巴德学院利维经济研究所-聚合生产函数与索洛的“三件牛仔”（英）-2024.3.docx

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1、aaI向Eo1.evyEconomics0InstituteofBardCollegeWorkingPaperNo.1045TheAggregateProductionFunctionandSolovv,suThreeDenials”byJesusFelipe(*)SchoolofEconomics,De1.aSalleUniversity(Manila,Philippines)andJohnMcCombie(*)UniversityofCambridge,Cambridge,UKMarch2024Authorcontactinformation:Felipe(iesus.felir)e(dl

2、su.edu.uh):McCombie(jslm2(5)cam.ac.uk)The1.evyEconomicsInstituteWorkingPaperCollectionpresentsresearchinprogressby1.evyInstitutescholarsandconferenceparticipants.Thepurposeoftheseriesistodisseminateideastoandelicitcommentsfromacademicsandprofessionals.1.evyEconomicsInstituteofBardCollege,foundedin19

3、86,isanonprofit,nonpartisan,independentlyfundedresearchorganizationdevotedtopublicservice.Throughscholarshipandeconomicresearch,itgeneratesviable,effectivepublicpolicyresponsestoimportanteconomicPrObIemSIhatPrOfbUndIyaffeciIhequalilyOfIifeinIheUnitedSlaIeSandabroad.1.evyEconomicsInstituteP.O.Box5000

4、Annandale-on-Hudson,NY12504-5000Copyright1.evyEconomicsInstitute2024AllrightsreservedISSN1547-366XABSTRACTThispaperoffersaretrospectiveviewofthekeypillarofSolow,sneoclassicalgrowthmodel,namelytheaggregateproductionfunction.Wereviewhowthistoolcametolifeandhowithassurviveduntiltoday,despitethreecritic

5、ismsthatundermineditsraisond,etre.TheyaretheCambridgeCapitalTheoryControversies,theAggregationProblem,andtheAccountingIdentity.Thesecriticismswereforgottenbytheprofession,notbecausetheywerewrongbutbecauseofthekeyroleplayedbyRobertSolowinthefield.Today,thesecriticismsarenotevenmentionedwhenstudentsar

6、eintroducedto(neoclassical)growththeory,whichispresentedinmosteconomicsdepartmentsandmacroeconomicstextbooksastheonlytheoryworthstudying.JE1.C1.ASSIFICATION:B22,B31,B32,B41,E13,E25KEYWORDS:AccountingIdentity,AggregationProblem,CambridgeCapitalTheoryControversies,SolowINTRODUCTIONRobertSolow,oneofthe

7、mostnotableeconomistsofthetwentiethcenturydiedDecember21,2023,attheageof99.Hewascertainlyagreatresearcher,someoneinterestedinsociety,srealproblems,andthosewhostudiedatMITduringhistenureconsiderhewasagreatinstructor.SolowarrivedatMITin1949asaprofessorofstatistics.TogetherwithPaulSamuelson,hebuiltoneo

8、fthebestregardedeconomicsdepartmentsintheworld.Botheconomistswereinstrumentalinlayingthefoundationsoftheneoclassicalsynthesis.WhilethistooksomeelementsofKeynes,GeneralTheory,itwas,insomerespects,areturntothepre-Keynesianworld.Theneoclassicalsynthesishadthreepillars:microeconomiccompetitivegeneralequ

9、ilibriumtheory,thePhillipscurve,andSolow,s(1956)growthmodel.ThesynthesisassertedtheefficacyofKeynesianpolicyintheshortrun,butassertedabeliefincompetitivemarketforcesandSay,s1.awinthelongrun(inparticularinthecaseofSolow,sgrowthmodel).Asaneconomistinterestedinsociety,srealproblems,Solowwasconcerned,in

10、teralia,withthecausesofunemployment(Solow1980),andviewedthelabormarketasasocialinstitutionandnotlikethetypicalmarketforagood(Solow1990).Hetookpartinthetwomostimportantintellectualdebatesineconomicsofthetwentiethcentury:theCambridgeCapitalTheoryControversies(CCTCs)(mainlywithJoanRobinsonintheUK)andwi

11、ththenewclassicalmacroeconomists(mainlywithMiltonFriedmaninChicago).SolowwasawardedtheNobelPrizein1987forhiscontributionstothetheoryofeconomicgrowth.Solow,s(1956)growthmodelincorporatedanaggregateproductionfunction(APF).Thisconceptbecameapillarofneoclassicalmacroeconomicsandcertainlyofsubsequentneoc

12、lassicalgrowthmodels.Productionfunctionsappearedineconomicsinthenineteenthcentury.Itwasnot,however,untilCobbandDouglas(1928)thatonewasestimatedfortheAmericaneconomyusingstatisticalmethods,whichrequiredusingaggregatedata(indices)foroutput,labor,andcapital.Inthisarticle,theyfoundtheelasticitiesofoutpu

13、twithrespecttolaborandcapitaltobe0.75and0.25,respectively,closetothefactorshares.Theirworkwasinitiallyreceivedwithgreathostility,tothepointthatDouglasconsideredgivingup.Hemovedfromtheoriginalworkwithtimeseriestocross-sectionaldata,whichproducedmuchbetterstatisticalresults(McCombie1998;FelipeandMcCom

14、bie2013,chapter4).AggregateproductionfunctionscontinuedbeingusedduringthefollowingdecadesbutitwasnotuntilSolow,s(1956,1957)twoseminalpapersthattheybecameastandardconceptinmacroeconomics.Thiswasdespitesomedoubtsabouttheirtheoreticalandempiricalfoundations,asweshallseebelow.Solow,s(1956)growthmodeliss

15、tillusedtodaytointroducestudentstogrowththeory.InSolow(1957),theAPFservedasthetooltoempiricallyapportionthecontributionsoftechnicalprogress(totalfactorproductivitygrowthorSolowresidual)andthoseofcapitalandlaborgrowth,tooutputgrowth,intheUSeconomybetween1909and1949.Althoughtotalfactorproductivityhadb

16、eencalculatedbefore,thiswasthefirsttimeithadbeenexplicitlylinkedtoproductiontheory.The1957paperlaunchedtheneoclassicalresearchprogramongrowth,inparticulargrowthaccountingexercisesandtheestimationoftotalfactorproductivitygrowth.ThepresentpaperoffersaretrospectiveviewoftheAPF,inparticularofthreefundam

17、entalcriticismsitwassubjectedto,andofhow,despitethesecriticisms,ithassurvivedthetestoftime.ThesecritiquesaretheCambridgeCapitalTheoryControversies(CCTCs),theAggregationProblem,andtheAccountingIdentity.Itisarguedthatthesethreecriticismsunderminedtheraisond,etreoftheAPF,Solow,sgrowthmodel,andgrowthacc

18、ountingexercises.WithouttheAPF,theneoclassicalmacroeconomicsedificewouldlargelycollapse.Hence,itsputativedefenseatthetimethatthesecritiqueswereadvancedbecameamatterOfcrucialimportance.However,allthreehavelongbeenforgottenbytheprofession,andnotbecausetheywerefundamentallyflawedbutbecauseofthekeyrolet

19、hatSolowplayedinthedebates.Obviously,Solowwasnottheonlyone,buthewasthefther“oftheneoclassicalgrowthmodel(forwhichhereceivedtheNoblePrize)andofthisliterature.Hewasawareofthethreecriticismsandplayedamostimportantroleindismissingthem.HeclearlydidsointhecaseoftheCCTCs,ignoredtheaggregationresults,andden

20、iedtheveracityoftheaccountingidentityargument.Today,theseargumentsarenotevenmentionedwhenstudentsareintroducedtoneoclassicalgrowththeory,whichispresentedinmosteconomicsdepartmentsandmacroeconomicstextbooksastheonlytheoryworthstudying.Thcstandardtextbooksongrowththeoryinthe1970ssuchasWan(1971),Jones(

21、1975)andHacche(1970),mentionedtheCCTCs.Wan(1971)andJones(1975)alsomentionedheaggregationproblems.Bythe1990s.therewasnodiscussioninthegrowthtextbooksofeitherofthese,e.g.,BarroandSala-i-Martin(1995),Jones(19982002),AghionandHowitt(1998),Wcil(2(X)5),orAcemoglu(2009).ForalternativegrowththeoriesseeSen(1

22、970),Scott(1989),andSetterfield(2010).ItshouldbeemphasizedthatthediscussionheredoesnotintendtoundermineallthemanyimportantcontributionsthatSolowmadetoeconomics.Yet,itisimportanttosettherecordstraightontheaboveissues.Therestofthepaperisstructuredasfollows.Section2discussestheCCTCs.Section3discussesth

23、eAggregationProblem.Section4discussestheAccountingIdentitycritique.Section5concludes.TheAppendixintroducesthealgebraoftheaccountingidentityargumentandrevisitsSolow(1957).2.DENIA1.1:THECAMBRIDGECAPITA1.THEORYCONTROVERSIES“Thestudentofeconomictheoryistaughttowrite0=f(1.,C)where1.isaquantityoflabour,Ca

24、quantityofcapitaland0arateofoutputofcommodities.Heisinstructedtoassumeallworkersalike,andtomeasure1.inman-hoursoflabour;heistoldsomethingabouttheindex-numberprobleminvolvedinchoosingaunitofoutput;andthenheishurriedontothenextquestion,inthehopethathewillforgettoaskinwhatunitsCismeasured.Beforeeverhed

25、oesask,hehasbecomeaprofessor,andsosloppyhabitsofthoughtarehandedonfromonegenerationtothenexf,(Robinson1953-54,81).“InherpaperTheProductionFunctionandtheTheoryofCapitalMrs.Robinsonwasannoyedatmanyofthepracticesofacademiceconomists.Wehavereasontobegratefulforherannoyance,forsheseemstohavewrittenherart

26、iclethewayanoystermakespearls-outofsheerirritation(Solow1955-56,101).TheCambridgeCapitalTheoryControversies(CCTCs)wereaseriesofexchangesbetweentwogroupsofeconomistsonbothsidesoftheAtlantic.Theyweretheoretical.CambridgeUKeconomists,ledinitiallybyRobinson,questionedtheverydeepfoundationsofneoclassical

27、macroeconomics.CambridgeUSAeconomistsprimarilyledbySamuelsonandSolow,counterargued.Summarizingtheexchangesbetweenthetwosidesisarathercomplicatedtask.Harcourt(1969,1972)providesanexcellentsummaryanddiscussionoftheliterature.TherearemanygoodsummariesoftheCCTCs.CohenandHarcourt(2003)andFelipeandMcCombi

28、e(2013)alsoprovidesummaries.Inthefinalanalysis,thedebateswereaboutdifferentvaluetheories,theclassical(Smith,Ricardo,Marx)versustheneoclassical(Bohm-Bawerk,Jevons,Clark,Wicksteed,Wicksell,Walras),andhowthosetwotheoriesexplainpricesanddistribution.Thedebatescenteredonaseriesofissuesderivedfromandlinke

29、dtothequestionofwhetheronecanuseanaggregatemeasureofcapitalinamacroeconomicproductionfunctionwithoutrunningintoapparentlyparadoxicalphenomena.TheAPFappearedintheCCTCsinRobinson,s(1953-54)article.Comingfromaclassicaltradition,capitalintheproductionfunctionneededtobeintheformofphysical,homogeneousmach

30、ines.Theseweretermed“leets(Steelspeltbackwards)byRobinson.However,shearguedthatthiscouldnotbethecaseattheaggregatelevel.Atthislevel,ithadtobeavaluemeasure,withtheconsequencethatthisnotionofcapitalwasconflatingthenotionsofphysicalcapital(alistofheterogeneousmachines)andfinancialcapital(afundofresourc

31、es,“money),whichwereverydifferentinclassicaleconomics.Theneoclassicaleconomistsusedthefirstnotionofcapitalinthestudyofinterestandportfolioadjustment;capitalinphysicaltermswasusedinthetheoreticalstudyofproduction(Clark1893).Clark,however,arguedthat,overlongperiodsoftime,changesinthevalueofcapitalrefl

32、ectedchangesinthestockofinvestmentgoods.Thiswasimperativeinordertoshowthat,inalaissez-faireeconomy,eachindividual(factorofproduction)whocontributedtoproductionreceivedthevalueofwhatheorsheproduced(inanormativesense,deserved).Thiswas,ofcourse,thepointofthemarginalisttheoryofproduction:thewagerateequa

33、lsthemarginalproductoflabor,andthereturnoneachdollarofcapitalequalsthemarginalproductofcapital.Hence,eachsocialclassgetswhatitcontributestoproduction(naturally,thereisaclearcontrastbetweenthisviewoftheworldandthatprovidedbythelabortheoryofvalue,inparticulartheMarxianversion).TheCambridgeCapitalContr

34、oversieswereplaguedwithconfusions.Themostimportantisbetweenthelegitimacyofpostulatinganaggregateproductionfunction,andthelegitimacyofthemarginalist-neoclassical,orthesupply-demand,approachtodistribution.Theimportantquestionisthesecondone.Itisonlywhenoneacceptsthemarginalistapproachthatonemayfeellike

35、usingaggregateproductionfunctionswhosemarginalproductsdeterminedistribution.So,onemustask:whatkindofaggregationisneededtorthevalidityoftheneoclassicalapproachto(macro)distribution?WhatwastheproblemRobinson(1953-54)pointedoutandwhichinitiatedtheCCTCs?Shecriticizedthatthedistinctionmadebytheneoclassic

36、aleconomistsbetweencapitalasamonetaryfundandcapitalasacollectionofdifferentcapitalgoodswascompletelylostaftertheKeynesianRevolution,inparticular,inempiricalanalyses.Infact,accordingtoRobinson,thetwoconceptionsofcapitalweremixed.Atsomepointintime,economistsbegananalyzingtheperformanceoftheeconomyinte

37、rmsofanaggregateproductionfunctionwith“capital”andlaborasfactorsofproduction,andbegandiscussingtheremunerationofthesefactorsintermsoftheirmarginalproductivities.Asaconsequence,itappearedthatthedivisionoftheaggregateproductbetweenlaborandcapitalcouldbeexplainedintermsofmarginalproductivities.Robinson

38、(1953-54)askedtheimportantquestionthattriggeredthedebate:inwhatunitis“capital“tobemeasured?Robinsonwasreferringtotheuseoftcapita,asafactorofproductioninaggregateproductionfunctions.Becausecapitalgoodsareaseriesofheterogeneouscommodities(physicalinvestmentgoods),eachhavingspecifictechnicalcharacteris

39、tics,itisimpossibletoexpressthestockofcapitalgoodsasahomogeneousphysicalentity.Robinsonclaimedthatitfollowedthatonlytheirvaluescouldbeaggregated.Suchavalueaggregate,however,isnotindependentoftherateofprofitandthusofincomedistribution.Thisheterogeneityofcapitalbecameanimportantpartofthecontroversies(

40、atleastinitiallyandcertainlyforRobinson).TheClarkianconceptofcapital,conceivedasafairlyhomogeneousandamorphousmasswhichcouldtakedifferentforms,Robinsonargued,cannotserveinamacroeconomicproductionfunctionbecauseitisessentiallyamonetaryvalue.Sheclaimed,perhapsimplausibly,thatalthoughlaborisnotahomogen

41、eousinput,inprincipleitcanbemeasuredinatechnicalunit,i.e.,man-hoursofwork(disregardingdifferentqualities).Thesamegoesforland(acresoflandofagivenquality).Thesearenaturalunits,sothatthemarginalproductsoflandandlaborcouldbedefinedindependentlyoftheequilibriumfactorprices.Butwhatabout(aggregate)capital?

42、Robinsonarguedthatthestatisticsofcapitalusedinpracticehadnothingtodowiththeprevioustwonotionsofcapital.Suchstatisticsarevalues(e.g.,dollars)andnomatterhowtheyaredeflated(toconvertthemintoconstantdollars),theycontinuetobemoney-asumofvalue.Therefore,thiscannotbemadetocorrespondtoaphysicalfactorofprodu

43、ction.Allthismattersbecause,itwasclaimed,itisimpossibletogetanynotionofcapitalasameasurablequantityindependentofdistributionandprices.Thatis,ifdistributionistobeexplainedbytheforcesofsupplyofanddemandforthefactorsofproduction,thenthelattermusteachhaveameasure.Thosemeasuresmustbehomogeneoussothataggr

44、egationispossible.Thiswasclaimednottobepossibleforcapitalasafactorofproduction,butonlywhenitisanamountoffinance.Thus,capitalhasnonaturalunit,akintolaborandland,whichcanapparentlybeaggregatedtogiveaquantityofaproductiveservice,thatcanthenbeusedforthedeterminationoftheirprices.Wenote,however,thatsucha

45、ggregationisillusory,andtheaggregationproblemisnotrestrictedtocapital.WasonelaborhourbyRobinsonreallythesameasonebyQueenElizabethIIoroneofBritneySpearsintermsofproductivity?Theanswerisno.TheargumentoftheCambridge,Englandeconomistswasthatinvestmentgoods,whichmakeupthestockofrealcapitalarethemselvespr

46、oduced(i.e.,producedmeansofproduction).Thesegoodsareproducedinamarketeconomywherecapitalistsrequireprofits.Thisimpliesthatinordertoprovidea“quantityofcapita,onemustfirstknowitsprice.Infact,thepriceofanycommoditycannotbedeterminedindependentlyofthetechnicalconditionsofproductionandoftherateofprofits.

47、Inotherwords,thepriceoftheaggregatefactorcapitalisaffectedbythedistributionofincomeamongthefactors.Thevalueofcapitalchangesastheprofitandwagerateschangesothatthesamephysicalcapitalcanrepresentadifferentvalue,whereasdifferentstocksofcapitalgoodscanhavethesamevalue(Robinson1956).Solongasthecapitalstoc

48、kisheterogeneous,itsmeasurementrequiresknowledgeoftherelativevaluesofindividualcapitalgoods.Thiscanonlybeachievedifthepricevectoroftheeconomyandtherateofprofitswereknownexante.Theconsequenceisthataggregatecapital,theaggregateproductionfunction,andthemarginalproductsofthefactorscanonlybedefinedwhenth

49、erateofprofitisgiven,implyingthattheycannotbeusedtobuildatheoryoftherateofprofitordistribution.Robinson,scritiqueledtoaseriesofintertwineddebatesthatlastedtwodecadesandwhichwentfarbeyondtheoriginalquestion.Themaindebateswereaboutthefollowingfiveissues.(i) Thetheoryofdistribution,inparticulartheneoclassicalclaimthatthedistributionofincomecouldbederivedfromsometechnicalpropertiesofaneconomy,embeddedintheproductionfunction,andthatfactorsharescouldbesomehowlinkedtothemargina