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 oEntrepreneurship
and
income
inequality
Daniel
Halvarsson
a,
Martin
Korpi
b,∗,
Karl
Wennberg
caRatioInstitute,P.O.Box3203,10364,Stockholm,Sweden bRatioInstitute,Stockholm,Sweden
cInstituteforAnalyticalSociology(IAS),LinköpingUniversity,60174Norrköping,Sweden
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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
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t
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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/).
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
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).
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,
0,1,2constitutethemostcommonvaluesinsimilarstudiesusingtheGE-index.Since˛=−1turnsthe3.1. 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 wjGEyj;˛ . (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 NYj (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 NYj (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.
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
yjsatisfiessixbasicassumptionsidentifiedbyShorrocks(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
yjby,
sjk≡ Sjk
yjk,yj
Iyj .
(9)
Sincesj1+sj2+...+sjK =1byconstruction,multiplyingthroughwithI
yjshowsthatsjkbecomestheloadingoffactor 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
yjfrommulticoliniarity,i.e.ifxjkiscorrelatedwithxjr forther /=kotherexplanatoryvariables;andthethirdterm representsthecontributiontoI
yj
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;˛= ˛2p−j ˛
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).
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
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
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,
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)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=1yj;˛ = J j=1 b
yj;˛ +w
yj;˛ =1. (17)
Basedontherulesofdecomposition,summingallcontributionsamountsto1(i.e.,100%).InTable3above,thisrepresents thesumoftheentriesintherowforTotal,presentedinthecolumnforTotal.Thesumsacrossthegroups’betweenand withincontributionsarecalculatedusingtheterms
J
j=1 byj;˛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.
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.
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
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
0.032×0.322/0.210forGE (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