Chapter3TheoryofEconomicGrowth主講：陳忠斌（博士）武漢大學經(jīng)濟發(fā)展研究中心武漢大學經(jīng)濟與管理學院ChapterHighlightsEconomicgrowthisduetogrowthininputs,suchaslaborandcapital,andtoimprovementsintechnology.Capitalaccumulatesthroughsavingandinvestment.Thelong-runlevelofoutputperpersondependspositivelyonthesavingsrateandnegativelyintherateofpopulationgrowth.Theneoclassicalgrowthmodelsuggeststhatthestandardoflivinginpoorcountrieswilleventuallyconvergetothelevelinwealthycountries.ChapterHighlightsRatesofeconomicgrowthvarywidelyacrosscountriesandacrosstime.Endogenousgrowththeoryattemptstoexplaingrowthratesasfunctionsofsocietaldecisions,inparticularsavingsrates.Incomeinpoorcountriesappearstobeconvergingtowardincomelevelsofrichcountries,butatextraordinarilyslowrates.1.LongTermGrowthinChina仍然屬于中低收入國家.發(fā)展不平衡：2003年，深圳市的人均GDP為6510美元，是全國平均值的6倍總量大，人均量低?？偭颗琶?，人均量排名第136。生活水準與美國相差100年（反映了中國經(jīng)濟增長質(zhì)量的欠缺）。粗放式經(jīng)濟增長為主：主要依靠增加物質(zhì)資源消耗和勞動力投入帶動GDP增長。加快轉(zhuǎn)變經(jīng)濟發(fā)展方式,推動產(chǎn)業(yè)結構優(yōu)化升級.堅持擴大國內(nèi)需求特別是消費需求的方針,促進經(jīng)濟增長由主要依靠投資、出口拉動向依靠消費、投資、出口協(xié)調(diào)拉動轉(zhuǎn)變；由主要依靠第二產(chǎn)業(yè)帶動向依靠第一、第二、第三產(chǎn)業(yè)協(xié)同帶動轉(zhuǎn)變；由主要依靠增加物質(zhì)資源消耗向主要依靠科技進步、勞動者素質(zhì)提高、管理創(chuàng)新轉(zhuǎn)變。發(fā)展現(xiàn)代產(chǎn)業(yè)體系,大力推進信息化與工業(yè)化融合,促進工業(yè)由大變強,振興裝備制造業(yè),淘汰落后生產(chǎn)能力；提升高新技術產(chǎn)業(yè),發(fā)展信息、生物、新材料、航空航天、海洋等產(chǎn)業(yè)；發(fā)展現(xiàn)代服務業(yè)，提高服務業(yè)比重和水平；加強基礎產(chǎn)業(yè)基礎設施建設，加快發(fā)展現(xiàn)代能源產(chǎn)業(yè)和綜合運輸體系。(資源來源：中國共產(chǎn)黨第17大報告，2007年10月15日)TheVarietyofGrowthExperiencesCopyright?2004South-Westernreturn亞當?斯密常常被認為是現(xiàn)代經(jīng)濟學之父。其《國民財富的性質(zhì)和原因的研究》于1776年出版。為什么各國的發(fā)展速度不同這一問題從那時起一直是經(jīng)濟探索的最重要問題。AdamSmithandincreasingreturns斯密最重要的貢獻之一是把以勞動分工為基礎的報酬遞增概念引入了經(jīng)濟學。他把勞動分工看作是社會經(jīng)濟的基礎，否則每個人都變成了RobinsonCrusoe,生產(chǎn)自己所需要的一切。正是以勞動分工為基礎的報酬遞增概念，成為了對作為自行產(chǎn)生過程的經(jīng)濟進步抱有樂觀主義觀點的核心。報酬遞增意味著勞動生產(chǎn)率和人均收入隨著產(chǎn)出和就業(yè)擴張而上升；而報酬遞減意味著勞動生產(chǎn)率和人均收入下降，勞動就業(yè)限制在某一點上－－在這一點之后，勞動的邊際產(chǎn)品下降到生存工資的水平。報酬遞增在大多數(shù)工業(yè)活動中普遍存在，而報酬遞則是農(nóng)業(yè)和采礦業(yè)等以土地為基礎的活動的特點，因為土地是一個固定的生產(chǎn)要素。(A.P.Thirlwall,GrowthandDevelopment(1999),p83-86.)Appendix:ClassicalgrowththeoryTheclassicalpessimists斯密以后對經(jīng)濟發(fā)展過程的古典主義觀點基本上悲觀主義的。它集中討論迅速的人口增長與由農(nóng)業(yè)報酬遞減和成本上升所造成的糧價上升對工業(yè)利潤率施加的影響。最大的悲觀主義者之一是托馬斯?馬爾薩斯(ThomasMalthus)。馬爾薩斯的著作分為兩部分：他的人口論和他的維持有效需求(effectivedemand)對發(fā)展的重要性的論述－－“有效需求”這個概念后來被凱恩斯所借用。事實上，馬爾薩斯是強調(diào)需求對決定產(chǎn)出的重要性的唯一的古典經(jīng)濟學家－－所有其他古典經(jīng)濟學家都信奉薩伊定律Say’sLaw:supplycreatesitsowndemand,sothatthelevelandgrowthofoutputisafunctionofthesupplyofphysicalinputsalone.(A.P.Thirlwall,GrowthandDevelopment(1999),p86.)Appendix:ClassicalgrowththeoryTheclassicalpessimistsMalthusisbestknown,however,forhisEssayonthePrincipleofPopulation(1798),inwhichheclaimedthatthereisa‘constanttendencyinallanimatedlifetoincreasebeyondthenourishmentpreparedforit’.(A.P.Thirlwall,GrowthandDevelopment(1999),p86-87.)Thatfoodproductiononlygrowsatanarithmeticrateimplies,ofcourse,diminishingreturnstoagriculture.Theimbalancebetweenpopulationgrowthandgrowthofthefoodsupplywouldleadtothepercapitaincomeofcountriesoscillating擺動aroundthesubsistencelevel,orbeingcaughtinwhatisnowsometimescalleda‘low-levelequilibriumtrap’.Anyincreasesinpercapitaincomebroughtaboutbytechnicalprogressleadtomorebirths,whichthenreducespercapitaincomebacktosubsistencelevel.Earlydevelopmentmodelsofthe‘bigpush’weredesignedtolifteconomiesfromthistrap.

TheclassicalpessimistsDavidRicardowasanotherofthegreatclassicalpessimists.In1817hepublishedhisPrinciplesofPoliticalEconomyandTaxation,inwhichhepredictedthatcapitalisteconomieswouldendupinanastationarystate,withnogrowth,alsoduetodiminishingreturnsinagriculture.(A.P.Thirlwall,GrowthandDevelopment(1999),p87-89.)FinallyweturntoKarlMarx,famousforhisbookDasKapital(1867),andhispredictionofthecollapseofcapitalism.LetusbrieflyconsiderMarx’smodelandhispredictionofcrisis.Grossoutputconsistsofthreeelements:Variablecapitalorthewagebill(v)Constantcapital(c),thatis,plantandmachinery.Surplusvalueorprofit(s)Thewageoflabouraredeterminedbytheminimumsubsistencelevel,andsurplusvalueisthedifferencebetweenoutputperworkerandminimumwageperworker.Therateofsurplusvalue,orwhatMarxcalledthe‘degreeofexploitation’,isgivenbys/v.Therateofprofitisgivenbytheratioofsurplusvaluetototalcapital,thatisWheretheratioofconstanttovariablecapital(c/v)isdefinedasthe‘organiccompositionofcapital’.Astechniquesofproductionbecomemorecapital-intensive,the‘organiccompositionofcapital’risesthroughtime,andasitdoessotherateofprofitfallsunlesssurplusvaluerises.Whilethereisnolimittotheriseinc/v,however,thereisalimittos/v.Marxforesawnomajorproblemaslongassurpluslabourexiststokeepwagesdown,buthepredictedthatascapitalaccumulationtakesplace,the‘reservearmyoflabour’,ashecalledit,woulddisappear,drivingwagesupandprofitsdown.Thecapitalist’sresponseistheneithertoattempttokeepwagesdown,leadingtothe‘immiseratinofworkers’andsocialconflict,ortosubstitutemorecapitalforlabour,whichwouldworsentheproblembyraisingc/v.

(A.P.Thirlwall,GrowthandDevelopment(1999),p88-89.)3.1.1.TheHarrod-DomargrowthmodelHarrod’soriginalmodelisadynamicextensionofKeynes’staticequilibriumanalysis.InKeynes’GeneralTheory,heconditionforincomeandoutputtobeinequilibrium(intheclosedeconomy)isthatplanstoinvestequalplanstosave.3.1.增長理論的模型分析

Whatifthepopulationisgrowingaswell?Inthiscasewemustmassage(3.16)alittlebittogetitintopercapitaterms.Letsy(t)=[Y(t)]/[P(t)]denotepercapitaincome.Thensimplybydividingbothsidesof(3.16)byP(t),weseethatSource:DebrajRay(1998),DevelopmentEconomics,PrincetonUniversityPress,Appendix3.A.1,pp90-91.AlsoRay:“What’sNewinDevelopmentEconomics?”–availableat/user/debraj/Papers/AmerEcon.pdf.AndRay:IntroductiontoAReaderinDevelopmentEconomics–availableat/user/debraj/Papers/DevReaderIntro.pdf.此式就是哈羅德-多馬增長模型的基本公式。g表示國民收入增長率或經(jīng)濟增長率，它等于儲蓄傾向除以增量資本-產(chǎn)出比。該模型表明，經(jīng)濟增長率是由儲蓄傾向和資本-產(chǎn)出比共同決定的，它與儲蓄傾向成正比關系，與資本-產(chǎn)出比成反比關系。如果資本-產(chǎn)出不變，經(jīng)濟增長率就決定于儲蓄傾向或儲蓄率，儲蓄傾向越高，則經(jīng)濟增長率越高。如果儲蓄傾向不變，資本-產(chǎn)出比越低，則經(jīng)濟增長率越高。哈羅德-多馬增長模型的批評:批評主要是針對它的假定前提：這個模型是建立在儲蓄能全部轉(zhuǎn)化為投資的假定之上的。這對發(fā)展中國家是特別不現(xiàn)實的。實際上儲蓄轉(zhuǎn)化為投資需要具備很多條件：(1)發(fā)展中國家往往存在著制度缺陷；(2)缺少投資所需的機器設備等物質(zhì)資本品、原材料以及關鍵的技術、而且由于外匯短缺也不可能都靠進口來解決；(3)社會基礎設施(交通通訊,電力等)十分落后，對投資造成了重大的障礙。這個模型是建立在資本-產(chǎn)出比不變的假定上的。實際上，隨著經(jīng)濟發(fā)展，資本-產(chǎn)出比不可能不變。發(fā)展中國家為了加速工業(yè)化和實行進口替代發(fā)展戰(zhàn)略，常常把大量的資金投入資本密集度很高的工業(yè)上，如汽車、鋼鐵等部門。因此。增量資本—產(chǎn)出比一般是趨于上升的。3.這個模型只有資本（儲蓄）一個變量，這實際上暗含地假定資本—勞動比例是不變的，即資本與勞動同比例地增加，資本增加百分之一，勞動也必須增加百分之一。這也是不現(xiàn)實的。的確，發(fā)展中國家的勞動力資源是豐富的，但是，豐富的是無技術的、非熟練的勞動者，而受過良好教育和訓練的技術人員和稱職的管理者卻是非常稀缺的。因此，即使投資所需的資本品能夠得到滿足，因缺乏有技能的勞動力和合格的管理者而不能形成實際投資，或者形成了實際投資，投資效率也是十分低下的。此外，假定資本－勞動比不變還意味著不能用勞動來代替資本，這不僅不符合實際，而且是十分有害的。因為發(fā)展中國家勞動力豐富，充分利用剩余勞動力資源是能創(chuàng)造出資本和增加產(chǎn)出的。Exercises(seechapter3,DebrajRay,)(1):Afirmissetuptoproduceandsellcottonshirts.Itbuysplantandmachineryfor$2millionandlandfor$1million,andconstructawarehouseforanother$1million.Eachyear,ithires100workersandpayseachofthem$2,000peryear.Itbuys$600,000worthofcottonfabrictobeusedinmakingtheshirts.Thefirmsells100,000shirtsayear,whichitpricesat$10pershirt.(a)Howmuchprofitdoesthefirmmakeonayearlybasis,ifyoudonotcountitssetupinvestment?(b)Howmuchincomedoesthefirmgenerateeveryyear?(c)Whatisthecapital-outputratioofthefirm?Explain,usingthisexample,whyacapital-outputratiothatexceeds1isperfectlycompatiblewithprofitmaking.Answers:(1)(a)Therunningcostsareforlabor($2000times100)andforcottonfabric,whichis$600,000.Thustotalcostsare$800,000peryear.Totalrevenuesare$1million.Thusprofits,notcountingsetupinvestment,are$200,000peryear.(b)Tofigureoutincomegenerated,wemustcountthewagepaymentstoworkersaswell,whichare$200,000.Thusincomegeneratediswagesplusprofits(therearenorentshere),whichis$400,000peryear.(c)Theoutputofthefirmis$1millionperyear.Thefirm’sinstalledcapitalis$4million.Thereforethecapital-outputratiois4.Noticethatthecapitalequipmentcanbeusedoverandoveragain(thoughitmightdepreciateovertime).Thereforeacapital-outputratiolargerthanoneisperfectlycompatiblewiththenotionofprofitability.3.1.2.TheNeoclassicalProductionFunctionY=F(K,L)Wesaythattheproductionfunctionisneoclassicalifthefollowingthreepropertiesaresatisfied.First,forallK>0andL>0,F(?)exhibitspositiveanddiminishingmarginalproductswithrespecttoeachinput:Second,F(?)exhibitsconstantreturnstoscale:Third,themarginalproductofcapital(orlabor)approachesinfinityascapital(orlabor)goesto0andapproaches0ascapital(orlabor)goestoinfinityTheselastpropertiesarecalledInadaconditions稻田條件,followingInada(1963).TheconditionofconstantreturnstoscaleimpliesthatoutputcanbewrittenasWherek=K/Listhecapital-laborratio,y=Y/Lispercapitaoutput,andthefunctionf(k)isdefinedtoequalF(k,1).Thisresultmeansthattheproductionfunctioncanbeexpressedinintensiveform集約形式

as(RobertJ.Barro&XavierSal-I-Martin,EconomicGrowth,p16-17.)3.1.2.TheNeoclassicalgrowththeoryTherearethreebasicpropositionsofneoclassicalgrowththeory:Inthelong-runsteadystate,thegrowthofoutputisdeterminedbytherateofgrowthofthelabourforceinefficiencyunits,thatis,bytherateofgrowthofthelabourforceplustherateofgrowthoflabourproductivity,andisindependentoftheratioofsavingandinvestmenttoGDP.Thisissobecauseahighersavingsorinvestmentratioisoffsetbyahighercapital-outputratioorlowerproductivityofcapital,becauseoftheneoclassicalassumptionofdiminishingreturnstocapital.(A.P.Thirlwall,GrowthandDevelopment(1999),p94.)Thelevelofpercapitaincome,however,doesdependontheratioofsavingandinvestmenttoGDP.ThelevelofPCYvariespositivelywiththesavings-investmentratioandnegativelywiththerateofgrowthofthepopulation.Givenidenticaltastes(thatis,preferencesforsavingvis-à-visconsumption)andtechnology(productionfunctions)acrosscountries,therewillbeaninverserelationacrosscountriesbetweenthecapital-labourratioandtheproductivityofcapital，sothatpoorcountrieswithasmallamountofcapitalperheadshouldgrowfasterthanrichcountrieswithalotofcapitalperhead,leadingtotheconvergenceofpercapitaincomesandlivingstandardsacrosstheworld.(A.P.Thirlwall,GrowthandDevelopment(1999),p94.)Letusnowconsiderhowthesefundamentalpropositionsarearrivedat.ThebasicneoclassicalgrowthmodelwasfirstdevelopedbyRobertSolowandTrevorSwanin1956,andhasbeenveryinfluentialintheanalysisofgrowtheversince----particularlytheuseoftheaggregateproductionfunction,asweshallcometosee.Themodelisbasedonthreekeyassumptions.Thelabourforcegrowsataconstantexogenousrate,l.Outputisafunctionofcapitalandlabour:Y=F(K,L).Theproductionfunctionrelatingoutputtoinputsexhibitsconstantreturnstoscale,diminishingreturnstoindividualfactorsofproduction,andhasaunitaryelasticityofsubstitutionbetweenfactors.Allsavingisinvested:S=I=sY.Thereisnoindependentinvestmentfunction.Whatthebasicneoclassicalgrowthmodelisdesignedtoshowisthataneconomywilltendtowardsalong-runequilibriumcapital-labourratio(k*)atwhichoutput(orincome)perhead(q*)isalsoinequilibrium,sothatoutput,capitalandlabourallgrowatthesamerate,l.Themodelthereforepredictslong-rungrowthequilibriumatthenaturalrate.(A.P.Thirlwall,GrowthandDevelopment(1999),p95.)Themostcommonlyusedneoclassicalproductionfunctionwithconstantreturnstoscaleistheso-calledCobb-Douglasproductionfunction:Whereistheelasticityofoutputwithrespecttocapital,1-istheelasticityofoutputwithrespecttolabour,andobviously+(1-)=1,thatis,a1percentincreaseinKandLwillleadtoa1percentincreaseinY,whichiswhatismeantbyoutputexhibitingconstantreturnstoscale.

(A.P.Thirlwall,GrowthandDevelopment(1999),p95.)Equationcanalsobewrittenin‘labourintensive’formbydividingbothsidesoftheequationbyLtogiveoutputperheadasafunctionofcapitalperhead:Thisisthe‘labour-intensive’formoftheneoclassicalproductionfunction,andcanbedrawnasinFigure.Thediminishingslopeofthefunctionrepresentsthediminishingmarginalproductofcapital.(A.P.Thirlwall,GrowthandDevelopment(1999),p95.)f(k)ykoyy*kk*Capital-laborratioy=f(k)Figure3-1.PERCAPITAPRODUCTIONFUNCTION(DebrajRay,DevelopmentEconomics,PrincetonUniversitypress,1998,p64.)k(2003)k(2002)k(2004)k*k(1+n)kt+1(1-σ)kt+syFigure3.2-aThedynamicsoftheSolowmodelSource:DebrajRay,DevelopmentEconomics(1998),p66.k(2005)k(2006)y當k<k*,實際人均資本量((1-)k+sy)超過了保持資本－勞動比不變所需要的人均資本量((1+n)k),這時,人均資本和人均產(chǎn)出都將增加。k(2005)k(2004)k(2006)k(1+n)kt+1(1-σ)kt+syFigure3.2-bThedynamicsoftheSolowmodelSource:DebrajRay,DevelopmentEconomics(1998),p66.k*y當k>k*,實際人均資本量[(1-)k+sy]小于為保持資本-勞動比不變所需要的人均資本量(1+n)k,結果是人均資本k和人均產(chǎn)出y都將下降。人均資本的凈變化是儲蓄超過必需投資的部分：k=sy-(n+d)k穩(wěn)態(tài)定義為k=0,并且在y*和k*的值滿足：sy=sf(k*)=(n+d)k*Fig3-3.STEADY-STATEOUTPUTANDINVESTMENT

圖3-3的穩(wěn)態(tài)出現(xiàn)在C點.儲蓄線與投資需求線相交在C點上.無論在哪里，只要儲蓄線高于需求線，資本在增加,經(jīng)濟就在增長。例如，從A點開始，隨著時間的推移，經(jīng)濟向右邊移動。由于資本的邊際產(chǎn)量遞減，生產(chǎn)函數(shù)與并行的儲蓄曲線逐漸變得平直。因為必需的投資線具有不變的正斜率，所以必需的投資線與儲蓄線會相交。圖3-4中，經(jīng)濟由C點的穩(wěn)態(tài)均衡起步。在C點，儲蓄與必需的投資恰好相等.現(xiàn)在人們愿意把收入中的更大部分儲蓄起來.這會引起儲蓄曲線向上移動到虛線的位置。圖3-4中，C點是初始的一個穩(wěn)態(tài)均衡?，F(xiàn)在，相對于必需的投資，儲蓄增加了，其結果是，儲蓄額比保持人均資本不變所需要的投資要多。儲蓄多到足以使人均資本量增加。人均資本量將持續(xù)增加，直到達到C'點。在C'點，經(jīng)濟已恢復到穩(wěn)態(tài)增長率n。Fig3-4A.Increaseinsavingsratemovesthesteadystateyy*kk*Capitalperheady=f(k)(n+d)ksys'ysy*k**s'y**OOutputperheadFig3-4B.Decreaseintherateofpopulationgrowthincreasethesteady-staterateofgrowthofaggregateoutput.Capitalperheady*kk*y=f(k)(n+d)ksysy*k**yy**OOutputperhead(n'+d)ksy**在規(guī)模報酬不變的生產(chǎn)函數(shù)條件下,在長期中,儲蓄率的增加只是提高人均產(chǎn)出水平和人均資本水平,而不是提高人均產(chǎn)出增長率.(Macroeconomics,8edition,byDornbusch,p57.）Figure3-5.ADJUSTMENTTONEWSTEADYSTATEFigure3-7.EXOGENOUSTECHNOLOGICALCHANGE引進了技術進步因素解決了人均收入的長期增長趨向于零的尷尬局面。但是，問題還沒有結束。在新古典增長模型中，技術進步是外生的，也就是說是從外部引入的，與模型中的任何變量沒有關系。新古典增長模型假定商品和要素是完全自由流動的。即使假定技術進步率最初在國家間存在很大差距，最終也應該趨于相同。然而，無論是收入水平還是增長率，趨同在全世界都沒有發(fā)生。而且除了少數(shù)幾個國家之外，發(fā)達國家與發(fā)展中國家之間的經(jīng)濟差距在近幾十年反而拉大了。Appendix3.1.2..Cobb-DouglasproductionfunctionOneformthatisespeciallypopularistheCobb-Douglasproductionfunction.Thus,theCobb-Douglasformsatisfiesthepropertiesofaneoclassicalproductionfunction.

(RobertJ.Barro&XavierSal-I-Martin,EconomicGrowth,p16-17.)(DebrajRay,DevelopmentEconomics,PrincetonUniversitypress,1998,p91-94.)Appendix3.1.2..Cobb-DouglasproductionfunctionwhereAisapositiveconstant.WhatdoestheCobb-Douglasproductionfunctioncapture?Firstofall,theparameterAisameasureofthedegreeoftechnologicalknowledgeintheeconomy.ThelargerisA,

thelargeristhemagnitudeofoutputforanyfixedcombinationofKandL.WiththeCobb-Douglasfunction,

Acanalso

beinterpretedasameasureoftheproductivityoflabor.Toseethis,notethatequationcanberewrittenasThenELisjusttheamountofeffectiveunitsoflaborusedinproduction.3.1.3.TheNew(endogenous)GrowththeoryThe‘new’growththeoryrelaxestheassumptionofdiminishingreturnstocapitalandshowsthat,withconstantorincreasingreturns,therecanbenopresumptionoftheconvergenceofpercapitaincomesacrosstheworld,orofindividualcountriesreachingalong-runsteady-stategrowthequilibriumatthenaturalrate.Iftherearenotdiminishingreturnstocapital,investmentisimportantforlong-rungrowthandgrowthisendogenousinthissense.(A.P.Thirlwall,GrowthandDevelopment(1999),p115.)3.1.3.TheNew(endogenous)GrowththeoryInthese‘new’modelsofendogenousgrowth,pioneeredbyRobertLucas(1988)andPaulRomer(1986,1990),thereareassumedtobepositiveexternalitiesassociatedwithhumancapitalformationandresearchanddevelopmentthatpreventthemarginalproductofcapitalfromfallingandthecapital-outputratiofromrising.WehaveaproductionfunctionincapitalofY=AK,where=1.Indeeditcanbeseenfromtheexpressionofthecapital-outputratio,thatis,(A.P.Thirlwall,GrowthandDevelopment(1999),p115.)3.1.3.TheNew(endogenous)GrowththeoryThatanythingthatraisestheproductivityoflabour(Y/L)inthesameproportionasK/Lwillkeepthecapital-outputratioconstant.LearningbydoingandembodiedtechnicalprogressinthespiritofArrow(1962)andKaldor(1957),aswellastechnologicalspilloversfromtrade(GrossmanandHelpman,1990,1991)anddirectforeigninvestment(deMello,1996),areadditionalpossibilitiestoeducationandresearchanddevelopment.除了教育和研究開發(fā)以外的另一些影響增長的因素.

(A.P.Thirlwall,GrowthandDevelopment(1999),p116.)3.1.3.TheNew(endogenous)GrowththeoryThefirstcrudetestofthe‘new’growththeoryistoseewhetherornotpoorcountriesdogrowfasterthanrichones,orinotherwordstoseewhetherthereisaninverserelationbetweenthegrowthofoutput(oroutputperhead)andtheinitiallevelofpercapitaincome.Ifthereis,thiswouldprovidesupportfortheneoclassicalmodel.Ifthereisnot,thiswouldsupportthenewgrowththeory’sassertionthatthemarginalproductofcapitaldoesnotdecline.Theequationtobeestimatedis

3.1.3.TheNew(endogenous)GrowththeoryWheregiistheaveragegrowthofoutputperheadofcountry-ioveranumberofyearsandPCYi

isitsinitiallevelofpercapitaincome.Asignificantlynegativeestimateofb1wouldevidenceofunconditionalconvergenceorbeta(β)convergenceasitiscalledintheliterature;thatis,poorcountriesgrowingfasterthanrichwithoutallowingfor不考慮

anyothereconomic,socialorpoliticaldifferencesbetweencountries.Aswesee,noneofthestudiestakinglargesamplesofdevelopedanddevelopingcountrieshavebeenabletofindevidenceofunconditionalconvergence.Theestimateofb1isnotsignificantlynegative;infactitisinvariablypositive,indicatingdivergence

(Thirlwall,GrowthandDevelopment(1999),p116.)3.1.3.TheNew(endogenous)Growththeory

Beforejumpingtotheconclusionthatthisisarejectionoftheneoclassicalmodel,however,itmustberememberedthattheneoclassicalpredictionofconvergenceassumesthatthesavingsorinvestmentratio,populationgrowth,technologyandallfactorsthataffecttheproductivityoflabourarethesameacrosscountries.Sincetheseassumptionsaremanifestlyfalse,therecanneverbethepresumptionofunconditionalconvergence(eveniftherearediminishingreturnstocapital),onlyconditionalconvergence,holdingconstantallotherfactorsthatinfluencegrowthofpercapitaincome,includingpopulationgrowth(p),theinvestmentratio(I/Y)andvariablesthataffectthe3.1.3.TheNew(endogenous)Growththeory

investmentratio(I/Y)andvariablesthataffecttheproductivityoflabour,forexampleeducation(ED),researchanddevelopmentexpenditure(R&D),trade(T)andevennon-economicvariablessuchaspoliticalstabilitymeasuredbythenumberofrevolutionsandcoups(PS).Theequationtobeestimatedistherefore3.1.3.TheNew(endogenous)GrowththeoryAndthequestiontobeaskediswhathappenstothesignoftheinitialpercapitaincomevariable(PCY)whentheseothervariablesareintroducedintotheequation?Ifthesignturnsnegative(b<0)whenallowanceismadefortheseotherfactors,thisissupposedtorepresentarehabilitation(n.復原)oftheneoclassicalmodel(seeBarro,1991);thatis,therewouldbeconvergenceifitwerenotfordifferencesbetweenrichandpoorcountriesinalltheseotherimportantvariablesinthegrowthprocess.‘New’growththeorywouldbesupportedbyfindingthateducation,researchanddevelopmentexpenditureandsoonmatter,anditisthesefactorsthatkeepthemarginalproductofcapitalfromfalling,producingactualdivergenceintheworldeconomy(Thirlwall,GrowthandDevelopment(1999),p116.).K.J.Arrow(1962)K.J.Arrow(1962)tookontheviewthatthelevelofthe"learning"coefficientisafunctionofcumulativeinvestment(i.e.pastgrossinvestment).UnlikeKaldor,Arrowsoughttoassociatethelearningfunctionnotwiththerateofgrowthininvestmentbutratherwiththeabsolutelevelofknowledgealreadyaccumulated.BecauseArrowclaimedthatnewmachinesareimprovedandmoreproductiveversionsofthoseinexistence,investmentdoesnotonlyinduceproductivitygrowthoflaboronexistingcapital(asKaldorwouldhaveit),butitwouldalsoimprovetheproductivityoflaboruponallsubsequentmachinesmadeintheeconomy.K.J.Arrow(1962)Thetrickistoutilizetheconceptthatwhilefirmsfaceconstantreturns,theindustryoreconomyasawholetakesincreasingreturnstoaccount.Thiscanbeeasilyformalized.TakingouroldCobb-Douglasproductionfunction,Y=AKaL1-a,thereisconstantreturnstoscaleforallinputstogether(sincea+(1-a)=1).Therefore,asnotedintheSolowmodel,itmightseemasifoutputpercapitalandconsumptionpercapitadoesnotgrowunlesstheexogenousfactor,A,growstoo.ToendogenizeA,letusfirstestablishtheCobb-Douglasproductionfunctionforeachindividualfirm:Yi=AiKiaLi1-a

where,onecannote,theoutputofanindividualfirmisrelatedwithcapital,laboraswellasthe"augmentation"oflaborbyAi.K.J.Arrow(1962)Arrow(1962)assumedthatAi,thetechnicalaugmentationfactor,mightthuswrittenlookspecifictothefirm,butitisinfactrelatedtototal"knowledge"intheeconomy.Thisknowledgeandexperience,Arrowargued,iscommontoallfirms:afreeandpublicgood(i.e.non-competitiveconsumption).Sothefirstquestionishowknowledgeisaccumulated.Arrowarguedthatitarisesfrompastcumulativeinvestmentofallfirms.LetuscallthiscumulativeinvestmentG.Thus,Arrowassumedthatthetechnicalaugmentationfactorisrelatedtoeconomy-wideaggregatecapitalinaprocessof"learning-by-doing".K.J.Arrow(1962)Inotherwords,theexperienceoftheparticularfirmisrelatedtothestockoftotalcapitalintheeconomy,G,bythefunction:Ai=Gz

thus,asthephysicalcapitalstockGaccumulates,knowledgeusedbyaparticularfirmalsoaccumulatesbyaproportionzsuchthatYi=GzKiaLi1-a

where,note,onlyGdoesnothaveasubscripti(i.e.isnotparticulartothefirm),itisaproductiveforceexternaltothefirms(i.e.aMarshallianexternality)andassumedafreepublicgood.Thisforceisfreeandanyfirmemployingitwillnotimplicateonanotherfirm'sconsumption:itisfreely-availableknowledge.K.J.Arrow(1962)Thus,westillmaintainCRSatthefirmlevel,butintheaggregate,however,G=K----sinceitisonlytheaccumulatedstockofcapitalfortheeconomy.Therefore,the"economy-wide"aggregateproductionfunctionis:Y=Ka+zL1-a

Arrow(1962)assumedthata+z<1.Therefore,increasingonlycapital(oronlylabor)doesnotleadtoincreasingreturns.Wecanobtainincreasingreturnstoscaleasa+z+(1-a)="z">0,butcapitalandlabormustbothexpand.However,byaddingthisrestriction,Arrow'soriginalmodelexhibitsnon-increasingreturnstoscaleinaggregateiftherateofgrowthinaneconomyissteady.SummaryNeoclassicalgrowththeoryaccountsforgrowthinoutputasafunctionofgrowthininputs,particularlycapitalandlabor.Therelativeimportanceofeachinputdependsonitsfactorshare.Laboristhemostimportantinput.Long-rungrowthresultsfromimprovementsintechnology.Absenttechnologicalimprovement,outputperpersonwilleventuallyconvergetoasteady-statevalue.Steady-stateoutputperpersondependspositivelyonthesavingrateandnegativelyontherateofpopulationgrowth.Economicgrowthinthemostdevelopedcountriesdependsontherateoftechnologicalprogress.Accordingtoendogenousgrowthmodels,technologicalprogressdependsonsaving,particularlysavingdirectedtowardhumancapital.Internationalcomparisonssupportconditionalconvergence.Adjustingfordifferencesinsavingsandpopulationgrowthrates,developingcountriesadvancetowardtheincomelevelsofthemostindustrializedcountries.Thereareextraordinarilydifferentgrowthexperiencesindifferentcountries.Highsaving,lowpopulationgrowth,outward-lookingorientation,andapredictableeconomicenvironmentareallimportantprogrowthfactors.DebrajRaychapter3-(6)ConsidertheSolowmodelwithaproductionfunction,whereAisafixedtechnologicalparameter.Explicitlysolveforthesteady-statevalueofthepercapitacapitalstockandpercapitaincome.Howdothesevalueschangeinresponsetoarisein(a)thetechnologicalparameterA,(b)therateofsavings,(c)α,(d)δ,thedepreciationrate,and(e)thepopulationgrowthraten?Answer:DebrajRaychapter3-(6)

ThisisamoremathematicalexercisethatwillhelpyouunderstandhowthesteadystateintheSolowmodelisdescribed.Wehavetheequationdescribinghowtotaloutputisproducedwithcapitalandlabor.Inthefirststep,wetransformthisintoaper-capitamagnitudebydividingthroughbythelaborforceL(thereisnotechnicalprogressheresothatlaborisjustthesameaseffectivelabor).Ifwedefiney=Y/Landk=K/L,weseethatThereforetheequationdescribingtheSolowmodelisInthesteadystate,k(t)=k(t+1)=.Consequently,Answer:DebrajRaychapter3-(6)

Inthesteadystate,k(t)=k(t+1)=.Consequently,Nowwesolvethisequationtofigureoutwhatthevalueof

mustbe.Tryit:youwillseethatorthatNowusingthisequation,youshouldbeabletoeasilytellthedirectioninwhich

moves,inresponsetoallthechangesaskedaboutinthequestion.DebrajRaychapter3-(10)

Thinkof