英國(guó)國(guó)家經(jīng)濟(jì)和社會(huì)研究所-論勞動(dòng)收入份額的計(jì)量 ON MEASURING THE LABOUR INCOME SHARE 2024

ONMEASURINGTHELABOURINCOMESHARE

DrBenjaminCaswell

NationalInstituteofEconomicandSocialResearch

NIESRDiscussionPaperNo.55630April2024

AbouttheNationalInstituteofEconomicandSocialResearch

TheNationalInstituteofEconomicandSocialResearchisBritain'slongestestablishedindependentresearchinstitute,foundedin1938.Thevisionofourfounderswastocarryoutresearchtoimproveunderstandingoftheeconomicandsocialforcesthataffectpeople’slives,andthewaysinwhichpolicycanbringaboutchange.Overeightyyearslater,thisremainscentraltoNIESR’sethos.Wecontinuetoapplyourexpertiseinbothquantitativeandqualitativemethodsandourunderstandingofeconomicandsocialissuestocurrentdebatesandtoinfluencepolicy.TheInstituteisindependentofallparty-politicalinterests.

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?NationalInstituteofEconomicandSocialResearch2024

OnMeasuringtheLabourIncomeShare

DrBenjaminCaswell

Abstract

Thelabourincomeshareplaysakeyroleasaparameterinmacroeconomicmodelsandhas

motivatedabodyofliteraturewithregardstoitsapparentdecline.Despiteitscrucial

importance,thereexistsnorobustconsensusonhowtoquantifythelabourincomeshareinpractice.Thispaperexploressomeoftheconceptualissuessurroundingmeasurementand

providesanovelempiricalapplicationutilisingUKsectorlevelnationalaccountsdata.

Specifically,thisinvolvesimputingproprietorlabourincomeatthesectorlevelandthenaggregatinguptothewholeeconomy.Thispaperdemonstratesthatthedisaggregated

approachamplifiesmeasurementerrorsundercertainimputationassumptions.

Classification:E01,E25,P2

Keywords:aggregateincome,labourincomeshare,nationalaccounts,measurement

1

Introduction

Theconceptofthelabourshareofincomedatesbacktoclassicaleconomics.Accordingly,Ricardo(1817)openshismagnumopusbywayofemphasisingitsimportance.

‘Indifferentstagesofsociety,theproportionsofthewholeproduce[…]underthenamesofrent,profit,andwages,willbeessentiallydifferent.Todeterminethelawswhichregulatethisdistribution,istheprincipalprobleminpoliticaleconomy.’

However,justovertwocenturieslater,thereremainsnoexactconsensusonhowtoquantifytheportionofaggregateincomewhichaccruestolabour.Theprimaryreasonforthisisthatwecannotdirectlyobservealllabourincome.

Specifically,unincorporatedenterprisesarenotseparatelegalentitiesfromtheirowners;assuch,theycanfreelymovefundsbetweenbusinessandpersonalaccounts.Forthisreason,itisnotpossibletodistinguishbetweentheirearningsfromworkandtheirentrepreneurialprofit.

Thismixednatureofself-employedincome,whichcontainsbothcapitalandlabourremunerations,necessitatesthatallestimatesofself-employedlabourincomebeimputed.Itistheseimputationassumptions,alongwithnovelempiricalestimatesfortheUKeconomy,whichareexploredinthispaper.

Thefindingsaretwofold.Firstly,thecarefultreatmentofproprietorincomeconfirmstherehasbeenadeclineintheUKlabourincomeshare.However,thisdeclinetookplaceoverthelastquarterofthe20thcentury.Sincethemillennium,theUKlabourincomesharehasbeennotablystable.

Secondly,imputingproprietorlabourincomeviaaveragehourlyemployeecompensationshouldbeavoidedunlesscompellingempiricalevidencestatesotherwise.Detailsector-leveldatademonstratessignificantmeasurementerrorassociatedwiththismethodofimputationwhichisnotcapturedattheaggregatelevel.

Background

Attemptstoformallymeasurethelabourincomesharebeganinthe20thcentury.Assuch,thefirsttaskundertakenbytheNationalBureauofEconomicResearchuponitsfoundationin

1920wastheestimationofthe‘a(chǎn)pproximatesizeand[functional]distributionofnationalincome’(King,1930).

Whiletheseearlymeasurementeffortswereoftenhamperedbytheoreticalconcernsandalackofcomprehensivedata,aconsensusgrewoverthedecadesregardingtheperceived

stabilityofthelabourincomeshare.Forexample,Keynes(1939)famouslyremarkedthat:

'Thestabilityofthe[labourincome]ratioforeachcountryischieflyremarkable,andthisappearstobealong-run,andnotmerelyashort-period,phenomenon.'

Decadeslater,Kaldor(1961)outlinedhis(noweponymous)six‘stylised’facts.Histhirdfactemphasisedtheconstancyoftheshareofnationalincomereceivedbylabour.

Consequently,thisobservedregularitybecameawidelyacceptedtruthinmacroeconomics.Itwasmathematicallyconvenientforthetractabilityofeconomicmodelsandhadsignificantempiricalsupport.Subsequently,thelabourincomeshareassumedanimportantroleasaparameterinbusinesscycleandgrowthmodels.

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However,inthelate20thcentury,atrendbegantoemergeacrossindustrialisedeconomies:thedeclineofthelabourincomeshare.Thistrendhasmotivatedabodyofliteraturedevotedtoaccountingforthedecline.Itcanbebroadlycategorisedintotwostrands-economicphenomenonandaccountingartefact.

Thefirststrandoftheliteraturearguesthatthefallinthelabourincomesharecanbeattributedtounderlyingeconomiccauses.Thesecondarguesthattheobserveddeclinecanbeexplainedthroughalackofconsistencyinaccountingpractices.

EconomicPhenomenon:

Blanchard(2006)arguesthatchangesinlabourmarketinstitutionsandthecurbingofunionpowersacrossindustrialisedeconomiesoverthelastquarterofthetwentiethcenturyreducedthecollectivebargainingpoweroflabourandsubsequentlybroughtaboutafallintheshareoflabourincome.

HarrisonandMcMillan(2006)suggestthatglobalisationhasopenedupgoodsandlabourmarketstocompetitionfromaroundtheworldandthatthishasexerteddownwardpressureonwagesandthelabourincomeshare.

Similarly,Elbsy,etal(2013)claimthatthedeclineinthelabourincomesharehasitsoriginsinglobalisationandtheoffshoringoflabour-intensiveproductiontoeconomieswithlowerlabourcosts.

KarabarbounisandNeiman(2014)arguethatinvestment-specifictechnologicalchangehasreducedtherelativepriceofcapitalovertimeandcausedfirmstosubstitutelabourforcapital.Thiscapitaldeepeningexertsdownwardpressureonthelabourincomeshare.

Alternatively,Lawrence(2015)proposesanexplanationthatdoesnotrelyoncapitalandlabourbeingsubstitutes.Heclaimsthattheeffectivecapital-labourratiohasfallenascapitaldeepeninghasbeenoffsetbyrapidlabour-augmentingtechnologicalchange.Thishasincreasedtheeffectivesupplyoflabourandproducedadeclineinthelabourshareofincome.

AccountingArtefact:

Bridgeman(2014)explainsthattheratioofconsumptionoffixedcapitaltoaggregateincomehasrisenovertimeduetotheincreasedprevalenceofITgoods-whichtypicallydepreciatemorequicklythanotherinvestmentgoods.

Subsequently,anincreaseintheratioofconsumptionoffixedcapitalcancreatetheappearanceofadeclininglabourincomesharebyimplicitlyanderroneouslyoverstatingthevalueofthedenominator.Aftercontrollingforthis,heshowsthatlabourincomesharesexhibitnopersistentdeclineacrossindustrialisedeconomies.

Armenter(2015)showsthatmethodologychangesforimputingproprietorlabourincomecanaccountforpartofthedeclineinthelabourincomeshare.Heclaimsthatimputationsbasedontheassumptionthatproprietorsarecompensatedfortheirlabouratthesameaveragehourlyrateasemployees,asopposedtoaconstantfractionoftheirincomeaccruingtolabour,significantlyimpactsthetrendofthelabourincomeshareintheUS.

Koh,etal(2020)notethatintellectualpropertyproductswerepreviouslyviewedasintermediateinputsbuthavegraduallybeenreclassifiedasinvestments.Thisrevisionreassignsaportionofintermediateinputstogrossvalueadded.

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Fromanarithmeticbasis,thisautomaticallyraisesthevalueofthedenominatorandthereforedecreasesthelabourincomeshare.Subsequently,theyarguethattheimplicitcapitalisationofintellectualpropertyproductsisthemaindriveroftheobserveddeclineinthelabourincomeshare.

ThispaperfallsintotheaccountingstrandoftheliteratureandbuildsontheworkofArmenter(2015)andMackenzie(2021).However,thefindingsofArmenter(2015)fortheUSeconomyareshowntobereversedfortheUKeconomy.

ExtendingthesectoralbasedworkofMackenzie(2021),itisshownthatimputationsbasedontheassumptionthattheself-employedreceivethesameaveragelabourcompensationasemployeeserroneouslyindicatetherehasbeennofallinthelabourincomeshareintheUK.

LabourIncomeShareMethodology

Howshouldweaccountforthelabourportionofself-employedincomewhenestimatingthelabourincomeshare?Theissueliesinseparatingself-employedincomeintoitslabourandcapitalcomponents.However,disentanglingself-employedincomerequiressubjectiveassumptionsregardingsourcesofincomewhicharenotwelldefined.ThefollowingdefinitionisausefulstartingpointforthinkingaboutthelabourincomeshareLIS:

LIS=

WhereCOEiscompensationofemployees,MIismixed(self-employed)incomeandθ∈[0,1]istheshareofself-employedincomewhichaccruestolabour.Yrepresentsgrossvalueadded.

Ascompensationofemployeesrepresentsunambiguouslabourincomeandmixedincomerepresentsambiguouscapital/labourincome,anyinternallyconsistentmeasureisboundbytheextremecasesofθ=0andθ=1.Theseloweranduppervaluesrepresenttheproductionboundary.

Twocommonmethodsforimputingself-employedlabourincomearedetailedbelow.ThefirstisfavouredbytheOfficeforNationalsStatisticsintheUK,andthesecondisfavouredbytheBureauofLabourStatisticsintheUS.

Method1:

Astraightforwardmethodforimputingself-employedlabourincomeinvolvesapportioningmixedincomebetweencapitalandlabourinequalproportiontotherestoftheeconomy.Simplyput,thisassumesthattherelativereturnstolabourandcapitalarethesameforthosewhoareemployedandself-employed(thelabourincomeshareisthesameintheincorporatedandunincorporatedsectoroftheeconomy).

COE+GOS

LIS1=COE

Pros:Method1bindsitsestimatesinsidetheproductionboundarybyonlyusingdatafromthenationalincomeaccountingidentity.Labourincomefortheself-employedcannotexceedtotalself-employedincome.

Cons:Method1doesnotdirectlyadjustforanychangesinthequantityofself-employedpeople,orthenumberofhoursworked(therelativereturnsareassumedtobeunaffectedbytheratio

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ofemployeestoself-employedintheeconomy).Whilethisisnotinherentlyanissue,onthesurface,itappearssomewhatna?ve.

Method2:

Anothermethodforimputingself-employedlabourincomeinvolvesestimatingaverage

employeecompensationandscalingituptothetotalworkforce.Thisassumesthattheself-

employedarecompensatedfortheirlabouratthesameaveragehourlyrateasemployees(thereturntolabourisequalintheincorporatedandunincorporatedsectors).

LIS2=

WhereEisthetotalnumberofhoursworkedbyemployeesandPisthetotalnumberofhoursworkedbytheself-employed(proprietors).

Pros:Adjustsattheextensiveandintensivemarginfortherelativehoursworkedbyemployeesandproprietors.

Cons:Itdoesnotbindestimatesinsidetheproductionboundaryasitmakesnodirectreferencetomixed(self-employed)income.Itisabletoimputeavalueofself-employedlabourincomewhichexceedstotalself-employedincome.

BothmeasuresofthelabourincomeshareareillustratedinFigure1withtheproductionboundaryshadedingrey.Thisarearepresentsthefeasibleregionforvaluesofthelabourincomeshare.Thelowerboundassumesthatallmixedincomeaccruestocapitalθ=0whiletheupperboundassumesthatallmixedincomeaccruestolabourθ=1.

Figure1:LabourIncomeShareMeasures1955Q1to2021Q4

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Method1requiresonlynationalaccountsdataandthereforehasalengthyhistoricalseriesfrom1955Q1to2021Q4.Theseriesdisplayssomestability,withthelabourincomesharehoveringaround0.65untilthemid-1970s.Afterwhich,thereisanotablespikeandthenaprotracteddeclineuntilthelate1990s.Fromaroundthemillenniumonwards,thelabourincomesharethenrecoversandstabilisesaround0.6.

Meanwhile,detaileddataonhoursworkedfortheself-employedlimitsourseriesformethod2fromtheearly1990sonwards.Bothmeasuresexhibitsimilarrelativemovementswithonlyminimalsignsofdivergence.Moreover,method2suggestsaslightlygreaterrecoveryinthelabourincomeshareafter2000,withahigheraveragevalueoverall,around0.63.

However,theLIS2seriessometimesexceedsthefeasibleproductionboundary(shadedgreyarea).Thismeansthatmethod2createsameasurewherebyimputedself-employedlabourincomeexceedstotalself-employedincome.

Subsequently,inpractice,wecanconcludethataverageemployeecompensationperhourworkedmustbesignificantlyhigherforthosewhoareemployedrelativetothosewhoareself-employed.

However,bothmethodsoutlinedaboveimposeimputationassumptionsuniformlyacrossallsectorsoftheeconomy.Thisisarestrictiveassumptionasitimpliesthatallself-employedpeoplesharethesamesplitbetweentheircapitalandlabourincome,regardlessofthesectorinwhichtheywork.

Anaturalsolutiontothisissueistoperformimputationsatthesectorlevelandthenaggregateuptothewholeeconomy.Thisincreasedgranularitycanaccountfortheheterogeneityacrosssectorsandthereforereduceinaccuraciesassociatedwithaggregateimputations.

ISIC4Disaggregation

Methods1and2areappliedusingISIC4dataforsectorsAthroughT.Wethencomparetheaggregateapproachwiththedisaggregatedapproach(superscriptD).

Method1(Disaggregated):

Method1imputationisperformedatthesectorlevel,wheresubscriptsdenoteISIC4sectorclassificationsj=A,...,T.ThelabourincomeshareineachsectoristhenweightedbyitsrelativeshareofoutputinthewholeeconomyYj/Ytoreflectthesectoralcompositionofvalueaddedintheaggregateeconomy:

LIS=+?+

Theassumptionformethod1(disaggregated)isthattherelativereturnstocapitalandlabourarethesameforthosewhoareemployedandself-employedineachsector.Thismeansthattherelativereturnstolabourfortheself-employedarepermittedtovaryacrosseachsector(reflectingthevariousproductionstructuresacrossdifferentsectorsoftheeconomy).

Method2(Disaggregated):

Applyingthesamenotation,Method2imputationisperformedatthesectorlevel.HoursworkedbyemployeesEjandproprietorspjineachsectorareobtainedfromthequarterly

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LabourForceSurvey.Thelabourincomesharesineachsectorarethenweightedandsummedinthesamemannerasabovetoobtaintheaggregatemeasure:

LIS=(CAEAPA)+?+(CTETPT)

Theassumptionformethod2(disaggregated)isthatineachsectortheself-employedarecompensatedfortheirlabouratthesameaveragehourlyrateasemployees.Thehourlyrateofcompensationispermittedtovaryacrosssectors,reflectingthevariationinaveragehourlywagecommandedbyworkersindifferentsectors.

ThedisaggregatedapproachesareappliedandplottedbelowinFigure2indashedlines,alongsidetheseriesfromFigure1.Thisallowsustoclearlyobservetheimpactofthedisaggregatedimputationofself-employedlabourincomeoneachmeasureofthelabourincomeshare.

ISIC4sectorlevelnationalaccountsdataonlyextendsbackto1997Q1.Therefore,inFigure2,wefocusonashortertimeframetoclearlydemonstratehowdisaggregationaffectsboth

methods.

Figure2:LabourIncomeShareMeasures1992Q2to2021Q4

Ascanbeseen,method1and2behavequitedifferentlywhensubjecttoimputationatthesectorlevel.LISyieldslowervalueswhiletheLISyieldsnotablyhighervalues,onaverage.

Subsequently,thesecondmethodunderdisaggregationsuggestsanotablerecoveryinthelabourincomeshareafter2000.However,uponinspectionwecanseethatthefrequencyatwhichtheproductionboundaryisviolatedundermethod2disaggregationisamplified,ratherthanreduced.Thiscanonlyleadustoconcludethatmethod2producesaspuriousmeasureofthelabourincomeshareintheUKanderroneouslyoverestimatesitstruevalue.

Tofurtheranalysetheseeffectsasetofafewdescriptivestatisticsforeachseriesaredetailed:

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Table1:DescriptiveStatistics1997Q1to2021Q4

DescriptiveStatistics

LIS1

LIS

LIS2

LIS

Mean

0.595

0.591

0.626

0.644

Median

0.597

0.592

0.628

0.647

StandardDeviation

0.014

0.013

0.013

0.015

Range

0.073

0.070

0.064

0.074

Autocorrelation

0.785

0.779

0.710

0.801

Overall,theimpactofthedisaggregatedimputationformethod1isminor.However,overtime,agrowinggapappearsbetweenLIS1andLIS.Thissuggestsincreasingheterogeneityintherelativefactorreturnsforproprietorsacrossdifferentsectorsoftheeconomy.

Moreover,fromTable1itcanbeobservedthatdisaggregationreducesthestandarddeviationandrangeformethod1,whileincreasingtheserialcorrelationoftheseries.Therefore,disaggregationmarginallyincreasesthestabilityofthelabourincomeshare.

Thedisaggregatedimputationundermethod2alsoincreasestherangeandstandarddeviationoftheseriesnotably.However,thisincreasecanbeattributedtoaclearupwardbiasasthefrequencyofexceedingthefeasibleregionisamplified.

Thisimpliesthataveragehourlyself-employedlabourcompensationissignificantlylowerthanaverageemployeecompensationinsectorswhichhaverelativelylargeroutputshares.Thisiscorroboratedbythefollowingscatterplot:

Figure3:AverageISIC4sectorsizeandself-employedtoemployeerelativereturns

Sectorswithlargersharesofoutputingrossvalueaddedtendtohaveahigherrelativehourlyreturntolabourforemployees.Subsequently,imputationswhichdonotaccountforthiscross-sectorheterogeneitycanmistakenly‘overweight’thesectorswherehourlyreturnstotheself-employedarerelativelygreater.

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Conclusion

ThispaperexplorestwocommonmeasuresofthelabourincomeshareandappliesthemtotheUK.Moreover,itprovidesnovelestimatesofthelabourincomeshareusingadisaggregatedapproach,utilisingLabourForceSurveyandISIC4sectorleveldata.Thefindingsaretwofold.

Firstly,thecarefultreatmentofself-employed(proprietor)incomesuggeststherehasbeenadeclineintheUKlabourincomeshare.However,thisoccurredinthelastquarterofthe20thcenturyandtherecoveryafterthemillenniumwasmodest.

Secondly,imputingself-employedlabourincomeviaaveragehourlyemployeecompensationfortheUKeconomyshouldbeavoidedunlesscompellingempiricalevidencestatesotherwise.Thegranularapproachemployedherehasuncoveredsystematicinconsistenciesinmethod2whensubjecttodisaggregation.

Thevalidityofmethod2hasthereforeshowntobeinaccuratefores