The Rise and Decline of General Laws of Capitalism

NBER WORKING PAPER SERIES

THE RISE AND DECLINE OF GENERAL LAWS OF CAPITALISM

Daron Acemoglu

James A. Robinson

Working Paper 20766 http://www.nber.org/papers/w20766

NATIONAL BUREAU OF ECONOMIC RESEARCH

1050 Massachusetts Avenue Cambridge, MA 02138

December 2014

We thank David Autor, Amy Finkelstein, Johan Fourie, Bengt Holmstrom, Chang Tai Hsieh, Chad Jones, Matthew Kustenbauder, Naomi Lamoureux, Ulrike Malmendier, Kalle Moene, Joel Mokyr, Suresh Naidu, Jim Poterba, Matthew Rognlie, Ragnar Torvik, Laurence Wilse-Samson, Francis Wilson and Timothy Taylor for The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.

NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

© 2014 by Daron Acemoglu and James A. Robinson. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.

The Rise and Decline of General Laws of Capitalism

Daron Acemoglu and James A. Robinson

NBER Working Paper No. 20766

December 2014

JEL No. O20,P16,P48

ABSTRACT

Thomas Piketty's (2014) book, Capital in the 21st Century, follows in the tradition of the great classical economists, like Marx and Ricardo, in formulating general laws of capitalism to diagnose and predict the dynamics of inequality. We argue that general economic laws are unhelpful as a guide to understand the past or predict the future, because they ignore the central role of political and economic institutions, as well as the endogenous evolution of technology, in shaping the distribution of resources in society. We use regression evidence to show that the main economic force emphasized in Piketty's book, the gap between the interest rate and the growth rate, does not appear to explain historical patterns of inequality (especially, the share of income accruing to the upper tail of the distribution). We then use the histories of inequality of South Africa and Sweden to illustrate that inequality dynamics cannot be understood without embedding economic factors in the context of economic and political institutions, and also that the focus on the share of top incomes can give a misleading characterization of the true nature of inequality.

Daron Acemoglu

Department of Economics, E18-269D

MIT

77 Massachusetts Avenue Cambridge, MA 02139 and CIFAR and also NBER daron@mit.edu

James A. Robinson

Harvard University Department of Government N309, 1737 Cambridge Street Cambridge, MA 02138 and NBER jrobinson@gov.harvard.edu

Economistshavelongbeendrawntotheambitiousquestofdiscoveringthegenerallawsof capitalism.DavidRicardo,forexample,predictedthatcapitalaccumulationwouldterminate ineconomicstagnationandinequalityasagreaterandgreatershareofnationalincomeaccrued tolandowners.KarlMarxfollowedhimbyforecastingtheinevitableimmizerizationofthe proletariat.ThomasPikettyís(2014)tome, Capitalinthe21stCentury,emulatesMarxinhis title,hisstyleofexposition,andhiscritiqueofthecapitalistsystem.Pikettyisaftergeneral lawswhichwilldemystifyourmoderneconomyandelucidatetheinherentproblemsofthe systemóandpointtosolutions.

Butthequestforgenerallawsofcapitalismismisguidedbecauseitignoresthekeyforces shapinghowaneconomyfunctions:theendogenousevolutionoftechnologyandtheinstitutions andthepoliticalequilibriumthatináuencenotonlytechnologybutalsohowmarketsfunction andhowthegainsfromvariousdi§erenteconomicarrangementsaredistributed.Despitehis erudition,ambition,andcreativity,Marxwasledastraybecauseofhisdisregardoftheseforces. ThesameistrueofPikettyíssweepingaccountofinequalityincapitalisteconomies.

Inthenextsection,wereviewMarxísconceptualizationofcapitalismandsomeofhis generallaws.WethenturntoPikettyísapproachtocapitalismandhisversionofthegeneral laws.WewillpointtovariousproblemsinPikettyísinterpretationoftheeconomicrelationships underpinninginequality,butthemostimportantshortcomingisthat,thoughhediscussesthe roleofcertaininstitutionsandpolicies,heallowsneitherforasystematicroleofinstitutions andpoliticalfactorsintheformationofinequalitynorfortheendogenousevolutionofthese institutionalfactors.WeillustratethisbyÖrstusingregressionevidencetoshowthatPikettyís centraleconomicforce,therelationshipbetweentheinterestrateandtherateofeconomic growth,isnotcorrelatedwithinequality(inparticular,withthekeyvariablehefocuseson, theshareofnationalincomeaccruingtotherichest1percent,henceforth,thetop1percent share).WethenusetheexamplesoftheSouthAfricanandSwedishpathsofinequalityover the20thcenturytodemonstratetwothings.First,thatusingthetop1percentsharemay missthebigpictureaboutinequality.Second,itisimpossibletounderstandthedynamicsof inequalityinthesesocietieswithoutsystematicallybringingininstitutionsandpolitics,and theirendogenousevolution.Weconcludebyoutlininganalternativeapproachtoinequality thateschewsgenerallawsinfavorofaconceptualizationinwhichbothtechnologyandfactor pricesareshapedbytheevolutionofinstitutionsandpoliticalequilibria,andtheinstitutions themselvesareendogenousandarepartlyináuencedby,amongotherthings,theextentof inequality.Wethenapplythisframeworktotheevolutionofinequalityandinstitutionsin SouthAfricaandSweden.

Weshouldnoteatthispointthatwebelievethetermìcapitalismînottobeausefulone

forthepurposesofcomparativeeconomicorpoliticalanalysis.Byfocusingontheownership andaccumulationofcapital,thistermdistractsfromthecharacteristicsofsocietieswhich aremoreimportantindeterminingtheireconomicdevelopmentandtheextentofinequality. Forexample,bothUzbekistanandmodernSwitzerlandhaveprivateownershipofcapital,but thesesocietieshavelittleincommonintermsofprosperityandinequalitybecausethenature oftheireconomicandpoliticalinstitutionsaresosharplydi§erent.Infact,Uzbekistanís capitalisteconomyhasmoreincommonwiththeavowedlynon-capitalistNorthKoreathan Switzerland,aswearguedinAcemogluandRobinson(2012).Thatsaid,giventheemphasis inbothMarxandPikettyoncapitalism,wehaveoptedtobearwiththisterminology.

CapitalFailures

ThoughmanyimportantideasinsocialsciencecanbetracedtoKarlMarxísoeuvre,his deÖningapproachwastoidentifycertainhard-wiredfeaturesofcapitalismówhatMarxcalled ìgenerallawsofcapitalistaccumulation.îThisapproachwasheavilyshapedbythehistorical contextofthemiddle19thcenturyinwhichMarxlivedandwrote.MarxexperiencedÖrsthandboththebewilderingtransformationofsocietywiththeriseofindustrialproduction,and theassociatedhugesocialdislocations.

Marxdevelopedarichandnuancedtheoryofhistory.Butthecenterpieceofthistheory, ìhistoricalmaterialism,îrestedonhowmaterialaspectsofeconomiclife,togetherwithwhat Marxcalledìforcesofproductionîóparticularlytechnologyóshapedallotheraspectsofsocial,economicandpoliticallife,includingtheìrelationsofproduction.îForexample,Marx famouslyarguedinhis1847book ThePovertyofPhilosophy,thatìthehand-millgivesyou societywiththefeudallord;thesteam-millsocietywiththeindustrialcapitalistî(asreprinted inMcLellan,2000,pp.219-220).Herethehand-millrepresentstheforcesofproductionwhile feudalismrepresentstherelationsofproduction,aswellasaspeciÖcsetofsocialandpolitical arrangements.Whentheforcesofproduction(technology)changed,thisdestabilizedtherelationsofproductionandledtocontradictionsandsocialandinstitutionalchangesthatwere oftenrevolutionaryinnature.AsMarxputitin1859in AContributiontotheCritiqueof PoliticalEconomy (McLellan,2000,p.425):

[T]hesumtotaloftheserelationsofproductionconstitutestheeconomicstructureofsocietyñtherealfoundation,onwhichriselegalandpoliticalsuperstructuresandtowhichcorresponddeÖniteformsofsocialconsciousness.Themodeof productionofmateriallifeconditionsthegeneralcharacterofthesocial,political andspiritualprocessesoflife.Atacertainstateoftheirdevelopmentthematerial forcesofproductioninsocietycomeintoconáictwiththeexistingrelationsofproductionorñwhatisbutalegalexpressionofthesamethingñwiththeproperty

relationswithinwhichtheyhadbeenatworkbefore.Fromformsofdevelopmentof theforcesofproductiontheserelationsturnintofetters.Thencomestheepochof socialrevolution.Withthechangeoftheeconomicfoundationtheentireimmense superstructureismoreorlessrapidlytransformed.

Marxhypothesizedthattheforcesofproduction,sometimesinconjunctionwiththeownershipofthemeansofproduction,determinedallotheraspectsofeconomicandpolitical institutionsóthedejureanddefactolaws,regulations,andarrangementsshapingsociallife.

Armedwiththistheoryofhistory,Marxmadeboldpredictionsaboutthedynamicsofcapitalismbasedjustoneconomicfundamentalsówithoutanyreferencetoinstitutionsorpolitics, whichhegenerallyviewedasderivativeofthepowerfulimpulsesunleashedbytheforcesof production.1

Mostrelevantforourfocusarethreeofthesepredictionsconcerninginequality.InVolume 1,Chapter25of Capital,Marxdevelopedtheideathattheìreservearmyoftheunemployedî wouldkeepwagesatsubsistencelevel,makingcapitalisminconsistentwithsteadyimprovementsinthelivingstandardsofworkers.Hisexactpredictionhereisopentodi§erentinterpretations.ThoughMarxviewedcapitalismastheharbingerofìmisery,agonyoftoil,slavery, ignorance,brutality,mentaldegradationîforworkingmen,itislessclearwhetherthiswas meanttoruleoutrealwagegrowth.Blaug(1997)statesthatMarxneverclaimedthatreal wageswouldbestagnant,butratherthattheshareoflaborinnationalincomewouldfallsince Marxsaysìrealwages...neverriseproportionatelytotheproductivepoweroflabor.îFoley (2008,Chapter3),ontheotherhand,arguesthatMarxdidstartbyassertingthatrealwages wouldnotriseundercapitalism,butthenweakenedthisclaimtoafallinglaborsharewhen herealizedthatwageswereindeedincreasinginEngland.Thismotivatesustostatethislaw inbothastrongandaweakform.

1: TheGeneralLawofCapitalistAccumulation StrongForm:Realwagesarestagnant undercapitalism. WeakForm:Theshareofnationalincomeaccruingtolaborwould fallundercapitalism.

Underitseitherstrongorweakform,thislawimpliesthatanyeconomicgrowthunder

1 ThereisnoconsensusonMarxísexactformulationoftherelationshipbetweentheìsubstructure,îcomprisingproductiveforcesandsometimestherelationsofproduction,andtheìsuperstructureîwhichincludeswhat wecallpoliticalinstitutionsandmostaspectsofeconomicinstitutions.InChapterIofthe CommunistManifesto,MarxandEngelswrotethatìThehistoryofallhithertoexistingsocietyisthehistoryofclassstrugglesî. Buttheideahere,sofarasweunderstand,isnotthatìclassstruggleîrepresentssomeautonomoushistorical dynamic,butratherthatitisanoutcomeofthecontradictionsbetweentheforcesofproductionandtheownershipofthemeansofproduction.Insomewritings,suchas TheEighteenthBrumaireofLouisNapoleon,Marx alsoallowedforfeedbackfrompoliticsandotheraspectsofsocietytotheforcesofproduction.Butitisclear fromhisworkthatheregradedthisassecondorder(seeSinger,2000,Chapter7foradiscussionofthis).Marx neverformulatedanapproachinwhichinstitutionsplaythecentralroleandthemselvesendogenouslychange.

capitalismwouldalmostautomaticallytranslateintogreaterinequalityóascapitalistsbeneÖt andworkersfailtodoso.

InVolumeIIIof Capital,Marxproposedanothergenerallaw:

2: TheGeneralLawofDecliningProÖt:ascapitalaccumulates,therateofproÖtfalls.

Thesetwolawscamealongwithathird,lessoftenstressedbuthighlyrelevant,lawpresentedinVolumeIof Capital:

3: TheGeneralLawofDecreasingCompetition:capitalaccumulationleadstoincreasedindustrialconcentration.

Marxísgenerallawsdidnotfarewell,however.AsMarxwaswriting,realwages,whichhad previouslybeenfallingorconstant,hadalreadybeenrising,probablyforabouttwodecades (Allen,2001,2007,2009a;Clark,2005;Feinstein,1998).Theshareoflaborinnationalincome, whichhadfallentounder50%by1870,alsostartedtoincreasethereafter,reaching2/3inthe 20thcentury.Allenís(2009a)calculationoftherealrateofproÖtsuggeststhattheproÖtrate wascomparativelylowattheendofthe18thcenturyandroseuntilaround1870reachinga maximumof25%,butthenfellbacktoaround20%whereitstabilizeduntilWorldWarI. Matthews,FeinsteinandOdling-Smee(1982,pp.187-188)suggestthattheseratesdidnot fallinthe20thcentury,thoughthereisalotofheterogeneityacrosssectors.(Thethirdlawís performancewasnobetteraswediscussbelow).

WhydidMarxísgenerallawsfail?Mostlybecausetheyignoredboththeendogenous evolutionoftechnology(despitehisgreatemphasisontheforcesofproduction)andtheroleof institutionsandpoliticsthatshapemarkets,pricesandthepathoftechnology.Theincrease inrealwagesinBritain,forexample,wasinpartaconsequenceofthechangeinthepace andnatureoftechnologicalchange,rapidlyincreasingthedemandforlabor(Crafts1985; Allen2009b;Mokyr2012).ItwasalsoaconsequenceoftheradicalpoliticalchangesBritain underwentatthetime,whichbothináuencedtechnologyanddirectlyimpactedwages.The rationalizationofpropertyrights,dismantlingofmonopolies,investmentininfrastructure,and thecreationofalegalframeworkforindustrialdevelopmentincludingthepatentsystemwere amongtheinstitutionalchangescontributingtorapidtechnologicalchangeanditswidespread adoptionintheBritisheconomy(AcemogluandRobinson,2012;Mokyr,2012).

Thedistributionofthegainsfromnewtechnologieswasalsoshapedbyanevolvinginstitutionalequilibrium.TheIndustrialRevolutionwenthand-in-handwithmajorpoliticalchanges, includingthedevelopmentofthestateandtheReformActsof1832,1867,and1884,which transformedBritishpoliticalinstitutionsandthedistributionofpoliticalpower.Forexample, in1833aprofessionalfactoryinspectoratewassetup,enablingtheenforcementoflegislation

onfactoryemployment.Thepoliticalfalloutofthe1832democratizationalsoledin1846to therepealoftheCornLawsówhichweretari§slimitingimportsoflower-pricedforeigncorn, loweringthepriceofbread,raisingrealwages,andsimultaneouslyundermininglandrents (Schonhart-Bailey,2006).TheFactoryActof1847tooktheradicalstepoflimitingworking hoursinthetextilemillsto10hoursperdayforwomenandteenagers.TheReformActof1867 ledtotheabolitionoftheMastersandServantsActsin1875ówhichhadimposedonworkers legally-enforceabledutiesofloyaltyandobedience,andlimitedmobilityówasanexampleof pro-workerlabormarketlegislationthatincreasedrealwages(NaiduandYuchtman,2013).

AnothertellingexampleisthefailureofMarxísthirdgenerallawintheUnitedStates:the predictionofincreasedindustrialconcentration.AftertheendoftheCivilWarcametheage oftherobberbaronsandthehugeconcentrationofeconomicownershipandcontrol.Bythe endofthe1890s,companiessuchasDuPont,EastmanKodak,StandardOilandInternational Harvestercametodominatetheeconomy,inseveralcasescapturingmorethan70percentof theirrespectivemarkets(Lamoreaux,1986,pp.3-4).ItlookedlikeaMarxianpredictioncome true.

Exceptthatthissituationwasonlytransitoryandwasdulyreversedaspopularmobilization,inparttriggeredbytheincreaseininequality,changedthepoliticalequilibriumand theregulationofindustry(Sanders,1999).Thepoweroflargecorporationsstartedbeing curtailedwiththeInterstateCommerceActof1887andthentheShermanAnti-TrustAct of1890,whichwereusedintheearly20th-centurytrust-bustinge§ortsagainstDuPont,the AmericanTobaccoCompany,theStandardOilCompanyandtheNorthernSecuritiesCompany,thencontrolledbyofJ.P.Morgan.Thereformscontinuedwiththecompletionofthe break-upofStandardOilin1911,andtheratiÖcationoftheSixteenthAmendmentin1913, whichintroducedtheincometax,andtheClaytonAnti-TrustActin1914andthefoundingof theFederalTradeCommission.Thesechangesnotonlystoppedfurtherindustrialconcentrationbutreversedit(CollinsandPreston1961;Edwards1975).White(1981)showsthatU.S. industrialconcentrationinthepost-WorldWarIIperiodchangedlittle(seeWhite,2002,for anupdate).

Crucially,thepoliticalprocessthatledtotheinstitutionalchangestransformingtheBritish economyandinequalityinthe19thcenturywasnotaforgoneconclusion.Norwastherisein inequalityintheUnitedStatesaftertheCivilWaraninevitableconsequenceofcapitalism.Its reversalstartingintheearly1900swasequallydependentonanevolvinginstitutionalequilibrium.Infact,whilethepowerofmonopolyandinequalitywerebeingcurtailedintheUnited States,inequalitycontinuedtoincreaserapidlyinneighboringMexicoundertheauthoritarian ruleofPorÖrioDiaz,culminatinginrevolutionandcivilwarin1910,anddemonstratingthe centralroleoftheendogenousandpath-dependentevolutionofinstitutions.

ThefailureofMarxísgenerallawswasforthesamereasonthatotherpreviousgeneral lawsbyeconomistsperformedpoorly.Theselawswereformulatedinane§orttocompress thefactsandeventsoftheirtimesintoagrandtheoryaimingtobeapplicableatalltimes andplacesówithlittlereferencetoinstitutionsandthe(partlyinstitutionally-determined) changingnatureoftechnology.Forexample,whenDavidRicardopublishedtheÖrstedition of OnthePrinciplesofPoliticalEconomyandTaxation in1817,andpredictedthatarising shareofnationalincomewouldaccruetoland,hehadindeedbeenlivingthroughaperiodof rapidlyrisinglandrentsinBritain.Butsoonthereafter,theshareofnationalincomeaccruing tolandstartedamonotonicdecline,andbythe1870srealrentsstartedarapidfallwhich wouldlastforthenext60years(Beckett,TurnerandAfton1999;Clark2002,2010).

Inshort,Marxísgenerallaws,likethosebeforehim,failedbecausetheyreliedonaconceptionoftheeconomythatdidnotrecognizetheendogenousevolutionoftechnologyandtherole ofchangingeconomicandpoliticalinstitutions,shapingbothtechnologyandfactorprices.In fact,evenMarxísemphasisonthedeÖningroleoftheforcesofproduction,soemblematicof hisapproach,wasofteninadequatenotonlyastheengineofhistory,butalsoasadescription ofhistory,includinghisparadigmaticexampleofhand-millsandsteam-mils.Forexample, Bloch(1967)arguedpersuasivelythatthehand-milldidnotdeterminethenatureoffeudal society,nordidthesteam-milldeterminethecharacterofthepost-feudalworld.

Seeking21st-CenturyLawsofCapitalism

ThomasPikettyisalsoaneconomistofhismilieu,withhisthinkingheavilycoloredbyincreasinginequalityintheAnglo-SaxonworldandmorerecentlyincontinentalEuropeóandin particularcomparedtothemoreequaldistributionoflaborandtotalincomesseeninFrance inthe1980sand1990s.Alargeliteratureinlaboreconomicshaddonemuchtodocument anddissecttheincreaseininequalitythatstartedsometimeinthe1970sintheUnitedStates (seethesurveysandtheextensivereferencestoearlierworkinKatzandAutor,1999,and AcemogluandAutor,2011).Thisliteraturehasdemonstratedthattheincreaseininequality hastakenplacethroughouttheincomedistribution,andthatitcanbeexplainedreasonably wellbychangesinthesupplyanddemandforskillsandinlabormarketinstitutions.Piketty andSaez(2003)broughtanewandfruitfulperspectivetothisliteraturebyusingdatafrom taxreturns,conÖrmingandextendingthepatternsthepreviousliteraturehaduncovered,and placingaheavyemphasisonriseininequalityattheverytopoftheincomedistribution.

In Capitalinthe21stCentury,Pikettygoesbeyondthisempiricalandhistoricalapproach too§eratheoryofthelong-runtendenciesofcapitalism.ThoughPikettyísdataconÖrmthe Öndingofthepreviousliteraturethatwideninginequalityinrecentdecades,atleastinadvancedeconomies,hadbeendrivenbyrisinginequalityoflaborincomes,hisbookpaintsa

futuredominatedbycapitalincome,inheritedwealthandrentierbillionaires.Thetheoretical frameworkusedtoreachthisconclusionisamixofMarxianeconomicswithSolowísgrowth model.PikettydeÖnescapitalisminthesamewaythatMarxdoes,andhasasimilarlymaterialistapproachlinkingthedynamicsofcapitalismtotheownershipofthemeansofproduction (inparticularcapital)andtheironcladnatureoftechnologyandexogenousgrowthdynamics. ItistruethatPikettysometimesmentionspoliciesandinstitutions(forexample,thewealth taxandthemilitaryandpoliticaldevelopmentsthatdestroyedcapitalandreducedtheratio ofwealthtoincomeduringtheÖrsthalfofthe20thcentury).Buttheirroleisadhoc.Our argumentisthat,toexplaininequality,thesefeaturesandtheirendogenousevolutionhaveto besystematicallyintroducedintotheanalysis.

ThisapproachshapesPikettyísanalysisandpredictionsaboutthenatureofcapitalism. Capitalinthe21stCentury startsbyintroducingtwoìfundamentallaws,îbutthemore majorpredictionsáowfromwhatPikettycallsaìfundamentalforceofdivergenceî(p.351) orsometimestheìfundamentalinequalityî(p.25),comparingthe(real)interestrateofthe economytothegrowthrate.

TheÖrstfundamentallawisjustadeÖnition:

capitalshareofnationalincome = r K Y ; where r isnetrealrateofreturnoncapital(therealinterestrate), K isthecapitalstock,and Y isGDP(orequivalently,nationalincomeastheeconomyistakentobeclosed).

Thesecondfundamentallawisslightlymoresubstantial.Itstatesthat

K Y = s g ; where s isthesavingrateand g isthegrowthrateofGDP.Asweexplainintheonlineappendix (availablewiththispaperathttp://e-jep.org),aversionofthislawdoesindeedfollowreadily fromthesteadystateofaSolow-typemodelofeconomicgrowth(butseeKrusellandSmith, 2014,andRay,2014).Atanintuitivelevel,thegrowthrateofthecapitalstock K willbegiven bynetinvestment,whichinaclosedeconomyisequaltosaving, sY .Thustheratio K=Y will reáectthechangein K tothechangein Y overtimeduetoeconomicgrowth, s=g

LetusfollowPikettyhereandcombinethesetwofundamentallawstoobtain

capitalshareofnationalincome = r s g Pikettypositsthat,evenas g changes, r and s canbetakentobeapproximateconstants(or notchangeasmuchas g).ThisthenleadstowhatcanbethoughtofashisÖrstgenerallaw, thatwhengrowthislower,thecapitalshareofnationalincomewillbehigher.

ThisÖrstlawisnotascompellingasonemightatÖrstthink,however.Afterall,onemust considerwhetherachangeinthegrowthrate g mightalsoalterthesavingrate s ortherate

ofreturn r sincealltheseareallendogenousvariableswhicharelinkedinstandardmodelsof economicgrowth.Pikettyarguesthat r shouldnotchangemuchinresponsetoadeclinein g, becausetheelasticityofsubstitutionbetweencapitalandlaborishigh,resultinginanincrease inthecapitalshareofnationalincome.2

However,thevastmajorityofexistingestimatesindicateashort-runelasticityofsubstitutionsigniÖcantlylessthanone(forexample,Hamermesh,1993,Mairesse,HallandMulkay, 1999,Chirinko,FazzariandMeyer,1999,Krusell,Ohanian,Rios-Rull,andViolante,2000, Chirinko,1993,Antras,2004,Klump,McAdamandWillman,2007,OberÖeldandRaval, 2014).Thisisalsotheplausiblecaseonintuitivegrounds:giventechnology,theabilityto substitutecapitalforlaborwouldbelimited(forexample,ifyoureducelabortozero,fora givenproductionprocess,onewouldexpectoutputtofalltozeroalso).Thoughthiselasticity couldbehigherinlongerhorizons,Chirinko(2008)andChirinkoandMallick(2014)Önditto besigniÖcantlylessthanonealsointhelongrun.Onereasonwhythelong-runelasticityof substitutionmightbegreaterthan1istheendogeneityoftechnology(e.g.,Acemoglu,2002, 2003).Inthiscontext,itisworthnotingthattheonlyrecentpaperestimatinganelasticity ofsubstitutiongreaterthan1,KarabarbounisandNeiman(2014),useslong-runcross-country variationrelatedtochangesininvestmentprices,makingtheirestimatesmuchmorelikelyto correspondtoendogenous-technologyelasticities.Nevertheless,asRognlie(2014)pointsout, evenanelasticityofsubstitutionsigniÖcantlygreaterthan1wouldnotbesu¢cienttoyield oftheconclusionsthatPikettyreaches.

Moreover,thoughitistruethattherehasbeenariseinthecapitalshareofnationalincome, thisdoesnotseemtoberelatedtotheforcesemphasizedin Capitalinthe21stCentury.In particular,Bonnet,Bono,ChapelleandWasmer(2014)demonstratethatthisriseinthecapital shareisduetohousingandtheincreasedpriceofrealestate,sheddingdoubtonthemechanism Pikettyemphasizes.

Thesecondgenerallawof Capitalinthe21stCentury isformulatedas r>g; statingthatthe(real)interestrateexceedsthegrowthrateoftheeconomy.Theoretically,in aneconomywithanexogenoussavingrate,orwithoverlappinggenerations(e.g.,Samuelson, 1958,Diamond,1965),orwithincompletemarkets(e.g.,Bewley,1983,Aiyagari,1994),the interestrateneednotexceedthegrowthrate.Itwilldosoinaneconomythatis dynamically e¢cient,meaninginaneconomyinwhichitisimpossibletoincreasetheconsumptionatall 2 However,theinterestrateandthegrowthratearelinkedfromboththehouseholdsideandtheproduction side.Forexample,witharepresentativehousehold,wehavethat r = g + ,where istheinverseofthe intertemporalelasticityofsubstitutionand isthediscountrate.Thefactthattherepresentativehousehold assumptionmaynotbeagoodapproximationtorealitydoesnotimplythat r isindependentof g.Onthe productionside, g a§ects r throughitsimpactonthecapitalstock,anditisthesecondchannelthatdepends ontheelasticityofsubstitutionbetweencapitalandlabor.

dates(thusachievingaParetoimprovement).Whetheraneconomyisdynamicallye¢cient isanempiricalmatter(Geerolf,2013,forexample,suggeststhatseveralOECDeconomies mightbedynamicallyine¢cient),anddynamicine¢ciencybecomesmorelikelywhenthe capital-outputratioisveryhighas Capitalinthe21stCentury predictsittobeinthefuture.

Finally,Pikettyísthirdandmostimportantgenerallawisthatwhenever r>g,therewill beatendencyforinequalitytodiverge.Thisisbecausecapitalincomewilltendtoincreaseat therateofinterestrate, r,whilenationalincome(andtheincomeofnon-capitalists)increases attherate g.Becausecapitalincomeisunequallydistributed,thiswilltranslateintoacapitaldrivenincreaseininequality,takingusbacktotheageofJaneAustenandHonorÈBalzac.In thewordsofPiketty:

ìThisfundamentalinequality[r>g]...willplayacrucialroleinthisbook.In asense,itsumsuptheoveralllogicofmyconclusions.

WhentherateofreturnoncapitalsigniÖcantlyexceedsthegrowthrateofthe economy...,thenitlogicallyfollowsthatinheritedwealthgrowsfasterthanoutput andincome.î(pp.25-26).

Heelaboratesthislater,writing:ìTheprimaryreasonforthehyperconcentrationofwealth intraditionalagrariansocietiesandtoalargeextentinallsocietiespriortoWorldWarI...is thattheseverylow-growthsocietiesinwhich[sic]therateofreturnoncapitalwasmarkedly anddurablyhigherthantherateofgrowthî(p.351),andproposinganexplanationforthe riseininequalityoverthenextseveraldecades:

ì...Thereasonwhywealthtodayisnotasunequallydistributedasinthepast issimplythatnotenoughtimehaspassedsince1945î(p.372).3

AswiththeÖrsttwogenerallaws,therearethingstoquibblewithinthepureeconomics ofthethirdgenerallaw.First,asalreadymentioned,theemphasison r g sitssomewhat uneasilywiththecentralrolethatlaborincomehasplayedintheriseininequality.Second, asweshowintheonlineappendix, r>g isfullyconsistentwithconstantorevendeclining inequality.Third, r g cannotbetakenasaprimitiveonwhichtomakefutureforecasts,as boththeinterestrateandthegrowthratewilladjusttochangesinpolicy,technologyandthe capitalstock.Finally,inthepresenceofamodestamountofsocialmobility,evenverylarge

3 Itisunclearwhether r>g isaforcetowardsdivergenceofincomesacrossthedistributionofincome,or towardsconvergencetoanewandmoreunequaldistributionofincome.Inmanyplaces,includingthosewehave alreadyquoted,Pikettytalksofdivergence.Butelsewhere,thepredictionisformulateddi§erently,forexample, whenhewrites:ìWiththeaidofafairlysimplemathematicalmodel,onecanshowthatforagivenstructure of...[economicanddemographicshocks]...,thedistributionofwealthtendstowardsalong-runequilibriumand thattheequilibriumlevelofinequalityisanincreasingfunctionofthegap r g betweentherateofreturnon capitalandthegrowthrate.î(p.364).Intheonlineappendix,wediscussavarietyofeconomicmodelslinking r g toinequality.

valuesof r g donotleadtodivergenceatthetopofthedistribution(asweshowintheonline appendix).

Butourmajorargumentisaboutwhattheemphasison r>g leavesoutóinstitutionsand politics.Pikettylargelydismissestheimportanceofinstitutionsagainstthecrushingforceof thefundamentalinequality,writing

ì...thefundamentalinequality r>g canexplaintheveryhighlevelofcapital inequalityobservedinthenineteenthcentury,andthusinasensethefailureof theFrenchrevolution....Theformalnatureoftheregimewasoflittlemoment comparedwiththeinequality r>g.î(p.365).

Inpassing,weshouldnotethattheavailableempiricalevidence,however,suggeststhatthe FrenchRevolutionnotonlyledtoadecreaseininequality(MorrissonandSnyder,2000),but alsoprofoundlychangedthepathofinstitutionalequilibriaandeconomicgrowthinEurope (Acemoglu,Cantoni,JohnsonandRobinson,2011).

Ifthehistoryofgrandpronouncementsofthegenerallawsofcapitalismrepeatsitselfó perhapsÖrstastragedyandthenfarceasMarxcolorfullyputitóthenwemayexpectthesame sortoffrustrationwithPikettyíssweepingpredictionsastheyfailtocometrueinthesame waythatthoseofRicardoandMarxsimilarlyfailedinthepast.Wenextprovideevidence suggestingthatthisisinfactquitelikelyaseventheexistingevidencegoesagainstthese predictions.

Cross-CountryDataon r>g andTop-LevelInequality

ThemajorcontributionofPiketty,mostlytogetherwithEmmanuelSaez,hasbeentobringto thetableahugeamountofnewdataoninequality(PikettyandSaez,2003).Thereadermay comeawayfromthesedatapresentedatlengthinPikettyísbookwiththeimpressionthatthe evidencesupportinghisproposedlawsofcapitalismisoverwhelming.However,Pikettydoes notpresentevenbasiccorrelationsbetween r g andchangesininequality,muchlessany explicitevidenceofacausale§ect.Therefore,asaÖrststepweshowthatthedataprovide littlesupportforthegenerallawsofcapitalismheadvances.

Webeginbyusingasadependentvariablethetop1percentshare(seeAtkinsonand PikettyísWorldTopIncomesDatabaseathttp://topincomes.parisschoolofeconomics.eu/).We combinethisvariablewithGDPdatafromMadisonísdataset.FortheÖrstpartofouranalysis wherewedonotuseexplicitdataoninterestratesthisgivesusanunbalancedpanelspanning 1870-2012,andthereafterourpanelcoversthepost-warperiod(andusesGDPdatafromthe PennWorldTables).4

4 ThenumberofcountriesvariesdependingonthemeasureoftheinterestrateusedandspeciÖcation.In

Weusethreedi§erentmeasuresof r g.First,weassumethatallcapitalmarketsareopen andallofthecountriesinthesamplehavethesame(possiblytime-varying)interestrate.Under thisassumption,cross-countryvariationin r g willcomeonlybecauseofvariationinthe growthrate, g.TheÖrstthreecolumnsinPanelAofthistablethensimplyexploitvariationin g usingannualdata(thatis,weset r g = g bynormalizing r =0).Throughout,thestandard errorsarecorrectedforarbitraryheteroscedasticityandserialcorrelationatthecountrylevel, andbecausethenumberofcountriesissmall(varyingbetween18and28),theyarecomputed usingthepairs-clusterbootstrapprocedureproposedbyCameron,GelbachandMiller(2008), whichhasbetterÖnite-samplepropertiesthanthecommonly-usedclusteredstandarderrors. (Thesameresultswithëtraditionalístandarderrorsthatassumenoheteroscedasticityand residualserialcorrelationarereportedinAppendixTableA1andshowverysimilarpatterns).

Incolumn1,welookattherelationshipbetweenannualtop1percentshareandannualgrowth inaspeciÖcationthatincludesafullsetofyeardummiesandcountrydummiesósothatpure time-seriesvariationattheworldlevelispurgedbyyeardummiesandnoneoftheresultsrely oncross-countrycomparisons.PikettyístheorypredictsapositiveandsigniÖcantcoe¢cient onthismeasureof r góincountrieswithhigher g,theincomesofthebottom99percent willgrowmore,limitingthetop1percentshare.5 Instead,weÖndanegativeestimatethatis statisticallyinsigniÖcant.

Incolumn2,weincludeÖveannuallagsoftop1percentshareontheright-handsideto modelthesigniÖcantamountofpersistenceinmeasuresofinequality.ThoughspeciÖcations thatincludethelaggeddependentvariableontheright-handsidearepotentiallysubjectto theNickel(1981)bias,giventhelengthofthepanelherethisisunlikelytobeanissue(since thisbiasdisappearsasthetimedimensionbecomeslarge).Thetestatthebottomofthetable showsthatlaggedtop1percentshareisindeedhighlysigniÖcant.Inthiscase,theimpactof r g isnegativeandsigniÖcantat10percentótheoppositeofthepredictionof Capitalinthe 21stCentury.Column3includesÖveannuallagsofGDPaswellasÖvelagsoftop1percent columns1-3PanelA,wehave27countries,Argentina,Australia,Canada,China,Colombia,Denmark,Finland, France,Germany,India,Indonesia,Ireland,Italy,Japan,Malaysia,Mauritius,Netherlands,NewZealand, Norway,Portugal,Singapore,SouthAfrica,Spain,Sweden,Switzerland,UnitedKingdom,andUnitedStates. Incolumn2PanelB,weloseChinaandColombia,andadditionallyPortugalincolumn3.Incolumn4PanelA, welosethenon-OECDcountries,China,Colombia,India,Indonesia,Malaysia,MauritiusandSingaporerelative tocolumns1-3,andadditionallyGermanyincolumns5and6.InPanelB,weadditionallylosePortugalin columns4and5,andPortugalinGermanyincolumn6.Incolumn7PanelB,wehaveUruguayinadditionto the27countriesincolumn1.Incolumns8and9,weloseGermanyandUruguay.InPanelB,weloseUruguay incolumn7relativetoPanelA,andadditionallyChinaandColombiaincolumn8,andArgentina,China, Colombia,IndonesiaandPortugalincolumn9.

5 Withreturnstocapitalincomedeterminedintheglobaleconomy,i.e., rit = rt (where i referstocountry and t thetimeperiod),variationin rt isfullyabsorbedbythetimee§ectsintheseregressionmodels,making the r =0 normalizationwithoutanylossofgenerality.Note,however,thatwhatdeterminesthedynamics ofinequalityinacountryaccordingtoPikettyísgenerallawisthatcountryísgrowthrate,supportingthe methodologyhere,whichexploitscountry-speciÖcvariationingrowthrates(conditionaloncountryandtime Öxede§ects).

sharesimultaneously.Thereisoncemorenoevidenceofapositiveimpactof r g ontop inequality.Onthecontrary,therelationshipisagainnegative,asshownbytheÖrstlagand alsobythelong-runcumulativee§ectreportedatthebottom.

WhatmattersforinequalitymaynotbeannualorÖve-yearvariationsexploitedinPanel A,butlonger-termswingsin r g.PanelBturnstoinvestigatethispossibilitybylookingat 10-year(columns1and2)and20-yeardata(column3).6 ThesespeciÖcationsdonotprovide anyevidenceofapositiverelationshipbetweenthismeasureof r g andtop1percentshare either.

Incolumns4-6inPanelA,weworkwithadi§erentmeasureof r g basedontherealizedinterestrateconstructedfromdataonnominalyieldsoflong-termgovernmentbonds andináationratesfromtheOECD.Therelationshipisagainnegativeandnowstatistically signiÖcantat5percentincolumns4and5andat10percentincolumn6.InPanelB,when weuse10-and20-yearpanels,therelationshipcontinuestobenegativebutisnowstatistically insigniÖcant.

Oneconcernwiththeresultsincolumns4-6isthattherelevantinterestrateforthevery richmaynotbetheoneforlong-termgovernmentbonds.Motivatedbythis,columns7-9 utilizetheprocedureproposedbyCaselliandFeyrer(2007)toestimatetheeconomy-wide marginalproductofcapitalminusthedepreciationrateusingdataonaggregatefactorsof production,andconstruct r g usingtheseestimates.Nowtherelationshipismoreunstable. InsomespeciÖcationsitbecomespositive,butisneverstatisticallysigniÖcant.

AppendixTablesA2andAyshowthattheseresultsarerobusttoincluding,additionally, GDPpercapita(asanothercontrolforthebusinesscycleanditsimpactonthetop1percent share),populationgrowth,andcountry-speciÖctrends,andtotheuseofthetop5percent measureofinequalityasthedependentvariable.AppendixTableA4veriÖesthattheresults aresimilarifwelimittheanalysistoacommonsampleconsistingofOECDcountriessince 1950,andAppendixTableA5showsthatfocusingonthecapitalshareofnationalincome, ratherthanthetop1percentshare,leadstoasimilarsetofresults,providingnoconsistent evidenceofanimpactfrom r g toinequality.7

Thoughthisevidenceistentativeandobviouslywearenotpretendingtoestimateanysort ofcausalrelationshipbetween r g andthetop1percentshare,itisquitestrikingthatsuch basicconditionalcorrelationsprovidenosupportforthecentralemphasisof Capitalinthe

6 Toavoidthemechanicalserialcorrelationthatwouldarisefromaveragingthedependentvariable,wetake thetop1%shareobservationsevery10or20years.Ifanobservationismissingatthosedatesandthereexists anobservationwithinplusorminustwoyears,weusetheseneighboringobservations.Theresultsarevery similarwithaveraging.

7 ThistableusestwoalternativemeasuresofthecapitalshareofnationalincomefromthePennWorldTables andfromtheOECD.WedonotpresentregressionsusingthemarginalproductofcapitalfromCaselliandFeyrer (2007)asthismeasureiscomputedusingthecapitalshareofnationalincome,makingitmechanicallycorrelated withthedependentvariableinthistable.

21stCentury.8 Thisisnottosaythatahigher r isnotaforcetowardsgreaterinequalityin societyóitprobablyis.Itisjustthattherearemanyotherforcespromotinginequalityand ourregressionssuggestthat,atleastinacorrelationalsense,thesearequantitativelymore importantthan r g

ATaleofTwoInequalities:SwedenandSouthAfrica

Wenowusethehistoriesofinequalityduringthe20thcenturyinSwedenandSouthAfrica toillustratehowthedynamicsofinequalityappearlinkedtotheinstitutionalpathsofthese societiesóratherthantotheforcesof r>g.Inaddition,thesecasesillustratethattheshare ofnationalincomegoingtothetop0.1percentortop1percentcangiveadistortedviewof whatisactuallyhappeningtoinequalitymorebroadly.Indeed,thisfocusoninequalityatthe topinevitablyleadstoalesserandinsu¢cientfocusonwhatistakingplaceinthemiddleor thebottomoftheincomedistribution.

Figure1showstheevolutionoftheshareofthetop1percentinnationalincomeinSweden andSouthAfricasincetheearly20thcentury.

Thereareofcoursesomedi§erences.Swedenstartedoutwithahighertop1percentshare thanSouthAfrica,butitstop1percentsharefellfaster,especiallyfollowingWorldWarI.The recentincreaseinthetop1percentalsostartsearlierinSwedenandislesspronouncedthan whatweseeinSouthAfricainthe1990sand2000s.Butinbroadterms,thetop1percent sharebehavessimilarlyinthetwocountries,startinghigh,thenfallingalmostmonotonically untilthe1980s,andthenturningup.

Suchcommondynamicsforthetop1percentshareintwosuchdi§erentcountriesóa formercolonywithahistoryofcoercedlaborandlandexpropriation,ruledformuchofthe 20thcenturybyaracistwhiteminority,ontheonehand,andthebirthplaceofEuropean socialdemocracy,ontheotherówouldseemtobolsterPikettyíscasethatthegenerallawsof capitalismexplainthebigswingsofinequality,withlittlereferencetoinstitutionsandpolitics. Perhapsonecouldevenclaimthat,justliketheFrenchRevolution,thee§ectsofapartheid andsocialdemocracyaretriáingdetailsagainstthefundamentalforceof r>g.

Exceptthattherealityisratherdi§erent.InSouthAfrica,forexample,theinstitutionalizationofwhitedominanceafter1910quicklyledtotheNativeLandActin1913whichallocated 93percentofthelandtotheëwhiteeconomyíwhiletheblacks(around59%ofthepopulation), got7percentoftheland.Inthewhiteeconomyitbecameillegalforblackstoownpropertyor abusiness,andmanytypesofcontractualrelationsforblackswereexplicitlybanned.Bythe

8 Oneimportantcaveatisthattheexpostnegativereturnsthatmayhaveresultedfromstockmarketcrashes andwarsarenotinoursample,becauseourestimatesfor r arefromthepost-WorldWarIIsample.Nevertheless, if r g isindeedafundamentalforcetowardsgreaterinequality,weshouldseeitsimpactduringthelast60 yearsalso.

1920stheëColorBaríblockedblacksfrompracticallyallskilledandprofessionaloccupations (vanderHorst,1942;Feinstein,2005,Chapters2-4).After1948theëapartheidístatebecame evenstronger,implementingawidearrayofmeasurestoenforcesocialandeducationalsegregationbetweenwhitesandblacks.Finally,in1994,theapartheidinstitutionscollapsedas NelsonMandelabecameSouthAfricaísÖrstblackpresident.However,anaÔvelookatFigure1 wouldseemtosuggestthatSouthAfricaísapartheidregime,whichwasexplicitlystructuredto keepblackwageslowandtobeneÖtwhites,wasresponsibleforagreatdecreaseininequality, whiletheendofapartheidcausedanexplosionininequality!

Howcanthisbe?Theansweristhatmeasuringinequalitybythetop1percentshare cangiveamisleadingpictureofinequalitydynamicsinsomesettings.Figure2showsthe top1percentsharetogetherwithothermeasuresofinequalityinSouthAfrica,whichbehave quitedi§erently.Tostartwith,Wilsonís(1972)seriesforrealwagesofblackworkersingold mines,akeyengineoftheSouthAfricaneconomyatthetime,showsthatduringtheÖrst halfofthe20thcentury,inequalitybetweenblackworkersandwhiteswasmassivelywidening (acontinuationof19th-centurytrends,seedeZwart,2011).ThisisconÖrmedbythewhiteto-blackpercapitaincomeratiofromcensusdata,whichdoeshavesomeupsanddownsbut exhibitsafairlylargeincreasefromabout10-foldto14-folduntil1970.Thereafter,itshows arapiddecline.Eventhetop5percentsharebehavessomewhatdi§erentlythanthetop1 percentshare(thoughavailabledataforthisvariablestartonlyinthe1950s).

IfonewantedtounderstandeconomicinequalityinSouthAfrica,changesinlabormarket institutionsandpoliticalequilibriaappearmuchmorerelevantthan r and g.Indeed,the alternativemeasuresofinequalityinFigure2showthatduringthetimethattheshareofthe top1wasfalling,SouthAfricabecameoneofthemostunequalcountriesintheworld.Aswe willdiscussinthenextsection,theturningpointsininequalityinSouthAfricainfacthave institutionalandpoliticalroots.

InSweden,thedeclineinthetop1percentshareisaccompaniedbyamuchmorepervasive fallininequality.Figure3showsthatforSweden,othermeasuresofinequality,includingtwo seriesfortheGiniindex,havesimilartrendstothetop1percentandthetop5percentshare. However,intheSwedishcaseaswell,thestoryofinequalityseemsrelatednottosupposed generallawsofcapitalismandchangesin r and g,butrathertoinstitutionalchanges.The initialfallinthetop1percentsharecoincidedwithlargechangesingovernmentpolicy:for example,arapidincreaseinredistributioninthe1920s,frompracticallynothinginthe1910s (Lindert,1994),andanincreaseintopmarginaltaxratesfromaround10percentin1910 to40percentby1930and60percentby1940(Roine,ValchosandWaldenstrˆm,2009,p. 982).Theexpandingroleofthegovernmentandofredistributivetaxationplausiblyhada negativeimpactonthetop1percentshare.ThedatainFigures1andFigure3areforpre-tax

inequality,butthesearelikelytobeimpactedbytaxes,whichináuencee§ortandinvestment (seetheevidenceisRoine,ValchosandWaldenstrˆm,2009,onthis),andalsodirectlybythe wagecompressioncreatedbySwedeníslabormarketinstitutions.Indeed,uniondensityrose rapidlyfromaround10percentofthelaborforceduringWorldWarIto35percentby1930 andover50percentby1940(DonadoandW‰lde,2012).

Pikettyemphasizestheroleofthedestructionofthecapitalstockandassetpricefallsinthe aftermathoftheworldwarsaskeyfactorsexplainingthedeclineoftopinequalityduringmuch ofthe20thcentury.ButsuchfactorscanhardlyexplainthetrendsinSwedenorSouthAfrica. Swedenwasneutralinbothwars,andthoughSouthAfricaprovidedtroopsandresourcesfor theAlliedpowersinboth,neithereconomyexperiencedanydirectdestructionoftheircapital stock.

TowardsanInstitutionalFramework

Asatisfactoryframeworkfortheanalysisofinequalityshouldtakeintoaccountboththeimpact ofdi§erenttypesofinstitutionsonthedistributionofresourcesandtheendogenousevolution oftheseinstitutions.Wenowáeshoutsuchaframeworkandthenapplyittotheevolution ofinequalityóandinstitutionsóinSwedenandSouthAfrica.Theframeworkwepresentis basedontheoneweproposedinAcemoglu,JohnsonandRobinson(2005).AdaptingFigure 1fromthatpaperourframeworkcanberepresentedschematicallyasfollows:

Inthisapproach,theprevailingpoliticalinstitutionsatacertaintimedeterminethedistributionofdejurepoliticalpower(seeAcemogluandRobinson,2000,2008;Acemoglu,2008; Acemoglu,EgorovandSonin,2012,2014):forexample,whichgroupsaredisenfranchised,how politicalpoweriscontested,andhowconstrainedtheeconomicandpoliticalelitesare,and soon.Politicalinstitutionsalsoa§ect,togetherwithinequalityinsociety,thedistributionof defactopoliticalpower.Forinstance,defactopower(whichdesignatespoliticalpowerand constraintsgeneratedbyaccesstothemeansofviolence,collectiveaction,informalinstitutions andsocialnorms)dependsontheextenttowhichdi§erentsocialandeconomicgroupsare organizedandhowtheyresolvetheircollectiveactionproblemsandhowresourcesináuence

theirabilitytodoso.Defactoanddejurepowertogetherdetermineeconomicinstitutions, andalsothestabilityandchangeofpoliticalinstitutions.

Inturn,economicinstitutionsa§ectthesupplyofskillsóacrucialdeterminantofinequality throughouthistoryandevenmoresotoday.Theyalsoináuence,throughregulationofboth pricesandmarketstructure,bytaxation,orbyimpactingthebargainingpowerofdi§erent factorsofproductionandindividuals,goodsandfactorprices.Finally,economicinstitutions impacttechnology,includingwhetherandhowe¢cientlyexistingtechnologiesareutilized,as wellastheevolutionoftechnologythroughendogenousinnovationsandlearningbydoing. Forexample,Zeira(1998)andAcemoglu(2010)showhowlowwages,resultingfromeither supplyorinstitutionalfactors,cansometimesreducetechnologyadoptionoreventechnologicalprogress,andHornbeckandNaidu(2014)provideevidenceconsistentwiththispattern. Throughtheirjointimpactontechnology,thesupplyofskillsandrelativeprices,economic institutionsa§ectnotonly r and g,butmoreimportantly,inequality.Inthisapproach,inequalityshouldnotbethoughtofasalwayssummarizedbyasinglestatistic,suchastheGini indexorthetop1percentshare.Rather,theeconomicandpoliticalfactorsstressedhere determinethedistributionofresourcesmoregenerally.

Wedonotmeantosuggestthatthisframeworkdeterminestheevolutionofinstitutions, technologyandinequalitydeterministically.Thearrowsdesignateináuences,whicharemediatedbyvariousstochasticeventsandpoliticaleconomyinteractions,andasourbriefdiscussion ofthecontrastofMexicoandtheUnitedStatesindicates,similareconomicdevelopmentswill resultinverydi§erentinstitutionalresponsesdependingontheprevailingpoliticalequilibrium.Nordoweimplythattheframeworkcapturesalleconomicimplicationsofimportóor allofthosethatarerelevantforinequality.Mostcentrally,technologywillevolveovertime notonlybecauseofinstitutionalfactors,butalsoduetoscientiÖcdevelopmentsandbecause itrespondstoothereconomicchanges,includingfactorprices,theabundanceandscarcity ofdi§erenttypesofskillsandmarketstructure(forexample,Acemoglu,2002,2003,2010). Itispossibleaswellthattechnologicaldevelopmentscouldinturntheimpactinstitutional dynamics(forexample,Acemoglu,AghionandViolante,2001,andHassler,Rodriguez-Mora, StorlesstenandZilibotti,2003).Nevertheless,thissimpleframeworkisusefulforhighlightingthepotentiallyimportantroleofinstitutionalequilibria,andtheirchanges,inshaping inequality.

LetusnowapplyittoSouthAfrica.Before1910,non-whitescouldvoteintheCapeand NatalaslongastheyfulÖlledcertainwealth,incomeorpropertyrestrictions(thoughthiswas moreheavilyrestrictedinNatal).After1910aspeciÖcallywhitefranchisewasestablishedinthe TransvaalandOrangeFreeState,andthengraduallyextendedtotherestofthecountrywith blacksÖnallybeingdeÖnitivelydisenfranchisedintheCapein1936.Theformalinstitutionsof

theapartheidstatecementedthepoliticalpowerofthewhiteminority,andsegregationistlaws andotheraspectsoftheregimecreatedeconomicinstitutions,suchastheskeweddistribution oflandandtheëcolorbar,íaimedatfurtheringtheinterestsofthewhiteminority.Sothen whydidthisandtheáourishingofsocialapartheidafter1948leadtoafallinthetop1percent share?

TheprimaryreasonisthatpoliticaldynamicsinSouthAfricaatthistimecannotbefully capturedasaconáictbetweenmonolithicgroupsofwhitesandblacks.Rather,apartheid shouldbeviewedasacoalitionbetweenwhiteworkers,farmersandmine-ownersóattheexpenseofblacks,butalsowhiteindustrialistswhohadtopayveryhighwagesforwhiteworkers (Lundahl,1982;Lipton,1985).Thus,onereasonforareductioninthetop1percentshare wasthatproÖtsweresqueezedbywagesforwhitelabor.Moreover,bydeprivingindustrialists ofalargerpoolofskilledworkers,andtiltingthepriceofwhitelaborhigher(becausethe supplyoflaborwasartiÖciallyrestricted),theserulesfurtherstuntedSouthAfricaneconomic development.

Inaddition,therewereforceswithinapartheidforredistributionfromtheveryrichtowards poorerwhites.Indeed,SouthAfricaíspoliticaldiscussionsinthe1920sthatledtothefurther spreadoftheëcolorbaríandsubsequentlytothevictoryoftheNationalPartyin1948were relatedtowhatwascalledtheëpoorwhiteproblem,íhighlightingtheimportanceofthespeciÖc coalitionunderpinningapartheid(seeAlvaredoandAtkinson,2010,fordiscussionofother factorssuchasthegoldprice).

ThecompressionofthehugewagegapsbetweenSouthAfricaíswhitesandblacksstarting inthe1970sshouldbeviewedwithinthecontextofthepoliticalweakeningoftheapartheid regimeanditsincreasingeconomicproblems(seealsoWilson,1980,Mariotti,2012).The domesticturningpointwastheabilityofblackworkerstoorganizeprotestsandriots,and exercisetheirdefactopower,particularlyaftertheSowetouprisingof1976,whichledtothe recognitionofblacktradeunions.Thisprocesswasaidedbymountinginternationalpressure, whichinducedBritishandU.S.ÖrmsbasedinSouthAfricatopushbackagainstworkplace discrimination.Ultimately,thisdefactopowerforcedthecollapseoftheapartheidregime, leadingtoanewsetofpoliticalinstitutionsandtheenfranchisementofblackSouthAfricans. Thenewsetofeconomicinstitutions,andtheirconsequencesforinequality,áowedfromthese politicalchanges.Consistentwithourframework,theinstitutionsofapartheidmayhavealso fedbackintotheevolutionoftechnology,forexampleinimpedingthemechanizationofgold mining(Spandau,1980).Asthepowerofapartheidstartedtoerodeinthe1970s,white businessmenrespondedrapidlybysubstitutingcapitalforlaborandmovingtechnologyina laborsavingdirection(SeekingsandNattrass,2005,p.403).

AscanbeseenfromFigure1,thetop1percentshareinSouthAfricashowsasteepriseafter

1994,coincidingwiththeÖnaloverthrowoftheformidableextractiveinstitutionsofapartheid. Noclearconsensushasyetemergedonthecausesofthepost-apartheidincreaseininequality, butonereasonisrelatedtothefactthataftertheendofapartheid,theartiÖciallycompressed incomedistributionofblacksstartedwideningassomeportionofthepopulationstartedto beneÖtfromnewbusinessopportunities,education,andaggressivea¢rmativeactionprograms (Leibbrandt,Woolard,Finn,andArgent,2010).Whateverthedetailsoftheseexplanations, itishardtoseethepost-1994riseinthetop1percentshareasrepresentingthedemiseofa previouslyegalitarianSouthAfrica.

TheroleofdefactoanddejurepoliticalpowerinshapingpoliticalandeconomicinstitutionsisnolesscentralinSweden,wheretheimportantturningpointwascreatedbytheprocess ofdemocratization.Adultmalesu§ragecamein1909,buttrueparliamentarydemocracydevelopedonlyaftertheReformActof1918,withsigniÖcantcurbsonthepowerofthemonarchy andmorecompetitiveelections.Boththe1909reformandtheemergenceofparliamentary democracyin1918wereresponsestounrest,strikesandthedefactopowerofdisenfranchised workers,especiallyintheatmosphereofuncertaintyandsocialunrestfollowingWorldWarI (Tilton,1974).Collier(1999,p.83)explains:ì[I]twasonlyaftertheeconomiccrisisof1918 andensuingworkerprotestsfordemocracyledbySocialDemocratsthattheReformActwas passed.Indeed,inNovember1918,laborprotestsreachedsuchapointastobeperceivedas arevolutionarythreatbySwedenísConservativePartyandupperclasses.î Swedishdemocracythenlaidthefoundationsformodernlabormarketinstitutionsand thewelfarestate,andcreatedpowerfuldownwardpressureoninequality,includingthetop 1percentshare.However,democraticconáictinSwedenwasnotasimplecontestbetween monolithicgroupsofworkersandbusinesseseither.AsMoeneandWallerstein(1995,2006) characterizeit,socialdemocracywasacoalitionoftheendsoftheincomedistributionó businessmenandunskilledworkersóagainstthemiddleclassandskilledworkers(seealso Saint-Paul,2000;Gourevitch,1986;Luebbert,1991,fortheoriesabouttheemergenceofsuch politicalcoalitions).Inconsequence,Swedisheconomicinstitutionsstronglycompressedskilled wagesrelativetounskilledwages,underpinningtherapiddeclineinbroad-basedmeasuresof inequality.SomebusinessesbeneÖttedfromthesearrangements,particularlythoseinsectors exposedtointernationalcompetition,whichusedcentralizedwagebargainingasatoolto stopwagepushfromnon-tradedsectors,suchasconstruction(Swenson,1991,2002).Swedish labormarketinstitutionsalsolikelyimpactedthepathoftechnology.Forinstance,Moene andWallerstein(1997)emphasizethatwagecompressionactedasataxonine¢cientplants andstimulatednewentryandrapidtechnologicalupgrading.Inthefaceofhighunskilled wagesandtheinstitutionsofthewelfarestate,itisnotasurprisethatthetop1percentshare declinedinSwedenaswell,evenifbusinessmenalsodidwelloutofsomeaspectsofSwedish

labormarketinstitutions.

Whatexplainsthefactthatthetop1percentshareappearstoincreasenotjustinSouth AfricaandSweden,butinalmostallOECDeconomiesoverthelast20yearsorso?Factorsleft outofourframeworkóglobalization,skill-biasedtechnologicalchangesandtheincreaseinthe sizeoflargecorporationsóarelikelytobeimportant.Butthesearethemselvesforcesthatare notironclad,buthavelikelyrespondedtootherchangesintheworldeconomy.Forexample, Acemoglu(2002)arguesthatskill-biasedtechnologicalchangecannotbeunderstoodwithout theincreaseinthesupplyofskilledworkersintheUnitedStatesandtheworldeconomy, makingthesetypesoftechnologiesmoreproÖtable,andglobalizationandtheincreasingsize ofglobalcorporationsarethemselvesconsequencesofregulatoryandtechnologicalchangesof thelastseveraldecades.Thissimplyunderscoresthattheframeworkpresentedherecannot capturethedynamicsofalldimensionsofinequalityóortherichdynamicsofpoliticaland economicinstitutionsforthatmatter.Nevertheless,thebasicforcesthatitstressesappearto beimportantnotjustinthecontextofSwedenandSouthAfrica,butmuchmoregenerally (asarguedinAcemogluandRobinson2006,2012).

Thisframeworkalsohelpstoclarifythereasonswhywemightcareaboutinequalityat theverytopoftheincomeandwealthdistributions.Mostrelevantisthatthefactorswhich undergirdahighshareofincomeforthetop1percentmightalsorepresentalackofequality ofopportunity,oralackofalevelplayingÖeld.Extendingtheframeworkpresentedabove,we arguedinAcemogluandRobinson(2012)thatlackofalevelplayingÖeld,includinglimited socialmobility,islikelytoholdbackcountriesintheirinvestments,innovationandthee¢ciencyofresourceallocation.However,thetop1percentsharemaynotbethemostrelevant dimensionofthedistributionofincomeforevaluatingequalityofopportunityandbarriersto thee¢cientallocationoftalentandresourcesinsociety.Forexample,ifasmallnumberatthe topbecamewealthierósay,ifBillGatesandWarrenBu§ettbecametwiceaswealthyóatthe expenseofotherrichindividuals,wouldthatmakeU.S.societynotablylessmeritocratic?This seemsunlikely.Indeed,Chetty,Hendren,KlineandSaez(2014b)showthatsocialmobility atthecommutingzonelevelintheUnitedStatesisunrelatedtoincomeinequality,especially inequalityatthetop.Their(2014a)evidencethatU.S.socialmobilityhasstayedthesame evenasthetop1percentsharehasincreasedrapidlyoverthelastseveraldecadesfurther corroboratesthisintuition.Othertypesofinequality,suchasthegapbetweenwhitesand blacksasinSouthAfricaorbetweenthebottomandthemiddleclassintheUnitedStates, maybemorerelevantforthinkingaboutwhethertherehavebeenchangesinsocialmobility andtheangleoftheplayingÖeld.

Butonedimensionofpoliticaleconomywherethetop1percentsharemaybecentral isthehealthofpoliticalinstitutions.Itmaybedi¢culttomaintainpoliticalinstitutions

thatcreateadisperseddistributionofpoliticalpowerandpoliticalaccessforawidecrosssectionofsocietyinasocietyinwhichasmallnumberoffamiliesandindividualshavebecome disproportionatelyrich.Acautionarytaleaboutthedangerscreatedbythistypeofinequality isdiscussedinPugaandTreáer(2014)andAcemogluandRobinson(2012):thestoryof latemedievalVenice.Here,theeconomicpowerofthemostprosperousandwell-established familiesultimatelymadeitpossibleforthemtoblocktheaccessofotherstopoliticalpower, andoncetheythusmonopolizedpoliticalpower,theycouldchangeeconomicinstitutionsfor theirbeneÖtbyblockingtheentryofotherfamiliesintolucrativebusinessesandbanning contractsthathadpreviouslymadeitpossibleforindividualswithlimitedcapitaltoenter intopartnershipsforlongdistancetrade.Thischangeinpoliticalinstitutions,feedingintoa deteriorationofeconomicinstitutions,heraldedtheeconomicdeclineofVenice.

Yetiftheprimarythreatfromthetop1percentshareispolitical,thenthemainresponse shouldberelatedtomonitoringandcontainingthepoliticalimplicationsoftheincreaseintoplevelinequalityónotnecessarilycatchallpoliciessuchaswealthtaxes.Suchpoliciesshouldbe explicitlyrelatedtotheinstitutionalfaultlinesofthespeciÖcsociety,andshouldbeconceived inthecontextofstrengtheninginstitutionalchecksagainstanypotentialpowergrab.

Conclusion

ThomasPikettyís(2014)ambitiousworkpro§ersabold,sweepingtheoryofinequalityapplicabletoallcapitalisteconomies.Thoughwebelievethatthefocusoninequalityandthe ensuingdebatesonpolicycanbehealthyandconstructive,wehavearguedthatPikettygoes wrongforexactlythesamereasonsthatMarx,andbeforehimRicardo,wentastray:these questsforgenerallawsignorebothinstitutionsandpolitics,andtheáexibleandmultifaceted natureoftechnology,whichmaketheresponsestothesamestimuliconditionalonhistorical, political,institutionalandcontingentaspectsofthesocietyandtheepoch,vitiatingthefoundationsoftheoriesseekingfundamental,generallaws.Wehaveargued,incontradictiontothis perspective,thatanyplausibletheoryofthenatureandevolutionofinequalityhastoinclude politicalandeconomicinstitutionsatthecenterstage,recognizetheendogenousevolutionof technologyinresponsetobothinstitutionalandothereconomicanddemographicfactors,and alsoattempttomodelhowtheresponseofaneconomytoshocksandopportunitieswilldepend onitsexistingpoliticalandinstitutionalequilibrium.

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OnlineAppendixforìRiseandDeclineofGeneralLawsofCapitalismî

InthisAppendix,wediscussthecoretheoreticalclaimsofPikettyís Capitalinthe21stCentury, inane§orttoclarifytherelationshipbetween r g andinequality.Theemphasiswillbeon fourissues:(1)whattypesofmodelsandeconomicforcesleadtoadivergenceofinequality when r>g;(2)theroleofsocialmobilityinthisprocess;(3)whattypesofmodelsleadinstead toarelationshipbetween r g andthe(right)tailofthestationarydistributionofincomeand wealth;(4)howdoes r g respondtopoliciesandcapitalaccumulation.

DivergenceofInequalitywhen r g> 0 (withoutSocialMobility)

TheÖrstpossiblereadingofthetheoreticalcoreof Capitalinthe21stCentury isthatif r g is positive(orsu¢cientlylarge)itwillleadtoadivergenceofwealthbetweentheveryrichandthe restofpopulation.TheapproachofthebookherebuildsonideasproposedbyNicholasKaldor, inparticular,Kaldor(1955).Aswewillsee,thismodelgivesaformalizationofthevarious intuitionsandstatementsmadein Capitalinthe21stCentury inaratherstraightforward manner,butalsoshowswhatthelimitationsofsomeoftheseintuitionsandclaimsare.

TheprototypicalKaldor-typeeconomyconsistsofìcapitalistsîandworkers(andnoland), andanimportantdimensionofinequalityisbetweenthesetwogroupsandisfueledbythe assumptionthatcapitalistshaveahighsavingrate(andworkershaveasavingrateofzero), andalloftheincomeofthecapitalistscomefromcapital.Aswewillsee,thereisnoneedto assumethatworkersdonothaveanycapitalincome;itissu¢cienttoallowdi§erentsaving ratesbetweenthesetwogroups.

Supposethattheeconomycomprisesasinglegood,sothatthereisnorelativepricefor installedcapital(relativetoÖnaloutputandconsumption).Wealsofocusonacontinuoustimeeconomyfornotationalconvenience.Letusdenotethecapitalstockheldbycapitalists by KC .Forfuturereference,wealsodenotethefractionofcapitalistsinthepopulationby m,andthusthefractionofworkersis 1 m,andwithoutlossofgenerality,wetaketheseto bethenumbersofcapitalistsandworkers(thusnormalizingtotalpopulationto1).Fornow, thereisnosocialmobilitybetweencapitalistsandworkers,butwewillrelaxthisbelow.

Sincealloftheincomeofthecapitalistscomesfromcapital,theirtotalincomeissimply givenbythecapitalstocktimestherentalpriceofcapital.Assumingthatcapitaldepreciates attherate andtheinterestrateis r,totalincomeaccruingtocapitalistscanbewrittenas

wherewearesuppressingtimeindices.9

9 PikettyspeciÖeseverything,includingthesavingrateinnetofdepreciationunits.ButasKruselland

Nowsupposingthatcapitalistshaveaconstantsavingrateof sC outoftheirincome,the evolutionofthecapitalstockheldbycapitalistscanbewrittenas

wheretheÖrstlinesimplyusesthefactthataconstantfraction sC ofcapitalistsíincome, IC ,is saved,butthenafraction oftheirexistingcapitalstockdepreciates.Thesecondlinesimply substitutesfor IC from(A1).

Toobtainthegrowthrateofcapitalistsíincome,wealsoneedtoknowhowtheinterest ratevariesovertime.Inparticular,thegrowthrateofcapitalistsíincomecanbeobtainedby di§erentiating(A1)withrespecttotimeas

Nowreturningtoworkers,theirincomeis

where KW isthecapitalstockheldbyworkers, w therealwage, L totalemploymentandwhere thesecondlinesimplyusesthefactthatlaborincomeisequaltonationalincomeminuscapital income.Then,thegrowthrateoftheincomeofworkerscanbeobtainedbystraightforward di§erentiationwithrespecttotimeandbyrearrangingtermsusingtheexpressionforthe incomeofthecapitalistsfrom(A1):

Oneadvantageofthisexpressionisthatitiswrittenwithoutreferencetothesavingrateof workers, sW ,becauseofthenationalincomeaccountingidentity.Butthisisalsoadisadvantage,because,aswediscussbelow,itmasksthatcomparisonsof r to g areimplicitlychanging thegrowthoflaborincomeandthesavingrateofworkers.

Denotethefractionofnationalincomeaccruingtocapitalistsby (= IC =Y ).Ifcapitalists correspondtotherichest1percentinthepopulation,then isthetop1percentsharemeasure Smith(2014)emphasize,thisisadi¢cultassumptiontomotivateandleadstotheunpleasantanduntenable implicationofallofnationalincomebeingsavedatlowgrowthrates.Inlightofthis,itismoreappropriateto thinkofPikettyísresultsasbeingsupportedbyassumingthat 0

usedextensivelybyPiketty.UsingthisdeÖnitionanddenotingthegrowthrateofGDP(and nationalincome)by g,wecanthenwrite g I W = g [sC (r + ) ] r r+ 1

Letusnowcomparethistothegrowthrateoftheincomeofthecapitalists.Asimple rearrangementgivesthat

Thisexpressionthusstatesthattherewillbedivergencebetweentheincomesofthecapitalists andtheworkerswhen(A2)holds.10 Note,however,thatthissortofdivergence,bydeÖnition, mustbetemporary,becauseifcapitalistsíincomesaregrowingfasterthantherestofthe population,atsomepointtheywillmakeuptheentireincomeoftheeconomy.11

Itisnowstraightforwardtoobservethattheclaimin Capitalinthe21stCentury about r g> 0 leadingtoexpandinginequalitywillholdundertwoadditionalconditions:

1. sC ' 1,whichwouldfollowiftheveryrichsaveaverylargefractionoftheirincomes.In practice,thoughtheveryrichsavemoreoftheirincomesthanthepoor, sC issigniÖcantly lessthan1,especiallyonceonetakesintoaccountcharitablecontributionsanddonations bytheveryrich.

2. r =0,sothattheinterestrateisconstant.Here,asdiscussedinthetext,muchofgrowth theorysuggeststhattheinterestrateisquiteresponsivetochangesinthecapitalstock (andotherfactorsofproductionaswellastechnology).

Underthesetwoassumptions,(A2)boilsdownto

g I C >gI W ifandonlyif r>g; asassertedbyPiketty.However,(A2)alsomakesitclearthatwithoutthetwosimplifying assumptionsabove,theevolutionoftopinequalitydependsonthesavingrateandchangesin theinterestrateaswellas r>g

10 SeealsoHomburg(2014)foranexplanationforwhy r g doesnottranslatetodivergenceinoverlapping generationsmodels.

11 Inparticular,when(A2)holdsforanextendedperiodoftime,thenallofnationalincomewillbeinterms ofcapitalincome,soitisimpossiblefor r>g andthusfor(A2)tobemaintainedforever.

DivergenceofInequalitywithSocialMobility

ThesimpleKaldor-typemodelpresentedintheprevioussubsectionenablesustopresenta transparentillustrationofhowsocialmobilitya§ectsinequality.Wewillnowshowthateven undertheassumptionsenumeratedabove,modestamountsofsocialmobilitycansigniÖcantly changetheconclusions.ThoughtheUnitedStatesisnotoneofthehighestsocialmobility countriesintheworld,itstillhasafairlysizablelikelihoodthatthoseatthetopofincome distributionwilllosetheirposition,andasmentionedinthetext,recentevidencebyChetty, Hendren,KlineandSaez(2014a,b)suggeststhatthisrateofsocialmobilityhasnotdeclined overtime,eventhoughoverallinequalityhasincreasedsharply.

Letusnowincorporatethepossibilityofsocialmobilityintothissimpleframework.To simplifytheexposition,letussupposethat =_ r =0 forthispartoftheanalysis.

Wemodelsocialmobilityasfollows.Weassumethatatsomeáowrate ,acapitalistishit byarandomshockandbecomesaworker,inheritingtheworkeríslaborincomeprocessand savingrate.Atthispoint,he(orshe)ofcoursemaintainshiscurrentincome,butfromthen onhisincomedynamicsfollowsthoseofotherworkers.Simultaneously,aworkerbecomesa capitalist(alsoattheáowrate ),keepingthefractionofcapitalistsinthepopulationconstant at m 2 (0; 1).

Wecannowwritethedynamicsofthetotalincomeofcapitalistsas

whereweareexploitingthefactthat,onaverage,acapitalistleavingthecapitalistclasshas income IC =m (totalcapitalistsíincomedividedbythemeasureofcapitalists),andaworker enteringthecapitalistclasshas,onaverage,income IW =(1 m).ThissigniÖcantlyfacilitates thecharacterizationofinequalitybetweencapitalistsandworkers(thoughthedetermination oftheexactdistributionofincomeismorecomplicatedbecauseoftheslowgrowthdynamics oftheincomeofindividualsthatchangeeconomicclass).12

Nowrearranging(A3),weobtain

Withasimilarreasoning,thegrowthrateofthetotalincomeofworkersis

12 Thisalsomeansthatthecomparisonoftheincomesofcapitalistsandworkersinthisworldwithsocial mobilityisonlyanapproximationtothetop1percentinequalitymeasures(evenwhencapitalistsmakeup1 percentofthepopulation),becauseworkerswhobecomecapitalistswilljointhetop1percentonlyslowly.

Combiningtheseexpressionsandrearrangingterms,wecanwrite

I C >gI W ifandonlyif sC r g> m m(1 m) ; (A4)

wherethetermontheright-handsideisstrictlypositiveinviewofthefactthat >m (i.e.,theshareoftop1percentinnationalincomeisgreaterthan1%).Thisexpressionthus showsthatevenwhen sC r g> 0 (or,fortiori,when r g> 0),itdoesnotfollowthat inequalitybetweencapitalistsandworkerswillincrease.Whetheritdoeswilldependonthe extentofsocialmobility.Infact,thequantitativeimplicationsofsocialmobilitycouldbequite substantialaswenextillustrate.

FromChetty,Hendren,KlineandSaezísdata,thelikelihoodthatachildwithparentsinthe top1percentwillbeinthetop1percentis9.6%.13 Ifwetakethegapbetweengenerationsto beabout30years,thisimpliesanannualrateofexitingthetop1percentapproximatelyequal to0.075(7.5%).Therearemanyreasonswhythismaybeanoverestimate,includingthefact thatchildrenaretypicallyyoungerwhentheirincomesaremeasuredandalsothatinpractice, familiesexitingthetop1percenttendtoremainattheverytopoftheincomedistribution (ratherthanfollowtheincomedynamicsofatypicalworkerasinthesimplemodelhere).But therearealsoreasonsforunderestimation,includingthefactthatwithin-generationtransitions inandoutofthetop1percentarebeingignored.Forourillustrativeexercise,wetakethis numberasabenchmark(withoutanyattempttocorrectitforthesepossibleconcerns).This numbercorrespondsto =m inourmodel(theprobabilitythatagivencapitalistishitbya shockandbecomesaworker),sowetake =0:00075.Usingthetop1percentísshareas20%, wecancomputethattheright-handsideof(A4)isapproximately0.072(72%).Thisimplies thatfortheleft-handsidetoexceedtheright-handside,theinterestratewouldhavetobe veryhigh.Forexample,withasavingrateof50%andagrowthrateof1%,wewouldneed theinterestratetobegreaterthan15%.Alternatively,ifweusethetop10percentsoasto reduceexitsthatmaybecausedbymeasurementerror,theequivalentnumberfromChetty, Hendren,Kline(2014)is26%,implyinganannualexitrateequalto4.4%.Usingashareof 45%ofincomeforthetop10percent,theright-andsideof(A4)canbecomputedas0.038, againmakingitverydi¢cultforrealisticvaluesof r g tocreateanaturalandpowerful forceforthetopinequalitytoincrease.Forexample,usingagainasavingrateof50%anda growthrateof1%,theinterestratewouldneedtobeover8.5%.Wethereforeconcludethat incorporatingsocialmobilitygreatlyreducesanyìfundamentalforceîthatmayhaveexisted from r g towardsmechanicallygreaterinequalityatthetopofthedistribution.

13 WethankNathanHendrenforprovidinguswiththedata.

r g andtheStationaryDistributionofIncomeandWealth

Asdiscussedinthetext, Capitalinthe21stCentury sometimespositsarelationshipbetween r g andthestationarydistributionofwealthinsteadoftherelationshipbetween r g anddivergenceofincomesandwealth.EmpiricallytheParetodistribution(withdistribution function 1 a withParetoshapecoe¢cient 1)appearstobeagoodapproximation tothetailoftheincomeandwealthdistributions.Forthisreason,existingmodelshave focusedonstochasticprocessesforwealthaccumulationthatgenerateaParetodistributionor distributionsforwhichtherighttailcanbeapproximatedbytheParetoform.Suchmodels havealonghistoryineconomics,andarediscussedinthecontextoftheissuesraisedin Capital inthe21stCentury inJones(2014),andwereferthereadertothispaperformoreextensive references.SomerecentpapersthatderiveParetowealthdistributionsincludeBenhabib,Bisin andZhu(2011),AokiandNirei(2013)andJonesandKim(2014).

Inthispartoftheappendix,weshowthataParetotailinthewealthdistributionemerges fromcertainclassesofmodels,andwill,undersomeconditions,correspondtogreatertop inequalitywhen r g ishigher,butwealsohighlightwhythesemodelsareoftennotagood approximationtothetypeoftopinequalityweobserveinthedataand/orrelyonimplausible assumptions.

Togivethebasicidea,consideraneconomyconsistingofacontinuumofmeasure1of heterogeneousindividuals.Supposethateachindividual i isinÖnitelylivedandconsumesa constantfraction ofherwealth, Ait.Shehasastochastic(possiblyseriallycorrelated)labor income Zit (with EZit 2 (0; 1) andÖnitevariance),andhasastochasticrateofreturnequal to r + "it,where "it isastochastic,returntermthatisalsopossiblyseriallycorrelated(with theunconditionalmean E"it equaltozeroasanormalization).Thus,thelawofmotionofthe assetsofindividual i isgivenby

DividingbothsidesofthisequationbyGDP(alsoaverageincomepercapita), Yt,weobtain ait+1 = 1+ r + "it 1+ g ait +~ zit; where ait Ait=Yt and zit Zit=Yt.Afurthernormalizationisalsouseful.Supposethat ait convergestoastationarydistribution(weverifythisbelow).Thenlet Ea betheaverage (expected)valueof ~ ait inthestationarydistribution.Thendividingbothsidesofthisequation by E~ a,weobtain ait+1 = 1+ r + "it 1+ g ait + zit; (A5) where ait ait=Ea and zit zit=Ea,andofcourse Eait+1 = Eait =1 inthestationary distribution.Thisalsoimpliesthat Ezit 2 (0; 1).

Equation(A5)isanexampleofaKestenprocess(Kesten,1973),discussed,forexample, inGabaix(1999).Kestenshowsthatprovidedthat 1+r 1+g < 1,(A5)convergestoastationary distributionwithaParetotailómeaningthattherighttailofthedistribution,corresponding to a a for a su¢cientlylarge,canbeapproximatedby 1 a forsomeendogenouslydeterminedParetoshapeparameter 0.

Toobtaintheintuitionforwhy(A5)generatesaParetotailinthestationarydistribution, weconsiderthefollowingheuristicderivation,whichfollowsGabaix(1999).Letusfocuson thecaseinwhich z and " areiid.LetusalsodeÖnethecounter-cumulativedensityfunction of(normalized)wealthinthiseconomytobe G

where 1fPg istheindicatorfunctionfortheevent P,wehavedeÖned 1+r+" 1+g fornotational convenience,andwehavedroppedtheindicesfor z and sincethestochasticlawsforthese variablesdonotdependontimeandareidenticalacrossindividuals.Then,bythedeÖnition ofastationarydistribution G,wehave

NowletusconjectureaParetotailwithshapeparameter ,i.e., G (a)= a forlarge a Thenforlarge a,wehave a = E(a z) h i , or 1= E a z a h i

Since Ez< 1 andhasÖnitevariance,wecanwrite lima!1 E a z a =1,whichconÖrms theconjectureanddeÖnes asthepositivesolutionto

Thisequationalsoexplainswhy E = 1+r 1+g < 1 isnecessaryforconvergencetoastationary distribution(asotherwisethewealthdistributionwoulddiverge).

Oncepinneddown,thisParetoshapeparameteroftherighttail, ,determineswealth inequality,aswellasincomeinequality,atthetopofthedistribution.Forexample,ifthe entirewealthdistributionwerePareto,thenthetop kíspercentileísshareoftotalwealthwould besimply: k 100 1 .Thisexpressionmakesitclearthatalower correspondstoaìthicker tailîoftheParetodistributionandthustoagreatershareofaggregatewealthaccruingto householdsinthehigherpercentilesofthedistribution.

Thequestionofinterestiswhetheranincreasein r g (orin r g )correspondingtoa rightwardshiftinthestochasticdistributionof willreduce ,thusleadingtogreaterinequalityinthetailofthewealthdistribution.Thoughingeneralthisrelationshipisambiguous,in anumberofimportantcasessuchrightwardshiftsdoreduce andincreasetopinequalityas wenextshow.

Recallthat(again "it and zit beingiid),wehave ait+1 = itait + zit:

Takingexpectationsonbothsides,usingthefactthat it isiidandthatinthestationary distribution Eait+1 = Eait =1,wehave E =1 z; where z = Ezit 2 (0; 1),asnotedabove.Thisequationalsoimpliesthat E 2 (0; 1).

Todeterminetherelationshipbetween r g and ,weconsidertwospecialcases.

First supposethat (or ")islognormallydistributed.Inparticular,supposethat ln has anormaldistributionwithmean ln(1 z) 2=2 andvariance 2 > 0 (sothat E =1 z). Thenwehave

E[ ]= E[e ln ]; whichissimplythemomentgeneratingfunctionofthenormallydistributedrandomvariable ln ,whichcanbewrittenas

ThenthedeÖnitionof , E[ ]=1,impliesthat [ln(1 z) 2=2]+ 2 2=2=0; whichhastworoots, =0 (whichisinadmissibleforthestationarydistribution),andthe relevantone, =1 ln(1 z) 2=2 > 1.

Finally,forsmallvaluesof r g < 0,wecanwrite 1+ r g + ", andthusfromtherelationshipthat E =1 z,wehavethat z = (r g ) > 0,sothat 1 ln(1+ r g ) 2=2 .

Itthenreadilyfollowsthat isdecreasingin r g ,thusimplyingthathigher r g and lowermarginalpropensitytoconsumeoutofwealth, ,leadtogreatertopinequality.14

Second,asimilarrelationshipcanbederivedevenwhen isnotlognormallydistributed, butonlywhen z issmall(andwewillseewhythismaynotbeveryattractiveinthecontext ofthestationarydistributionofwealth).LetusstartbytakingaÖrst-orderTaylorexpansion of E[ ]=1 withrespectto around =1 (whichalsocorrespondstomaking z liecloseto zero).Inparticular,di§erentiatingwithintheexpectationoperator,wehave

E[ + ln ( 1)] 1; wherethisapproximationrequires tobecloseto1.15 Thenagainexploitingthefactthat E =1 z,wehave 1+ z E[ ln ] > 1 (wherethefactthat E[ ln ] > 0 followsfromthefactthat z isclosetozero).16 Thisexpression clariÖeswhy iscloseto1when z iscloseto0.

Moreover,notethatthederivativeof ln is 1+ln .For z small, ln > 1 with su¢cientlyhighprobability,andthus E[ ln ] increasesas shiftstotheright(inthesense ofÖrst-orderstochasticdominance).Therefore,when iscloseto1orequivalentlywhen z is closeto0,ahigher r g increases E[ ln ] andreducestheshapeparameter ,raisingtop inequality.However,itshouldalsobenotedthatthiscaseismuchlessrelevantforstationary wealthdistributionswhichhaveParetotailsmuchgreaterthan1.

Benhabib,BisinandZhu(2011)extendtheresultonthePareto-tailofthewealthdistributiontoasetupwithÖnitely-livedagentswithbequestmotives.Inthiscase,thetailofthe distributionisinpartdrivenbywhichindividualshavebeenaccumulatingforthelongesttime. Theyalsoderivetheconsumptionchoicesfromoptimizationdecisions,considertheequilibriumdeterminationoftheinterestrate,andconÖrmtheresultsderivedheuristicallyhere.In addition,theyshowthatonetypeofsocialmobilityórelatedtotheserialcorrelationof ",thus makingÖnancialreturnslesscorrelatedforahouseholdovertimeótendstomakethetailless thick,hencereducingtopinequality.TheseissuesarealsodiscussedinJones(2014).

Thereareseveralreasonswhythesemodelsmaynotbeentirelysatisfactoryasmodelsoftop inequality,however.First,totheextentthatveryrichindividualshavediversiÖedportfolios,

14 Thesameconclusionfollowswithouttheapproximation 1+ r g + ".Inthiscase,wewouldsimply have

whichyieldsthesamecomparativestatics.

15 Formally,wehave E[ + ln ( 1)+ o( )]=1:

16 Bynotingthat ln isaconvexfunctionandapplyingJensenísinequality, E[ ln ] > E ln E =(1 z)ln(1 z).For z closeenoughtozero, (1 z)ln(1 z)=0,andthus E[ ln ] > 0

variabilityinratesofreturnsasadriverofthetailofthedistributionmaynotbethemost dominantfactor.Second,thestructureofthesemodelsimpliesthatlaborincomeplaysnorole inthetailofthestationarywealthdistribution,butthismaybeatoddswiththeimportance ofwagesandsalariesandìbusinessincomeîinthetop1percentoreventop0.1percent shareofthenationalincome(PikettyandSaez,2003).Thirdandrelatedly,thesemodelsdo nothavearoleforentrepreneurship,whichisoneoftheimportantaspectsoftheinterplay betweenlaborandcapitalincome(see,forexample,JonesandKim,2014).Fourth,andmost importantlyinouropinion,thesemodelsdonotfeaturesocialmobility(exceptthelimited typeofsocialmobilityrelatedtothecorrelationofÖnancialreturnsconsideredinBenhabib, BisinandZhu,2011),whichappearstobeanimportantdeterminantoftopinequalityand itspersistence.Finally,inmorerealisticversionssuchasBenhabib,BisinandZhu(2011)and JonesandKim(2014),akeydeterminantoftheextentoftopinequalityturnsouttobethe ageorsomeothercharacteristicofthehouseholdwhichdetermineshowlongthehouseholdhas beenaccumulating.Butthisisalsoatoddswiththesalientpatternsofthetailoftheincome andwealthdistributionintheUnitedStates,wherebysuccessfulentrepreneursorprofessionals aremorelikelytoberepresentedatthistalethanindividualsorhouseholdsthathavebeen accumulatingcapitalforalongwhile.

From r g totheImplicationsofLowGrowth

AkeypartofPikettyísargumentisthatthefuturewillbringevengreaterinequalitybecauseit willbecharacterizedbyloweconomicgrowth(atleastinthedevelopedëcapitalistíeconomies). Thisargumentreliesontwopillarsóinadditiontothelinkfrom r g toinequalityortop inequalityasexplicatedabove.TheÖrstisthatthefuturewillbecharacterizedbylowgrowth. Thisisnottheplacetoenterintoalongdebateabouttheforecastsoffuturegrowthrates, butitsu¢cestonotethatwedonotÖndforecastsaboutfuturegrowththatdonotmake anyreferencetothefutureoftechnology,innovation,andtheinstitutionsthatshapethem particularlyconvincing.ThoughthedemographictrendsPikettyemphasizesarewellknown, theirimplicationsforeconomicgrowtharemuchlesswellunderstood.

Thesecondimportantpointisthat,evenifoneweretotakethelinkbetween r g and inequalityonfaith,thisdoesnotimplythatalower g willtranslateintoahigher r g.As wenotedinthetext,therearetworeasonsforthis.First,changesin g willimpact r from thehouseholdside.Forexample,ifconsumptiondecisionsaremadebyoptimizinghouseholds, thentheinterestrateispinneddownas r = g + ,where istheinverseoftheintertemporal elasticityofsubstitution.Ifonlysomefractionofhouseholdsoptimizeandtherestarehandto-mouthconsumers,thisequationwillstillapplybecauseitwillbetheoptimizingconsumers who,atthemargin,determinetheequilibriuminterestrate.Incaseswhere > 1, r g would

actuallydecreasewithdeclinesin g

Second,evenignoringthelinkagebetween r and g comingfromthehouseholdside,changes in g willimpact r throughtheirináuenceonthecapital-outputratio(since r isrelatedtothe marginalproductofcapital).ThisiswherePikettyassertsthattheelasticityofsubstitution betweencapitalandlaborisveryhigh,ensuringthatchangesinthecapital-laborratioin theeconomydonottranslateintosigniÖcantchangesintherateofreturntocapitalandthe interestrate.Aswenotedinthetext,however,thesestrongclaimsarenotbackedbythe existingevidence.Therefore,weareparticularlyskepticalofPikettyísconclusionfromhis theoreticalediÖce,evenwiththecentralroleassignedto r g

Theseconsiderationssuggestthatevenif r g maybeausefulstatisticinthecontextoftop inequality,itcannotbeusedeitherforcomparativestatictypeanalysis(becauseitwillrespond endogenouslyanddependingontechnologyandinstitutionstothechangesbeingconsidered) orevenformedium-termforecasting.Inaddition,theKaldor-typemodelpresentedabove highlightsanotherdi¢cultyofreasoningintermsof r g.Forthisquantitytobeconstant,we needtospecifynotonlywhatthesavingrateofworkershastobebutalsohowitischanging.

Inparticular,giventhesavingrateofcapitalistsandothervariables, g isafunctionofthe capitalistsísshareofnationalincome, ,thesavingrateofworkers, sW ,andtherateofgrowth oftheirlaborincome.Thisimpliesthatif r>g,thenbecause ischanging,thesavingrate and/orthegrowthrateoflaborincomeofworkersmustbealsoimplicitlychanging.

Allofthissuggeststhat r and g mustbetreatedasendogenousvariables,andpredictions aboutthefutureorcomparativestaticsmustbeconductedintermsofexogenousvariables, notintermsofendogenousobjects.

PikettyísSecondFundamentalLawofCapitalism

TheÖnalpointwewouldliketocommentonisPikettyíssecondfundamentallawofcapitalism, linkingthecapital-GDPratiotothesavingrateandthegrowthrateoftheeconomy.Piketty usesthissecondfundamentallawtoassertastronglinkbetweenthesizeofthecapitalstock relativetoGDPandthegrowthrateoftheeconomy,andthenonthebasisofhisforecasts oflowereconomicgrowthinthefuture,reachestheconclusionthatthefuturewillbringa pronouncedincreaseinthesizeofthecapitalstockrelativetoGDPinadvancedeconomies. Givenaconstantinterestrate, r,thisalsoimpliesthecontinuationoftherecentincreasein theshareofcapitalinnationalincome.Thus,whilethefundamentalforceof r g providesan accountofagrowingtop1percentshare,thesecondfundamentallawofcapitalismprovides predictionsaboutthefutureofcapital-GDPratioandtheshareofnationalincomeaccruing tocapitaloverall.

Inthispartoftheappendix,weshowhowsomethingakintothesecondfundamentallaw

followsfromtheSolowgrowthmodel,butalsothatwhyitismisleadingtoderivepredictions abouttheevolutionofthecapital-GDPratio(orthecapitalshareofnationalincome)from thisrelationshipbecauseitrelatestheseobjectstoendogenousvariablesthatwillalltendto changetogetherinresponsetoshocksorchangesinparameters.

Pikettyíssecondfundamentallawofcapitalismis

g = s Y K ;

where s istheaggregatesavingrate.Then,combiningthiswithhisÖrstfundamentallaw (whichisjustanidentityasnotedinthetext),heobtainsthat

capitalshareofnationalincome = r s g :

Holding r and s constant,ifthereisadeclineinthegrowthrateoftheeconomy, g,thencapital shareofnationalincomewillincrease.Inparticular,ifthegrowthrateishalved,thencapitalís shareofnationalincomeshoulddouble.

Letusstartwiththesteady-stateequilibriumofastandardSolowgrowthmodel,where thereisaconstantsavingrate, s,anddepreciationofcapitalattherate .Theninthis steady-stateequilibrium,wehave K Y = s g + (A7)

Toseethis,simplynotethat,assumingaconstantsavingrate,aggregatesavingis

= I = K + K; sothat

Y K = _ K K + :

Ifwealsohave g = K K ,then(A7)follows.

Pikettyísversionisthespecialcaseofthiswell-knownrelationshipwhen =0óorwhen thingsarespeciÖedinìnetîunits,sothatwhatwehaveisnotnationalincome,butnational incomenetofdepreciation,andthesavingrateisinterpretedasthesavingrateabovethe amountnecessaryforreplenishingdepreciatedcapital.KrusellandSmith(2014)provideamore detailedcritiqueofPikettyíssecondfundamentallawformulatedinthisway.Inparticular,as wenotedinthetext,Pikettyíssecondfundamentallawhasuntenableimplications,particularly inthecaseswherethegrowthrateoftheeconomybecomeslow(anditisthesecasesonwhich Pikettybaseshisconclusionsabouttheimplicationsoflowgrowthonthecapitalshareof nationalincome).

Weshouldalsonotethatthesecondfundamentallawapplieswhenthecapital-GDPratio isconstant,andthus g = K K asjustnoted.Outofsteadystate(orbalancegrowthpath),itis notexactlytrue.Nevertheless,therelevantconclusionóthattherewillbeanincreaseinthe

capital-GDPratiofollowingadeclinein g providedthat r and s remainconstantóstillholds. Thisfollowsfromthefactthatthenewsteadystatefollowingalowergrowthrate,say g0 <g, willinvolveahighercapital-GDPratioof K0

Y 0 = s g0 + ; andconvergencetothisnewsteadystateinthebaselineSolowmodelismonotone,soover timethecapital-GDPratiowillmonotonicallyincrease(thoughwithasmallsavingrate,the transitioncantakealongtime).

Observealsothatbecauseofthedepreciationrate, ,inthedenominator,theimpactof changesinthegrowthratearelessthantheverylargee§ectsPikettyíssecondfundamental lawofcapitalismimplies(seeagainKrusellandSmith,2014).

However,eventhoughwehaveshownhowaversionofPikettyíssecondfundamentallaw ofcapitalismfollowsfromtheSolowgrowthmodel,thisdoesnotjustifytheconclusionthata slowdownineconomicgrowthwillautomaticallyincreasethecapital-GDPratioorthecapital shareofnationalincomebecause,asalreadynoted,almostanychangethatwillreducethe rateofeconomicgrowthwillalsoimpacttheinterestrateandthesavingrate.

AdditionalReferencesfortheOnlineAppendix

Aoki,ShuheiandMakotoNirei(2013) ìParetoDistributionandtheEvolutionofTop IncomesintheUSîUniversityLibraryofMunich,Paper47967.

Benhabib,Jess,AlbertoBisin,ShenghaoZhu(2011) ìTheDistributionofWealth andFiscalPolicyinEconomieswithFinitelyLivedAgentsî Econometrica,79(1),123-157.

Gabaix,Xavier(1999) ìZipfísLawforCities:AnExplanationî QuarterlyJournalof Economics,114(3),79-767.

Homburg,Stefan(2014) ìCriticalRemarksonPikettyísëCapitalintheTwenty-Örst Centuryíî,DiscussionPaperNo.530(InstituteofPublicEconomics,LeibnizUniversityof Hannover,Germany)andISSN0949-9962.

Jones,CharlesI.(2014) ìTheMacroeconomicsofPikettyîforthcoming Journalof EconomicPerspectives.

Jones,CharlesI.andJiheeKim(2014) ìASchumpeterianModelofTopIncome InequalityîStanfordmimeo.

Kaldor,Nicholas(1955) ìAlternativeTheoriesofDistributionî ReviewofEconomic Studies,23(2),83-100.

Kesten,Harry(1973) ìRandomDi§erenceEquationsandRenewalTheoryforProduct toRandomMatricesî ActaMathematica,131,207-248.

Nirei,Makoto(2009) ìParetoDistributionsinEconomicGrowthModelsîHitotsubashi University,mimeo.

Inequality

in South Africa and Sweeden

Top 1 percent share in Sweeden

Top 1 percent share in South Africa, married adults

Top 1 percent share in South Africa, all adults

Figure1: Top1percentshareofnationalincomeinSwedenandSouthAfrica. Thefigure plotsthetop1percentshareofnationalincomeforSouthAfricaandSweden.Theseriesfor SouthAfricaisfromAlvaredoandAtkinson(2010).TheseriesforSwedenisfromRoineand Waldenstr¨om(2009).

Inequality in South Africa

Top 1 percent share

Top 5 percent share

Ratio between whites’ and blacks’ wages in mining

Ratio between whites’ and blacks’ income per capita

Figure2: Topincomesharesandbetween-groupinequalityinSouthAfrica. Thefigureplotsthe top1and5percentsharesofnationalincomeforSouthAfricaintheleftaxis,obtainedfrom AlvaredoandAtkinson(2010).Therightaxisplotstheratiobetweenwhites’andblacks’wages inmining(obtainedfromWilson,1972),andtheratiobetweenwhites’andblacks’incomeper capita(obtainedfromLeibbrandtetal.,2010).

Inequality in Sweden

Top 1 percent share

Top 5 percent share

Gini coefficient for household disposable income (LIS)

Gini coefficient for household disposable income (Statistics Sweeden)

Figure3: TopincomesharesandoverallinequalityinSweden. Thefigureplotsthetop1and5 percentsharesofnationalincomeforSwedenintheleftverticalaxis,obtainedfromRoineand Waldenstr¨om(2009).TherightaxisplotstheGinicoefficientforhouseholddisposableincome, fromtheLuxembourgIncomeStudy(seeMilanovic,2013),andfromStatisticsSweden(SCB).

Table1:Regressioncoefficientsofdifferentproxiesof r g.Thedependentvariableisthetop1percentshareofnationalincome.

Nocross-countryvariationin r OECDdataoninterestrates r = MPK δ (1)(2)(3)(4)(5)(6)(7)(8)(9)

PanelA:Estimatesusingannualpanel

r g at t 4

Long-runeffect[p-valueestimate> 0] -0.16[0.13]-0.18[0.15] -0.39[0.29]-0.47[0.34]-0.04[0.68]0.03[0.89]

Persistenceoftop1percentshare[p-valueestimate< 1] 0.89[0.00]0.89[0.00] 0.90[0.31]0.89[0.30] 0.90[0.11]0.92[0.18]

Observations 1646123312266275204701162905860

Countries 2727 271918 182826 26

PanelB:Estimatesusing10-yearand20-yearpanels(columns3,6,9)

Average r g 0.055-0.036-0.252-0.114-0.121-0.1100.0690.1480.238 (0.110)(0.118)(0.269)(0.138)(0.132)(0.320)(0.118)(0.100)(0.164)

Long-runeffect[p-valueestimate> 0] -0.05[0.76] -0.25[0.44] 0.29[0.22] Persistenceoftop1percentshare[p-valueestimate< 1]

Notes-: Thetablepresentsestimatesofdifferentproxiesof r g onthetop1percentshareofnationalincome.Thedependentvariableisavailablefrom1871onwardsforthe countriescoveredintheWorldTopIncomesDatabase.Weusedifferentproxiesof r g:Columns1to3usegrowthratesfromMadisson,andassumenovariationinrealinterest ratesacrosscountries.Thesedataareavailablefrom1870onwards.Columns4to6userealinterestratescomputedbysubtractingrealizedinflationfromnominalyieldsonlong-term governmentbonds,andgrowthratesfromthePennWorldTables.Thesedataareonlyavailablesince1955forOECDcountries.Columns7to9use r = MPK δ,constructedas explainedinthetextusingdatafromthePennWorldTables,andgrowthratesfromthePennWorldTables.Thesedataareavailablefor1950onwards.PanelAusesanunbalanced yearlypanel.Columns2,5and8addfivelagsofthedependentvariableandreporttheestimatedpersistenceofthetop1percentshareofnationalincomeandtheestimatedlong runeffectof r g onthedependentvariable.Columns3,6and9addfourlagsof r g ontheright-handside,andalsoreportthelong-runeffectofapermanentincreaseof1%in r g andatestforthejointsignificanceoftheselags(withitscorresponding χ2 statisticandp-value).PanelBusesanunbalancedpanelwithobservationsevery10yearsor20years (columns3,6,9).Columns1,2,4,5,7and8presentestimatesfromaregressionofthetop1percentshareofnationalincomeattheendofeachdecadeinthesample(thatis,1880, 1890,...,2010,dependingondataavailability)ontheaverage r g duringthedecade.Columns2,5,and8addonelagofthedependentvariableontheright-handside.Finally, columns3,6and9,presentestimatesfromaregressionofthetop1percentshareofnationalincomeattheendofeach20-yearperiodinthesample(thatis,1890,1910,...,2010, dependingondataavailability)ontheaverage r g duringtheperiod.Allspecificationsincludeafullsetofcountryandyearfixedeffects.Standarderrorsallowingforarbitrary heteroscedasticityandserialcorrelationofresidualsatthecountrylevelarecomputedusingthepairs-clusterbootstrapprocedureproposedbyCameron,GelbachandMiller(2008) andarereportedinparentheses.

TableA1:Regressioncoefficientsofdifferentproxiesof r g.Thedependentvariableisthetop1percentshareofnationalincome. Traditionalstandarderrorsassuminghomoscedasticityandnoserialcorrelation.

Nocross-countryvariationin r OECDdataoninterestrates r = MPK δ (1)(2)(3)(4)(5)(6)(7)(8)(9)

PanelA:Estimatesusingannualpanel

r g at t 4

Long-runeffect[p-valueestimate> 0] -0.16[0.00]-0.18[0.05] -0.39[0.03]-0.47[0.06]-0.04[0.67]0.03[0.89]

Persistenceoftop1percentshare[p-valueestimate< 1] 0.89[0.00]0.89[0.00] 0.90[0.00]0.89[0.00] 0.90[0.00]0.92[0.00]

Observations 1646123312266275204701162905860

PanelB:Estimatesusing10-yearand20-yearpanels(columns3,6,9)

Average r g 0.055-0.036-0.252-0.114-0.121-0.1100.0690.148∗ 0.238 (0.095)(0.098)(0.228)(0.132)(0.118)(0.247)(0.091)(0.088)(0.172)

Long-runeffect[p-valueestimate> 0] -0.05[0.72] -0.25[0.32] 0.29[0.11]

Persistenceoftop1percentshare[p-valueestimate< 1] 0.32[0.00] 0.52[0.00] 0.48[0.00]

Observations 2131811068280 4313512461

Countries 2725 241818 17272522

Yearspercountry 7.97.24.44.64.42.55.05.02.8

Notes-: Thetablepresentsestimatesofdifferentproxiesof r g onthetop1percentshareofnationalincome.Thedependentvariableisavailablefrom1871onwardsforthecountries coveredintheWorldTopIncomesDatabase.Weusedifferentproxiesof r g:Columns1to3usegrowthratesfromMadisson,andassumenovariationinrealinterestratesacross countries.Thesedataareavailablefrom1870onwards.Columns4to6userealinterestratescomputedbysubtractingrealizedinflationfromnominalyieldsonlong-termgovernment bonds,andgrowthratesfromthePennWorldTables.Thesedataareonlyavailablesince1955forOECDcountries.Columns7to9use r = MPK δ,constructedasexplained inthetextusingdatafromthePennWorldTables,andgrowthratesfromthePennWorldTables.Thesedataareavailablefor1950onwards.PanelAusesanunbalancedyearly panel.Columns2,5and8addfivelagsofthedependentvariableandreporttheestimatedpersistenceofthetop1percentshareofnationalincomeandtheestimatedlongruneffect of r g onthedependentvariable.Columns3,6and9addfourlagsof r g ontheright-handside,andalsoreportthelong-runeffectofapermanentincreaseof1%in r g anda testforthejointsignificanceoftheselags(withitscorresponding χ2 statisticandp-value).PanelBusesanunbalancedpanelwithobservationsevery10yearsor20years(columns 3,6,9).Columns1,2,4,5,7and8presentestimatesfromaregressionofthetop1percentshareofnationalincomeattheendofeachdecadeinthesample(thatis,1880,1890,..., 2010,dependingondataavailability)ontheaverage r g duringthedecade.Columns2,5,and8addonelagofthedependentvariableontheright-handside.Finally,columns3,6 and9,presentestimatesfromaregressionofthetop1percentshareofnationalincomeattheendofeach20-yearperiodinthesample(thatis,1890,1910,...,2010,dependingon dataavailability)ontheaverage r g duringtheperiod.Allspecificationsincludeafullsetofcountryandyearfixedeffects.Traditionalstandarderrors,imposinghomoscedasticity andnoresidualautocorrelation,arereportedinparentheses.

TableA2:Regressioncoefficientsofdifferentproxiesof r g controllingforGDPpercapita, populationgrowthandcountrytrends.

Novariationin r OECDinterestrates r = MPK δ (1)(2)(3)(4)(5)(6)

PanelA:Baseline

Estimateof r g at t

∗ -0.066∗∗ -0.038∗∗ 0.029-0.004 (0.012)(0.010)(0.027)(0.017)(0.033)(0.009)

Long-runeffect[p-valueestimate> 0] -0.16[0.13] -0.39[0.29]-0.04[0.68]

Persistenceoftop1percentshare[p-valueestimate< 1]

Observations 164612336275201162905

Countries 272719182826

PanelB:logofGDPpercapita

Estimateof r g at t -0.006-0.018∗ -0.035-0.039∗∗ 0.032-0.006 (0.011)(0.010)(0.028)(0.017)(0.031)(0.009) logGDPpercapitaat t -0.1690.0223.270-0.0960.145-0.199 (0.767)(0.166)(2.149)(0.809)(1.152)(0.281)

Long-runeffect[p-valueestimate> 0] -0.16[0.14] -0.41[0.36]-0.06[0.55]

Persistenceoftop1percentshare[p-valueestimate< 1]

0.89[0.00] 0.91[0.35] 0.90[0.14]

Observations 164612336205141151898

Countries 272719182826

PanelC:Populationgrowth

Estimateof r g at t 0.004-0.017∗ -0.039-0.034∗ 0.030-0.006 (0.013)(0.009)(0.027)(0.018)(0.031)(0.008)

Populationgrowthat t 0.2550.0330.5440.1170.140-0.055 (0.225)(0.060)(0.464)(0.139)(0.310)(0.067)

Long-runeffect[p-valueestimate> 0] -0.15[0.11] -0.37[0.34]-0.05[0.51]

Persistenceoftop1percentshare[p-valueestimate< 1] 0.89[0.00] 0.91[0.30] 0.90[0.10]

Observations 164612336085031134885

Countries 272719182726

PanelD:Countrytrends

Estimateof r g at t -0.002-0.018∗ -0.022-0.0240.015-0.006 (0.010)(0.011)(0.015)(0.017)(0.016)(0.009)

Long-runeffect[p-valueestimate> 0] -0.10[0.15] -0.06[0.07]-0.02[0.52]

Persistenceoftop1percentshare[p-valueestimate< 1] 0.82[0.00] 0.62[0.00] 0.70[0.00]

Observations 164612336275201162905

Countries 272719182826

Notes-: Thetablepresentsestimatesofdifferentproxiesof r g onthetop1percentshareofnationalincome.Thedependent variableisavailablefrom1871onwardsforthecountriescoveredintheWorldTopIncomesDatabase.Weusedifferentproxiesof r g:Columns1and2usegrowthratesfromMadisson,andassumenovariationinrealinterestratesacrosscountries.Thesedata areavailablefrom1870onwards.Columns3and4userealinterestratescomputedbysubtractingrealizedinflationfromnominal yieldsonlong-termgovernmentbonds,andgrowthratesfromthePennWorldTables.Thesedataareonlyavailablesince1955for OECDcountries.Columns5and6use r = MPK δ,constructedasexplainedinthetextusingdatafromthePennWorldTables, andgrowthratesfromthePennWorldTables.Thesedataareavailablefor1950onwards.Columns2,4and6addfivelagsofthe dependentvariableandreporttheestimatedpersistenceofthetop1percentshareofnationalincomeandtheestimatedlongrun effectof r g onthedependentvariable.PanelApresentsthebaselineestimates.PanelBaddsthelogofGDPpercapitaasa control.PanelCaddspopulationgrowthasacontrol.Finally,PanelDaddscountry-specifictrendsascontrols.Allspecifications includeafullsetofcountryandyearfixedeffects.Standarderrorsallowingforarbitraryheteroscedasticityandserialcorrelationof residualsatthecountrylevelarecomputedusingthepairs-clusterbootstrapprocedureproposedbyCameron,GelbachandMiller (2008)andarereportedinparentheses.

TableA3:Regressioncoefficientsofdifferentproxiesof r g.Thedependentvariableisthetop5percentshareofnationalincome.

Nocross-countryvariationin r OECDdataoninterestrates r = MPK δ (1)(2)(3)(4)(5)(6)(7)(8)(9)

PanelA:Estimatesusingannualpanel

Long-runeffect[p-valueestimate> 0] 0.12[0.67]0.34[0.37] -0.48[0.30]-0.25[0.66]0.08[0.80]0.34[0.41]

Persistenceoftop1percentshare[p-valueestimate< 1] 0.92[0.01]0.92[0.01] 0.92[0.28]0.91[0.27] 0.93[0.12]0.93[0.13]

Observations 1307988988590489440985786749 Countries 2421 211817 17242020

PanelB:Estimatesusing10-yearand20-yearpanels(columns3,6,9)

Average r g -0.019-0.147-0.602-0.151-0.075-0.0430.1020.252

(0.207)(0.207)(0.514)(0.224)(0.217)(0.500)(0.199)(0.128)(0.256)

Long-runeffect[p-valueestimate> 0] -0.24[0.49] -0.19[0.73] 0.50[0.14]

Persistenceoftop1percentshare[p-valueestimate< 1]

Notes-: Thetablepresentsestimatesofdifferentproxiesof r g onthetop5percentshareofnationalincome.Thedependentvariableisavailablefrom1871onwardsforthe countriescoveredintheWorldTopIncomesDatabase.Weusedifferentproxiesof r g:Columns1to3usegrowthratesfromMadisson,andassumenovariationinrealinterest ratesacrosscountries.Thesedataareavailablefrom1870onwards.Columns4to6userealinterestratescomputedbysubtractingrealizedinflationfromnominalyieldsonlong-term governmentbonds,andgrowthratesfromthePennWorldTables.Thesedataareonlyavailablesince1955forOECDcountries.Columns7to9use r = MPK δ,constructedas explainedinthetextusingdatafromthePennWorldTables,andgrowthratesfromthePennWorldTables.Thesedataareavailablefor1950onwards.PanelAusesanunbalanced yearlypanel.Columns2,5and8addfivelagsofthedependentvariableandreporttheestimatedpersistenceofthetop5percentshareofnationalincomeandtheestimatedlong runeffectof r g onthedependentvariable.Columns3,6and9addfourlagsof r g ontheright-handside,andalsoreportthelong-runeffectofapermanentincreaseof1%in r g andatestforthejointsignificanceoftheselags(withitscorresponding χ2 statisticandp-value).PanelBusesanunbalancedpanelwithobservationsevery10yearsor20years (columns3,6,9).Columns1,2,4,5,7and8presentestimatesfromaregressionofthetop5percentshareofnationalincomeattheendofeachdecadeinthesample(thatis,1880, 1890,...,2010,dependingondataavailability)ontheaverage r g duringthedecade.Columns2,5,and8addonelagofthedependentvariableontheright-handside.Finally, columns3,6and9,presentestimatesfromaregressionofthetop5percentshareofnationalincomeattheendofeach20-yearperiodinthesample(thatis,1890,1910,...,2010, dependingondataavailability)ontheaverage r g duringtheperiod.Allspecificationsincludeafullsetofcountryandyearfixedeffects.Standarderrorsallowingforarbitrary heteroscedasticityandserialcorrelationofresidualsatthecountrylevelarecomputedusingthepairs-clusterbootstrapprocedureproposedbyCameron,GelbachandMiller(2008) andarereportedinparentheses.

TableA4:Regressioncoefficientsofdifferentproxiesof r g.Thedependentvariableisthetop1percentshareofnationalincome. SamplerestrictedtoOECDcountriessince1950.

Nocross-countryvariationin r OECDdataoninterestrates r = MPK δ (1)(2)(3)(4)(5)(6)(7)(8)(9)

PanelA:Estimatesusingannualpanel

Long-runeffect[p-valueestimate> 0] -0.61[0.31]-1.02[0.32] -0.39[0.29]-0.47[0.34]-0.24[0.53]-0.47[0.63]

Persistenceoftop1percentshare[p-valueestimate< 1] 0.91[0.34]0.89[0.33] 0.90[0.31]0.89[0.30] 0.91[0.39]0.91[0.44]

Observations 627520470627520470627520470 Countries 1918 181918 181918 18

PanelB:Estimatesusing10-yearand20-yearpanels(columns3,6,9)

(0.256)(0.208)(0.599)(0.138)(0.132)(0.320)(0.208)(0.157)(0.279)

Long-runeffect[p-valueestimate> 0] -1.30[0.11] -0.25[0.44] 0.04[0.92]

Persistenceoftop1percentshare[p-valueestimate< 1] 0.51[0.02] 0.52[0.02]

Notes-: Thetablepresentsestimatesofdifferentproxiesof r g onthetop1percentshareofnationalincome.WerestrictoursampletoOECDcountriesforwhichinterestrates dataisavailablefrom1955onwards.ThecountriesinoursampleincludeAustralia,Canada,Denmark,Finland,France,Germany,Ireland,Italy,Japan,Netherlands,NewZealand, Norway,Portugal,SouthAfrica,Spain,Sweden,Switzerland,UnitedKingdomandUnitedStates.Weusedifferentproxiesof r g:Columns1to3usegrowthratesfromthePenn WorldTables,andassumenovariationinrealinterestratesacrosscountries.Columns4to6userealinterestratescomputedbysubtractingrealizedinflationfromnominalyields onlong-termgovernmentbonds,andgrowthratesfromthePennWorldTables.Columns7to9use r = MPK δ,constructedasexplainedinthetextusingdatafromthePenn WorldTables,andgrowthratesfromthePennWorldTables.PanelAusesanunbalancedyearlypanel.Columns2,5and8addfivelagsofthedependentvariableandreportthe estimatedpersistenceofthetop1percentshareofnationalincomeandtheestimatedlongruneffectof r g onthedependentvariable.Columns3,6and9addfourlagsof r g on theright-handside,andalsoreportthelong-runeffectofapermanentincreaseof1%in r g andatestforthejointsignificanceoftheselags(withitscorresponding χ2 statistic andp-value).PanelBusesanunbalancedpanelwithobservationsevery10yearsor20years(columns3,6,9).Columns1,2,4,5,7and8presentestimatesfromaregressionofthetop 1percentshareofnationalincomeattheendofeachdecadeinthesample(thatis,1880,1890,...,2010,dependingondataavailability)ontheaverage r g duringthedecade. Columns2,5,and8addonelagofthedependentvariableontheright-handside.Finally,columns3,6and9,presentestimatesfromaregressionofthetop1percentshareofnational incomeattheendofeach20-yearperiodinthesample(thatis,1970,1990,...,2010)ontheaverage r g duringtheperiod.Allspecificationsincludeafullsetofcountryandyear fixedeffects.Standarderrorsallowingforarbitraryheteroscedasticityandserialcorrelationofresidualsatthecountrylevelarecomputedusingthepairs-clusterbootstrapprocedure proposedbyCameron,GelbachandMiller(2008)andarereportedinparentheses.

TableA5:Regressioncoefficientsofdifferentproxiesof r g.Thedependentvariableisthecapitalshareofnationalincome.

Dep.var:capitalsharefromPennWorldTables Dep.var:capitalsharefromKarabarbounisandNeiman(2013) Nocross-countryvariationin r OECDdataoninterestratesNocross-countryvariationin r OECDdataoninterestrates (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)

PanelA:Estimatesusingannualpanel

Long-runeffect[p-valueestimate> 0] -0.05[0.41]-0.15[0.19] -0.28[0.03]0.46[0.13]

Persistenceofcapitalshare[p-valueestimate

Observations

268726192611412412397173512391239495430406

Countries 123123123191919999292191919

PanelB:Estimatesusing10-yearand20-yearpanels(columns3,6,9,12)

Average r g -0.137-0.136-0.2580.2070.1870.560∗ -0.026-0.534-0.2690.2540.086-0.046 (0.124)(0.122)(0.307)(0.185)(0.196)(0.331)(0.156)(0.339)(0.742)(0.275)(0.385)(0.374)

Long-runeffect[p-valueestimate> 0]

Observations 3503502085555341515940563926

Countries 123123104191917572220181413

Notes-: Thetablepresentsestimatesofdifferentproxiesof r g onthecapitalshareofnationalincome.Thedependentvariableisthecapitalshareofnationalincome.Incolumns 1to6,weusedatafromthePennWorldTablestocomputethecapitalsharefor1990onwards.Incolumns7to12,weusethecapitalsharedatafromKarabarbounisandNeiman (2013).Weusedifferentproxiesof r g:Columns1to3and7to9usegrowthratesfromMadisson,andassumenovariationinrealinterestratesacrosscountries.Thesedataare availablefrom1870onwardsformostofthecountriesinthesample.Columns4to6and10to12userealinterestratescomputedbysubtractingrealizedinflationfromnominal yieldsonlong-termgovernmentbonds,andgrowthratesfromthePennWorldTables.Thesedataareonlyavailablesince1955forOECDcountries.PanelAusesanunbalanced yearlypanel.Columns2,5,8and11addfivelagsofthedependentvariableandreporttheestimatedpersistenceofthecapitalshareofnationalincomeandtheestimatedlongrun effectof r g onthedependentvariable.Columns3,6,9and12addfourlagsof r g ontheright-handside,andalsoreportthelong-runeffectofapermanentincreaseof1%in r g andatestforthejointsignificanceoftheselags(withitscorresponding χ2 statisticandp-value).PanelBusesanunbalancedpanelwithobservationsevery10yearsor20years (columns3,6,9,12).Columns1,2,4,5,7,8,10and11presentestimatesfromaregressionofthecapitalshareofnationalincomeattheendofeachdecadeinthesample(thatis,1980, 1990,...,2010,dependingondataavailability)ontheaverage r g duringthedecade.Columns2,5,8and11addonelagofthedependentvariableontheright-handside.Finally, columns3,6,9and12,presentestimatesfromaregressionofthecapitalshareofnationalincomeattheendofeach20-yearperiodinthesample(thatis,1990and2010)onthe average r g duringtheperiod.Allspecificationsincludeafullsetofcountryandyearfixedeffects.Standarderrorsallowingforarbitraryheteroscedasticityandserialcorrelation ofresidualsatthecountrylevelarecomputedusingthepairs-clusterbootstrapprocedureproposedbyCameron,GelbachandMiller(2008)andarereportedinparentheses.