Seconddraft
Version:31January2016
Contribution to Heather Boushey,
Bradford DeLong and Marshall
Steinbaum(eds.),AfterPiketty’s‘Capital
in the 21st century’: The agenda for
fighting inequality, Harvard University
Press,2017.
Increasingcapitalincomeshareanditseffecton
personalincomeinequality
BrankoMilanovici
Piketty's r>g implies an increase in capital-output ratio
and in the share of capital income in net output. But it
stilldoesnotguaranteetheincreaseinpersonalincome
inequality. We derive the conditions for the "passthrough" of the rise in the share of capital income to
greater personal income inequality. They have to do
with the concentration of income from capital and its
association with higher overall income. A key way to
breaking the "transmission" into higher personal
inequalityistodiversifyownershipofcapital("people's
capitalism").
1
1.MethodologicalcontributionsofPiketty’s“Capital…”
Whendiscussing“Capitalinthe21stcentury”weneedtodistinguish
betweenitsanalyticsandmethodology,itsrecommendations,anditsforecasts.
Onecanagreewithanalyticswithoutagreeingwiththerecommendations,orthe
reverse.Themethodologyintroducedby“Capital…”,becauseitseemstofitquite
wellthelikelyevolutionoftherichworldinthedecadestocome,andmore
importantlybecauseitprovidesanovelwaytolookateconomicphenomena,is
probablythemostsignificantcontributionofthebook.Itwillaffectnotonlyhow
wethinkofincomedistributionandcapitalisminthefuturebutalsohowwethink
abouteconomichistory,fromtheAncientRometopre-revolutionaryFrance.(In
effect,wecanalreadyseesomeofthesedevelopments).
ThemostimportantmethodologicalcontributionofPiketty’sbookishis
attemptattheunificationofthefieldsofeconomicgrowth,functionalincome
distributionandpersonalincomedistribution.iiInthestandardWalrasiansystem,
thethreeareformallyrelated,butintheactualworkineconomicstheywere
generallytreatedseparately,orsomewereevensimplyleftout.Functional
incomedistributionwasstudiedmuchmorebyMarxisteconomists.Neoclassical
economiststendedtoassumethatcapitalandlaborshareswerebroadlyfixed.
Thisviewchangedonlyfairlyrecentlyandwearenowwitnessinganupsurgeof
interestinthetopic(KarabarbounisandNeiman2013;Elsby,HobijnandŞahin
2013).Piketty’semphasisontherisingshareofcapitalincomecontributedtothis
efflorescence.
Personalincomedistributiontendedtobestudiedalmostasdivorcedfrom
therestofeconomicsbecauseinaWalrasianworldagentscometothemarket
withthealreadygivenendowmentsofcapitalandlabor.Sincetheoriginal
distributionoftheseendowmentsisnotthesubjectofeconomics(narrowly
defined),personalincomedistributionwasassumedtobewhateverthemarket
generates.Butin“Capital..”themovementsinthecapital-incomeratio,drivenby
“thefundamentalinequality”or“centralcontradictionofcapitalism”,namelyr>g
(returnoncapitalgreaterthanthegrowthrateofoverallincome)iii ,leadtothe
risingshareofcapitalincomeinnetproductandthisinturnleadstoagreater
inter-personalinequality.
2
Thispaperconcentratesonthelastpoint—implicitlytakenforgranted:
greatershareofcapitalisassociated,itisthoughtalmostimplicitly,witharising
inter-personalinequality.Thisviewisunderstandablebecauseduringmostof
economichistorypeoplewithhighcapitalincomewerealsopeoplewithhigh
overallincome.Therefore,agreatershareofnetproductgoingtocapitalists
cametobeassociatedwithgreaterinter-personalinequality.
Inarecentpaper,investigatingtheassociationbetweenhighercapital
sharesandincomeinequalityoverthelongrun(goingback,insomecasestothe
mid-19thcentury),BengtssonandWalderström(2015),find,inacountryfixed-
effectsetting,thatthecorrelationhastypicallybeenpositiveandfairlystrong.For
theentiresampleof15advancedeconomies,theyfindthat,ontheaverage,each
percentagepointincreaseinthecapitalsharewasassociatedwith0.86point
increasein(thelog)oftop1%incomeshare.Whenothercontrolsareintroduced,
thesizeofthecoefficientisreduced,butitremainspositiveandstatistically
significant.JacobsonandOcchino(2012)similarlyfindthatfortheUnitedStates,
aonepercentincreaseinthecapitalsharetendedtoincreaseGinibybetween
0.15and0.33percent.
FranceseandMulas-Granados(2015)usemorerecent1970s-2010
LuxembourgIncomeStudymicrodatafrom43countries,anddecomposethe
overallchangeindisposableincomeGiniintoitsaccountingcomponents:
concentrationcoefficientsoflaborandcapital,laborandcapitalshares,and
changesintaxationandsocialtransfers.UnlikeBengtssonandWalderström
(2015),theyfindanegligibleimpactofhighercapitalshare,andconcludethat
mostoftheincreaseindisposableincomeGiniwasdrivenbytherising
concentrationofwages.Theycomplementthedecompositionanalysisbya
regressiononasampleof93countries,fortheperiod1970s-2013,ofcapital
(labor)shareonGini.Oncecontrolsareintroduced,labor(capital)shareis
insignificant(p.15).
Sothelinkbetweengreatercapitalshareandincreasedinter-personal
inequalityisnotassimpleandunambiguousasitseems.Evenwhenthepositive
relationshipbetweenthetwoexists,thestrengthofthatrelationshipvaries.
Thepaperisorganizedasfollows.Section2discussesingeneralthelink
betweentherisingshareofcapitalinnetincome(Piketty’sα)andGinicoefficient
3
ofinter-personalincomeinequality.Section3looksatthisrelationshipinthree
ideal-typicalsocieties:socialist,classicalcapitalist,and“new”capitalist.(The
termsaredefinedthere).Section4presentstheempiricalanalysisofthe
relationshipusing138harmonizedhouseholdsurveysfrom17advanced
economies.Section5discussespolicyimplications.
Itmaybeuseful,evenbeforeweembarkonthestudyoftherelationship
betweenαandGini,toindicatewhythisisimportant.Theincreaseinαisnot,by
itself,a“problem”ifitdoesnotleadtoanincreaseininequalitybetween
individuals.Ineffect,whentheunderlyingdistributionofcapitalisegalitarian,an
increaseinαmaycauseadecreaseininter-personalinequalityorleaveit
unchanged.Hence,evenfortheproponentsofstrongegalitarianism,theincrease
incapitalsharecannotbeaproblemassuch.Itbecomesa“problem”only
becauseinmostofreal-worldsituationstheunderlyingdistributionofcapital
assetsisextremelyskewed.Therealizationofthisfactleadsme,inthe
prescriptivepart,toargueinfavorofequalizationofownershipofassetsamongst
individuals.Thisprovidesarealisticagendaforfightinginequalityandisespecially
relevantfortherichsocietieswhererisingwealth/incomeratioimpliesthat,
unlessthereturnoncapitaldecreasessufficiently,agreatershareofnationalnet
productwillbereceivedbyasset-holders.Thuswehaveachoicebetween
acquiescingintherisinginter-personalinequality,tryingtoreduceitthrough
taxation,orworkingonthedeconcentrationofassetownership.
Focusingonthedistributionofassetsis,inmyopinion,amorepromising
policythanPiketty’semphasisontaxationofcapital.Butregardlessofwhether
onetoolisbetterthantheother,theyaretwocomplementarywaystoaddress
risinginequalityintheevermoreaffluentsocieties(thatis,insocietieswitha
risingK/Yratio).
4
2.Goingfromfunctionaltopersonalincomedistribution
Themainlinkbetweenthefunctionalandpersonalincomedistributionis
providedbytherelationshipr>g.Butinordertoleadtoarisinginter-personal
inequalityitneedshowevertosatisfythethreefollowingrequirements.ivv
First,rmustbeoverwhelminglyusedforinvestment,andnotfor
consumption.Clearly,ifallofrwassimplyconsumedbycapitalists,theK/Yratio
inthenextcyclewillremainunchanged,anddynamicallytherewouldbeno
increaseineitherβ=K/Yorintheshareoftotalincomederivedbycapital(α).This
thepointonwhichDebrajRayinhiscritiqueof“Capital…”hasstronglyinsisted.vi
Ng(2015)makesthesamepoint.Itisindeedaformallycorrectargument,but
missestheentirepointofwhatcapitalismandcapitalistsare.Ifcapitalistswere
interestedsolelyinconsumption,inspendingmostoftheirincomeonwhatAdam
Smithnicelytermed“baublesandtrinkets”,theprocesswouldplayoutasRay
imagines.Butcapitalistsarepreciselycapitalistsbecausetheydonotconsumeall
surplus,areinterestedinexpandingthescopeoftheiroperations,andthusin
investingallormostofr.Theassumptionofsavingrateoutofrbeingcloseto1is
notonlywell-foundedintheprecedentsfromtheoreticaleconomics(inmodern
times,fromKalecki1942,Solow1956andKaldor1957,andobviouslyalltheway
backtoRicardoandMarx)butisequallywell-foundedintheempiricalbehaviorof
therich,andinwhatarethecentralfeaturesofcapitalismasasystem.viiviii
Buttherisingβandevenarisingαdonotensurebythemselves
transmissionintogreaterinter-personalinequality.Forthistohappen,
concentrationofcapitalincomehastobeveryhigh.Workingwithonlytwofactor
incomes,thatoflaborandcapital,fortheoverallinequalityofpersonalincometo
goup,therequirementisthatthemoreunequallydistributedsourcehastogrow
relativelytothelessunequallydistributedsource.Withcapitalincome,this
conditionisrelativelyeasilysatisfiedsinceinallknowncases,theconcentrationof
capitalincomeisgreaterthantheconcentrationoflaborincome.IntheUS,for
example,Giniofincomefromcapital(calculatedacrosshouseholdpercapita
incomes)isinexcessof80,whilesimilarlycalculatedGinioflaborincomeis
around40.Thesituationisidenticalinothercountries.Thisissimplyareflection
ofthewell-knownheavyconcentrationofcapitalassetsandofthefactthatabout
5
athirdofAmericanshavezeronetcapitalassets,andhencedrawnoincomefrom
ownership.
Thethirdrequirementisthattheassociationbetweencapital-richand
overallincome-richpeoplebehigh.Asimplehighconcentrationofagivenincome
sourcewillnotguaranteethatthatsourcecontributestoinequality.
UnemploymentbenefitshaveaGiniwhichisgenerallyinexcessof90(sincemost
peoplereceivenounemploymentbenefitsduringanygivenyear),butsince
recipientsofunemploymentbenefitsaregenerallyincome-poor,anincreasein
theshareofunemploymentbenefitsintotalincomereducesincomeinequality.
Technically,thethirdrequirementis(inthecaseofGinicoefficientwithwhichwe
workhere)expressedintheformofahighcorrelationbetweenrankings
accordingtocapitalincomeandrankingsaccordingtototalincome.Putsimply,
thisrequirementmeansthatpeoplewhoreceivelargecapitalincomesshould
alsoberich.Empirically,thisrequirementiseasilysatisfiedinmostcountries.
Itisthuspreciselybecausewetendtotakeasgiven
(1)highsavingoutofcapitalincome,
(2)highconcentrationofassets,and
(3)highcorrelationbetweenone’sdrawingalargecapitalincomeand
beingrich
thatwetendtoseethetransmissionfromarisingcapitalincomeshareinto
anincreasinginter-personalinequalityasaforegoneconclusion.Butthisisnot
alwaysso,oratleastthestrengthofthattransmissionisvariable.Wemovetoa
moreformalderivationoftherelationship.
WeknowthattotalincomeGinicanbedecomposedintoinequalities
contributedbyeachincomesource,inourcasecapital(c)andlabor(l)asin(1):
𝐺 = 𝑠! 𝑅! 𝐺! + 𝑠! 𝑅! 𝐺!
(1) wheresi=shareofagivenincome(i-th)source,Ri=correlationratiobetweenthe
sourceandtotalincome,Gi=Ginicoefficientofanincomesource,andG=overall
incomeGini.Riinturnisequaltotheratiooftwocorrelationcoefficients(ρ’s),
namely,betweenincomesourceandrecipients’ranks(fromthepooresttothe
richest)accordingtototalincome,andbetweenincomesourceandrecipients’
6
ranksaccordingtoincomesourceitself.Forcapitalincome,thecorrelationratio
canbewritten:
𝑅! =
𝑐𝑜𝑣𝑎𝑟(𝑟 𝑦 , 𝑐) 𝜌 𝑟 𝑦 , 𝑐 𝜎!(!) 𝜎! 𝜌 𝑟 𝑦 , 𝑐
=
=
𝑐𝑜𝑣𝑎𝑟(𝑟 𝑐 , 𝑐) 𝜌(𝑟 𝑐 , 𝑐)𝜎!(!) 𝜎!
𝜌(𝑟 𝑐 , 𝑐)
(2)
Noticethatifpeople’sranksaccordingtototalincomeandincomefrom
capitalcoincide,Rc=1.Inallothercases,𝜌 𝑟 𝑦 , 𝑐 < 𝜌(𝑟 𝑐 , 𝑐)andRc<1.For
unemploymentbenefitsmentionedaboveRi<0.
Fortherisingshareofcapitalincome(sc)ixtoincreaseoverallincomeGini,
weneedthereforetohavetwo“transmission”tools,Ginicoefficientofcapital
income(Gc)andRc,positiveandhigh.x
Therestofthepaperwilldealwiththesetwo“transmission”tools.
Equation(2)givesthedefinitionofRc,whichIalsocall“elasticityoftransmission”
betweenthechangeincapitalshareandchangeinpersonalincomeinequality.
ThedefinitionofGcisastandardone,withtheGinicoefficientcalculatedacross
theentiredistributionbutwithindividualsrankedbytheiramountofcapital
income(ratherthanbytotalincomeaswenormallydoincalculationsofoverall
incomeGini).NotethateveryGinipointincreaseintheconcentrationofcapital
incomewillbetranslatedintoRcscGinipointincreaseintotalincomeGini.
Similarly,astheshareofcapitalintotalincomeincreasesbyapercentagepoint,
GiniwillgoupbyRcGc-RlGl.
7
3.Transmissionofhighercapitalincomeshareintopersonalinequality:three
socialsystems
Itisusefultoconsiderthreeideal-typicalsocialsystemsandtoobservehow
they“transmit”anincreasedshareofincomefromcapitalintopersonalincome
distribution.
Socialism.Weassumethatinsocialismreturnsfromcapitalaredistributed
equallypercapita.Thiscouldhappenintwoways:allcapitalcanbestate-owned
andthereturnsfromitcanbedistributedequallyamongmembersofa
community,oreverymembercanhavethesameamountof(privately-owned)
capitalonwhichshereceivesthesamereturn.xiAvariantofthatisa“social
dividend”proposedbyJamesMeadeinthe1970sand1980s(seee.g.,Meade,
1986)andmorerecentlythe“minimuminheritance”ideaproposedbyTony
Atkinson(2014).Theydifferhoweverfromourideal-typicalsocialisminthat
underthelatterallcapitalincomeisdistributedequallypercapitawhereasin
MeadeandAtkinson’sschemesonlyapartofnationalincomefromcapitalisthus
distributed.
Now,r>gwillnotbe“transmitted”intogreaterinter-personalinequality
becauseGc=0.Insuchasociety,wecanwriteincomeofanindividuali(𝑦! )as
𝑦! = 𝑙! + 𝑐 wherelaborincome(ormorerealistically,logoflaborincome)lis
distributednormallywiththemean𝑙andstandarddeviation𝜎! 𝑙: 𝑁(𝑙 , 𝜎! )and
incomefromcapitalisaconstant𝑐.Rcwillbeequaltozerobecausethe
correlationbetweentheranksaccordingtototalincomeandamountsofcapital
incomewillbe0andthenumeratorof(2),𝜌 𝑟 𝑦 , 𝑐 ,willbeequaltozero.
Thesameresultobtainsifwedistributecapitalrandomlyacrossindividuals,
regardlessoftheirlaborincome.Inthatcase,Gcwillbepositive,andindividual
incomebecomes𝑦! = 𝑙! + 𝑐! wherenowbothlaborincome(orlogoflabor
income)andcapitalincomearenormallydistributedwith𝑙: 𝑁(𝑙 , 𝜎! )and
𝑐: 𝑁(𝑐 , 𝜎! )butarebasicallyuncorrelated.The“transmission”willagainfail
becausetherewouldbenoclearassociationbetweenbeingacapitalistand
havingahigheroverallincome.Rcmaybepositiveornegative(itwilljustdepend
onhowthelotteryofcapitalincomesgetscorrelatedwiththedistributionof
laborincomes)butitwouldbeverysmallintheabsoluteamount.xii
8
Inanycase,thetransmissionfromgreatershareofcapitaltointer-personal
incomedistributionwillbeweak:nilorquasinilacrossanyvalueofsc.Thisis
showninFigure1bythelinedenoted“socialism”whichwedrawtobealmost
undistinguishablefromRc=0forallvaluesofsc.Basically—andthisiskey—we
havefullindependenceofpersonalincomedistributionfromtherisingshareof
capitalinnetoutput.Theformeris“insulated”fromthelatter.
Figure1.Transmissionofrisingcapitalshareintointer-personalinequality
Correlationratio(Rc)
Newcapitalism
1
US2013
Classicalcapitalism
Socialism
0
1
Capitalincomeshare(sc)
Classicalcapitalism.Weconsidernextclassicalcapitalismwhere
ownershipsofcapitalandlaboraretotallyseparated,inthesensethatworkers
9
drawtheirentireincomefromlaborandhavenoincomefromtheownershipof
assets,whilethesituationforthecapitalistsisthereverse.Moreover,weshall
assumethatallworkersarepoorerthanallcapitalists.Thisgivesus,asshownin
Figure2,twosocialgroups,non-overlappingbyincomelevel.Whenthegroups
arenon-overlapping,Giniisexactlydecomposableacrosstherecipients(see
equation3),andthissimplifiestherelationshipbetweenGinicalculatedacross
incomesourcesandGinicalculatedacrosstherecipients.
Figure2.Socialstructureofclassicalcapitalism(simplified)
Numberof
people
Workers
Capitalists
Income(inlogs)
Ingeneral,Ginicalculatedacrossrecipientsbelongingtogroupsi(1,2,…r)is
equalto
1
𝐺=
𝜇
!
!
!
𝑝! 𝑠! 𝐺! + 𝐿
𝑦! − 𝑦! 𝑝! 𝑝! +
!!! !!!
!!!
whereμ=overallmeanincome,𝑦! =meanincomeofi-thgroup,𝑝! =
populationshareofi-thgroup,𝑠! =shareofi-thgroupintotalincome,andL=the
overlaptermthatisgenerallycalculatedasaresidualandispositivewhenthere
arerecipientsfromthemean-poorergroupwhoarericherthan(overlapwith)
10
somerecipientsofamean-richergroup.Sinceinourcaseallworkersarepoorer
thanallcapitalists,LdisappearsandtheexpressionfortheGinisimplifies:
𝐺=
1
𝑦 − 𝑦! 𝑝! 𝑝! + 𝑝! 𝑠! 𝐺! + 𝑝! 𝑠! 𝐺! =
𝜇 !
= 𝑠! 𝑝! − 𝑠! 𝑝! + 𝑝! 𝑠! 𝐺! + 𝑝! 𝑠! 𝐺! = 𝑠! 𝑝! + 𝑝! 𝐺! + 𝑠! −𝑝! + 𝑝! 𝐺!
(3)
whereweusesubscriptswforworkers,andkforcapitalists.
Overallinequality,whethercalculatedacrossincomesourcesoracross
recipients,mustbethesame,so(3)mustbeequalto(1),andthus
𝑠! 𝑝! + 𝑝! 𝐺! + 𝑠! −𝑝! + 𝑝! 𝐺! = 𝑠! 𝑅! 𝐺! + 𝑠! 𝑅! 𝐺! 𝑠! 𝑝! + 𝑝! 𝐺! − 𝑅! 𝐺! + 𝑠! −𝑝! + 𝑝! 𝐺! − 𝑅! 𝐺! = 0
(4)
wherewemakeuseofthefactthattheshareoflaborincome(sl)isexactly
thesameastheshareofincomereceivedbyworkers(sw)andtheshareofcapital
incomeisequaltotheshareofincomereceivedbycapitalists,sc=sk.Similarly,
Gk=GcandGl=Gw.Annex1showsfurthermanipulationsoftherelationship.Atthe
endweobtainapositiveandconcaverelationshipbetweenscandRc(asshownin
Figure1bythecurvedenoted“classicalcapitalism”).Thetransmissionfroman
increasedcapitalshareintoahigherinter-personalinequalityincreasesinscbut
doessoatthediminishingrate.Itasymptoticallytendstoward1whensc
approachesunity.
Someintuitionwillhelpexplaintheresult.Supposethatclassicalcapitalism
issuchthatthereisonlyaninfinitesimallysmallnumberofcapitalists(atthe
extreme,justoneperson)andthatallotherindividualsareworkerssothatboth
skandscarelow.xiii Byassumingasolecapitalistwealsoassumethathe/sheisthe
richestpersoninthecommunity(butnotsoextravagantlyrichtodrivescvery
high).ThecorrelationcoefficientinthenumeratorofRc,cov(r(y),c),willbelow
becauseranksaccordingtototalincome,runningfrom1to100,willnotbe
correlatedwiththeamountofincomefromcapital.Weshallhavetwovectors,
thatofranks[123……n]andthatofcapitalincome[0000….K]whereK=total
capitalincome(receivedbyonepersononly).Now,thedenominatorofRcwillbe
obtainedfromacorrelationbetweenavectorwheretheranksforallrecipients
butthetopwillbethesame(sincetheyallhavethesame,nil,amountofincome
11
fromcapital),thatisbetweenavectorsuchas
!
!
,
… . 𝑛 ,and[000..K].
(!)/! (!)/!
Suchacorrelationwillbemuchhigher(actually,equalto1)andtheratiobetween
thetwocorrelationcoefficientwillthusbelow.Wecanillustrateitwitha
numericalexample.Letn=100andKanyrandomnumberbutwhichweselected
tobe100.Thecorrelationinthenumeratoris0.17,thatofthedenominator1.
HenceRc=cov(r(y),c)=0.17.
Considernowtheotherextremewhereclassicalcapitalistsocietyis
composedmostlyofcapitalistsandaninfinitesimallysmallnumberofworkersso
thatscapproachesunity.Itisclearthatperson’srankaccordingtocapitalincome
willentirely(oralmostentirely)coincidewithhisrankaccordingtototalincome,
andcov(r(y),c)≈cov(r(c),c)andthusRc≈1.Inotherwords,therewouldbe
practicallynodifferencebetweentotalandcapitalincomesinceatthelimitthey
arethesame.Thismakesthetwocorrelationcoefficientsalmostthesameand
theirratioRc≈1.
Newcapitalism.Weassumethatnewcapitalismdiffersfromtheclassical
capitalisminthatallindividualsreceiveincomefrombothcapitalandlabor.Thus,
insteadofthetwosharplydelineatedgroups,workerswithincome(li,0)and
capitalistswithincome(0,ci),wehaveforallindividualspositivelaborandcapital
incomes(li,ci).Weassumefurtherthattheamountsofbothlaborandcapital
incomereceivedincreasemonotonicallyaswemovetoward(totalincome-)richer
individuals.Apoorperson’sincomewouldbeforexample(2,1),middle-income
person’s(7,3)andrichperson’sincome(24,53).
12
Figure3.Laborandcapitalincomeacrossrecipientsinnewcapitalism
(simplified)
Income
level(in
logs)
Capitalincome1
Laborincome
Capitalincome2
Poorestpeople
Richestpeople
Recipients
rankedby
totalincome
Monotonicincreasesoflabor,capitalandtotalincome(suchthatif𝑦! > 𝑦! thenwemusthave𝑙! > 𝑙! and𝑘! > 𝑘! )ensurethattheranksaccordingtocapital,
laborandtotalincomearethesame.Thus,Rc=Rl=1.ThisiswhyinFigure1we
drawthe“transmission”functionfornewcapitalismatRc=1throughout.
Howevertwoelaborationsofthissituationarepossible.Forexample,we
canhaveasituationillustratedinFigure3bylaborincomeandcapitalincome2
lines:theproportionsoflaborandcapitalincomestayconstantthroughoutthe
distribution,thatis,bothamountsofcapitalandlaborincreasebythesame
percentageaswemovefrompoorertoricherrecipients.Aperson’sincomecan
bewrittenas𝑦! = ϛ! 𝑙 + 𝑐 whereϛiincreasesini,indicatingthateverybody
receivesaspecificportionofbothoveralllaborandcapitalincome.Inother
words,aswemoveupalongincomedistribution,wemovefromincomethatcan
bewrittenas(2,1)to(10,5)to(200,100)etc.,whereeveryindividualreceives
twiceasmuchoflaborincomeasofcapitalincome,buttheabsoluteamountsof
13
bothdiffer.Obviously,richerpeoplereceivemoreofboth.Inthatcase(let’scall
it,“newcapitalism2”),Ginisofbothlaborandcapitalwillbethesameandthe
Ginicoefficientoftotalincomecanbewrittenas
𝐺 = 𝑠! 𝐺 + 𝑠! 𝐺 = 𝐺
(5)
Whenr>gandtheshareofcapitalincomegoesupoverallinequalityis
unaffected.Thus,inthe“newcapitalism2”whereeverybody(poorandrichalike)
hasthesamecompositionoftotalincome(e.g.everybody’stotalincomeis
composedofe.g.70%oflaborincomeand30%ofcapitalincome),arisingshare
ofcapitalincomedoesnotgettransmittedintoanincreasedinter-personal
inequality.NotethathappensbecausetherisingcapitalshareleavesGiniof
capitalincomeunchanged(andGiniofcapitalincomeisthesameasGinioflabor
income).Insocialism,thishappensbecauseGc=0.
Amorerealisticversionofthenewcapitalism(named“newcapitalism1”)
istheonewheretheproportionofcapitalincomeincreasesaspersonbecomes
!
(total-income)richer.Thiscanbewritten(inacontinuouscase)as
!"
!"
!"
!
!
!"
> 0with
> 0 and!" > 0 ensuringthatabsoluteincomesfrombothcapitalandlabor
arehigherforricherindividuals.xivTherelationshipcov(r(y),c)=cov(r(c),c)then
stillholdssincetherankingsaccordingtototalincomeandtherankingaccording
tocapitalincomecoincideandthusRc=1,butnowanincreaseinthecapitalshare
pushestheoverallGiniup.Thishappensbecausecapitalincome(depictedby
capitalincome1lineinFigure3)hasagreaterGinithanlaborincomeandasthe
shareofamoreunequallydistributedsourceincreases,sodoestheoverallGini.
TheactualincreaseinGiniwillbeGc-Gl.
Newcapitalismrepresentsastrongdeparturefromthemodelofclassical
capitalism.xvEveryindividualreceivesbothlaborandcapitalincome,andin
principle(iftheirshareswerethesameacrossthedistribution),wecouldobtain
thesameoutcomeasinsocialism,namelyfullorthogonalityofpersonalincome
distributionfromtherisingshareofcapitalincome.Thishoweverseemsunlikely
asrichcountriestodayareineffectcloserto“newcapitalism1”,wheretheshare
ofcapitalincomeisgreaterfortherichhouseholds.
Under“newcapitalism1”thetransmissionfromincreasedcapitalshare
intogreaterinter-personalinequalitymaybeasstrongasinclassicalcapitalism.
14
Supposethatsc=0.3andthatitincreasesto0.35.Underclassicalcapitalismwith
Rc(say)around0.6,these5additionalpercentagepointsofnetincomereceived
bycapitalistswillincreasetheoverallGinibyabout3points.Underthe“new
capitalism1”,theincreasewillbe(Gc-Gl)times5.TheGc-Glgapisempirically
about0.3-0.5(0.8-0.9minus0.4-0.5),sotheGiniincreasemaybe1.5-2.5points.
Thenewcapitalismmaybejustmarginallymoresuccessfulthanclassical
capitalismincheckingthespill-overfromtherisingcapitalshareintoagreater
inter-personalinequality.
4.Transmissionofhighercapitalincomeshareintopersonalinequality:empirical
results
Howdoesthetransmissionofhighercapitalincomeintopersonal
inequality,summedupintheelasticityparameter,lookempiricallyinthe
advancedcapitalisteconomies?Iuseasampleof138standardizedhousehold
surveysproducedbyLuxembourgIncomeStudy(LIS)covering17capitalist
economiesovertheperiod1969-2013andcalculatealltherelevantstatistics(Gini
coefficients,concentrationcoefficients,correlationratiosforcapitalandlabor
income;seeLuxembourgIncomeStudyDatabase,2014).Thenumberofsurveys
bycountryrangesfrom12forCanada,and11fortheUnitedStatesto5for
SwitzerlandandGreece.Foralmostallcountries,themostrecentsurveysare
from2010or2013.ThelistofsurveysisgiveninAnnex2.
Onehastokeepinmindhoweverthatdespitethebesteffortsat
harmonizationconductedbyLIS,theamountofcapitalincomesisinmanycases
probablyunderestimated.Thisisduetothefactthattheoriginalsurveysoutof
whichLISdataarebuiltunderestimatecapitalincome,bothbecausetherich(who
receiveahighshareofincomefromcapital)refusetoparticipateinsurveys,or
richrespondents,whenparticipating,underestimatestheircapitalincome.For
example,LISdatafortheUnitedStatesgiveanaverageshareofcapitalincome
(exclusiveofcapitalgains)intotalmarketincomeof7percentwhichisabout2/3
ofthevalueobtainedfromfiscalsources.xviDespitethat,comparisonsofUSdata
obtainedfromLISandfromfiscalsourcesshowveryclosecorrespondence
betweenthevaluesoftheGinicoefficientforcapitalincomeandcorrelation
ratios(Rc),thetwofactorsthatdeterminethetransmission.Thelatterthereforeis
likelytobeverysimilarwhethercalculatedfromhouseholdsurveysorfromfiscal
sources(seeTable1).
15
Table1.ComparisonofLISsurveyandfiscaldatafortheUnitedStates
Inequalityofmarket
incomewithoutcapital
gains(inGinipoints)
Capitalincomesharein
marketincome(in%)
Giniofcapitalincome(in
Ginipoints)
Capitalcorrelationratio,Rc
2000
2004
Surveys
53
Fiscal
55
Surveys
54
Fiscal
55
7
11
6
10
90
92
92
94
0.63
0.76
0.64
0.78
Note:Calculationsfromhouseholdsurveysarebasedonhouseholdpercapitaincome;calculationsfrom
fiscaldataarebasedonfiscalunits(whichareveryclosetohouseholds).Thefiscalseriesendsin2005.
Forcomparison,IchoosethetwomostrecentyearsforwhichIhadbothsurveyandfiscaldata.Source:
LIShouseholdsurveysbasedonUSCurrentPopulationSurveys:myowncalculations.Fiscaldata:
personalcommunicationbyChristophLakner.
Figure4showsthedataontheelasticity(Rc)overtimeforfouradvanced
economies.InadditiontotheUnitedStates,IselectedGermanyasanexampleof
acontinental-corporatistwelfarestate,SwedenasaprototypesofaScandinavian
welfarestate,andSpainasanadvancedMediterraneanwelfarestate.Theresults
showtheUSwitharatherhighelasticitythroughout.USelasticitysteadily
increases,passingfrom0.54inthelate1970sto0.64in2013.Mostinteresting
howeverisSwedenwheretheelasticitywasinthemid-1970saslowas0.2but
increasedto0.5by2000.Thisparallelsthewell-knownincreaseinincome,and
especiallywealth,inequalityinSweden(seeOECD,2015,Piketty2013,p.549).
Germanelasticityalsoincreasedsignificantly,from0.4tothepeakof0.65.
Finally,Spanishelasticitywentupaswell,fromlessthan0.3inthe1980stojust
shortof0.5in2010.Therewasinthesefourcases,aclearupwardtrendoverthe
pastthirtyyears.Inaddition,thegapsbetweencountries’elasticitiesintheearly
2010saresmallerthantheywereinthe1970s.Weshallfindverysimilarresults
forthewholesampleof17countries.
16
Figure4.Elasticityofinter-personalincomeGinitochangesincapitalincome
share;fouradvancedeconomies1967-2013
0.80
0.70
USA
Correla1onra1o,Rc
0.60
Germany
0.50
Spain
0.40
Sweden
0.30
0.20
0.10
0.00
1960
1970
1980
1990
2000
2010
2020
Year
Source:calculatedfromhousehold-leveldataavailablefromLuxembourgIncomeStudy(seeAnnex2).
Allunderlyingvariablesnormalizedbyhouseholdsize,thatisexpressedinpercapitaterms.
17
Figure5showstheaverageelasticitybycountry,rankedinincreasingorder.
Italy,UnitedStatesandFinlandhavethehighestelasticitiesofaround0.6;atthe
otherextremeareBelgium,SwedenandSwitzerlandwiththeaverageelasticities
ofjustunder0.35.Notethattheperiodoverwhichtheseelasticitiesare
calculatedisnotidenticalacrosscountries(thefirstdatapointfortheUnited
Statesgoesbackto1979,forGreecetoonly1995)noristhenumberof
observationspercountrythesame.
.4
0
.2
mean of elasticity
.6
Figure5.Averageelasticityoverthepastapproximately40years,by
country
BELSWECHEESPNLDGBRGRCCANFRA IRLDNKDEUAUSNORFINUSA ITA
Countriesarerankedbymeanelasticity.BEL=Belgium,SWE=Sweden,CHE=Switzerland,ESP=
Spain.NLD=Netherlands,GBR=GreatBritain,GRC=Greece,CAN=Canada,FRA=France,IRL=Ireland,
DNK=Denmark,DEU=Germany,AUS=Australia,NOR=Norway,FIN=Finland,USA=UnitedStates,
ITA=Italy.Source:seeAnnex2.
18
Figure6showsthescatterplotofelasticitiesobtainedfrom138surveys
againstthecapitalsharescalculatedfromthesamesurveys.Asimpliedbyour
derivationinSection3,highercapitalshareisassociatedwithgreaterelasticity,
butthescatterplotshowsthattherelationshipisconcaveandthatafterthe
capitalsharereachesabout0.12,theelasticityincreasesbyverylittleorisstable.
Whatthismeansisthatanyincreaseinthecapitalshare(say,by1percentage
point)willbeassociatedwithagreaterincreaseininter-personalGiniathigher
levelsofcapitalshare.Butoncethatlevelisreasonablyhigh,furtherincreasesin
thecapitalsharewillproduceaboutthesameeffectoninter-personalinequality.
Figure6.Elasticitywithwhichcapitalshareis“transmitted”intohigher
interpersonalinequality,andcapitalshare
(17advancedeconomies,1967-2013)
.8
NOR
DNK
.4
.6
FIN
ITA
FIN
ITA
AUS
NLD
DEU
FIN
USA
ITA
DEU
ITA
USA
USA
FIN
DNK
USA
AUS
USA
NOR
ITA
AUS
USA
DNK
USA AUS ITA
DEU
ITA
FIN NOR
DEU
USA
USA
ITAUSA
IRL DNK
ITA
DEU
ITA USA
DEU
IRL IRL
SWE
DNK
AUSDEU FRA
GBR
FRA
IRL ESP
CAN
IRL
ESP
FRA
FRA CAN
GBR
NLD
SWE
AUS
GBR
BEL
GBR
AUS
BELGRC
GBRCAN
CAN
NLD
GBR
IRL
ESP NLDFRA
DEU
CAN
GRC
FIN ESP
NLD
CAN
GRC
FIN CAN
SWECAN NOR
DEU
GBR
CAN
DNK
ESP
GRC
CAN
GRC
IRL NLD
DNK BEL
CHE
IRL
NOR
CAN
CHE
SWEFRAESP
NOR
FRA CAN
SWE
BEL
CHE
GBR
SWE
ESP
GBR ESP
BEL
SWE
NLD
SWE
CHE
NLD
GBR
.2
elasticity
NOR
NOR
ITA
CHE
AUS
0
BEL
0
.05
capital share
.1
.15
bandwidth = .8
Source:calculatedfromhousehold-leveldataavailablefromLuxembourgIncomeStudy(seeAnnex2).
Allunderlyingvariablesnormalizedbyhouseholdsize,thatisexpressedinpercapitaterms.NonparametriclowessfunctioninStatawithdefaultbandwidthshown.Capitalshareisexpressedasaratio
(0.05=5%).Asinglecountryabbreviationappearsforallyearsforwhichsurveysforsuchacountryare
available.ForthelistofcountryabbreviationseeNotetoFigure5.
19
Mostelasticitiesarebetween0.3and0.6withboththemedianandthe
meanelasticityof0.46(implyingafairlysymmetricaldistributionofelasticities).
ThedistributionofelasticitiesisshowninFigure7.
1.5
0
.5
1
Density
2
2.5
Figure7.Distributionofelasticities(Rc)inadvancedcapitalisteconomies
0
.2
.4
elasticity
.6
.8
1
kernel = epanechnikov, bandwidth = 0.0482
Source:calculatedfromhousehold-leveldataavailablefromLuxembourgIncomeStudy(seeAnnex2).
Straightlinedrawnatmeanelasticityof0.46.
Howiselasticityrelatedtothecapitalshare?Inotherwords,canwe
estimatetherelationshipshowninFigure6parametrically?Table2showsthe
regressionresultsforseveralspecifications.Inthesimplestlinearspecification
whereelasticityisregressedoncapitalshareandtimeonly,wefindasteepslope
oncapitalshareofabout3,andastatisticallysignificantpositivecoefficienton
time.Thisformermeansthat,onaverage,eachpercentagepointincreaseinthe
capitalshareisassociatedwithanincreaseofelasticityofalmost3points:for
example,ifthecapitalshareincreasesfrom0.05to0.06(from5%to6%),the
elasticityincreasesfrom0.4to0.43.Thepositivesignonthetimevariableimplies
thatthetransmissionfunctionhasrecentlybecomestronger.Perhapsmore
20
realistic(inlightofthepatterninFigure6)isaquadraticformulation,andindeed
wefindasignificantquadraticterminregression2.Anotheralternativeisa
countryfixedeffectregressionwhichallowsforheterogeneitybetweenthe
countries(reflectedinthecountry-specificintercepts).Thecoefficientonthe
capitalshareisquitesimilar(2.68)towhatwehaveobtainedinthesimplepooled
regression.Thecoefficientontimeremainsstronglypositive.Finally,specification
(4)repeatsthesquaredcapitalshareformulation,nowincountryfixedeffects,
withbasicallyunchangedresults.Wecandrawtwoconclusionsfromthisexercise:
first,arisingcapitalshareisassociatedwithincreasing(butconcave)transmission
intopersonalinequality,andsecond,therelationshiphasrecentlybecome
stronger.
Table2.Regressionresults:elasticityoftransmissionandcapitalshare
Dependentvariable:elasticity
Capitalshare
Squaredcapital
share
Time
Constant
Adjusted(or
within)R2
(F-value)
Numberof
observations
Numberof
countries
Pooledregressions
1
2.95
(0.00)
Countryfixedeffects(unbalanced
panel)
3
4
2.68
4.99
(0.00)
(0.00)
-15.81
(0.03)
0.004
0.004
(0.00)
(0.00)
-7.84
-7.17
(0.00)
(0.00)
0.43
0.45
(45)
(32)
0.005
(0.00)
-9.19
(0.00)
0.41
(48)
2
5.81
(0.00)
-20.69
(0.01)
0.004
(0.00)
-8.45
(0.00)
0.43
(36)
138
138
138
138
17
17
Note:p-valuesbetweenparentheses.Timeismeasuredbytheyearwhenthesurveywasconducted
(seeAnnex2).
Wecannowcomparetheelasticitiesfromreallifetothosethatwe
obtainedearlierfromourfourideal-typicalsocialsystems(Table3).Thisenables
21
ustoseebetterwhere,comparedtodifferentidealtypes,domoderncapitalist
economieslie.GreatBritainin1969,Netherlandsin1987,Switzerlandin1982,
andSwedenin1981hadelasticitiessmallerorequalto0.2andwerequiteclose
tothesocialistmodel.One-halfofallobservedelasticitiesfallbetweenthevalues
of0.36and0.57(withthemedian,aswehaveseen,of0.46).Thislevelof
elasticitycorresponds,withinourideal-typicalworld,toanintermediateposition
betweensocialismandclassicalornewcapitalism1.Countrieswiththehighest
elasticities,whichareNordiccountriesintheyearsafter2000andItalyin1998
and2000,havevaluesabove0.7andarethusclosesttotheclassicalornew
capitalism1,andfurthestfromsocialism.xviiTheUSisclosetothesecountries
withitshighestelasticityvalueof0.65,reachedin1997,anditsmostrecent2013
elasticityat0.64,justslightlybelowthepreviouspeak.
HowmuchGiniwillincreasewilldependnotonlyontheelasticitybutalso
onotherparameterslikeGinioflaborandcapitalincomeandthecorrelationratio
forlabor(Rl).However,theseparameters,andespeciallyGinisforlaborand
capitalincomedonotdiffergreatlybetweenthecountriesandwecanmakean
easyapproximation:theaverageGiniforlaborincomeinoursampleis0.5and
theaverageGiniforcapitalincomeis0.9.Takingthesevaluesandtheaverage
correlationratioforlabor,givesusanestimatedincreaseof0.16Ginipointfor
eachpointincreaseinthecapitalshare(seeTable3).
Table3.Elasticityoftransmissionofrisingshareofcapitalincomeintopersonal
incomeinequality
Economicsystem
“Newcapitalism1”(withGc>Gl)
Classicalcapitalism
“Newcapitalism2”(with
Gc=Gl)*
Richcountriestoday
Socialism
Elasticity
Around1
<1
1
Ginichange
Gc-Gl
RcGc-RlGl
0
0.51
RcGc-RlGl=(0.51)(0.9)–(0.6)(0.5)=0.16*
Around0 Around0ornegative**
*ThemeanRcintheperiodafter2000is0.51;Ialsotaketheaveragevaluesforothervariables.
**SinceGinioflaborincomeissupposedtobepositive(Gl>Gc=0).
22
5.PolicyImplications
Theimplicationofthisanalysisisthatthewaytherisingshareofcapital
incomegetstransmittedintogreaterinter-personalinequalityvariesbetween
differentsocialsystemsinfunctionoftheunderlyingassetdistribution.Weare
usedtoimplicitlymakingtheassumptionthatcapitalincomesarevery
concentratedandthattheassociationbetweenbeingcapital-richandoverallincomerichisveryclose.Bothoftheseassumptionsarereasonablegiventhe
empiricalevidence.Indeed,asweseeintheideal-typicalworldofnewcapitalism,
theincreaseinscalmostdirectlytranslatesintoahigherGini(becauseGiniof
capitalincomeismuchgreaterthanGinioflaborincome).Intheclassical
capitalism,thisisalsotrueoncetheshareofcapitalistsbecomessufficientlyhigh.
Butinasocialistworldrisingscdoesnotimplyrisinginter-personalGini;ineffect,
givenourassumptionofequalpercapitadistributionofcapitalassets,itimpliesa
reductioninincomeinequality.Similarly,innewcapitalism2whereevery
individualreceivesanequalshareofherincomefromassetownership,arising
capitalsharedoesnotaffectinter-personalincomedistribution.
Thiscarries,Ithink,clearlessonsfortherichsocietiesinparticular.The
definitionofrichsocietiesisthattheyhavehighK/Y(β)ratios.Ascurrently
advancedsocietiesbecomeevenricher,ther>gdynamicwillleadtotherising
betaandalpha.Onewaytoensurethatthisdoesnotspilloutintoincreased
incomeinequalityisthroughtaxation,asadvocatedbyPiketty,butanotherway—
perhapsamorepromisingoneoratleastcomplementary—istoreducethe
concentrationofownershipofcapitalandthusofincomefromcapital.
Intheframeworkdiscussedhere,reducedGcwillalsoreducethe
associationbetween(high)capitalincomeand(high)overallincomes.Thusboth
GcandRcwouldbereducedandanincreaseincapitalsharewillhaveasmallor
evenaminimaleffectonpersonalincomedistribution.UltimatelyifGc=Gl,itmay
havenoeffectonoverallincomeGiniatall.
Inturn,thismeansthatmuchgreaterattentionshouldbepaidtopolicies
thatwouldredistributeownershipofcapitalandmakeitlessconcentrated.In
principle,therearetwokindsofsuchpolicies:onewouldbegivinggreater
importancetoESOPs(EmployeeStockOwnershipPlans)andsimilarplansthat
23
wouldgiveacapitalstaketoworkerswhocurrentlyhavenone.Awell-known
Swedishtradeunionplanwherebycompanieswouldissuespecialsharestogo
intoafundwhichwouldsupportworkers’pensionswasrecently“resuscitated”by
Taylor,ÖmerandRezai(2015,p.23).Thisapproachhoweverrunsintothewellknownproblemofnon-diversificationofrisk,whereindividuals’incomedepends
entirelyonworkinginagivencompany.Thisisindeedthecaseformostpeople
todaywhohaveonlylaborincomes,sohavingbothlaborandcapitalincome
comingfromthesamecompany,itcouldbeargued,doesnotexposethemto
moreriskthantheypresentlyexperience.Whilethismaybetrue,itbegsthe
questionofwhysuchpro-laborownershipwouldbeintroducedifitdoesnot
manifestlyimprovethesituationofthosewhocurrentlyholdnocapitalassets.It
thereforeseemstomethatthisapproach,whilevaluable,runsquicklyintosome
limits.
Amorepromisingapproachmaybetofocusonwidershareownership
divorcedfromone’sworkplace.Thiscouldbedonethroughvariousincentives
thatwouldencouragesmallshareholdings,andpenalizeheavyconcentrationof
assets.Indeed,Piketty’ssuggestionofaprogressivewealthtaxcouldbe
combinedwithimplicitandexplicitsubsidiestothosewhoholdsmallamountsof
wealth.xviii
Inrichsocietieswhosecapital-outputratiowilltendtorise,theshareof
capitalincomeinnetincomemaybeexpectedtogoupaswell.xixIfso,efforts
shouldbedirectedtowardensuringthatthisinevitableupwardmovementinthe
K/Yratiodoesnotproduceunsustainablelevelsofincomeinequality.Awayto
achievethisistoequalizeasmuchaspossibleindividuals’positionsatthepredistributionstage,ortoputitintermsintroducedinthispaper,tomoveaway
from“newcapitalism1”,whichisinmanywayssimilartotheactually-existing
capitalismtoday,andgetcloserto“newcapitalism2”.Thisinvolvesprimarily
lesserconcentrationofcapitalassets,butalso(atopicwhichIdidnotdiscuss
here)moreequalaccesstoeducationanddeconcentrationofthereturnstoskills.
24
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27
Annex1.Derivationofthetransmissionfunctioninthecaseofclassicalcapitalism
(withtwonon-overlappingincomeclasses)
𝑠! 𝑝! + 𝑝! 𝐺! − 𝑅! 𝐺! = −𝑠! −𝑝! + 𝑝! 𝐺! − 𝑅! 𝐺! 𝑠! 𝑝! + 𝑝! 𝐺! − 𝑅! 𝐺! = −(1 − 𝑠! ) −𝑝! + 𝑝! 𝐺! − 𝑅! 𝐺! 𝑠! 𝑝! + 𝑝! 𝐺! − 𝑅! 𝐺! = −(1 − 𝑠! ) 𝐴 𝑠! 𝑝! + 𝑝! 𝐺! − 𝑅! 𝐺! − 𝐴 = −𝐴
−𝑠! 𝑅! 𝐺! = −𝑠! 𝑝! + 𝑝! 𝐺! − 𝐴 − 𝐴
𝑠! 𝑅! 𝐺! = 𝑠! 𝑝! + 𝑝! 𝐺! − 𝐴 + 𝐴
𝑅! 𝐺! = 𝑝! + 𝑝! 𝐺! − 𝐴 +
𝑅! =
𝐴
𝑠!
𝑝! − 𝐴
𝐴
+ 𝑝! +
𝐺!
𝑠! 𝐺!
𝑑𝑅!
𝐴 1
=−
> 0
𝑑𝑠!
𝑠! 𝐺! !
Since𝐴 = −𝑝! + 𝑝! 𝐺! − 𝑅! 𝐺! = − 1 − 𝑝! + 𝑝! 𝐺! − 𝑅! 𝐺! =𝑝! 1 +
𝐺! − 1 − 𝑅! 𝐺! willtendtobenegative.Inoneextremecasewhenpk→1this
wouldbeclearlythecase.Intheotherextremecasewhenpk→0,𝐴 = 𝐺! ( 1 −
𝑅! ) → 0.Thislastcaseisclearlyirrelevantbecauseitimpliesthatthereareno
capitalistsatall.Butforallsensiblesituationswhere0<pk<1,A<0.
Thesecondderivativeis
𝑑 ! 𝑅!
𝑑𝑠! !
=
2𝐴 1
< 0
𝑠! 𝐺! !
Allsymbolsareasexplainedinthetext.
28
Annex2.ListofLISSurveysused
Country
Australia
Years
1981198519891995200120032006
2010
198519881992199519972000
1971197519811987199119941997
19982000200420072010
19821992200020022005
1973197819841989199420002004
20072010
1987199219952000200420072010
1980198519901995200020042007
20102013
1987199119952000200420072010
1978198419891994200020052010
1969197419791986199119941999
200420072010
19952000200420072010
1987199419951996200020042007
2010
1986198719891991199319951998
2000200420082010
1983198719901993199920042007
2010
1979198619911995200020042007
2010
1967197519811987199219952000
2005
1974197919881991199419972000
2004200720102013
Belgium
Canada
Switzerland
Germany
Denmark
Spain
Finland
France
GreatBritain
Greece
Ireland
Italy
Netherland
Norway
Sweden
UnitedStates
29
i
GraduateCenterCityUniversityofNewYorkandLuxembourgIncomeStudy.Iamgratefulforcommentsby
HeatherBoushey,BradDeLong,ChristophLakner,SalvatoreMorelli,EricNielsen,MarshallSteinbaum,andother
participantsattheconferenceinBellagio,December2015.
ii
Theterms“personal”and“inter-personal”incomedistributionwillbeusedinter-changeably.
iii
p.57Frenchedition.“Thecentralcontradictionofcapitalism”isthetitleintheConclusionsof“Capital…”
iv
AslightlydifferentapproachtothisissueisadoptedbyAtkinson2009,seeespeciallypp.10-11.
v
Iassumehereamodelofhomogeneouscapital.Piketty(2016,p.8),probablyreactingtothecritiques(e.g.
Stiglitz,2015andseveralotherfollow-uppapers)thathavepointedoutthatitistheheterogeneousnatureof
capital,moreparticularlytheroleofhousing,thatisresponsiblefortheriseinthecapital-incomeratio,prefers
nowmulti-sectormodelsofcapitalaccumulation.Suchmodelsallowrelativepricesofvariouscapitalgoodstovary
differentlyand,asinthecaseofrisingrealestateprices,todrivetheobservedK/Yratio.Theyalsodonotdepend
onthegreaterthanunitaryelasticityofsubstitutionbetweencapitalandlabortogenerateanincreasingcapital
share.Whilethatapproachcertainlyhastheadvantageofbeingmorerealistic,itfailstoprovidethepowerfuland
focusedsimplicityoftheone-sectormodel.
vi
SeeRay(2014a,2014b).
vii
ForthispointseeMilanovic(2014)critiqueofDebrajRay’scritiqueofPiketty.
viii
Inhistworecentpapers,Piketty(2015,2016)addressesthispointexplicitly.Heallowsforcapitalists’
consumptionoutofrbutnotesthatafamilyneedsonlyto“reinvestafractiong/rofitscapitalincome..toensure
thatitscapitalstockwillgrowatthesamerate…asthe…economy”(Piketty2016,p.3).Obviously,anygreater
savingwillincreasethecapitalstockandmakecapital’sincomeshareinnetproductgoup.Bothpapersalso
deemphasize,comparedtothebook,theimportanceofther>grelationshipinexplainingtheincreaseinincome
inequality,butseeitsroleashavingmostlytodowiththelong-runlevelofwealthinequality:“[s]pecifically,a
higherr-ggapwilltendtogreatlyamplifythesteady-stateinequalityofwealthdistribution”(Piketty,2016,p.3).
ix
scisthesameasPiketty’salpha.
x
Theconditionis𝑅! 𝐺! > 𝑅! 𝐺! .
xi
Initsimplications,thisissimilartothesituationwherecapitalisprivately-ownedbutthereturnoncapitalis
assessedatconfiscatory(100percent)taxratesandtheproceedsaredistributedequallypercapita.Obviously,
endowmentsofcapitalwillnotbeequalized,butincomefromcapitalwould.IowethisideatoChristophLakner.
xii
Weimplicitlyassumethattheamountofrandomlydistributedcapitalincomeisequaltotheusualshareof
capitalincomeintotalnetincome(say,upto30%).Obviously,ifrandomlydistributedcapitaldwarfslaborincome
thenitcouldhappenthatpeoplewhohaverandomly“drawn”largeallotmentofcapitalincomebecomealsototal
incomerich.Inthat,ratherextravagantcase,Rccouldbehigh,andindeedevenapproach1.
xiii
Obviously,havingjustonecapitalist(lowsk)doesnotensurethatscwillbealsolow:itcouldbethatthatsole
capitalistissorichthatthecapitalshareishigh.Intherestofthisintuitivediscussion,Iassumehoweverthatthe
twomovebroadlytogether.
30
xiv
Fortheevidenceonnewcapitalism,seeAtkinsonandLakner(2014)whoshowanincreasingassociationofhigh
laborandcapitalincomeintheUnitedStatesduringthepasthalfcentury.SuchasocietyisalsoevokedbyPiketty
(2013;Chapter7,p.416inFrenchedition).
xv
Thesefeaturesof“newcapitalism”aresimilartothepointrepeatedlymadebyPikettythatthepost-Warperiod
isdistinguishedbytheemergenceofaproperty-owningmiddleclassevenifitsshareofcapitalownershiphas
remainedrelativelysmall(seePiketty,2013,pp.410,552).
xvi
PersonalcomunicationbyChristophLakner.
xvii
Notethatwecannotjudgehowclosetheycometo“newcapitalism2”becauseunder“newcapitalism2”Rc
wouldbestill1althoughthetransmissionlinkbetweengreatercapitalincomeshareandinter-personalinequality
issevered.
xviii
Pikettynoticestheneedforcomplementaritybetweentaxationandredistributionpoliciesingeneralandthe
needtochangeformsofgovernanceofprivatecapital.Heclosesthelastchapterofhisbookbystatingthat
“withoutarealrighttointerveneincorporatedecision-making(includingseatsforworkersonthecompany’s
boardofdirectors),[financial]transparency(broughtaboutbytaxationofwealth]isoflittleuse”(p.570).
xix
Assumingsomestickinessintherateofreturn.
31