalityhavetendedtofocus onincomeinequalitywithinfirms—mostoftenmeasuredbythetraditionalGinicoefficient—anditseffectsonworkers’ mobilitytoentrepreneurship.Studiesusingcountrycomparisonshavesuggestedthatentrepreneurshipispositivelyrelated toaggregateincomeinequality,buttheyhavebeensilentinregardtowhichpartsoftheincomedistributionmightbe affectedandhowdifferenttypesofentrepreneurshipmayaffectoverallinequality.Inthisliterature,therehasalsobeen noattemptofanykindtolinkindividual-leveldevelopmentstoeitherwithin-groupinequalityorchangesinaggregate outcomes.Theseempiricalpuzzlesformthebasisofourresearchquestions,towhichwenowturn.

3. Empiricalstrategyandmethod

Firstly,sincetherearenumerouswaystoconceptualizeandmeasureinequality,eachwithauniquesetofproperties, weneedtobeginbychoosinganinequalitymeasureappropriatetotheresearchquestion.Themostcommonmeasureis certainlytheGinicoefficient(Akitaetal.,1999).Inspiteofitsprevalenceandsimplicity,theGinicoefficientdoesnotfitour purposesfortworeasons.First,itdoesnoteasilydecomposeintosub-groupsandfactorsources(Cowell,2011),andsincewe wanttogaugeboththedifferentcontributionsofentrepreneursandsalariedworkerstoaggregateinequalityaswellashow differentfactorscontributetoinequality,decomposabilityiscrucial.Second,sincewewanttoestimateofoursub-groups’ respectivecontributiontoinequalityatvariousrangesoftheincomedistribution,theGinicoefficientisalsoinappropriate sinceitmostlyreflectsvariationinmiddlerangeincome.

Wethusneedamoreflexiblemeasureandthegeneralizedentropyindex(GE-index)fulfilsbothrequirements,allowing forthestudyofinequalitywithineachgroupseparatelyandalsoforanassessmentofhowmucheachgroupcontributes totheaggregate.Further,theGE-indexisdefinedasafunctionofasensitivityparameter˛ ∈ (−∞,∞),whichallowsus toadjustitssensitivitytospecificpartsofthedistribution.Bychoosingdifferentvaluesof˛whendecomposinginequality intosub-groups,wecandiscernwhichpartoftheincomedistributionismostaffectedbyeachseparateoccupationalgroup. Specifically,thelowerthevalueof˛,themoresensitivetheGE-indexistodispersioninthelowerpartsoftheincome distribution.Conversely,thehigherthelevelof˛,themoresensitivetheGE-indexistodispersionintheupperpartsofthe incomedistribution(Cowell,2000).AlthoughtheGE-indexisdefinedontherealline,welimitourstudytothefollowing subsetofvalues:{−1,0,1,2}.OfparticularinterestistherelativecontributionofSEandISEtooverallinequalitywhen˛is tunedtoeitherthebottomortoppartsofthedistribution(i.e.,˛ ∈



−1,2



)ascomparedtothemiddle(i.e.,˛ ∈



0,1



).4 TobetterdescribethepropertiesoftheGE-indexweincludeaformaldefinition.Lety= [y1...yN] beavectorofincomes foratotalofNindividualsinthepopulation.AsampleanalogueoftheGE-indexcanthenbedefinedasafunctionof˛by theexpression GE(y,␣)=␣ (˛11)N N



i=1



y i  (y)



˛ −1



,␣∈(−∞,∞){0,1}. (1)

Thesumistakenoverindividualincomesyi(i=1,...,N)withexponent˛scaledbythemeanincomeofthepopulation  (y).Wecaninterpretthedifferentvaluesof˛asfollows.Startingwith˛=2andGE (y;2),theexpressionin(1)corresponds tohalfthesquaredcoefficientofvariation(CV),whichisgivenbyvar (y) /2 (y) andissynonymouswiththe Hirschman-Herfindahlconcentrationindex(Quintanoetal.,2005).When˛takesthevalues1or0,inturn,GE (y;1) andGE (y;0) is evaluatedinthelimitas˛→1and˛→0,respectively.At˛=1,theGE-indexisidenticaltotheso-calledTheilindex,and at˛=0,itcorrespondstothemeanlogarithmicdeviation(MLD).Inthislistedorder,theseentropymeasuresaresensitive tochangesinthetop,upper-middle,andlower-middleincomeranges,respectively.Lastly,at˛=−1,theemphasisofthe indexGE (y;−1) isonthebottomrangesofthedistribution,asitcontainstheexpectedvalueofreciprocalincome(1/y).

4 Withthepossibleexceptionof˛=−1,



0,1,2



constitutethemostcommonvaluesinsimilarstudiesusingtheGE-index.Since˛=−1turnsthe

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3.1. Sub-groupdecompositionofthegeneralizedentropy(GE)index

Havingchosenaninequalitymeasure,thissectiondiscussesthesub-groupdecomposabilityoftheGE-index,anadditive propertythatiscrucialforevaluatingthecontributionfromeachsub-grouptooverallinequality.5

LetusconsideratotalofJsub-groups(J=3throughoutthisstudy).TheGE-indexcanthenbedividedintotwoaggregate parts,

GE (y;˛) =GEb(y;˛) +GEw(y;˛) , (2)

onebetween-grouppartGEb(y;˛) ,whichreflectsinequalityasmeasuredbyvarianceinmeanincomebetweendifferent groups,andonewithin-grouppartGEw(y;˛),whichreflectsthedispersionofindividualincomewithineachseparategroup. Here,thelatterexpression,GEw(y;˛),isaweightedsumoftheGE-indexcomputedforeachofthesub-groups(j=1,...,J) using GEw(y;˛) = J



j=1 wjGE

yj;˛

. (3)

Theweightisinturndefinedbywj=pjrj˛,wherepj=Nj/Ncorrespondstoapopulationweight,andrj=

Yj

/ (Y) correspondstotheratiobetweenmeanincomeinsub-groupjandthemeanincomeofthepopulation(CowellandFiorio, 2011).Substitutingthisexpressionforthepopulationweightintoexpression(3)andusing(1)yieldsthefollowingformula fortotalwithin-groupinequality:

GEw(y;˛) = 1 ˛2˛ J



j=1 Nj N



Yj

 (Y)

˛ 1 Nj Nj



i=1

yji 

yj

˛ −1



. (4)

ThisexpressionthusreflectstheshareoftotalinequalityGE (y;˛) thatresultsfromincomedispersionwithineachofthe separatesub-groupscombined.UsingtheidentityinEq.(2)andtheexpressionforGEw(y;˛) inEq.(4),thebetweenpart GEb(y;˛) canbebackedoutto

GEb(y;˛) = ˛21˛ J



j=1 Nj N



Yj

 (Y)

˛ −1



, (5)

whichinturncapturesresidualinequalityoncewithin-groupinequalityisaccountedfor.6TheGE-indextherebyaccounts forthedifferencesinmeanincomesacrossthesub-groups—namely,between-groupinequality.7

Note alsothat thesub-groupdecomposition in(4)and (5)allowsforanalternativedecomposition bydefiningthe contributiontototalinequalityGE (y;˛) fromagivengroupj,as

˜ GE

yj;˛

= pj

rj˛−1

˛2˛ +wjGE

yj;˛

. (6)

Thefirstterminthisexpressionreflectsgroupj’scontributiontothebetweencomponentofinequality,andthesecond termreflectsthegroup’scontributiontothewithincomponent.Thisexpressionisusefulwheneverweareinterestedin thetotalcontributionfromoneparticularsub-groupratherthanthecombinedwithin-orbetweenpartofallsub-groups takentogether.TogetbacktoaggregateinequalityGE (y;˛) fromthisexpression,wesimplytakethesumovertheJgroups. Ifnotmentionedotherwise,itisthisexpressionwerefertowhendiscussingaparticularsub-group’stotalcontributionto aggregateinequality.

5GE (y;˛) isstrictlydecomposableindicesbecauseits’between-groupcomponentsmeasurethechangeinoverallinequalitywhengroupmeansare

equalizedwhilekeepingthewithin-groupcomponentconstant.

6The“betweenpart”inEq.(5)iswrittenslightlydifferentherecomparedtoCowellandFiorio(2011),wherethepopulationweightisincludedwithin

thesquarebracketsasfollows: 1

˛2−˛

J



j=1



Nj N



(Yj) (Y)



˛



−1

.Althoughthetwoexpressionsareequivalent,itislessclear,usingtheirexpression, howtocalculatethecontributiontoaggregateinequalityfromoneparticulargroup’s“betweenpart”sincetheirequationleavesoutthe“residualterm”of

−1

˛2−˛thatalsoneedstobedistributedamongthegroups.Usingtheexpressionin(5)instead,itneatlytakescareofthisinconveniencebyportioningthe residualtermbetweenthegroupsbytheamountof−Nj/N

˛2˛

.

7Usingtheexpressioninfootnote4,similarexpressionscanbereachedfortheMLDandTheilindex.Wedonotshowseparatederivationsforthese

measureshere.Aslongas˛>1,itisapparentthatforgroupswithalowermeanincomethanthepopulationaverage,the“betweenpart”contributes negativelytooverallinequality.Theconverseistrueforgroupswithmeanincomeslargerthanthepopulationaverage.For˛<1,therelationshipbecomes theopposite.

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3.2. Factorsourcedecompositionofasub-group’swithininequality

Inthissection,weturntoinequalitydecompositionbyfactorsources,somethingthatoftenaccompaniesasub-group decompositionanalysis.Traditionally,afactor-sourceanalysisisusedtodecomposeinequalityintoincomesourcessuch assalariedincome,capitalincome,ortransferpayments.Toallowforamuch widersetofpossiblefactorswerelyon Fields(2003)andCowellandFiorio(2011)whodeveloparegression-basedapproachtoinequalitydecomposition.When specifyingtheinequalitymodel,thisapproachallowsustoincludedeterminantsofincometypicallyusedinMincer-type wageregressionsbutarerarelyincorporatedinstudiesoninequality.

Theregression-basedapproachforfactor-sourcedecompositioncanbedescribedasfollows.Lettheincomeforindividual i (i=1,...,N) insub-groupj(j=1,...,J)besplitintoasumofKdifferentfactorsources(i.e.,components):

yji=yij1+yij2+···+yijK. (7)

ProvidedthataninequalityindexdenotedbyI

yj

satisfiessixbasicassumptionsidentifiedbyShorrocks(1982,see AppendixA),theindexcanbedecomposedintoasumofKinequalitycomponents,heredenotedbySjk

yjk,yj

fork= 1,...,Kas I

yj

=Sj1

yj1,yj

+Sj2

yj2,yj

+···+SjK

yjK,yj

, (8)

whereyjk referstothekth incomesourceforthejth group.Infact,providedtheassumptionsarefulfilled,this typeof decompositionisinvarianttothechoiceofinequalitymeasureI (y) (Shorrocks,1982).Toseethis,definethesharethe proportionalcontributionofSjktoI

yj

by,

sjk≡ Sjk

yjk,yj

I

yj

.

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Sincesj1+sj2+...+sjK =1byconstruction,multiplyingthroughwithI

yj

showsthatsjkbecomestheloadingoffactor ktotheinequalityI

yj

decomposedinto I

yj

=sj1I

yj

+sj2I

yj

+...+sjKI

yj

. (10)

Furthermore,forthisclassofinequalitymeasures(theGE-indexamongthem),thetermsjkcanbeexpressedintermsof thecovariancebetweentheincomecomponentyjkandtotalincomeyjdividedbythevarianceofyj,asfollows

sjk= 

yjk,yj

2

y j

. (11)

Thisresultcomesfromtheorem3ofShorrocks(1982)andwasfirstusedbyFields(2003)toconnectincomeregression analysiswithtraditionalfactor-sourcedecompositionofincomeinequality.Inthenextsectionwepresentabasicincome modelandshowhowtheresultinEq.(11)canbeusedtodecomposetheinequalityofincomeintoK−1explanatorysources usinglinearregressionanalysis.

3.3. Factorsourcedecompositionusingregressionanalysis

Weconsideralinearmodelofincomeforindividualiingroupjgivenby yij=bj0+

K−1



k=1

bjkxijk+uij, (12)

whichincludesK−1numberof(potentiallyendogenous)explanatoryvariablesxkji,andani.i.d.errorterm,uij.Becausethe modelhasthesamelinearformastheexpressioninEq.(7)wecandecomposetheinequalityofyj,i.e.I

yj

,intofactor sourcesbymappingbjkxijkinEq.(12)toyjkinEq.(7).ByexpandingthecovarianceinEq.(11),Fields(2003)showsthat differentpartsofthelinearincomemodelarerelatedtosjkasfollows(CowellandFiorio,2011)

sjk=b2jk 2

x jk

2

y j

+bjk K−1



r/=k bjr

xjr,xjk



xjr



xjk

2

y j

+bjk

uj,xjk



uj



xjk

2

y j

, (13)

wherethefirsttermgivesthedirectcontributionofbjkxjktoI

yj

;thesecondtermisasumandrepresentsthecontribution toI

yj

frommulticoliniarity,i.e.ifxjkiscorrelatedwithxjr forther /=kotherexplanatoryvariables;andthethirdterm representsthecontributiontoI

yj

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thelastterm,sjK,itrepresentsthecontributiontoinequalityfromtheunobservedpartofEq.(12)expressedintermsofthe residual’sdirectcontributionaswellasthevariationresultingfromanyendogenousexplanatoryvariables,givenby8

sjK = 2

u j

2

y j

+ K−1



k=1 bjk

uj,xjk



uj



xjk

2

y j

. (14)

TofindthesampleversionofsjkandsjK,weestimatethe(no-log)incomemodelwithOLSandcollectthepointestimates. Thesearecombinedwithinformationfromthecovariancematrixofallvariablesincludedintheempiricalmodeltoform estimates ˆskand ˆsK.

Whenitcomestothestandarddeviationsoftheestimates ˆskand ˆsK,CowellandFiorio(2011)suggestabootstrapping procedureconsideringthedifficultyofcomputinganalyticalstandarderrors.Sincethecomputationoutlinedinthissection involvesnumerousseparatecomputationsand,inourcase,almost3.5millionobservations,bootstrappingbecomesless attractive.InBigottaetal.(2015)theauthorsprovideanalyticalstandarderrorsfor ˆsk.Withourinclusionof3-digitindustry codesalongwithdummiesforlocal-labormarkets,eventhecalculationsofthesebecometoocumbersomewithordinary statisticalsoftwareandcomputationalpower.9Wethereforeshowdecompositionresultswithouttheattachedstandard errors.Thisisinlinewithmuchofthepreviousliteratureusingregressiondecompositiontechniquesinwhichthereporting ofsignificancelevelshasyettobecomestandard.

3.4. Decompositionofwithin-groupinequalityinseveralsub-groups

Inthelastsectionwekeptthesub-groupindexationjinthetermsjkandsjK inEqs.(13)and(14)inlinewithCowell andFiorio(2011)whoshowthatitispossibletoreconcilewithin-groupdecompositionofinequalityintofactorssources withthesub-groupdecompositionpresentedinSection3.1,usingregressionanalysisandOLS.Inparticular,using regres-sioncoefficientsexpressing

yj

= K−1



k=1 bjk

xjk

,Eq.(6)theyshowthattheinequalitycontributionfromgroupjtototal inequalityI (y) canberestatedasfollows,

˜ GE

yj;˛

= ˛2pj ˛



K−1 k=1bjk

xjk



K−1 k=1bk (xk)



˛ −1

+wj K



k=1 GE

yj;˛

sjk. (15)

Thefirstexpressionstillcapturesthegroup-componenttobetween-groupinequality,butherethisisexpressedinterms ofparametersfromtwoseparateregressions,onerestrictedtoindividualsinsub-groupjandoneunrestrictedonthefull population.Asbefore,thesecondtermcaptureswithin-groupinequality,buthereexpressedasthepopulationweighted (wj)sumofKnumberofinequalitycomponentseachscaledwiththeloadingfactorsjk.Exceptforthepopulationsharesthat canbecalculateddirectlyfromthedata,allinformationregardingthesub-groupfactor-sourcedecompositionareprovided byregressingincomeonthesetofexplanatoryvariablesinEq.(12)foreachofthejsubgroups.

4. Dataanddescriptivestatistics

4.1. Data

TheempiricaltestforourmodelisbasedonmicrodatafromSwedenfortheyears2005and2013.TheSwedisheconomy hasoneoftheworld’slowestratesofincomeinequality.However,inequalityinSwedenincreasedmarkedlybetween1985 andtheearly2010s(OECD,2015).10Duringthesameperiod,thecountrysawincreasingratesofentrepreneurshipinthe formofISE,makingSwedenaninterestingcasetoprobetheroleofentrepreneurshipinincomeinequality.

8Sincealldirectcontributionsaresquared,anecessaryconditionfors

ktobenegativeisthatxjkiseithercorrelatedwithatleastoneofthexr(r/=k)

resultinginmulticollinearity,oritiscorrelatedwiththeerrortermresultinginendogeneity(CowellandFiorio,2011).Ontheotherhand,ifallstandard assumptionsinOLSaresatisfied(i.e.,nomulticollinearityandnoendogeneity)skjandsKjarereducedtotheirrespectivefirstterms,sjk=b2jk2

xjk

/2

y j

andsjK=2

uj

/2

y j

.

9WhencomputingBigottaetal.(2015)standarderrorsforoursmallersamples,wefindthemtobeverysmallinmagnitude.Exceptforafewcaseswhen

theOLSestimateisinsignificant,andthepercentagecontributionisminiscule,sjktendtobehighlysignificant.

10OurinequalityestimatesaresomewhatdifferentfromtheOECD’scountryanalyses,whichreportaslightincreaseinGiniformarketincomefrom

2004to2011(0.369–0.371).OECDchangedtheirdefinitionofmarketincomein2012toamoredetailedbreakdownofhouseholdincometransfersanda reviseddefinitionofhouseholdincome.AmainsourceofdivergencebetweentheOECD’sestimatesofincomeinequalityandoursisduetotheirusageof equivalizedincomedata(bythesquarerootofhouseholdsize)andconstantprices,whereasweuseindividualnominalincomedata.Inouranalysis,we alsofocusonworkforceinequalityofnon-zeromarketincome,whereasOECDanalysesalsoincludethoseunemployedandoutsidetheworkforce.Taken together,theaggregateOECDstatisticsarefairlyconsistentwithoursthatshowaslightlydecliningGinicoefficientformarketincomebetween2005and 2013(0.318–0.309,seeTable2below).

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OurpaperreliesondatafromtheLISAdatabase,whichincludesallindividualsresidinginSwedenaged16andolder. TheLISAdatacomesfromgovernmentalregistersandismaintainedforresearchpurposesbyStatisticsSweden.Thedata containsawealthofdemographicandincome-relatedinformationandisgeneratedfromanumberofsources,including individualtaxstatements,birthplaceregistries,andschoolrecords.Thedatabaseoffersinformation onemploymentas wellasindustrialandoccupationalstructures,andittracksflowsinthelabormarket.Whileincome-relatedinformation datesbackto1990,thedatabasedoesnotincludeentrepreneurialincomeandoccupationaldatauntilmorerecently.In ouranalysis,wethereforefocusontwocrosssections,2005and2013,thefirstandlastyearstheLISAdatabaseincluding comprehensivedataontheincomeandoccupationvariablesusedinouranalysis.Thesetwodatapointsalsorepresenta fulleconomiccycle.Usingthemethodologydescribedintheprevioussection,wecanaccountforthelevelofinequalityfor eachoftheseyearsaswellasprobeanychangethatoccurredoverthenine-yearperiod.

Weuseallindividualsintheworkforcebetween25and64yearsofageintherespectiveyearsforwhichlabormarketdata isavailable.Fromthisdata,wethenexcludeanumberofindividualswhoarenotassociatedwithanemployingorganization, suchassailorsandseasonalworkers.Thesampleusedforanalysiscomprises3,619,132individualsin2005and3,746,272 individualsin2013.Exceptforage,theonlycriteriaweusetoexcludeindividualsfromthesampleiswhenanindividual reportedzeroincomeontheirincomestatement.Wealsoexcludeahandfulofindividualsattheverytopoftheincome distribution(seediscussionbelow).

Thisrichdataenablesustodistinguishbetweentwotypesofentrepreneurs:thoseindividualswhoareself-employed(SE) inaprivatebusiness(soleproprietorships)andthosewhoareself-employedinanincorporatedbusiness(ISE)(Blanchflower, 2000).Sinceweincludeallindividualswithincomestatementsabovezero,ourcategoryforsalariedworkersneedstoinclude individualswhowerenotonlyemployedatthetimeofmeasurement(whichcorrespondstothemonthofNovemberfor eachseparatecalendaryear)butwhoalsoworkedsometimeduringthatsameyear.

Consistentwithgovernmentclassifications,wedefineanentrepreneurasanindividualwhosemainsourceofincome comesfromacompanyinwhichheorshehasamajorityownershipstakeandworksfulltime(Foltaetal.,2010).11With thisclassification,weuseinformationfromtwodifferentsources.First,weuseinformationfromgovernmentregisterdata (LISA)regardingthesourcesfromwhichanindividualderivesthelargestshareofhisorherincome.12Basedonthese data,weonlyincludeentrepreneursreportingtheirownbusinessasthesourceofthemajorityoftheirincome.Part-time entrepreneurswhoseincomestemsprimarilyfrompaidemploymentarecodedasworkers.Second,weuseinformation fromRAMS(Swedishlaborforceregisterdata)onwhethertheentrepreneurconsidershim-orherself“active”inthesense thatheorsheworksatleast600hayearinhisorherownbusiness.Unlessentrepreneursactivelyreportdoingbusinessin thismanner,theyareputintotheworkercategory.

ThisratherstrictdefinitionofwhatconstitutesentrepreneurshipmayreducethenumberofindividualsinbothourSE andISEcategories,butitensuresthatwecanbecertainthatrunningtheirrespectivebusinessisthemainoccupationof theseentrepreneurs.

Similartostudiesoninequalityby,forexample,theOECD(2015),theprimaryincomevariableinourmodelsismarket income,definedasthesumofgrosswageincomeplusnetincomefromanactivebusinesspluscapitalincome.Allthree variablesareincludedinmarketincometobeabletobettercompareincomefrombothtypesofentrepreneurship:while SE-entrepreneursreceive100%oftheirearningsintheformofnetincomefromanactivebusiness,ISE-entrepreneursreceive theirearningsasbothgrosswageincome(fromtheirbusiness)andcapitalincome(AlstadsæterandJacob,2016;Edmark andGordon,2013).

Althoughourmainfocusinthepaperisonmarketincome,inasupplementaryanalysis,wealsoestimateourmodels usingdisposableincome,toaccountforentrepreneurships’effectsoninequalityposttaxesandgovernmenttransfersandasa robustnesstesttoensurethatourresultsarenotoverlyaffectedbythepotentialproblemoftaxevasionamongentrepreneurs (EngströmandHolmlund,2009).DisposableincomeismeasuredbyStatisticsSwedenbyequalizeddisposablehousehold income,potentiallygivingdifferentmembersofthehouseholddifferentconsumptionweights.Eachfamilymember’s per-sonaldisposableincomeismultipliedwithanindividualconsumptionweight(ascalculatedbyStatisticsSweden)andthen dividedbythefamily’stotalconsumptionweight.Disposableincomeincludesbothfactorincomes,suchasnetwages, business-relatedincome(netdeficit),andnetcapitalprofits,andtaxableandnon-taxabletransfers,suchasrehabilitation compensation,pensions,andchildallowances(e.g.,housingbenefits,socialsecurity,andstudyallowances).

Intheempiricalmodel,weconsiderthefollowingexplanatoryvariables:ageandagesquared,jobtenureandjobtenure squared,jobchanges,andyearsofeducation(e.g.,Foltaetal.,2010;Yamauchi,2001;Åstebroetal.,2011).Allindividuals livinginSwedenreceiveapersonalidentificationnumberbasedontheirdateofbirth.Weusethisinformationtocalculate

11 Incorporationprocessesandtaxratesdifferacrosscountriesandhaveimplicationsforentrepreneurs’choiceoflegalform(seee.g.DeNardietal.,

2007;EdmarkandGordon,2013;Herranzetal.,2009).Theseprocesseshasbeencomparedbye.g.WorldBankscholarsintermsofdifferencesinare significantdifferencesintheincorporationprocessforSwedenandothernationsintermsofcost,timeandcoverageofincorporation,suggestingthat(i) costsforincorporatingafirminSwedenwassignificantlyhigherthancomparablecountriesin2005,butnotin2013aftertheminimumequityrequired whenforminganincorporatedbusinesswasloweredfrom100,000to50,000SEKasofOctober1,2010,(ii)timerequiredtoincorporateafirminSwedenis shorterthanmostcountries(Djankovetal.,2002),and(iii)coverageofincorporationiscomparabletoothernations,howeverEdmarkandGordon(2013)

notethatalthoughlower-incomeindividualsfacerelativelyneutralincentives,higher-incomehouseholdsfacetaxincentivestoincorporate.

12 Inthisclassification,reportedbusinessincomeisweightedbyafactorof1.6tocompensateforthefactthatbusinessincomecomparedtoworkersis

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anindividual’sage(inyears)aswellasthesquaredterm.JobtenureandjobchangesarecomputedfromLISAandare definedasthenumberofyearsofexperiencegainedataworkplaceandthenumberofworkplaceswitchessince1990.13 Yearsofeducationisthemostcommonoperationalizationofgeneralhumancapitalbothin theentrepreneurshipand inequalityliteratures(ArumandMüller,2004;CowellandFiorio,2011;VanPraagetal.,2013).Ourvariableiscreatedfrom educationalcodes(availableforallindividualsintheLISAregister)thatprovideinformationonthelengthofanindividual’s highestattainededucation(commensuratewiththeInternationalStandardClassificationofEducation[ISCED]97).Further, wecontrolforthenumberofchildrenlivingathome,maritalstatus(1=married/cohabitant)andgender(1=male;0=female) aswellasindustry(usingthree-digitNACEcodes)andregionaldifferences.OurregiondummyvariableisbasedonStatistics Sweden’s2006definition,whichassertsthatSwedencanbedividedinto79separatelocallabormarkets.14

Finally,wenotethatouranalysisofincomeinequalityissensitivetotheverytopincomesineachyear.Wetherefore excludeanumberoftopincomeearnerswhoseverelyskewtheincomedistribution,theinclusionofwhichalsoviolatesthe ordinaryleastsquares(OLS)assumptions.Still,wedonotwanttoexcludetoomanyindividualswithtopincomesbecause theymayreflectimportantdifferencesbetweenW,SE,andISE,andincludingmostindividualswithinthiscategoryisalso motivatedbytheliterature’srecentinterestintopincomeearnersandthedebateregardingthetoponepercent(seee.g. Atkinsonetal.,2011;Quadrini,1999;RoineandWaldenström,2008).Thus,thereisatradeoffbetweendroppingtopincome earners,whichincreasesR2andtherelevanceofourstudyintermsofencompassingtheentiredistributionofwageincome earners(includingalltopearners’resultsinzeroR2forourMincerregressionsfornon-logarithmicmarketincome).We settleonafairlygenerousrestrictionbykeeping99.9999%ofthefullsample,merelyexcluding366and377individualswith thehighestmarketincomein2005and2013,respectively.15

InthestandardMincer-typeregression,thedependentvariableisusuallyexpressedinlogarithmicform.However,inour contextofregressiondecomposition,usinglog-incometogenerateproportionaldecompositionweightshastheconsequence thatthedecompositionthencorrespondstoinequalityoflog-income,whichismuchlessinformativeandnotstandardin thedecompositionliterature.Therefore,weopttoestimateourMincerregressionswithincomeexpressedinabsoluterather thanlogarithmicform.

4.2. Descriptivestatistics

Table1showsthedescriptivestatisticsforthreesub-groupsofthepopulation—salariedworkers(W),self-employed(SE), andincorporatedself-employed(ISE)—forallvariablesintheyears2005and2013.Overtheperiod,weseethatthenumber ofSE,asashareofthetotalworkforce,decreasesfrom3.86%to3.32%,whereastheshareofISEincreasesfrom2.22%to2.47%. AsnotedinFootnote11,thispartlyreflectsthechangesinminimumequityrequiredforforminganincorporatedbusiness in2010.

Mostvariablesdisplayfairlymoderatechangesacrossthetwotimeperiods,whichistobeexpectedwhenworking withpopulation-sizeddatasets.However,thereareafewnoteworthydifferences:theaverageshareofmarried/cohabiting individualsdecreasesoverthetimeperiodforallgroups,andeventhoughSE-entrepreneursexhibitsomewhatlowerlevels ofeducationcomparedtoWandISE-entrepreneursinbothperiods(aresultoftenfoundinotherstudies[e.g.,seeRobinson andSexton,1994]),averageyearsofeducationforallgroupsincreases.16Finally,withlittlechangeovertime,bothSE-and ISE-entrepreneursarepredominatelymenwithahigheraverageageofaround48and47,respectively,comparedtoWwho areconsiderablyyounger(44)onaverage.WhencomparingSEandISEentrepreneurs,wenotethattheirdemographics arequitesimilar,albeitwithahigheraveragejobtenureforISEentrepreneurs.Furthermore,theproportionofimmigrants amongSEentrepreneursis7.0%(10.1%)in2005(2013)butamongISEentrepreneursisonly1.6%(1.8%)in2005(2013). AverageeducationisonlyslightlyhigheramongISEentrepreneurs.

Turningourattentiontothedescriptivestatisticsofaggregateinequality,Fig.1showsLorentzcurvesformarketincome inequalityin2005and2013,andTable2displaysasetofcommoninequalitymeasures.TheLorentzcurvesshowaslight inwardshiftbetweenthetwoyears,indicatingthattheoveralldispersionofmarketincomeactuallybecomeslessunequal overtheperiod.TheGinicoefficientdecreasesfrom31.8to30.9,whichcorrespondstoa2.8%decrease(Table2).Inour supplementaryanalysisofdisposableincome,theLorentzcurvedisplaysaslightoutwardshift(seeFig.A1inAppendixB). SincethetwoLorentzcurvesareclosetogether,theyaredifficulttodifferentiatevisually.IntherightpanelofFig.1(b), wethereforeplottheverticaldistancebetweenthetwocurves,computedasthedifferencebetweenthecurvesfor2013and

13Toaccountforpotentialbiasarisingfromleftcensoringthejobtenurevariable,inunreportedrobustnesstests,wereplicatetheresultsfromthefactor

sourceregressionanalysesinTables5and6withanadditionaldummyvariabletakingthevalue1forthoseindividualswiththemaximumyearsofjob tenure(Wennbergetal.,2010).Theseresults—availableuponrequest—areconsistentwiththeresultsreportedhere.

14Fordetailedinformationonindustryandlocallabormarketclassificationcriteria,seeEurostat(2008)andSCB(2010),respectively.Thesecontrols

marginallydecreasedthesamplesizeby40,282(1%)ofallindividualsin2005and26,470(0.7%)ofallindividualsin2013sincesomeindividuals’lackdata onindustryaffiliation.

15Coefficientestimatesofourmodelsarenotoverlysensitivetothiscut-offbutthemorerestrictiveoursampledefinition,thelargertheincreaseinR2.

Forexample,droppingthetop0.5%intermsofmarketincome(20,000individuals)nearlydoublesR2forallthreecategoriesofindividualsexamined

(Tablesavailableuponrequest).

16Thefactthataveragejobtenureincreasesfrom2005to2013ismainlyduetothefactthatthetenurevariableisleft-censoredin1990,whichmeans

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Table1

Descriptivestatistics:workers(W),self-employedentrepreneurs(SE)andincorporatedself-employedentrepreneurs(ISE).

Occupationalgroups 2005 2013

Mean St.dev Min Max Mean St.dev Min Max

Workers(W) Marketincome(in 100sSwedishkrona) 2,453.165 2,13.554 0.909 1,14150.68 2,827.492 2,252.876 0.812 108,732.242 Age 43.996 10.875 25 64 44.08 10.944 25 64 Agesquared (demeaned) 132.879 134.89 0.033 520.699 135.425 142.842 0.001 530.632 Jobtenure 6.241 5.294 0 15 7.535 7.092 0 23 Jobchanges 1.938 1.693 0 14 2.735 2.176 0 20

Childrenlivingathome 0.976 1.095 0 12 1.008 1.085 0 14

Gender(1=Men) 0.507 0.5 0 1 0.503 0.5 0 1 Maritalstatus (1=Married/cohabitant) 0.488 0.5 0 1 0.468 0.499 0 1 Yearsofeducation 12.332 2.312 9 20 12.728 2.312 9 20 Immigrants 0.037 0.188 0 1 0.064 0.245 0 1 Obs. 3,437.021(93.92% oftheworkforce) 3,554.138(94.21% oftheworkforce) Self-employed(SE)

Marketincome(in 100sSwedishkrona) 1,728.648 2,470.781 0.909 111,326.797 1,861.262 2,555.928 0.812 106,108.648 Age 47.918 10.42 25 64 48.155 10.531 25 64 Agesquared (demeaned) 108.589 108.348 0.033 520.699 110.911 115.275 0.001 530.632 Jobtenure 6.465 5.291 0 15 8.839 6.877 0 23 Jobchanges 1.75 1.6 0 12 2.489 2.076 0 18

Childrenlivingathome 0.987 1.141 0 12 0.986 1.114 0 11

Gender(1=Men) 0.686 0.464 0 1 0.66 0.474 0 1 Maritalstatus (1=Married/cohabitant) 0.559 0.497 0 1 0.52 0.5 0 1 Yearsofeducation 11.393 2.06 9 20 11.755 2.107 9 20 Immigrants 0.069 0.253 0 1 0.102 0.302 0 1 Obs. 141,261(3.86%of theworkforce) 125,293(3.32%of theworkforce) Incorporatedself-employed(ISE)

Marketincome(in 100sSwedishkrona) 3,480.648 4,159.77 0.909 113,410.617 3,909.648 3,860.34 0.812 107,112.789 Age 47.251 9.705 25 64 47.262 9.384 25 64 Agesquared (demeaned) 94.515 97.33 0.033 520.699 88.656 100.552 0.001 530.632 Jobtenure 8.261 5.068 0 15 8.927 7.059 0 23 Jobchanges 1.741 1.588 0 13 3.043 2.189 0 16

Childrenlivingathome 1.06 1.104 0 10 1.146 1.091 0 10

Gender(1=Men) 0.795 0.404 0 1 0.788 0.409 0 1 Maritalstatus (1=Married/cohabitant) 0.618 0.486 0 1 0.582 0.493 0 1 Yearsofeducation 11.951 2.245 9 20 12.376 2.25 9 20 Immigrants 0.016 0.126 0 1 0.33 0.178 0 1 Obs. 81,132(2.22%ofthe workforce) 93,311(2.47%ofthe workforce)

2005,respectively.Theincreasingverticaldistancereflectsasmallerareabetweenthe45◦lineandtheLorentzcurve,i.e.a

decreaseininequality.Fromthefigure,wealsoseethatthisdecreasemainlyinvolvesthebottom40percentofindividuals

intheincomedistribution(forwhichtheverticaldistancebetweenthetwocurvesisthelargest).Forincomelevelsabove

the40thpercentilethedistanceisstillpositivehoweversmallerinmagnitude.

TheslightinwardshiftanddecreaseinoverallincomeinequalityinFig.1representstheaggregatechangesacrossall

occupationalgroups.WeattendtothesechangesinTable2,whichshowstheGinicoefficient,percentileratios,andGE indicesforourseparatesub-groupsofW,SEandISEintheyears2005and2013.

Beginningwithworkers(W),weseeaslightdecreaseininequalityovertheperiodacrossalmostallinequalitymeasures. Thedecreasemaybesmallbutisneverthelesspresent.Theexceptionsareforinequalityasmeasuredbythepercentileratio p90/p50,whichdisplaysaslightincreaseof1%.

Table2revealssimilardevelopmentsforSE-entrepreneursasforW,withdecreasinginequalityregisteredforallmeasures exceptp50/p10andGE(-1).Thissuggestssomeformofcontractionoftopincomes,whereasbottomincomesbecomemore dispersedamongSE.ThelatterappearssignificantastheGE(-1)-indexincreasesbyatotalof34.9%.AsforISE,inequality amongthisgroupofentrepreneursincreasesforp50/p10aswellasforp75/p25by4.5%.NoneoftheGEindices,however,

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Fig.1. Lorentzcurveforworkforcemarketincomein2005and2013.

Table2

IncomeinequalitystatisticsofmarketincomeforW,SEandISEin2005and2013.

2005 Total 2013 Total W SE ISE W SE ISE (1) (2) (3) (4) (5) (6) (7) (8) p90/p10 4.073 15.321 4.483 4.331 3.805 14.948 4.483 4.047 p90/p50 1.748 2.494 2.148 1.765 1.765 2.348 2.058 1.783 p50/p10 2.33 6.143 2.086 2.451 2.156 6.367 2.178 2.268 p75/p25 1.771 3.716 1.891 1.813 1.719 3.583 1.976 1.754 GE(-1) 0.73 3.858 0.433 0.906 0.59 5.203 0.407 0.829 GE(0) 0.202 0.527 0.260 0.219 0.185 0.526 0.233 0.201 GE(1) 0.198 0.446 0.322 0.212 0.185 0.429 0.264 0.197 GE(2) 0.371 1.021 0.714 0.405 0.317 0.943 0.487 0.341 Gini 0.318 0.309

Notes:Allinequalitymeasuresarecomputedasrawfiguresforeachofthesubgroups,withoutweightsthataccountsfortheircontributiontotheaggregate incomeinequality.ThesubgroupsarecreatedsuchthatW+SE+ISE=totalworkforce(population),wheretheSEandISEgroupscorrespondtothenumber ofindividualspresentedinTable1,andW=totalworkforce–(SE+ISE).

reflectthisincreaseforISE,suggestingthattheGiniisanimperfectmeasureswhenitcomestodistributionsmarkedwith ‘fattails’suchasisprevalentindatasetsonentrepreneurs.

5. Results

5.1. Sub-groupdecompositionoftheGEindex

TofurtherexaminewhatliesbehindthechangesinlevelsofinequalitypresentedinTable2,wemodeloutcomesin twostages.First,forourtwocrosssections,2005and2013,weusethedecomposabilityoftheGEindextodisaggregate theinequalityofGE (y;˛) intobetween-groupandwithin-grouppartsforoursub-groupsW,SE,andISE,probingtheir contributiontoinequalityatdifferentpartsoftheincomedistributionatdifferentpointsintime.Second,usingtheregression frameworkoutlinedabove,weestimatethecontributionofourexplanatoryvariablestowithinandoverallinequalityfor eachseparateyear.Finally,wediscusshowtheimpactoftheseexplanatoryvariableschangesovertime.

Inthefirststepinthisanalysis,insteadofreportingthecontributionsintermsofinequalitypoints,wecalculatethe percentagecontributionsforeachtermof ˜GE(yj,˛)inEq.(15),whichgreatlyfacilitatesinterpretation.Dividingbothsides of ˜GE

yj;˛

withaggregateinequality,GE (y;˛),wedefine

yj;˛

as

(yj;˛)≡ ˜ GE(yj;˛) GE(y;˛) = pj([



K−1 k=1bjk(xjk)



K−1 k=1bk(xk) ] ˛ −1) (˛2˛)GE(y;˛)







b(yj;˛) +wjGE(yj ;˛) GE(y;˛)







w(yj;˛) K



k=1 sjk. (16)

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Table3

PercentagedecompositionofGE (y;˛) intothesub-groupsW,SEandISEformarketincome,2005and2013.

2005 Total 2013 Total W SE ISE W SE ISE (1) (2) (3) (4) (5) (6) (7) (8) GE(-1) 0.73 3.858 0.433 0.906 0.59 5.203 0.407 0.829 Between:b

yj;˛

−0.11 0.887 −0.363 0.414 −0.107 1.035 −0.415 0.512 Within:w

yj;˛

75.548 23.292 0.746 99.586 66.993 31.616 0.878 99.488 Total:

yj;˛

75.438 24.179 0.383 100 66.886 32.651 0.463 100 GE(0) 0.202 0.527 0.26 0.219 0.185 0.526 0.233 0.201 Between:b

yj;˛

−0.908 6.131 −3.562 1.661 −0.883 6.877 −4.01 1.983 Within:w

yj;˛

86.419 9.284 2.636 98.339 86.472 8.682 2.862 98.017 Total:

yj;˛

85.511 15.416 −0.927 100 85.589 15.559 −1.148 100 GE(1) 0.198 0.446 0.322 0.212 0.185 0.429 0.264 0.197 Between:b

yj;˛

0.939 −4.468 5.227 1.698 0.903 −4.63 5.672 1.945 Within:w

yj;˛

87.791 5.726 4.786 98.302 88.7 4.768 4.586 98.055 Total:

yj;˛

88.729 1.258 10.012 100 89.604 0.138 10.258 100 GE(2) 0.371 1.021 0.714 0.405 0.317 0.943 0.487 0.341 Between:b

yj;˛

0.492 −2.387 2.794 0.898 0.522 −2.754 3.336 1.105 Within:w

yj;˛

86.355 4.85 7.896 99.102 88.106 3.998 6.792 98.895 Total:

yj;˛

86.847 2.463 10.69 100 88.628 1.244 10.128 100

Note:Thetableshowsthepercentagecontribution (1=100%) ofthebetween-andwithin-inequalitycomponentfromthesub-groupsworkers(W), self-employed(SE),andincorporatedentrepreneurs(ISE).SeparatecontributionsarecalculatedforthevariousGE-indiceswith˛=



−1,0,1,2



.The inequalitylevelsforeachofthesubgroupsarecalculatedusingEq.(16)withtheappropriateweights.Theseinequalitylevelsdifferfromthosepresented inTable2thatcompriserawcalculationsbasedonEq.(1)appliedtoarestrictedsample.

Thetermb

yj;˛

representsthepercentagecontributiontoaggregateinequalityfromgroupj’sbetweenpartand w

yj;˛

,thecontributionfromitswithinpart.Thetotalcontributionfromaspecificgroupisgivenby

yj;˛

.These calculationsarepresentedformarketincomeinTable3,correspondingtotherowslabeledBetween,Within,andTotal.The tableshowsseparatecalculationsforeachoftheinequalityindices—GE (−1),GE (0),GE (1),andGE (2)—withindexvaluesfor thedifferentsub-groupspresentedinthefirstrow.TheresultsinColumns1–4arebasedonincomedatafortheyear2005, andtheresultsinColumns5–8arebasedonequivalentdatafor2013.

Wealsocalculatethecontributionstooverallinequalitywhenthebetween-andwithin-grouppartsaresummedacross groups.BytakingthesumoverallJgroups,theequationtakesthefollowingidentity:

 (y;˛) = J



j=1 

yj;˛

= J



j=1



b

yj;˛

+w

yj;˛



=1. (17)

Basedontherulesofdecomposition,summingallcontributionsamountsto1(i.e.,100%).InTable3above,thisrepresents thesumoftheentriesintherowforTotal,presentedinthecolumnforTotal.Thesumsacrossthegroups’betweenand withincontributionsarecalculatedusingtheterms

J



j=1 b

yj;˛

and J



j=1

w

yj;˛

,whicharepresentedinthecolumn TotalastheysumthecorrespondingrowsforBetweenandWithinentries.

Asastart,lookingatGE (−1),thetotalcontributionstoinequalityfromW,SE,andISEare79.06%,20.53%,and0.42%, respectively.Hence,whenemphasizingthebottompartsoftheincomedistribution,thelargestshareofinequalitycomes fromsalariedworkers(W).However,consideringtheirrelativelysmallshareofthetotalworkforce—amere3.64%in2005 (Table1)—the contributionfromSE-entrepreneurstototal inequalityis sizable.Further,usingGE(-1),itisthe within-inequalitycomponentofeachgroupthataccountsforalmostallofthetotalinequality.

Turningthesensitivityparametertohigherlevelsoftheincomedistribution(froman˛of−1to0,and1–2),weseethat thetotalcontributionstoinequalityfromentrepreneursasagroup(i.e.,SEandISEtogether)formaU-shapedrelationship. Beginningat20.94%forGE (−1),entrepreneurs’contributiontoinequalityshrinksto13.24%forGE (0) and11.23%forGE (1) butincreasesagainforGE (2) to13.0%.Asweincreasethevalueof˛,therearetwootherpatternsthatstandout.Thefirst isthatthebetween-inequalitycomponentplaysamoreprominentroleforGE (0) andGE (1) inthemiddlerangesofthe distribution.ThesecondisareversalbetweenSEandISEintermsoftheirrespectivetotalcontributiontoinequality.ISE accountsforanincreasinglylargershareofinequality,whereasSEaccountsforadecreasingshare,exceptfortheGE (2) measure.For thismeasure,thetotalpercentagecontributionstoinequalityfromW,SE,andISEare86.98%,2.13%,and 10.87%,respectively.

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Fig.2. Proportionalcontributionfromworkers(W),SE-andISEentrepreneurstooverallinequality(100%)ofmarketincome.

Thissamepatternisevenmorepronouncedintheequivalentdecompositionanalysisfor2013.Thatis,thecombined effectofentrepreneurshipisU-shaped,goingfromsmalltolargervaluesof˛.Asignificantpartofthecontributionstemsfrom SEwhenwefocusonthebottomendoftheincomedistribution.Comparingthetwotimeperiods,therelativecontribution ofentrepreneurship(SE+ISE)tototalinequality,asmeasuredatthebottomoftheincomedistribution( (y;−1)),increases substantiallyby8.55percentagepointsfrom2005to2013.Further,thisincreaseisalmostcompletelyduetochangesinthe within-inequalitycomponentforSE-entrepreneurs.

WecanillustratetheabovefindingsregardingincomedynamicsforW,SE,andISEbyplotting thetotalpercentage contributiontoaggregateincomeinequalityfordifferentvaluesof˛.TheplotsareshowninFig.2,withtheresultfor2005 in(i)andfor2013in(ii).ThecontributionfromWtooverallincomeinequalityishererepresentedbyasolidline,and thecontributionsofSEandISEarerepresentedbyadottedlineandadashedline,respectively.Forbothyears,thefigure illustrateshowadownwardshiftintheinequalitycontributionfromW,asmeasuredbyGE (−1),correspondstoanupward shiftforSE,whereastheISEcontributionatlowincomelevelsremainslargelyunchanged.

5.2. Estimatesfromregression-baseddecompositionofincomeinequalityforsub-groupsW,SE,andISE

Thefinalstepinouranalysisistoestimateanincomemodelforthesamesampleofsub-groupsasinourdecomposition analysisabove.Here,ourempiricalmodelisbasedonEq.(12),withthedependentvariableyitgivenby(non-logarithmic) marketincomein levels.Werunseparateregressionsforeachofthethreesub-groupsofworkers(W),self-employed entrepreneurs(SE),andincorporatedself-employedentrepreneurs(ISE).Asabove,themodelisestimatedfortwocross sections:2005and2013.TheresultsarepresentedinTable4for2005andTable5for2013,withrobustOLSestimates showninColumns1–3andthecorrespondingproportionalcontributiontoincomeinequality,givenbysjkfromEq.(13), showninColumns4–6.

Weshouldnotethattheproportionalcontributionstoinequalityforourexplanatoryvariablesrefertothecombined “price”and“quantity”effectofeachvariable.Usingyearsofeducationasanexample,thismeansthatwedonotattempt toseparatethepriceeffectcorrespondingtotheestimatedcoefficient,whichcapturestheeffectofoneadditionalyearof educationineachgroup,fromthequantityeffect,whichresultsfromtheaveragelevelofeducationamongindividualsin eachrespectivegroup.17

First,indecomposinginequalitytoincomefactors ˆbkj

xkj

,itisimportanttorememberthattheregressionapproach islimitedbytheexplanatorypowerofthemodel,givenbytheR2.Thus,foragivensub-group,addingupthecontributions (sjk)amountstotheR2.Theunexplainedpartofthemodel(1−R2)equalstheproportionalcontributionoftheresidual,

17Sincewecannotensurethatourexplanatoryvariablesarestrictlyexogenous,interpretationofouroutcomesshouldgenerallybedonewithsome

measureofcaution.Aproblemwithourdataisofcoursethatwedonothaveinformationonunderlyingability.Inotherwords,whenestimatingour modelsusingourcurrentdata,wecannotcontrolforself-selectionanddonotknowtowhichextenttheoutcomesofourtwoentrepreneurialcategories reflectorganizationalform(SEorISE)orvariationinthecapabilitiesoftheentrepreneursthemselvesotherthantotheextentthatourobservables,primarily educationlevels,indeeddoreflectunderlyingability.Tobettergaugethisissue,asarobustnesstest,wehavererunourmodelonadifferent2005sample ofindividualsforwhichwehaveadditionaldataonresultsfrommilitaryserviceconscriptiontestsregardingintelligenceandpsychologicability(i.e.,very goodproxiesforunderlyingability)aswellashighschoolgrades.Theresultsusingthismuchsmallerdatasetindicatethatourstudydoessufferfrom endogeneityproblemsinregardtotheeffectofeducationforSE-entrepreneurs(yearsofeducationisnotstatisticallysignificantforSE-entrepreneurswhen controllingforinnateabilityintermsofourtwoaptitudetestsandGPA),thisislessofaconcernforISE-entrepreneursorworkers.Inotherwords,using ourmodel,wearelikelymuchsafestoinfercausalityinregardtoISE-ascomparedtoSE-entrepreneurs.Theserobustnesstestsareavailablefromthe authorsuponrequest.

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Table4

Regressionresultsformarketincomein2005andpercentagecontributiontowithin-groupinequality.

Regressionestimates 100×skj W SE ISE W SE ISE (1) (2) (3) (4) (5) (6) Age 15.951*** 5.151*** 20.624*** 0.953+ 0.092+ 0.283+ (0.163) (0.917) (2.064) (0.000) (0.003) (0.004) Agesquare −1.277*** -0.812*** −1.501*** 0.994+ 0.18+ 0.189+ (0.010) (0.063) (0.157) (0.000) (0.001) (0.001) Jobtenure 24.227*** 27.570*** 18.197*** 0.312+ 0.332+ 0.048+ (0.297) (1.866) (4.471) (0.000) (0.001) (0.002) Jobchanges 70.268*** 46.425*** 7.118 0.169+ 0.021+ −0.002+ (0.886) (5.143) (12.530) (0.000) (0.001) (0.001) No.children −36.747*** 15.911*** 23.893 0.016+ 0.001 0.007+ (1.172) (5.757) (16.823) (0.000) (0.001) (0.001) Gender 972.655*** 555.585*** 889.601*** 4.809+ 1.01+ 0.61+ (2.245) (14.071) (31.585) (0.000) (0.001) (0.002) MaritalStatus 149.939*** 76.653*** 119.245*** 0.277+ 0.019+ 0.053+ (2.252) (14.823) (33.620) (0.000) (0.001) (0.001) Yearsofeducation 225.328*** 109.860*** 299.721*** 5.074+ 0.593+ 2.417+ (0.606) (3.983) (7.722) (0.000) (0.004) (0.004) Immigrant −393.522*** -606.254*** −900.441*** 0.178+ 0.409+ 0.083+ (3.851) (16.601) (65.419) (0.000) (0.000) (0.000) Constant −1660.521*** -338.908*** −1888.220*** (13.269) (71.781) (148.455) Obs. 3437021 141261 81132 R-sq. 0.128 0.027 0.037 Res.(=1-R-sq) 87.218 97.344 96.311

Note:Standarderrorsinparenthesiswithsignificancelevels***p<0.01,**p<0.05,*p<0.1,andwhere+issignificantaccordingtoa95%confidenceinterval. Columns(1)to(3)givestherobustOLSresultsfromeachofthegroupsW,SEandISE,estimatedseparately.Columns(4)to(6)showtheproportional contributionsofthecorrespondingexplanatoryvariabletothetotalwithin-groupinequalityforW,SEandISErespectively.Becauseofthelargesample sizes,almostallpercentagecontributionsarestronglysignificant.Forthisreasonwedisplaytheirstandarderrorswithoutasterisksdenotinglevelof significance.

Table5

Regressionresultsformarketincomein2013andpercentagecontributiontowithin-groupinequality.

Regressionestimates 100×skj W SE ISE W SE ISE (1) (2) (3) (4) (5) (6) Age 21.309*** 1.904* 12.559*** 1.544+ 0.035+ 0.208+ (0.174) (1.012) (1.686) (0.00) (0.006) (0.004) Agesquare −1.244*** -0.757*** −2.184*** 1.258+ 0.186+ 0.433+ (0.011) (0.068) (0.129) (0.00) (0.001) (0.001) Jobtenure 21.283*** 25.491*** 44.617*** 0.51+ 0.442+ 0.566+ (0.232) (1.616) (2.577) (0.00) (0.002) (0.001) Jobchanges 63.239*** 44.848*** 13.706* 0.403+ 0.091+ −0.009+ (0.699) (4.451) (7.188) (0.00) (0.002) (0.001) No.children −12.198*** 33.609*** 62.088*** −0.009+ 0.014+ 0.056+ (1.241) (6.985) (13.552) (0.00) (0.001) (0.001) Gender 960.778*** 462.213*** 835.323*** 3.809+ 0.707+ 0.591+ (2.396) (15.190) (28.301) (0.00) (0.002) (0.001) MaritalStatus 168.084*** 78.253*** 201.475*** 0.349+ 0.022+ 0.146+ (2.400) (16.044) (26.231) (0.00) (0.001) (0.001) Yearsofeducation 240.263*** 69.692*** 307.739*** 4.886+ 0.178+ 2.693+ (0.603) (4.041) (6.298) (0.00) (0.005) (0.003) Immigrant −396.395*** −463.896*** −592.389*** 0.298+ 0.354+ 0.095+ (3.380) (16.911) (59.261) (0.00) (0.00) (0.00) Constant −1858.759*** 365.506*** −1566.253*** (13.961) (72.788) (126.334) Obs. 3,554,138 125,293 93,311 R-sq. 0.13 0.02 0.048 Res.(=100-R2*100) 86.953 97.971 95.222

givenbysjKinEq.(14).Theseestimatesareprovidedinthebottomrowofeachtableandshowhowmuchofthevariance

inincomeinequalitycannotbeattributedtothefactors(explanatoryvariables)includedinouranalysis.

Also,forfurtherclarification,sjkrepresentstherawcontributiontoinequalitycomputedforaparticularsub-group.Since thegroupsW,SE,andISEdifferinsize,theproportionalcontributionattributedtoasinglefactor,sjk,foraparticulargroup

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Table6

Inequalityweights(wj)forGE-indexindices.

2005 2013 W SE ISE W SE (1) (2) (3) (4) (5) (6) GE(−1) 0.937 0.055 0.016 0.94 0.05 0.018 GE(0) 0.939 0.039 0.022 0.942 0.033 0.025 GE(1) 0.941 0.027 0.032 0.944 0.022 0.034 GE(2) 0.943 0.019 0.045 0.946 0.014 0.047

Note:Standarderrorsinparenthesiswithsignificancelevels***p<0.01,**p<0.05,*p<0.1,andwhere+issignificantaccordingtoa95%confidenceinterval. Columns(1)to(3)givestherobustOLSresultsfromeachofthegroupsW,SEandISE,runseparately.Columns(4)to(6)showtheproportionalcontributions ofthecorrespondingexplanatoryvariabletothetotalwithin-groupinequalityforW,SEandISErespectively.Becauseofthelargesamplesizes,almostall percentagecontributionsarestronglysignificant.Forthisreasonwedisplaytheirstandarderrorswithoutasterisksdenotinglevelofsignificance.

mustbescaledtoassessitscontributiontoaggregateinequality,herecapturedby (y;˛) inEq.(17).18Thescalefactoris

givenby wjGE

yj;˛

GE (y;˛) , (18)

wherewjistheweightdefinedinconnectiontotheexpressioninEq.(3)andpresentedinTable6.AsforthetermsGE

yj;˛

andGE (y;˛),theyaregiveninTable3abovefordifferentvaluesof˛.

Althoughtheproportionalcontributionstoincomeinequalityforagivenincomefactor(skj)isinvarianttotheinequality measureused,providedthebasicassumptionsformulatedbyShorrocks(1982)aresatisfied(seeAppendixA),weseefrom theexpressionofthescalingfactorthatitisnecessarytospecifyagivenindextodeterminehowmuchafactorsource inonesub-groupcontributestotheaggregateinequalityof (y;˛).Thus,whencalculatingthecontributiontoaggregate inequalityforW+SE+ISEfromsomegroup-specific ˆbkj

xkj

,wechosetherelativelycommonG (y,1) index(Theilindex) usingsub-group-andyear-specificvaluesfromTable3andinequalityweightsfromTable6.

Beginningwiththeresultsforinequalityin2005,Table4showsthatalmostallvariablesarestatisticallysignificantin theregressions,whichisnotsurprisinggiventhelargenumberofobservations.Commonforallsub-groups,therearethree explanatoryvariablesthatstandoutasmajorcontributorstoinequality.Theseareyearsofeducation,gender(1=Male), andage.Thevariableforyearsofeducationshowsamarginaleffectintheindividual-levelestimatesof24,571SEKhigher yearlyincomeforeachadditionalyearofeducation.19AmongSE-andISE-entrepreneurs,eachadditionalyearofeducation translatesintoahigherincomeof7616SEKand22,790SEK,respectively.20Althoughwefindalmostaslargeamarginaleffect ofeducationonearningsamongISEasamongW,inspectingtheproportionalcontributionsofeducationtoincomeinequality withineachofthesub-groups(Columns4–6),weobservehoweducationinpercentagetermscontributessubstantially moretoinequalityamongW(with5.06%),whereasthecorrespondingnumberforSE-andISE-entrepreneursisonly0.38% and1.67%,respectively.AsmuchastheseresultsinformusaboutthecontributiontoinequalityofGE

yj,˛

—thatis,tothe within-groupinequalityofeachsub-group—theirestimatedcontributiontoaggregateinequalityintermsofpercentage—that is,outof (y;˛) =100%—stillneedstobecomputed.

For2005,thescalingfactorgiveninEq.(18)fortheTheilindexamountsto0.884forW(0.942×0.197/0.210,0.053for SE(0.026×0.426/0.210),and0.049forISE

0.032×0.322/0.210

forGE (y;1).Oncemultipliedwiththeweight,education amongWaccountsfor4.47%(0.884×5.056)ofoverallwithininequalitygivenby (y;1),0.02%(0.053×0.38)forSE,and 0.08%(0.049×1.671)forISE.Although,educationamongSEandISEaccountsforasizableportionofthesegroups’within inequality,thecontributiontoaggregateinequalitystemmingfromdifferencesineducationlevelnaturallydropsbecause thetwoentrepreneurialgroupsaresmallcomparedtoW.Togaugethetotalcontributionfromoneexplanatoryvariable toaggregateinequality,wecanaddtheweightedcontributionsfromallgroups.Foryearsofeducation,thisamountsto 4.57% (4.47+0.02+0.08) outof100%.21

18Thecontributiontoaggregateinequalityonlyreferstothecontributiontow(y;˛).Hence,ifanincomefactorshouldbeimportantforthedetermination

ofthebetween-inequalitypartb(y;˛),wedonotaccountforithere.However,inTable3,weshowintermsofpercentagepointsthatw(y;˛) accounts

for98.3%and98.1%ofaggregateinequalityfor˛=1in2005and2013,respectively.Anycontributionofasinglefactorinagivengrouptoaggregate inequality (y;˛) thatgoesviab(y;˛) isthereforenegligible.

191Swedishkrona(SEK)was$0.11and0.11DinNovember2005and$0.15and0.11DinNovember2013.

20Inourrobustnesstestsusing462,242individualsin2005forwhichwehavedataonhighschoolGPAandinnateabilityasmeasuredbyconscription

records,wefindreturnstoeducationwhichis40%lowerforWandISEandalmost80%lowerforSE.Comparatively,returnstoonepointhigherGPA(on a1–100scaleyieldsareturninearningofabout1005SEKforW,748SEKforSE,and1784SEKforISEwhilereturnstoonepointhigher‘psychological ability’(ona1–9scale)is8346forW,4135SEKforSE,and8162forISE.Itthusappearsthatasignificantproportionofreturnstoeducation–almosthalf forWandISEandmorethanthree-quartersforSE,comesfromhigh-abilityindividualshavinglongereducation.

21Asacomparison,thecontributionfromeducationisroughlyinlinewiththeresultsinCowellandFiorio(2011),whoestimatethecontributionfrom

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