高级宏观经济学\新增长理论\新增长理论Ⅱ：人力资本模型\Lucas-1988

JournalofMonetaryEconomics22(1988)3-42.North-HollandONTHEMECHANICSOFECONOMICDEVELOPMENT*RobertE.LUCAS,Jr.UniuersiwofChicago,Chicago,IL60637,USAReceivedAugust1987,finalversionreceivedFebruary1988Thlspaperconsiderstheprospectsforconstructinganeoclassicaltheoryofgrowthandinterna-tionaltradethatisconsistentwithsomeofthemainfeaturesofeconomicdevelopment.Threemodelsareconsideredandcomparedtoevidence:amodelemphasizingphysicalcapitalaccumula-tionandtechnologicalchange,amodelemphasizinghumancapitalaccumulationthroughschool-ing,andamodelemphasizingspecializedhumancapitalaccumulationthroughlearning-by-doing.1.IntroductionBytheproblemofeconomicdevelopmentImeansimplytheproblemofaccountingfortheobservedpattern,acrosscountriesandacrosstime,inlevelsandratesofgrowthofpercapitaincome.Thismayseemtoonarrowadefinition,andperhapsitis,butthinkingaboutincomepatternswillneces-sarilyinvolveusinthinkingaboutmanyotheraspectsofsocietiestoo,soIwouldsuggestthatwewithholdjudgmentonthescopeofthisdefinitionuntilwehaveaclearerideaofwhereitleadsus.Themainfeaturesoflevelsandratesofgrowthofnationalincomesarewellenoughknowntoallofus,butIwanttobeginwithafewnumbers,soastosetaquantitativetoneandtokeepusfromgettingmiredinthewrongkindofdetails.UnlessIsayotherwise,allfiguresarefromtheWorldBank'sWorldDevelopmentReportof1983.Thediversityacrosscountriesinmeasuredpercapitaincomelevelsisliterallytoogreattobebelieved.Comparedtothe1980averageforwhattheWorldBankcallsthe'industrialmarketeconomies'(IrelandupthroughSwitzerland)ofU.S.$10,000,India'spercapitaincomeis$240,Haiti'sis$270,*ThispaperwasoriginallywrittenfortheMarshallLectures,givenatCambridgeUniversityin1985.!amverygratefultotheCambridgefacultyforthishonor,andalsofortheinvitation'slongleadtime,whichgavemetheopportunitytothinkthroughanewtopicwiththestimulusofsodistinguishedanaudienceinprospect.Sincethen,versionsofthlslecturehavebeengivenastheDavidHorowitzLecturesinIsrael,theW.A.MackintoshLectureatQueensUniversity,theCarlSnyderMemorialLectureattheUniversityofCaliforniaatSantaBarbara,theChung-HuaLectureinTaipei,theNancySchwartzLectureatNorthwesternUniversity,andtheLionelMcKenzieLectureattheUniversityofRochester.Ihavealsobasedseveralseminarsonvariouspartsofthismaterial.0304-3932/88/$3.5001988,ElsevierSciencePublishersB.V.(North-Holland)4R.E.Lucas,Jr.,Onthemechanicsofeconomicdevelopmenlandsoonfortherestoftheverypoorestcountries.Thisisadifferenceofafactorof40inlivingstandards!Theselatterfiguresaretoolowtosustainlifein,say,EnglandortheUnitedStates,sotheycannotbetakenatfacevalueandIwillavoidhangingtoomuchontheirexactmagnitudes.ButIdonotthinkanyonewillarguethatthereisnotenormousdiversityinlivingstan-dards.'RatesofgrowthofrealpercapitaGNParealsodiverse,evenoversustainedperiods.For1960-80weobserve,forexample:India,1.4%peryear;Egypt,3.4%;SouthKorea,7.0%;Japan,7.1%;theUnitedStates,2.3%;theindustrialeconomiesaveraged3.6%.Toobtainfromgrowthratesthenumberofyearsittakesforincomestodouble,dividethesenumbersinto69(thelogof2times100).ThenIndianincomeswilldoubleevery50years;Koreanevery10.AnIndianwill,onaverage,betwiceaswelloffashisgrandfather;aKorean32times.Thesedifferencesareatleastasstrikingasdifferencesinincomelevels,andinsomerespectsmoretrustworthy,sincewithin-countryincomecompari-sonsareeasiertodrawthanacross-countrycomparisons.Ihavenotcalculatedacorrelationacrosscountriesbetweenincomelevelsandratesofgrowth,butitwouldnotbefarfromzero.(Thepoorestcountriestendtohavethelowestgrowth;thewealthiestnext;the'middle-income'countrieshghest.)Thegeneralizationsthatstriketheeyehavetodowithvariabilitywithnthesebroadgroups:therichcountriesshowlittlediversity(Japanexcepted-elseitwouldnothavebeenclassedasarichcountryin1980atall).Withinthepoorcountries(lowandmiddleincome)thereisenormousvariability.*Withintheadvancedcountries,growthratestendtobeverystableoverlongperiodsoftime,providedoneaveragesoverperiodslongenoughtoeliminatebusiness-cycleeffects(orcorrectsforshort-termfluctuationsinsomeotherway).Forpoorercountries,however,therearemanyexamplesofsudden,largechangesingrowthrates,bothupanddown.Someofthesechangesarenodoubtduetopoliticalormilitarydisruption:Angola'stotalGDPgrowthfellfrom4.8inthe60sto-9.2inthe70s;Iran'sfellfrom11.3to2.5,comparingthesametwoperiods.Idonotthnkweneedtolooktoeconomictheoryforanaccountofeitherofthesedeclines.TherearealsosomestrikingexampleshheincomeestimatesreportedinSummersandHeston(1984)aremoresatisfactorythanthoseintheWorldDevelopmentReports.In1975U.S.dollars,theseauthorsestimate1980U.S.realGDPpercapitaat$8000,andfortheindustrializedeconomiesasagroup,$5900.ThecomparablefiguresforIndiaandHaitiare$460and$500,respectively.Incomedifferencesofafactorof16arecertainlysmaller,andIthnkmoreaccurate,thanafactorof40,butIthinktheyarestillfairlydescribedasexhibiting'enormousdiversity'.'~aumol(1986)summarizesevidence,mainlyfromMaddison(1982)indicatingapparentconvergenceduringthiscenturytoacommonpathoftheincomelevelsofthewealthiestcountries.ButDeLong(1987)showsthatthiseffectisentirelydueto'selectionbias':Ifoneexaminesthecountrieswiththehighestincomelevelsatthebeginningofthecentury(asopposedtocurrently,asinMaddison's'sample')thedatashowapparentdivergence!R.E.Lucus.Jr..Onthemechanicsofeconomicdeoelopmenl5ofsharpincreasesingrowthrates.ThefourEastAsian'miracles'ofSouthKorea,Taiwan,HongKongandSingaporearethemostfamiliar:forthe1960-80period,percapitaincomeintheseeconomiesgrewatratesof7.0,6.5,6.8and7.5,respectively,comparedtomuchlowerratesinthe1950'sandearlier.3,4Betweenthe60sandthe70s,Indonesia'sGDPgrowthincreasedfrom3.9to7.5;Syria'sfrom4.6to10.0.Idonotseehowonecanlookatfigureslikethesewithoutseeingthemasrepresentingpossibilities.IstheresomeactionagovernmentofIndiacouldtakethatwouldleadtheIndianeconomytogrowlikeIndonesia'sqrEgypt's?Ifso,what,exactly?Ifnot,whatisitaboutthe'natureofIndia'thatmakesitso?Theconsequencesforhumanwelfareinvolvedinquestionslikethesearesimplystaggering:Onceonestartstothinkaboutthem,itishardtothinkaboutanythingelse.Thisiswhatweneedatheoryofeconomicdevelopmentfor:toprovidesomekindofframeworkfororganizingfactslikethese,forjudgingwhichrepresentopportunitiesandwhichnecessities.Buttheterm'theory'isusedinsomanydifferentways,evenwithineconomics,thatifIdonotclarifywhatImeanbyitearlyon,thegapbetweenwhatIthinkIamsayingandwhatyouthinkyouarehearingwillgrowtoowideforustohaveaseriousdiscussion.Iprefertousetheterm'theory'inaverynarrowsense,torefertoanexplicitdynamicsystem,somethingthatcanbeputonacomputerandrun.ThisiswhatImeanbythe'mechanics'ofeconomicdevelopment-theconstructionofamechanical,artificialworld,populatedbytheinteractingrobotsthateconomicstypicallystudies,thatiscapableofexhibitingbehaviorthegrossfeaturesofwhichresemblethoseoftheactualworldthatIhavejustdescribed.Mylectureswillbeoccupiedwithonesuchconstruction,anditwilltakesomework:Itiseasytosetoutmodelsofeconomicgrowthbasedonreasonable-lookingaxiomsthatpredictthecessationofgrowthinafewdecades,orthatpredicttherapidconvergenceofthelivingstandardsofdifferenteconomiestoacommonlevel,orthatotherwiseproducelogicallypossibleoutcomesthatbearnoresemblancetotheoutcomesproducedbyactualeconomicsystems.Ontheotherhand,thereisnodoubtthattheremustbemechanicsotherthantheonesIwilldescribethatwouldfitthefactsaboutaswellasmine.ThlsiswhyIhavetitledthelectures'OntheMechanics...'ratherthansimply'TheMechanicsofEconomicDevelopment'.Atsomepoint,then,thestudyofdevelopmentwillneedtoinvolveworkingouttheimplicationsofcompetingtheoriesfordataotherthanthosetheywereconstructedtofit,andtestingtheseimplicationsagainstobservation.Butthisisgettingfaraheadofthe3~heWorldBanknolongertransmitsdataforTaiwan.Thefigure6.5inthetextisfromHarberger(1984,table1,p.9).4~ccordingtoHestonandSummers(1984),Taiwan'sper-capitaGDPgrowthrateinthe1950swas3.6.SouthKorea'swas1.7from1953to1960.6R.E.Lucas,Jr.,OnthemechanicsofeconomicdevelopmentstoryIhavetotell,whichwillinvolveleavingmanyimportantquestionsopenevenatthepurelytheoreticallevelandwilltouchuponquestionsofempiricaltestinghardlyatall.Myplanisasfollows.Iwillbeginwithanapplicationofanow-standardneoclassicalmodeltothestudyoftwentiethcenturyU.S.growth,closelyfollowingtheworkofRobertSolow,EdwardDenisonandmanyothers.Iwillthenask,somewhatunfairly,whetherthismodelasitstandsisanadequatemodelofeconomicdevelopment,concludingthatitisnot.Next,Iwillconsidertwoadaptationsofthisstandardmodeltoincludetheeffectsofhumancapitalaccumulation.Thefirstretainstheone-sectorcharacteroftheoriginalmodelandfocusesontheinteractionofphysicalandhumancapitalaccumulation.Thesecondexaminesatwo-goodsystemthatadmitsspecializedhumancapitalofdifferentkindsandoffersinterestingpossibilitiesfortheinteractionoftradeanddevelopment.Finally,Iwillturntoadiscussionofwhathasbeenarrivedatandofwhatisyettobedone.Ingeneral,Iwillbefocusingonvariousaspectsofwhateconomists,usingthetermverybroadly,callthe'technology'.Iwillbeabstractingaltogetherfromtheeconomicsofdemography,takingpopulationgrowthasagiventhroughout.Thisisaseriousomission,forwhichIcanonlyoffertheexcusethataseriousdiscussionofdemographicissueswouldbeatleastasdifficultastheissuesIwillbediscussingand1haveneitherthetimenortheknowledgetodoboth.Ihopetheinteractionsbetweenthesetopicsarenotsuchthattheycannotusefullybeconsideredseparately,atleastinapreliminaryway.5Iwillalsobeabstractingfromallmonetarymatters,treatingallexchangeasthoughitinvolvedgoods-for-goods.Ingeneral,Ibelievethattheimportanceoffinancialmattersisverybadlyover-stressedinpopularandevenmuchprofessionaldiscussionandsoamnotinclinedtobeapologeticforgoingtotheotherextreme.YetinsofarasthedevelopmentoffinancialinstitutionsisalimitingfactorindevelopmentmoregenerallyconceivedIwillbefalsifyingthepicture,andIhavenoclearideaastohowbadly.Butonecannottheorizeabouteverythingatonce.IhadbettergetonwithwhatIdohavetosay.2.Neoclassicalgrowththeory:ReviewTheexample,ormodel,ofasuccessfultheorythatIwilltrytobuildonisthetheoryofeconomicgrowththatRobertSolowandEdwardDenisondevelopedandappliedtotwentiethcenturyU.S.experience.Thistheorywillserveasabasisforfurtherdiscussioninthreeways:asanexampleoftheformthatIbelieveusefulaggregativetheoriesmusttake,asanopportunityto'~eckerandBarro(1985)isthefirstattemptknowntometoanalyzefertilityandcapitalaccumulationdecisionssimultaneouslywithnageneralequilibriumframework.Tamura(1986)containsfurtherresultsalongthisline.R.E.Lucm,Jr.,Onthemechanicsofeconomicdeuelopmenr7explainexactlywhattheoriesofthisformcantellusthatotherkindsoftheoriescannot,andasapossibletheoryofeconomicdevelopment.Inthisthirdcapacity,thetheorywillbeseentofailbadly,butalsosuggestively.Followinguponthesesuggestionswilloccupytheremainderofthelectures.BothSolowandDenisonwereattemptingtoaccountforthemainfeaturesofU.S.economicgrowth,nottoprovideatheoryofeconomicdevelopment,andtheirworkwasdirectedataverydifferentsetofobservationsfromthecross-countrycomparisonsIcitedinmyintroduction.ThemostusefulsummaryisprovidedinDenison's1961monograph,TheSourcesofEconomicGrowthintheUnitedStates.Unlessotherwisementioned,thisisthesourceforthefiguresIwillcitenext.Duringthe1909-57periodcoveredinDenison'sstudy,U.S.realoutputgrewatanannualrateof2.9%employedmanhoursat1.3%,andcapitalstockat2.4%.Theremarkablefeatureofthesefigures,ascomparedtothosecitedearlier,istheirstabilityovertime.EvenifonetakesasastartingpointthetroughoftheGreatDepression(1933)outputgrowthto1957averagesonly5%.Ifbusiness-cycleeffectsareremovedinanyreasonableway(say,byusingpeak-to-peakgrowthrates)U.S.outputgrowthiswithinhalfapercentagepointof3%annuallyforanysizeablesubperiodforwhichwehavedata.Solow(1956)wasabletoaccountforthisstability,andalsoforsomeoftherelativemagnitudesofthesegrowthrates,withaverysimplebutalsoeasilyrefineablern~del.~Therearemanyvariationsofthlsmodelinprint.Iwillsetoutaparticularlysimpleonethatischosenalsotoservesomelaterpurposes.Iwilldosowithoutmuchcommentonitsassumedstructure:Thereisnopointinarguingoveramodel'sassumptionsuntiloneisclearonwhatquestionsitwillbeusedtoanswer.Weconsideraclosedeconomywithcompetitivemarkets,withidentical,rationalagentsandaconstantreturnstechnology.AtdatetthereareN(r)personsor,equivalently,manhoursdevotedtoproduction.TheexogenouslygivenrateofgrowthofN(t)isA.Real,per-capitaconsumptionisastreamc(t),t20,ofunitsofasinglegood.Preferencesover(per-capita)consumptionstreamsaregivenby6~olow's1956paperstimulatedavastliteratureinthe1960s,exploringmanyvariationsontheoriginalone-sectorstructure.SeeBurmeisterandDobell(1970)foranexcellentintroductionandsurvey.Byputtingarelativelysimpleversiontoempiricaluse,as1shallshortlydo,Idonotintendanegativecommentonthisbodyofresearch.Onthecontrary,itisexactlythiskindoftheoreticalexperimentationwithalternativeassumptionsthatisneededtogiveonetheconfidencethatworkingwithaparticular,simpleparameterizationmay,forthespecificpurposeathand,beadequate.8R.E.Lucas,Jr.,Onthemechanicsofeconomicdevelopmentwherethediscountratepandthecoefficientof(relative)riskaversionuarebothpositive.'Productionpercapitaoftheonegoodisdividedintoconsumptionc(t)andcapitalaccumulation.IfweletK(t)denotethetotalstockofcapital,andd(t)itsrateofchange,thentotaloutputisN(t)c(t)+~(t).[Hered(t)isnetinvestmentandtotaloutputN(t)c(t)+d(t)isidentifiedwithnetnationalproduct.]ProductionisassumedtodependonthelevelsofcapitalandlaborinputsandonthelevelA([)ofthe'technology',accordingtowhere00.Theresourceallocationproblemfacedbythlssimpleeconomyissimplytochooseatimepathc(t)forper-capitaconsumption.Givenapathc(t)andaninitialcapitalstockK(O),thetechnology(2)thenimpliesatimepathK(t)forcapital.ThepathsA(t)andN(t)aregivenexogenously.Onewaytothinkaboutthisallocationproblemistothinkofchoosingc(t)ateachdate,giventhevaluesofK(t),A(t)andN(t)thathavebeenattainedbythatdate.Evidently,itwillnotbeoptimaltochoosec(t)tomaximizecurrent-periodutility,N(t)[l/(l-u)][c(t)-I]'-",forthechoicethatachievesthisistosetnetinvestment~(t)equaltozero(or,iffeasible,negative):Oneneedstosetsomevalueorpriceonincrementstocapital.Acentralconstructinthestudyofoptimalallocations,allocationsthatmaximizeutility(1)subjecttothetechnology(2),isthecurrent-valueHamiltonianHdefinedbywhichisjustthesumofcurrent-periodutilityand[from(2)]therateofincreaseofcapital,thelattervaluedatthe'price'B(t).AnoptimalallocationmustmaximizetheexpressionHateachdatet,providedtheprice8(t)iscorrectlychosen.Thefirst-orderconditionformaximizingHwithrespecttociswhichistosaythatgoodsmustbesoallocatedateachdateastobeequallyvaluable,onthemargin,usedeitherasconsumptionorasinvestment.Itisheinversea-'ofthecoefficientofriskaversionissometimescalledtheintertemporalelasticityofsubstitution.Sinceallthemodelsconsideredinthspaperaredeterministic,thslatterterminologymaybemoresuitable.R.ELucas,Jr.,Onthemechanicsofeconomicdeuelopmenlknownthattheprice8(t)mustsatisfyateachdatetifthesolutionc(t)to(3)istoyieldanoptimalpath(c(t))S",,.Nowif(3)isusedtoexpressc(t)asafunctionf?(t),andthisfunction8-'/"issubstitutedinplaceofc(t)in(2)and(4),thesetwoequationsareapairoffirst-orderdifferentialequationsinK(t)andits'price'B(t).Solvingthissystem,therewillbeaone-parameterfamilyofpaths(K(t),B(t)),satisfyingthe&eninitialconditiononK(0).Theuniquememberofthsfamilythatsatisfiesthetransversalitycondition:istheoptimalpath.IamhopingthatthisapplicationofPontryagin'sMaxi-mumPrinciple,essentiallytakenfromDavidCass(1961),isfamiliartomostofyou.Iwillbeapplyingthesesameideasrepeatedlyinwhatfollows.Forthisparticularmodel,withconvexpreferencesandtechnologyandwithnoexternaleffectsofanylund,itisalsoknownandnotatallsurprisingthattheoptimalprogramcharacterizedby(2),(3),(4)and(5)isalsotheuniquecompetitiveequilibriumprogram,providedeitherthatalltradingisconsum-matedinadvance,Arrow-Debreustyle,or(andthisistheinterpretationIfavor)thatconsumersandfirmshaverationalexpectationsaboutfutureprices.Inthisdeterministiccontext,rationalexpectationsjustmeansperfectfore-sight.Formypurposes,itisthisequilibriuminterpretationthatismostinteresting:IintendtousethemodelasapositivetheoryofU.S.economicgrowth.Inordertodothis,wewillneedtoworkoutthepredictionsofthemodelinmoredetail,whichinvolvessolvingthedifferentialequationsystemsowecanseewhattheequilibriumtimepathslooklikeandcomparethemtoobserva-tionslikeDenison's.Ratherthancarrythisanalysisthroughtocompletion,IwillworkoutthepropertiesofaparticularsolutiontothesystemandthenjustindicatebrieflyhowtherestoftheanswercanbefoundinCass'spaper.Letusconstructfrom(2),(3)and(4)thesystem'sbalancedgrowthpath:theparticularsolution(K(t),8(t),c(t))-suchthattheratesofgrowthofeachofthesevariablesisconstant.(Ihaveneverbeensureexactlywhatitisthatis'balanced'alongsuchapath,butweneedatermforsolutionswiththisconstantgrowthratepropertyandthisisasgoodasany.)LetKdenotetherateofgrowthofper-capitaconsumption,E(t)/c(t),onabalancedgrowth10R.E.Lucas,Jr.,Onthemechanicsofeconomicdevelopmentpath.Thenfrom(3),wehaveB(t)/e(t)=-OK.Thenfrom(4),wemusthaveThatis,alongthebalancedpath,themarginalproductofcapitalmustequaltheconstantvaluep+OK.WiththisCobb-Douglastechnology,themarginalproductofcapitalisproportionaltotheaverageproduct,sothatdividing(2)throughbyK(t)andapplying(6)weobtainBydefinitionofabalancedpath,~(t)/~(t)isconstantso(7)impliesthatN(t)c(t)/K(t)isconstantor,differentiating,thatThusper-capitaconsumptionandper-capitacapitalgrowatthecommonrateK.Tosolveforthiscommonrate,differentiateeither(6)or(7)toobtainThen(7)maybesolvedtoobtaintheconstant,balancedconsumption-capitalratioN(t)c(t)/K(t)or,whichisequivalentandslightlyeasiertointerpret,theconstant,balancednetsavingsratesdefinedbyHencealongabalancedpath,therateofgrowthofper-capitamagnitudesissimplyproportionaltothegivenrateoftechnicalchange,p,wheretheconstantofproportionalityistheinverseoflabor'sshare,1-P.Therateoftimepreferencepandthedegreeofriskaversionahavenobearingonthislong-rungrowthrate.Lowtimepreferencepandlowriskaversionainduceahghsavingsrates,andhghsavingsis,inturn,associatedwithrelativelyhighoutputlevelsonabalancedpath.Athriftysocietywill,inthelongrun,bewealthierthananimpatientone,butitwillnotgrowfaster.Inorderthatthebalancedpathcharacterizedby(9)and(10)satisfythetransversalitycondition(5),itisnecessarythatp+OK>K+A.[From(lo),oneseesthatthisisthesameasrequiringthesavingsratetobelessthancapital'sR.E.Lucas,Jr.,Onthemechanicso/economicdevelopment11share.]Underthiscondition,aneconomythatbegnsonthebalancedpathwillfinditoptimaltostaythere.Whatofeconomiesthatbeginofthebalancedpath-surelythenormalcase?Cassshowed-andthisisexactlywhythebalancedpathisinterestingtous-thatforanyinitialcapitalK(0)>0,theoptimalcapital-consumptionpath(K(t),c(t))willconvergetothebalancedpathasymptotically.Thatis,thebalancedpathwillbeagoodapproximationtoanyactualpath'most'ofthetime.Nowgiventhetasteandtechnologyparameters(p,a,A,Pandp)(9)and(10)canbesolvedfortheasymptoticgrowthrateKofcapital,consumptionandrealoutput,andthesavingsratesthattheyimply.Moreover,itwouldbestraightforwardtocalculatenumericallytheapproachtothebalancedpathfromanyinitialcapitallevelK(0).Thisistheexercisethatanidealizedplannerwouldgothrough.Ourinterestinthemodelispositive,notnormative,sowewanttogointheoppositedirectionandtrytoinfertheunderlyingpreferencesandtechnologyfromwhatwecanobserve.Iwilloutlinethis,takingthebalancedpathasthemodel'spredictionforthebehavioroftheU.S.economyduringtheentire(1909-57)periodcoveredbyDenison'sstudy.8Fromthispointofview,Denison'sestimatesprovideavalueof0.013forA,andtwovalues,0.029and0.024forK+A,dependingonwhetherweuseoutputorcapitalgrowthrates(whichthemodelpredictstobeequal).Inthetraditionofstatisticalinference,letusaveragetogetK+X=0.027.Thetheorypredictsthat1-Pshouldequallabor'sshareinnationalincome,about0.75intheU.S.,averagingovertheentire1909-57period.Thesavingsrate(netinvestmentoverNNP)isfairlyconstantat0.10.Then(9)impliesanestimateof0.0105forp.Eq.(10)impliesthatthepreferenceparameterspandasatisfy(Theparameterspandaarenotseparatelyidentifiedalongasmoothconsumptionpath,sothisisasfaraswecangowiththesampleaveragesIhaveprovided.)ThesearetheparametervaluesthatgivethetheoreticalmodelitsbestfittotheU.S.data.Howgoodafitisit?Eitheroutputgrowthisunderpredictedorcapitalgrowthoverpredicted,asremarkedearlier(andinthetheoryofgrowth,ahalfaperce