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LecturenotesinDevelopmenteconomics

Course aims This course is meant to provide students, by means of theoretical approach, with the understanding of the issues characterizing economic development. It is composed of two modules addressing the relationship between growth, development and inequality, more and more at the core of the economic discourse. At the end of the course students, through: a) the Module Developmet will be able to understand the role of the main economic variables in the virtuous dynamics within the sustainable development process in the medium-long run. b) the Module Inequality will be able to employ the main tools meant to describe inequality and to highlight the related concepts so to better understand the nature of the complex relationships linking inequality to growth and development.

Programme The Development Module is composed of the following issues:

1. Exogenous and endogenous growth theories 2. Development theories 3. Sustainable development and globalization 4. Human Development Index

so to understand the links between economic variables and their role in yielding economic development. The Inequality Module, by examining various ways to describe inequality, as listed below:

1. The assessment of income inequality: methods and results 2. Issues about world-wide health and education inequality and its

implications on economic development 3. Does gender matter? 4. The complex link between economic growth and income inequality

aims at understanding the multidimensional nature of economic development.

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REFERECENCESTO:Development Module

1. Exogenous and endogenous growth theories Lecture notes

2. Development theories Ray

3. Sustainable development and globalization Ray

4. Human Development Index Appendix 2016

Inequality Module1. The assessment of income inequality: methods and results

2. Issues about world-wide health and education inequality and its implications

on economic development

3. Does gender matter?

4. The complex link between economic growth and income inequality

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Development economics 2016/17

1.ExogenousandendogenousgrowththeoriesEconomictheoryoffersmanyexplanationsonthestartandtheprocessofpercapitaincomegrowth.Yet,theoryisdividedontheinterpretationofthedynamicprocessesthatfavoureconomicgrowth,andthereforealsoinsuggestingtheeconomicpoliciestopromotelongtermgrowth.Intheneoclassicmodel,whichisthelongrunversionofthetheoreticalmodelthatgavebirthtotheNewClassicalEconomics(NCE),capitalaccumulationisnotsufficienttosustaineconomicgrowth.Thereasonisthattheneoclassicmodelisfoundedonmarginalreturnsoffactors.Asaconsequence,productivitycannotriseindefinitely.Therefore,themodelismoreusefulfortheanalysisofmarketequilibriathanforexaminingsustainedincreasesinproductivitythatraiseoutputinthelongterm.Endogenousgrowthmodels,whichusesomeoftheelementsinNewKeynesianEconomics(NKE)theory,tryandfindthefactorsthatendogenouslyfavourgrowth.Thisapproachcanindicatepoliciestosustainincreasesinproductivitythatdirectlycontributetotheincreaseofthewagelevelandspreadwealth.Endogenousgrowthmodelsarenotnecessarilyrelatedtoahypothesisofdecreasingmarginalreturns.Thisimpliestherearenolimitstoeconomicgrowth.

1.1.NeoclassicgrowththeoryTheinitialformulationoftheneoclassicgrowththeoryowestothecontributionsofSwann(1956)andSolow(1957).BothauthorswereinspiredbytheseminalessaybyRamsey(1928)ontheroleofsavinginobtainingmaximalutility.Theneoclassictheoryofgrowthisalsoknownasatheoryofexogenousgrowth.Thecontinuousincreaseofpercapitaincomethathasbeenthedistinctivefeatureofcountrieswithamarketeconomyinthelasttwocenturiesisattributedtoanexogenousflowoftechnologicalinnovation.Theelementsthatwouldbeabletostimulatethistechnologicalprogressorthefavourableconditionsforitsdevelopmentaretakenforgranted.Thestabilityofthelong-termequilibriumandtheexogeneityofthedeterminantsofeconomicgrowthimplythattheSolow-Swannmodelgiveslittleadvicetoeconomicpolicy.Aproductionfunctionwithconstantreturnstoscaleanddecreasingmarginalreturnstofactorsimplicitlyassumesthattheproductiontechnologycanbeperfectlyreplicatedineachproductionplant.Anincreaseinproductioncanbeexplainedonlybyanincreaseintheendowmentoffactors.

1.1.1.ConstantreturntoscaleproductionfunctionLa teoria neoclassica della crescita si fonda sulla funzione di produzione caratterizzata darendimentidiscalacostantiedarendimentidecrescentideifattori.Siassumedunquechelaproduzionedibeninell’economiaavvengasecondounatecnologia identicamentereplicabiledaogniimpiantoproduttivoecheunaumentodellaproduzionesiaspiegatodaunaumentodiuno o di entrambi i fattori. La convessità, assicurata dalla decrescenza dei rendimentimarginali dei fattori, è la caratteristica della funzione che determina il limite nella crescitadellaproduzione.

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Figure1.Productionfunctionwithdecreasingmarginalreturns

1.1.2.ThecontributiontogrowthofproductionfactorsHowdotheproductionfactors,labourandcapital,contributetooutputgrowth?Withsomehypothesesonavailabletechnology,i.e.theproductionfunction,wemayattributetoeachfactoritscontributiontoeconomicgrowth.Thisdecompositionisbasedonthechangeinfactorinputovertwodifferentperiods(tandt+1),hereindicatedwithΔ.This‘growthaccounting’exerciseattributesoutputgrowthtoeachinput.Thegrowthrateofincome(g)ismeasuredbythegrowthrateofGDPandshowsthechangeinincome(ΔY/Y)overaperiodoftime.Itisgivenbythesumofitscomponents:thegrowthrateoftotalfactorproductivity(ΔA/A),thegrowthrateofcapital(ΔK/K)andthegrowthrateofthelabourforce(ΔL/L).Thelattertwoareweightedbytheirshareintotalincomeαand(1-α)respectively:

[1]LL

KK

AA

YYg Δ

−+Δ

+Δ

=Δ

= )1( αα

Growthdependsontechnologicalchangethatreflectsthegrowthrateofthetotalfactorproductivity,andtheaccumulationofcapitalandlabouratfullemployment.Thesharesαand1-αarethedistributionofoutputbetweenthefactorscapitalandlabour.Thesesharesalsodescribetherelationbetweenthegrowthratesofoutputandinput.Eventhoughitisnotnecessarytoassumethatthesesharesarestable,itisanempiricalregularitythattherelationbetweenlabourandcapitalincome–theratio(1-α)/α–isconstantovertime.Growthaccountingrevealsthatnotallproductorincomegrowthisduetogrowthintheproductionfactors.Growthinexcessofthecontributionofindividualfactorsisalsoknownasthe‘Solowresidual’: )/( 1 αα −= LKYRS .SolowmeasuredthisresidualonUSdatafortheperiod1909-49.HecalculatedgrowthratesaccordingtothereconstructionofhistoricalsequencesofbothGDPandcapitalperworkedhour(i.e.,Y/LandK/L)andoftheportionshareofcapitalintototalproduction(K/Y).Theincreaseofincomepercapitainthosefortyyearswasfor12.5%duetocapital.Theremaining87.5%couldnotdirectlyberelatedtoachangeinoneoftheinputsbutcouldratherbeattributedtotechnologicalprogressembedded

Y3

Y2

Y1

PML

1

Y

L0 L1 L2 L3 L4

Y4

5

intheproductionfactors.Hence,residualgrowththatisnotexplainedbythegrowthofeachofthefactorsLandK,isassignedtototalfactorproductivity(TPF).Thegrowthequation[1]canbederivedfromtheSolowmodelifwesimplyrewritetheproductionfunctionintermsoftheratesofchange.FortheCobb-Douglasfunctionwithconstantreturnstoscale αα −= 1LAKY achangeinproduction(ΔY)isgivenbythesumofthechangesinitscomponents: LAFKAFLKAFY LK Δ+Δ+Δ=Δ ),( .Ifwedividebothsidesbytotalproductionandrearrange,weget:

[2]LL

YLAF

KK

YKAF

AA

YLAF

YKAF

YLKAF

YY LKLK Δ

+Δ

+Δ

=Δ

+Δ

+Δ

=Δ ),(

Recalltheexpressionsofformarginalproductivity.Wemayreorder[2]andwritethegrowthrateasfollows:

[2’]YLPML

YKPMK

AA

YYg Δ

+Δ

+Δ

=Δ

=

SinceinaperfectlycompetitiveeconomywehavethatMPK=randMPL=w/pwebtainthefollowingsharesintotalincome:

[3a] α==YKr

YKPMK andfrom[3b] α−== 1

YL

pw

YLPML

Inthiswayweobtainthegrowthrateinrelationtothechangesinproductionfactorsin[1]:

[1]LL

KK

AA

YYg Δ

−+Δ

+Δ

=Δ

= )1( αα

Themarginalproductivityofthetwofactors(MPKandMPL)isamultipleoftheiraverageproductivity(PMK=αY/K,PML=(1-α)Y/L).Iffactorsarerewardedbytheirrespectivemarginalproductivities,thesharesofcapital(K/Y)andlabourincome(L/Y)areconstant(PMK·K/Y=α,PMLL/Y=(1-α).TheSolowresidualcanbeclarifiedbyanumericalexample.Imaginethatthegrowthratesofincomeandproductionfactorsareasfollows:ΔY/Y=0.5;ΔK/K=0.4;ΔL/L=0.2.Elasticitiesareestimatedtobe:α=0.3and(1-α)=0.7.Thecontributionofcapital(αΔK/K)willbegivenby(0.3·0.4=0.12)andthecontributionoflabour((1-α)ΔL/L)by(0.7·0.2=0.14).Inordertomatchtheobservedgrowthrate(equalto0.5),theremustbesomeresidualpartthatisneitherduetoKnortoL.ThismustthenbeattributedtoΔA/A.Thisrepresentstheimprovementintotalfactorproductivity:ΔA/A=ΔY/Y-αΔK/K-(1-α)ΔL/L 0.24=0.5-0.12-0.14Anincreaseintotalfactorproductivity(TPF)increasesthelevelofoutputthatmightpotentiallybereachedwiththesameinput.Itcausesanupwardshiftoftheproductionfunction.

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Farmer(1999)estimatedthatintheUSaverageGDPgrowthwas1.64%peryearbetween1890and1995.About0.55%couldbeassignedtocapital,0.17%tolabourand0.92%tototalproductivity.TheestimatedincomesharesfortheUSwere:α=0.33and(1-α)=0.66.Hence,theratios(1-α)/α=0.66/0.33=2.RossiandToniolo(1996)didthesameexerciseforItalybetween1893and1990.Economicgrowthrateaveraged3.27%peryear.About1.19%couldbeattributedtocapital,0.62%tolabourand1.46%tothetotalproductivityoffactors.TheincomesharesforItalyare:α=0.3and(1-α)=0.7sotheratiobetweenincomefromlabourandcapitalis(1-α)/α=0.7/0.3=2.3.IncontrasttotheUSA,Italyshowsalargercontributionoflabourthancapitalinaggregateproduction.

1.1.3.TheNeoclassicalgrowthequationAsweconsideredconstantreturnstoscale,weimplicitlyassumedthatfirmsizeisirrelevantforproduction.Wecanrepresenttheproductionfunctionintermsofpercapitaquantitiesassuminglabourasgiven.Ifwedividetheproductionfunction αα −= 1LAKY bylabour,percapitaoutput(Y/L)isproportionaltopercapitainput:

[4]αα −

⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛=1

LL

LKA

LY

Percapitaoutput(Y/L)equalsthecapitalperworker,raisedtoitsincomeshare(K/L)αandmultipliedbythetotalproductivityoffactors(A).Therefore,ifweputy=Y/Landk=K/Lwemayrewrite[5.4]inpercapitaterms:

[5] αAky = Wecanrepresent[5]inaCartesianplanewherewemeasurethecapital-labourratio(k=K/L)ontheXaxisandpercapitaproduct(y=Y/L)ontheYaxis(Figure1andFigure2).Wewillhenceforthuselowercaseletterstoindicatepercapitavaluesforconsumption(c=C/L)andforinvestment(ι=I/L).Figure2.Thesteadystateequilibrium

y=Y/L

k=K/Lk*0

y*

ι*

Productionfunctiony=f(k)

Effectiveinvestmentfunctionι=sf(k)

Depreciationfunctionδk

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Inequilibrium,thesupplyofgoods(y)givenbytheproductionfunctionhastobeequaltothedemandforgoods.Tosimplifymatters,weconsiderdemandasbeingmadeupbyconsumption(c)andinvestment(ι)only.Investmentisequaltosaving:y=c+ι.Wecanrepresentconsumptionasaportionofproduction(i.e.,income)withthefollowingconsumptionfunctionc=(1-s)y.Thisexpressionimpliesthatι=syandindicatesthatinequilibriumtheportionofincomeassignedtoinvestmentisconstant.Thisshareisthesavingrate(s=S/Y).Investmentdependsontherelationbetween,savingandproduction(ι=sy).Usingthegeneralnotationfortheproductionfunctiony=f(k),wecanderivearelationshipι=sf(k)intheCartesianplane(k,y)thatliesundertheproductionfunction.Thedistancetotheproductionfunctiondependsonthesavingrate(s)where0<s<1(Figure2).Weshoulddistinguishbetweendepreciationandnetinvestmentandrelatethecapitalstocktothegrossinvestmentflow.Foragivenlabourforce,thegrowthofcapitalisthesameasthegrowthofcapitalperworker.i.e.,thechangeintotalcapitalstock(Δk)fromyearttoyeart+1correspondstonetinvestment.Thisistheinvestmentinnewcapitaloncethesubstitutionofdepreciatedcapitalhasbeensubtracted(δk).Theequilibriumcondition(alsocalledthesteadystate)isobtainedbyresolvingtheaccountingidentitythatdescribesthegrowthofcapital(Δk=ι-δk)for(Δk=0).Inotherwords,weputkt+1=kt=k.Whennetinvestmentiszero,growthinthecapitalstockcomestoahalt.Allsavingsarededicatedtoreplacingcapital.Weneedtofindthenthestockofcapitalperworker(k*)thatdeterminesalevelofinvestment(ι*)wherenetinvestmentiszero(Δk=0)andthereplacementofexistingcapitalistheonlyinvestmentleft(δk).InFigure2,actualinvestment(ι=sy)increasesasincomerises.Thestraightline(δk)definestheinvestmentthatisrequiredtokeepconstantthelevelofcapitalperworker.Theequilibrium,calledstationarystateormorecommonlysteadystate,isreachedattheintersectionofthetwocurves((ι=sy)and(δk)forthosevaluesofι=ι*andk=k*forwhichι*=δk*.Whenthesavingrateisknownfromcondition:[6]ι*=sf(k*)=δk*wecanimmediatelyderivethepercapitaincomelevelinthesteadystate(y*=f(k*)).Sincethesavingrate(s)andtherateofdepreciation(δ*)aregivenparameters,fromtheratio[7]k*/f(k*)=s/δwecanderivethecapitalperworker(k*).Itisstraightforwardtofindthecorrespondingpercapitaincomeofthestationarystate(y*).TheequilibriumatwhichtheconditionΔk=0issatisfieddoesnotdependontheinitialcapitalstockperworker(k).Iftheinitialratio(K/L)islowerthantheratioinsteadystate(k<k*),actualinvestmentwillincreasemorethandepreciation(ι>δk).Thisimpliespositivenetinvestment(Δk>0).Theaccumulationofcapitalexceedstherequiredamountfordepreciation.Thedepreciationrateisaconstantproportionofthestockofcapital.Depreciationthusincreasesascapitalaccumulates.Instead,iftheinitialK/Lratioishigherthaninsteadystate(k<k*),investmentwillnotbeenoughtocoverthedepreciation(ι<δk).Capitalwilldecrease(Δk<0)thatprogressivelytore-establishbalance.Theconvexityoftheproductionfunction(duetodecreasingmarginalreturnsoffactors)putsalimitongrowth.Itistheincreaseofcapitalperworker(k=K/L)thatcreatesgrowthofpercapitaincome(y=Y/L).Thisincreasecannotcontinuewithoutlimits:itwearsoutwhensaving(hence,investment)isentirelyassignedtosubstitutingcapital.Anincreaseinthesavingrateimmediatelyincreasestheamountofsavingabovetheamountnecessarytokeepthecapital

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stockatitsexistinglevel.Sincesavingsaretransformedintoinvestment,thisresultsinanincreaseofthecapital-labourratio.Asaconsequence,thepercapitaincomegrowthratetemporarilyincreases.Duringtheadjustmentprocess,percapitaincomeandthecapitalstockperworkercontinuetogrowaslongassavingsarehigherthantheamountneededforfinancingdepreciation.Theadjustmentendswhenthenewsteadystateequilibriumisreached.Inordertoimprovestandardsoflivinginthelongrun,investmenthastorise.ButtheexpansionofinvestmentcangoonforlongerthehigheristheK/Lratio.Thereasonisthattheincreaseofinvestmentbringsabouttwoeffects.First,duetothedecreasingmarginalproductivityofcapital,incomeincreasesatadecliningrate.Second,asitisnecessarytoassignalwaysalargerpartofincometodepreciation,consumptionfallsmorethanproportionally.

1.1.4.TheGoldenRuleForeachpossiblesavingrate(s)thereisadifferentsteadystate.Isitpossibletochooseasteadystatethatmaximizesthewealthofcitizensbyreachingthehighestpossiblelevelofconsumption?Thegoldenruledefinesthecriteriatobeemployedinordertochoosethesavingratethatallowsmaximizingconsumptioninaneconomy.Toincreaseconsumption,itisnecessaryforincometogrowmorethansaving.Butforincometoincrease,savinghastoincrease.Ink*/f(k*)=s/δtheratiok/yisadirectfunctionofthesavingrate(s)andaninversefunctionofthedepreciationrate(δ).Hence,byaccumulatingmore,ariseinthesavingrateand/orafallofthedepreciationrateproduceahighersteadystateincome.Ifweexpressconsumptioninpercapitatermsasthedifferencebetweenproductionandinvestmentc=y-ιandifwewritebothexpressionsintermsofthecapital-labourratio,weobtaintherelation.Fromthis,wecancalculatetheoptimallevelofpercapitaconsumption(cº).Figure3.Thegoldenrule

Percapitaconsumption(cº)isatitsmaximumwhenthedistancebetweenf(k)andislargest.Thisoccursatthepointwherethetangentsofthesetwofunctionsareparallel.Theslopeof

y=Y/L

y*

y°

c°

c*

y=f(k)

k=K/L0 k*

ι=sf(k)

δk

k°

ι=s°f(k)

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thestraightlineisconstantandequalto.Theslopeoftheproductionfunctionvariesandismeasuredbythemarginalproductivityofcapital.Sinceconsumptionishighest(cº)atthepointwhereMPK=,atthegoldenrulevalue,thecapital-labourratioisequaltokº.InFigure3,wehaveputthedifferentvaluesofthesteadystatethatcorrespondtothegoldenrule.IntheexampleshowninFigure3,thedashedstraightlineparalleltoistangenttothecurvey=f(k)atapointwhichistotheleftoftheprevioussteadystatevalue(k*).Hence,atkº<k*,consumptionpercapita(c*)islowerthantheoptimallevel(cº)definedbythegoldenrule.Evenifthemodelpostulatesconvergenceoftheeconomytothesteadystate,thereisnomechanismthatputstheeconomyonthegoldenruleautomatically.Theeconomycanwellfinditselfinasteadystatedifferentfromtheoneinthegoldenrule,withacapital-labourratiodifferentfromthegoldenruleone.Ifthesteadystatehasacapital-labourratiohigherthanthegoldenrulelevel(k*>kº)theeconomyinveststoomuch.Toincreasepercapitaconsumption(c),thesavingrate(s)hastodecrease.Thiswillbefollowedbyafallinpercapitainvestment(ι),andascapitalshrinks,output(y)willfallaswell.Overtime,consumptionandinvestmentalsofall.Aftertheadjustmentthatbringsthecapital-labourratiotokº,consumptionwillbehigherthanbefore.Thereasonisthattheinitialincreaseexceedsthefalllateronduetothefallinoutput.Ifinsteadthecapital-labourratioislowerthanthegoldenlevel(k*<kº)thesavingrate(s)needstorisesothatinvestment(ι)andconsumption(c)canrise.Accumulationbooststhecapital-labourratioandhenceproduction.Theexpansionofoutput(y)triggersanincreaseinconsumption(c)andinvestment(ι).Therefore,untilthecapital-labourratioreachesthegoldenlevelvalue(kº),allvariables(c,ι,y)growbuttheincreaseinconsumptionisrealisedonlyattheendoftheadjustmentprocess.Ofcourse,thechoicebetweenconsumptionandsavingcreatesanintertemporalequityconflictbetweendifferentgenerations.Thereisanintergenerationaldistributionofconsumptionpossibilities.Ifbychangingthesavingrate,aneconomycouldincreasebothcurrentandfutureconsumption;theexistingsteadystateisnotoptimal.Allgenerationscouldbemadebetteroff.Theequilibriumwouldbedynamicallyefficientiftheeconomyfacesatrade-offbetweenconsumptionofthecurrentandfuturegenerations.Theoretically,thisproblemofthesustainabilityoflivingstandardscanbesolvedwiththeusualoptimisationtools.

1.1.5.LabourgrowthAfterashock,growthacceleratestoreturntothesteadystate.Oncethesteadystateisreachedandtheadjustmentofthecapital-labourratiocomestoanend,thistemporarygrowthfinishes.Howcanwepossiblyexplainthecontinuousgrowthweobserveinrealeconomies?Wemaydropthesimplifyinginitialhypothesisofaconstantlaboursupply.IntheSolowmodel,anincreaseoflaboursupplycanactuallyoccureitherfordemographic,naturalandmigratoryreasons,orduetoanincreaseintheactivityrateofthepopulation,orasubstitutionoflabourforleisure.Iflabourincreasesforsomeexogenousreason,thecapital-labourratio(K/L)falls.Tokeepthisratioconstant,capitalshouldgrowfasterthanlabour(n).Theadditionalcapitalwillgotodepreciationontheonehand,andtoendowthenewworkerswiththecapitaltheyneedontheotherhand.Netinvestmentisgivenbythedifferencebetweentotalinvestment(ι)andthesumofdepreciation(δk)andadditionalinvestment(nk)duetotheincreaseofthelabourforceatraten.WehavetomodifytheexpressionforcapitalgrowthintoΔk=ι-δk-nk.Asinthepreviousanalysis,steadystateisreachedwhen:ι=(δ+n)k.Insteadystate,wehavethat:c*=f(k*)-(δ+n)k*.Atthesteadystate,theoptimalityconditionisgivenby:PMK=δ+n.Iflabourincreases

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atraten>0,capital(K)andincome(Y)mustalsoincreaseatrateninordertomaintaintheratiosk*andy*ofsteadystate.Itisthegrowthoflabourthatspursthegrowthofthecapitalstocktokeepthelevelcapitalperworkerconstant.Thisinturndeterminesthegrowthofoutput.Ifweallowforanincreaseinlabour,wecanavoidthattotaloutputgrowthislimitedindefinitelybytheupperboundonthesavingrate.Amodelwithlabourgrowthisabletoexplaincontinuedoutputgrowthwithouthavingtorelyuponthesavingrateasgrowthpromoter.However,thismodeldoesnotsayanythingontheeconomictoolstoactuallyensureaconstantcapital-labourratioandeconomicgrowth.Enduringeconomicgrowthcomesfromtheexogenousgrowthoflabouratraten.Growthislimitedtoanincreaseintotaloutputanddoesnotimplygrowthofpercapitaincome.Itremainsconstant.Thisshouldnotcomeasasurprise:anincreaseofthepopulationforgiveneconomicconditions,impliesadecreaseofpercapitaincome.Thisfallcanbeavoidedonlywithadditionalinvestment.A(constant)positivegrowthrateofthepopulationimpliesasteeperslopeoftheline(δ+n)k.Thisslopeissteeperthestrongerispopulationgrowth.Asa

consequence,thegoldenrulevaluesarefoundatadifferenttangentpointbetweeninvestmentandtheproductionfunction.Sincetheslopehasincreased,suchpointsarefoundontheleftofthepreviousvalueandwillcorrespondtolowervaluesofcapitalperworker.Thiscorrespondstoalowerpercapitaincome.InFigure4,thecapital-labourratio(k°’)inthenewequilibriumisontheleftoftheratio(kº)intheprevious(goldenrule)steadystate.Alowerpercapitaincome(yº’<yº)wouldbetheconsequence.Tokeepincomeatitslevel–inthepresenceofaconstantgrowthofpopulation–thesavingrate(s’>s)wouldneedtoincrease.Thiswouldproduceanupwardshiftofthefunctionofactualinvestment,butalsoimpliesacontractionofconsumption.Thegoldenruleisinconflictwithactionstokeeppercapitaincomeconstantforn=0.Thecapitalstockadjuststothegrowthofpopulation.Thisconstancyoftheproductionfunctionimpedespursuingbothgoals.Investmentonthebalancedgrowthpathisjusttheinvestmentnecessarytokeepconstantthecapital-labourratio,andthisassuresthesteadystatelevelofoutput.

y°y°’

y*

y=Y/L

c°'

δk

c°

c*

y=f(k)

k=K/L0 k*

ι=sf(k)

(δ+n)k

k°' k°

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1.1.6.TechnologicalprogressTechnologicalprogressisthethirdelementthatappearsintheCobbDouglasproductionfunction.Theneoclassicalgrowthmodelattributestotechnologicalprogressthegrowthinoutputnotexplainedbythegrowthofoneofthefactorsofproduction.Thisisthe‘Solowresidual’.Theeffectsoftechnologicalprogressaddtoeconomicgrowth.Thisprogressmakesthecontributionofeachworkerincreasebyimprovedworkefficiency,thankstohighereducationandpersonalexperience,abetterorganizationofsociety,etc.Technologicalprogressthatincreasesworkefficiencycanbeeasilymodelledbyaddinganewvariable(E)indicatingtheefficiencyofwork.Letusassumetheefficiencyofworkincreasesataconstantrate(g).Wetakethisgrowthrateasexogenous,anddonotexplainitwithinthemodelitself.Theaugmentedproductionfunctionmayberewrittenas:Y=F(K,L,E).Aslabour(L)increasesatratenanditsefficiency(E)increasesatrate(g),thenlaboursupplyisgivenbytheproductbetweenthosevariables(L·E).Wethusmeasurelaboursupplybythenumberofworkedhoursandbyan‘efficiencyunit’orbyan‘actuallabourunity’.Foragivenleveloftechnology(foreverylevelofE)theproductionfunctionhasconstantreturnstoscaleanddecreasingreturns.Wecanredefinethemodelintermsof‘actuallabour’,ratherthansimplylabour.Wesubstitutethefactorlabour,previouslyconsideredashomogenous,fortheproductbetweenhoursworkedandactualworkinghours(L·E).Thecapital-labourratioistransformedintotheratioofcapitalperunitoflabourefficiency(k=K/(L·E)).Theproductivityoflabouristransformedintooutputperunitoflabourefficiency(y=y/(L·E)),andthegrowthrateofactuallabourisgivenbythesum(n+g)ofgrowthinthe‘efficiencyunits’.TheintroductionofthevariableEpermitsavaryingcontributionoflabourtogrowthevenasthenumberofworkedhoursperworkerisconstant.Itispossiblethatareductioninhoursworkediscompensatedbymoreefficientlabour.Thelatterphenomenonhasoccurredinmanycountriesoverhistory.Theaugmentedproductionfunctionthenlinkstheeffectiveproductperunitoflabourtothecapitalperunitofactuallabourasfollows:

[8]ααα

⎟⎠

⎞⎜⎝

⎛⋅

=⎟⎠

⎞⎜⎝

⎛⋅

⋅⎟⎠

⎞⎜⎝

⎛⋅

=⋅

−

ELKA

ELEL

ELKA

ELY 1

Thegrowthofcapitalperunitofactuallabourfollowsfromthebehaviourofnetinvestment.ThisisgivenbythedifferenceΔk=ι-δk-nk-gkbetweentotalinvestment(ι)andthesumofdepreciation(δk)andthenecessaryinvestmenttoputatworknewworkers,consideringalsotechnologicalprogress(n+g)k.Thesteadystateconditionbecomessf(k*)=k*(δ+n+g).Incomparisontothebaselinemodel,thegrowthrateofactuallabour(g)nowdeterminessteadystate.Thisisanalogoustotheinclusionofthegrowthrateoflabour(n)presentedabove.Thesteadystateisstillidentifiedbythevalueofk*,definedinthiscaseaccordingtotheunitofeffectivelabourratherthanintermsoflabour.Inordertokeepconstantbothk*andy*,itisnecessaryforboththecapital-labourratioandpercapitaincometoincreaseatthesamerateaslabourefficiency(g).Also,capital(K)andproduct(Y)shouldincreaseattherate(g+n).Insteadystate,capitalperunityofefficiency(k=K/(L·E))canonlybekeptconstantifthecapital-labourratioincreasesatthesamerate(g)astheefficiencyoflabour(E).Forthesamereason,theproductperunitofefficiency(y=Y/(L·E))staysconstantwhenpercapitaincomeincreasesatrateg.Acontinuousgrowthofpercapitaincomeandpersistentincreasesinthestandardoflivingareduetoendogenousincreasesinproductivity.Technologicalprogress,byincreasingtheefficiencyoflabour,allowsacontinuousgrowthofoutputperworkerandsustainscontinuedeconomicgrowthinthelongrun.

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Theaccumulationofcapitalthatmaximizessteadystateconsumptionperunitofefficientlabourchangesalsothegoldenrule.Thisrulenowbecomes:c°=f(k°)-(δ+n+g)k°.Themaximumconsumptioninsteadystate–keepinginmindtheroleofthetechnologicalprogress–isobtainedwhenMPK==δ+n+g.Hence,themarginalproductofcapitalnetofdepreciation(MPK–δ)hastoincreaseattherate(g+n).Asfactorsarerewardedtheirmarginalreturns,thenetmarginalproductivityofcapitalhastoequaltherealinterestrate(r).Hence,thegoldenruleimpliestheequalitybetweentheinterestrateandtheeconomicgrowthrateMPK–δ=r=g+n.Insummary,accordingtoneoclassictheory,factorsofeconomicgrowthare:1.thesavingrate:anincreaseofinvestmentleadtotheaccumulationofcapital.Thisincreasesthecapitallabourratio(k)andleadstoahigherpercapitaincome(y)andhence,largerpercapitaconsumption(c).Asthesavingratecannotberaisedindefinitely,growthhastodampenouteventually;2.populationgrowth:anincreaseinpopulationrequiresalargeraccumulationofcapitalsoastokeepthecapital-labourratiofixed(k).Ifthisdoesnotoccur,theriseinpopulationreducespercapitaincome(y)andconsumption(c);3.technologicalprogress:thegrowthoflabourefficiencyatrategincreasesthecapital-labourratio(k),raisespercapitaincome(y)andconsumption(c)inthesteadystate.Ontheonehand,technologicalprogressincreasespercapitaincome(y)forthesamek.Ontheotherhand,savingmightincreaseaswellandthusbooststhecapital-labourratioagain.Inthiscase,theproductionfunctionmovesupwardswithhighervaluesofE,andthegrowthofpercapitaincomecanbesustainedovertime.

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1.2. EndogenousgrowththeoryIntheneoclassicalapproach,continuedgrowthofpercapitaincomecanonlycomefromtechnologicalprogress,althoughthesourceofthisprocessisexogenous.TheSolowresidualisoftenrelevantinexplainingeconomicgrowth.Actually,itscontributiontogrowthisoftenlargerthanthatoftheinputs.Thisisanimportantlimitonneoclassicaltheory:itcannotexplaintheconstantgrowthinproductivity.Empiricalevidenceshowsthatinindustrializedcountries,observedgrowthratesofincomehavealwaysbeenpositiveinthelong-run.ThisstandsincontrastwiththepredictionsoftheSolowmodel.Modelsthatincludeanexplanationfortechnologicalprogress,forexamplethroughimprovedlabourefficiency,stilldonotgiveananswertothequestionwhyefficiencyeventuallygrows.Endogenousgrowththeoryhasadoublegoal:

• First,thetheoryaimstounderstandwhatfactorscausesustainedgrowth.• Second,technologicalprogressismodelledastheoutcomeofeconomicchoicesby

individualagents.Asaconsequence,endogenousgrowththeoriesarequitevaried.Therearemanydifferenttheoreticalmodels,withveryheterogeneouspremisesandhypotheses.SomeofthesemodelsarerelatedindifferentwaystoNewKeynesianEconomics(NKE)theory.Someoftheassumptionsattherootofexogenousgrowthmodels,andespeciallythoseonproductionandmarkets,areabandonedforotherhypotheseslikeincreasingreturns,economiesofscaleandimperfectlycompetitivemarkets.Newtheoriesofgrowththatlookfortheoriginsoftechnologicalprogressaredividednotonlybytheirassumptions,butalsobythedifferentimplicationstheyhave.Theoriginsoftechnologicalprogressmaybefoundintheaccumulationofknowledge(learning),theincreaseofhumancapital(education),ofpublic(infrastructures)orsocialcapital(interpersonalrelationsbasedontrustthatgeneratesthereductionofuncertainty),orinalargervarietyofproductsorinproductsofhigherquality.Thesehypothesesimplyadifferentapproachinmodellingeconomicgrowth.Thesemodelsalsohavedifferent,oftencontrasting,implicationsforlong-rungrowth.Asaconsequence,policyadvicebasedonendogeneousgrowthmodelsisquitedifferentfromneo-classicalpolicyrecommendations.BOX:Kaldorstylizedfacts(1963)Kaldor asks a fundamental requirement to economic growth theory. It should be able toexplain some observed facts which are a common feature experienced by industrializedcountries’economicgrowthpaths.Thesestylizedfactsemergefromempiricalregularitiesobservdinthelongrun.1)Thegrowth rateofoutputperworker (Δy/y>0) is roughly constantover longperiodsoftime2)The growth rateof the capital stockperworker (Δk/k>0) is roughly constant over longperiodsoftime3)Thecapital/outputratio(v=K/Y)isroughlyconstantoverlongperiodsoftime4)Therateofreturnoninvestment(r=KMP)isroughlyconstantoverlongperiodsoftime5)Thesharesofnationalincomereceivedbylabour(L)andcapital(K)areroughlyconstantoverlongperiodsoftime6)Thereareappreciablevariations in the rateof growthof laborproductivityandof totaloutputamongcountriesandthesedifferencesdonotseemtobefadingout

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1.2.1.ThelimitstogrowthIntheneoclassicalmodel,decreasingreturnsimposealimitoneconomicgrowth.TheAKmodel(Rebelo,1991)canresolvethisproblem.TheAKmodelissocalledforitsfunctionalformoftheproductiontechnology.Physicalcapital,humancapital,knowledge,infrastructureandallfactorsthatcontributetotheproductionabilityofaneconomyaresummedupinasingleproductionfactorcapital,hereindicatedwithK.AllfactorscontributeinfixedproportionstoK.Themarginalproductivityofeachoftheelementsthatmadeupthiscompositecapital(K)canstillhavedecreasingreturns.However,intheaggregatetheproductionfunctioniswrittenwiththefollowingform:Y=AK,wheretotalproduction(Y)dependsonthecompositionandonthelevelofthefactor(K)andapositiveconstant(A)thatindicatestheleveloftechnology.Inpercapitaterms,theproductiontechnologybecomesy=Ak.Percapitaincome(y=Y/L)dependsbothonthesupplyofcompositecapitalperunitoflabour(k=K/L)andonthepositiveconstant(A).Thisentailsthatthemarginalproductivityisconstantandequalsaverageproductivity:y/k=A.AlthoughthisseemstobeanapparentlysmallchangeoftheSolowmodel,ithaslargeeffects.Theaccumulationofcapitalperworker:

1) intheneoclassicalmodelwasgivenby:Δk=sf(k)-(δ+n)k.Asaconsequence,thegrowthrateoftheaccumulationofcapitalperworkerisΔk/k=sf(k)/k-(δ+n).

2) intheAKmodel,averageproductivityf(k)/kisconstantandequaltoA.Ifwesubstitutethetermthatreferstoproductivity,thisexpressionbecomes:Δk/k=sA-(δ+n).Asaresult,theaccumulationrate–thegrowthrateofcapitalperunitoflabour–dependsuponagivensavingrate(s),thedepreciationrate(δ)andthepopulationgrowth(n).

IntheAKmodel,themarginalproductivitydoesnotfallwhentheavailablecapitalperunitoflabourincreases.ThereforethelimitoftheSolowmodelthatpredictsthephasingoutofgrowthisovercome.Incomeincreasesinalinearpattern,asitisdirectlyrelatedtocompositecapitalK.IncontrasttotheSolowmodel,theincreaseofthecapitalstock(derivedfromthesavingfunction)doesnotdeclineascapitalintensityrisesintransitiontothenewsteadystateequilibrium.Instead,accumulationfurthernourishesthegrowthofproductivityandisthereforeabletosustainthegrowthrateoftheeconomy.Apositivegrowthratethusfollowsendogenouslywithinthemodel.Thisgrowthratecanbekeptinthelong-runwithouthavingtoresorttosomeexplicithypothesesabouttheappearance,developmentandenduringoftechnologicalprogress.UnliketheSolowmodel,theeffectofanincreaseinthesavingratedoesnotwearoutandcanproduceapermanenteconomicgrowth.Growthitselffeedsbackintomoregrowthifactualinvestment(sf(k)=sA)ishigherthantheinvestmentnecessarytosubstituteexistingcapital(δk).ThisisshowninFigure5wherethenewproductiontechnologyAKoverlapswiththesimpleststeadystateequilibriumpreviouslyconsideredinFigure2.Eachlineisidentifiedbyitsequationandthereadershouldnoticethatbothproductionfunctions(thelineary=Akandthey=f(k)curvewithdiminishingmarginalreturnsarerepresentedbyacontinuousline,botheffectiveinvestmentfunctionsarerepresentedbyabrokenline,whilethedepreciationrate(δk)iscommontobothparadigm.Theconditionthatallowsgrowthtofeedbackintoevenmoregrowth,iseasilyfulfilledasnosteadystatecanbedeterminedundertheAKmodel.Positivenetinvestmentwillbethenecessaryconsequenceoftheincentivetoinvestcontinuously,giventheabsenceofdecreasingmarginalreturnsofcapital.ApositivesavingrateissufficienttogeneratecontinuedgrowthintheAKmodel.Throughtheaccumulationof(agenericmeasureof)capitalK,savingissufficienttosustainunlimitedgrowth.Technologicalprogressisnotnecessarytoexplaineconomicgrowth:itisstillexogenousatalevelindicatedbytheconstantA.

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Figure 5. Unlimited growth in AK model

1.2.2.ThefactorsbehindtechnologicalprogressTheAKmodelcanovercomesomeofthelimitationofneoclassicalgrowthmodels,butdoesnottoexplaintheroleoftechnologyanditsdeterminingfactors.Infact,thereisonlyoneinput:compositecapital(K).Thisfactortransmitstheeffectsoftechnologicalprogress.AsthecompositionofKisconstant,itisnotpossibletoattributegrowthtooneofitscomponentsseparately.Asaconsequence,thismodeldoesnotgivesuggestionsforgrowth-enhancingpolicies.Factorsbehindtechnologicalprogresscanbeendogenouslyincludedinthemodel.Thishasbeenanalysedthroughthestudyofinnovationandthedifferentwaysinwhichinnovationcanoccur.First,laboursupplycanimprove,forexampleifthelabourforceishealthier,well-educatedandtrained(Harrod,1961).Second,theproductionprocesscanbeenhanced.Newproductscanbeinvented(productinnovation)andnewtechnologiescanbeputtobetteruseviaare-organization(processinnovation).Differentformsofinnovationcaneventuallybeattributedtotheaccumulationofhumancapital.Thisfactorcanbeadirectenginebehindgrowthifanewandmoresophisticatedorganisationofworkspreadsamongthelabourforce.Italsohasanindirecteffectiftheaccumulationofhumancapitalisincludedincapital,throughtheintroductionofnewmachineriesandplants,orinproductsofnewdesignorimprovedquality.Thetheoreticalanalysisofinnovationisquitecomplex,however.Endogenousgrowthmodelscanbedividedintomodelsthatdifferintheir:

1.roots:whicharetheincentivestowhichinnovatorsrespond?2.consequences:whobenefitsfrominnovation?3.modes:howdothematerialfactor(usually,capitalK)andthenon-materialfactor

(forexample,humancapitalHorlabourefficiencyL·E)interactwitheachother?Labourefficiencyreflectstheknowledgeandskillsacquiredbyworkerswithgrowingexperienceintheproductionprocess.Increasesintheefficiencyoflabour,thatareassumed

y=Y/L

y*

y=f(k)

k=K/L0 k*

ι=sf(k)

δk

sf(k)=sA

y=Ak

16

butnotexplainedinneoclassicaltheory,haveapredominantplaceintheoriesofendogenousgrowth.Newlyacquiredskillsincreasehumancapital,whichistheprincipalfactorofgrowth.Innovation–whetherradicalorincremental,genericorspecific,theconsequenceoftheexperienceaccumulatedbyworking,offormaleducation,orrelatedtotheintensityofcapital–requiresinvestmentinknowledgewhichtranslateintofixedcoststhatinturngeneratedecreasingcostscurvesinthelong-run.Thisaspectraisestheissueofincreasingreturns,andthedoubleissueoftheprovisionofresourcestoproducehumancapitalandhowtogetholdofitsbenefits.Infact,ifbenefitscanbegainedcompletely,andhumancapitalcanbeanalysedinasimilarwayasphysicalcapital(withunlimitedpositivereturns)aproblemofmarketorganisationoccurs.Howshouldpublicauthoritiesdealwiththemonopolythatcomesfromincreasingreturns?Isthiscompatiblewithsupposedlyperfectlycompetitivemarkets?Instead,ifthebenefitscannotbeobtainedentirely,thenthespreadofknowledgelookslikeapublicgood.Thequestionthenbecomeshowthispublicgoodcanbeprovided.Boththepublicsectorandtheprivatesector(orfirmsorworkersthemselves)mayhaveaspecificsystemofincentivestoprocurefortheaccumulationofknowledgewhichmustbeunderstood.

ScalereturnsandexternalitiesTheproblemofkeepingaproductiontechnologycharacterizedbynon-decreasingreturnswiththeassumptionsofcompetitivemarketsisaddressedbyendogenousgrowththeoriesthatintroducepositiveexternalities.Theseexternalitiesimplyincreasingreturns,andareachievedattheaggregatelevelintheproductionprocess–persectorratherthanperfirm.Thisgivesrisetoefficiencyimprovementsoverthedifferentphasesofproduction.Theseendogeneousgrowthmodelsarenecessarilydynamic,inordertogiveeconomicmeaningtogradualimprovementsinproductionactivity.Theroleofexternalitiescanbeanalyzedfromdifferentperspectives.Eachfirm,simplybyitsproductionactivity,causessomebeneficialeffectsontheproductionofotherfirms.Theseeffectsarenotvaluedinanymarket(whichistheverycharacteristcofexternalities).Hence,theproductioncostforeachfirmoperatingindividuallyishigherthanthecostwhenotherfirmsareactive.Ariseinprivatemarginalcostsafterafirmexpandsitsownactivity,causesareductionofthetotalcostsofotherfirms.Themarginalcostoftheindustryislowerthantheprivatemarginalcostofthefirm.ThemodelclearlyreferstoMarshalldistricts(Marshall,1890)andtothepositiveexternalitiesdeterminedbythecontiguityoflocalizingfirmsofthesamesector.Firmsbenefitfrompositiveexternalities.Analternativeexplanationisthattheamountproducedbyeachfirmexplainsthebeneficialeffectforthefirmitselfinreducingitsunitcosts.Ahigherproductionvolumeovertimetranslatesintolowercosts.Firmsareableto‘learnbydoing’(Arrow,1962).Afirmcanreducecostsbyhavingmoreexperienceintheproductionofagood.Thisincreasesproductivitybymorethanthesimpleadditionofproductionfactors.Increasingreturnsinaggregateproductionareusefultodealendogenouslywithtechnologicalprogress.However,theycanonlybemadecompatiblewithperfectcompetitionifincreasingreturnsareinterpretedaspositiveproductionexternalitiesoccurringattheaggregateindustrylevelratherthanatthefirmlevel.Increasingreturnswouldinterferewiththeproblemofthefirm’schoiceoffactorstominimizecosts(inanatomisticenvironment).Instead,increasingreturnsneedoccuratindustrylevel.Externalitiesalloweachfirmtotakeadvantageoftheactivityoftheircompetitors.Hence,increasingreturnsareexternaltotheindividualchoiceoffirms.Costsareperceivedbyeachfirmaspositiveexternalities.Inthisway,decreasingcostsforhigheroutputatthefirmleveldonotlimiteconomicgrowth.Ifmarginalfactorproductivityisanincreasingfunctionofoutputandishigherthanaverageproductivity,theremunerationoffactorsexceedstotalproductioni.e.,K·MPK+L·MPL>F(K,L).IfwedescribetheproductiontechnologywithaCobb-Douglasfunction,thisrequiresthatin

17

thefunctionY=AKαLβwhere0<α<1and0<β<1wehavethatalsoα+β>1.Inthissituation,moreinvestmentalwayspaysoff.Hence,continuedlong-rungrowthispossiblewithouttheneedtoexplicitlyconsidertechnologicalprogress.Aproductionfunctionwithincreasingreturnstoscaleassociatesincreasesinproductivitytoincreasesinoutput.Thisimpliesthatwecanmorethandoubleoutputbydoublingtheuseofinputs.Ifreturnstoscalewereincreasingwithoutlimitsandduetoeconomieswithinthefirm,thiswouldnotbecompatiblewithcompetitivemarkets.Inthelongrun,monopolieswouldappear.Underthehypothesisthatpositiveexternalitiesareduetotheproductionofafirmthathaspositiveeffectsonsimilarfirms,knowledgeisanon-remuneratedinput.Indifferentways,knowledgeproducesincreasingreturnsforanentiresector.Externaleconomiesenhancetheinvestmentofafirmincapital,whetherphysicalorhuman,asitimprovestheproductionskillsofotherfirmsaswell.Firmsdonotconsiderthisexternalityintheirproductiondecision.Therefore,knowledgeislikeapublicgood.The‘social’returnforthesectorofinvestingishigherthantheprivatereturn.Theconsequenceisthateachfirmwillinvestlessthanwhatisoptimalfortheentireeconomy.Theassumptionofexternaleconomiesisnecessarytokeepthehypothesisofcompetitivemarkets.However,itisdifficulttojustifyexternalitiesfortworeasons.First,giventhatknowledgeisapublicgood,thereisnorationalchoiceforaccumulatingknowledge(andhenceboosttechnologicalprogress).Second,itisevenhardertoexplainlearning,i.e.theaccumulationofhumancapital,atadisaggregatelevel.Thisproblemcanbecircumventedbystrictlyrelatingknowledgetoinnovation.Thisgivessometangiblemeaningtoanintangiblevariablelikeknowledge.Theassumptionisthatknowledgerelevantforproductionisinevitablyaccompaniedbyproductorprocessinnovation.Technologicalprogressisincludedinnewplantsandmachineriesthatthroughnewproductionprocessesrequirenewskills.Thisinduceslearningandtheaccumulationofhumancapital.Yet,howisitpossibletoreconciletheexistenceofconstantreturnsfortheeconomicsystem,butdecreasingreturnsforthefirm?Thegrowthlimitsoftheneoclassicalmodelcanbecircumventedbyassigninghumancapitaladecisiverole,leavingthehypothesisofdecreasingreturnsforaggregateproduction,whilemaintainingitfortheproductionofindividualfirms.ThepositiveexternalitiesproducedbytheaccumulationofhumancapitalforthewholeeconomyaccordingtoanY=AKfunctionaretakenintoaccountbythehypothesisthattheproductionofindividualfirmsoccursaccordingtoaCobb-Douglasfunctionwithconstantreturnstoscaleanddecreasingmarginalreturns,whiletheexternalitiestakeplaceoutsidethefirmbutinsidethesector.LetusimaginethatthereareNfirmsandeachoftheseproducesanequalportionofoutput:Y/N=A(K/N)α(L·E/N)1−α.Inaggregate,withconstantreturnstoscale,outputwillbe:Y=AKα(L·E)1−α.Weassumethatlabourefficiency(E)isproportionaltothecapitalaccumulatedperworkeraccordingtothefunctionofknowledge(E=K/L)thatrelatestheproductivityoflabourwiththeintensityofcapital.Wecanassociatetheefficiencyoflabour(E)withthelevelofcapitalintheeconomy(K).Inthisway,wecananalysethespreadofknowledgeinsociety.Thisdiffusioniseasedforhigherlevelsofcapital,whichincreasestheproductivityofeachfirm.Theaccumulationofcapital–apartfromtheusualeffectshownbytheterm(Kα)–haseffectsalsoontheefficiencyoflabour(E)throughtraining.Bysubstitutingtheexpression(E=K/L)intheproductionfunctionY=AKα(L·E)1−αtoobtainY=AKα(L·K/L)1−αonecansimplifyandeliminatethelabourterm(L).InthisexpressionY=AKαK1−αthetermK1−αappears.Thisrepresentstheexternalityforanyindividualproducerandreflectsthespreadofknowledgein

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society.Incomecanincreaseinproportiontotheincreaseofcapital,andtheamountoflabourstaysunchanged.SinceKαK1−α=K,theproductionfunctionfortheoveralleconomywouldbetheY=AKfunctionwithconstantreturns.Eachindividualfirmownsatechnologywithdecreasingmarginalreturns.ThetermK1−αhastobeconsideredasgiventothefirm,sinceitdependsonthedecisionsofotherproducers.Afirmthatincreasesitsowncapitalthereforeobtainsasmallerincreaseinoutputthanallfirmsjointly.Theeffectofitsincreaseisnotlimitedtothefirmitself,butspreadsoverthewholeeconomicsystem.Ifallfirmsexpandatthesametime,eachwouldbenefitnotonlyfromitsowndecisiontoexpandbutalsofromtheexpansionofallotherfirms.

ProductionandtheuseofhumancapitalInendogenousgrowthmodels,innovationdependsindifferentwaysontheaccumulationofhumancapital.Thereshouldbemorefocusontheroleofinnovationtounderstanditsroleintheeconomy,especiallythroughtheanalysisoftheconditionsunderwhichinnovationisproducedandtheroleoffeaturesintheproduction.Labour(L)increasesaccordingtothepopulationgrowthrate(n)whichisconsideredexogenous.Acquiringhumancapital(H)isinsteadaneconomicdecision,andisthereforesubjecttoeconomicincentives.However,modelsdonotagreeonthereasonswhyhumancapitalgrows.Itcangrowinapassiveandimplicitwaywhenitderivesfromtherenewalofphysicalcapital,sothatlearningisstrictlyrelatedtothegrowthofphysicalcapital.Humancapitalcanalsoriseinanintentionalandactivewayifitisduetoahighereducationlevelacquiredbythepopulation.Inthefirstcase,theincreaseofproductivityderivesfromtrainingontheworkplaceandisincludedinphysicalcapital.Thehumancapitalofworkersisaccumulatedbylearningnewtechnologies.Technologicalprogressessentiallydependsonthefirm’sinvestmentdecisionsandthecharacteristicsofthehumancapital(thevariableH)differlittlefromthoseoflabour(thevariableL).Thereasonwhyworkersacquirenewskillsorimprovetheiracquiredskillsislessrelevantcomparedtothereasonwhyfirmsarepushedtoinnovate.Itseffects–andhowandwhylearningbydoingtakesplace–arestilltheobjectofongoingresearch.Inthesecondcase,weneedtoexplainwhyaworkerdecidestoassignpartofitstimetotheaccumulationofhumancapital.Itisnotunreasonabletoassumethattherearedifferenttypesoflabour,whichcorrespondtodifferentlevelsofhumancapital(skilledandunskilled).Theincentiveforaworkertoinvestineducationisahigherwagelevel.Insuchacase,humancapital(thevariableH)sharessomefeatureswithphysicalcapital(thevariableK).Theaccumulationofboth,humanandphysicalcapital,occursinananalogousway.Accordingtohumancapitaltheory,educationisaninvestmenttowardstheproductionofskills.Aneducatedworkforcelearnsfasterandmoreeasily,andisthereforemorelikelytoadoptnewtechnologies.Thedirectconsequenceofahigheraveragelevelofinstructionofthepopulationaswellasofthelargernumberofworkersthatobtainacertainlevelofeducationisacontinuedgrowthofoutputandincome.Thegrowthrateofproductivitycanbedirectlyrelatedtoameasureofthelevelofeducation.Forexample,aroundathirdoftheSolowresidualcalculatedfortheUnitedStatesbetween1940and1967canbeattributedtoahigherlevelofeducation(Griliches,1970).Yet,iftheincreasesinproductivityderivefromindividualdecisionstoacquireknowledge,weshouldalsorecognizethatamorequalifiedworkforcehasenhanced‘socialskills’(Abramowitz,1986).Investmentinhumancapitalisawaytoincreasetheproductivityoftheworker.Atthesametime,humancapitallookslikeapublicgoodsincethespreadofknowledgehasnon-competitiveandnon-excludablefeatures.Itisimpossibleforaworkertoentirelyappropriatethebenefitsfromeducation,orforafirmfromthetrainingofferedtoworkers.Asaconsequence,privatedecisionsareunlikelytoleadtooptimalsocialoutcomes.

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IntheSolowmodel,physicalcapital(K)isapartofanundifferentiatedgood(Y)thatisinvestedratherthanconsumed.Unlikephysicalcapital,humancapital(H)hastobeproducedaccordingtothedecisionsofoptimisingagents.Iftheaccumulationofhumancapitalisscarce,actualgrowthcouldbelowerthanthepotentialone.Theprivatesectorcouldbeunabletoproduceenoughpublicgoodsforlackofincentives,sothatitsproductioncanonlybeassuredbythepublicsector.Differentmeasureshavebeenattemptedtoboostincentivesfortheprivateproductionofhumancapital(evenifithaselementsofapublicgood).Inthisway,theeconomycouldexploittheexistenceofincreasingreturnsandreachunlimitedgrowth,whileatthesametimehavingcompetitivemarketsnecessarytopreservethesocialoptimum.Onepathfollowedwastoaddhumancapital(H)tophysicalcapital(K)andlabour(L)intheproductionfunction.Withthreeinputs,theproductionfunctionbecomes:

βαβα −−= 1)(ALHKY andbydividingby(AL)theproductionfunction( βαhky = )intermsofbothpercapitafactorsphysical(k=K/L)andhumancapital(h=H/L)isobtained.Theadditionofhumancapitaltotheproductionfunctionraisesafirstproblemfortheappropriationofincometothedifferentfactorsinagrowthaccountingexercise.Thesharethatbelongstophysicalcapital(α)shouldnotchange.Theshareforhumancapital(β)ismoredifficulttomeasure,asitshouldbedecomposedintohumancapitalandtheefficiencyincludedinlabourunits.Ifthewagereflectslabourproductivity,humancapitalcouldbemeasuredaccordingtoitsretribution(similartophysicalcapital).Therefore,theunitaryhumancapital(h)reflectstheaveragewagedistribution.Theunitsoflabour(L)reflectthenumberofworkers,orworkedhours.FortheUnitedStatesthesevalueswereassessedasbeing:α=1/3and1/3<β<1/2.Thesumoftheexponentsoftheproductionfunctioncanstillbeconsistentwithahomogenousfirstgradefunction(Mankiwetal.,1992).Ifwesolvetheequationthatdescribesinlogarithmictermspercapitaincomegrowthforthevaluesofhevariableskandhinsteadystate,thiscanbewrittenas:

[1] )ln(1

)ln(1

)ln(1

)0(ln)ln( δβα

βαβα

ββα

α++

−−

+−

−−+

−−++= gnssgAy hktt

Aportionofincome(sh)issavedtofinancetheinvestmentinhumancapital,i.e.theexpenseforeducation.Anotherpartofincome(sk)issavedtofinanceinvestmentinphysicalcapital.BothinvestmentsplaythesameroleasthesavingrateintheSolowmodel.However,itisnotclearhowtoattributetheincomesharestoeachproductionfactor.Whatistherelationshipbetweenthesavingrates(skandsh)andthesumofthegrowthratesofthepopulation(n),technology(g)andthedepreciationrate(δ)inthegrowthequation?Withthepreviouslygivenvalues,e.g.α=β=1/3,andsubstitutinginα/(1-α–β)wewouldobtainacoefficientequalto1forphysicalcapitalandthesamewithβ/(1-α-β)forhumancapital.IntheSolowversion,thevalueα/(1-α)wouldhavebeenlower.Inthisformulation,percapitaoutputdependsonthecapital-labourratio(k)andonthehumancapitalperworker(h)ratio.Theformerisafunctionofspendingoninvestmentandthedepreciationrate.Thelatterisdeterminedbyspendingoneducationandthedevaluationofhumancapitalnetofitslearningskill.However,ifhumancapitalentersintheproductionfunctioninasimilarwayasphysicalcapitalandreflectstheendowmentoffactors,themodelwouldarriveatasteadystatewithahigherlevelofpercapitaincome.Inthissteadystatethereisnocontinuousgrowth.Instead,ifweincludehumancapitalintechnologicalprogressbymodellingitaseffectivelabour,growthiscontinuous.Yet,intheabsenceoftheincentivesabletoendogenouslydefinethetimetobededicatedtotheacquisitionofknowledgeandskills,themechanismbehindgrowthisstillexogenous,asisthelearningprocessandtheaccumulationofknowledge.

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Thisisstillnotaverysatisfactoryexplanation.Ifweadmitthatknowledgeisapublicgood,newknowledgecanbeproducedaccordingtoatechnologywithdecreasingreturns,but,itcanstillshowincreasingreturnswhenitisusedaproductionfactor(Romer,1986).TheadditionofhumancapitaltotheproductionfactorsdoesnotreallyrespondtotheobjectionstotheSolowmodel.Infact,itisactuallyraisingevennewobjections.Anotherresearchpathfindstheengineofgrowthintheproductionofinnovationbyfirmsengagedintotheresearchofproductswithpatents.Firmsexpecttoearnmonopolisticeffectswiththesenewlyproducedgoods(Aghion,Howitt,1992).Let’sdefineaperiodasthetimepassingbetweenonediscoveryandanother.Theamountofresearchineachperioddependsontheexpectationsfirmshaveontheamountofresearchinthefollowingperiod,whenthecurrentrightsonaninnovationhowevercannolongerbeexploited.ThistakesuptheSchumpeterconceptofcreativedestruction.Theunderlyingassumptionisapositiverelationbetweenmonopolyrentsandresearchactivity(Schumpeter,1942).Moreresearchdonebyqualifiedworkersismorelikelytogiveresultsthehighertheexpensesonresearchanddevelopment.Innovationincreasesproductivitypermanentlyinthewholeeconomy,accordingtoanaccumulationprocess.However,permanentgrowthcannotbetakenforgranted.Theperiodoverwhichreturnstoresearchthroughpatentslastandthewagespaidtoresearchersarecloselyrelated.Thereturnsarelowerthemoreresourcesarededicatedtoresearch.Costlyprojectsreduceprofits,but,moreresearchproducesevenmoreresults.Thisreducestheperiodinwhichafirmcangainrentsonaspecificproduct.Thehigherwagespaidtoresearchers,thehigherisresearchactivity.Theprobabilityofsuccessdetermineswhetherresearchcanleadtocontinuedgrowthorjusttoacyclicalboomoragradualstagnationoftheeconomy.Humancapitalisthefactorbehindtechnologicalprogress,butitcorrespondstodifferentconcepts.Differentformsofhumancapitalareonlypartiallyalternatives.Publicandprivateeducation,trainingonthejobandlearningbydoingallfavouritsproduction.Thecloseraneconomyistothetechnologicalfrontier,thehighertheboosttoproductivitygrowthandmoreinvestmentinuniversityandpost-universityeducationonthewholeofeducationspending(Aghion,Howitt,2006).Theaccumulationofhumancapitalcanbeexplicitlypursued,butitisnecessarytodesignasystemofincentivestofavoureducation.Accumulationcanalsohappenaccidentally,e.g.bylearningbydoing,butthisdoesnotgivemuchindicationstoeconomicpolicy.Privateeducationisanindividualdecision,anditisaninvestmentchoiceonlyifitsaimisproductiveactivity.Otherwise,educationisaconsumptiongood.Whenweconsiderhumancapitalasainputusefultogrowth,itsheterogeneouscompositionmakesatractableanalysisdifficult.Itisunlikelythatatheoreticalmodelcouldanalysehumancapitalinsuchmodelsandgivereasonableempiricalpredictions.Theaccumulationofhumancapitalmaintainsitsowncharacteristicsevenwhentheanalysisisverysimilartotheaccumulationofphysicalcapital.Onecanpossiblyextendtheanalysistoothermodels,e.g.theAKmodelwherecapitalisbothphysicalandhuman,andmakethegrowthratefeedbackintoitself.Butthispropertydependsontheimpossibilitytofullyappropriatetherents,sincemarginalcostsdecreasewhenproductionrises.So,itisnecessarytodiscernthewayinwhichhumancapitalcontributestoproductionandaffectsthegrowthrate.Thefallinproductioncostscanberelatedtotheincreaseofthelevelofhumancapitalortogrowingexperience(i.e.,theaccumulationofoutput,asunder‘learningbydoing’).Insummary,thereisacommonresultofmodelswithdifferentstructuresanddifferentanalyticalimplications:themarginalproductofcapitalisconstantandnotdecreasing.Proportionalincreasesincapitalcauseproportionalincreasesinoutput.Outputcanincreasealsointheabsenceofexogenoustechnologicalprogress.Lucas(1988)addstheaccumulationofhumancapitaltotheneoclassicalmodelandstudiesitsinteractionwithphysicalcapital.Therearetwoproductionfunctions.Oneisforoutput(y),

21

wherehumancapital(h)isplacedamongtheinputsandproducedthroughanadditionalproductionfunction.Theaccumulationofhumancapital(h)hasaninternaleffectontheproductivityoftheindividual.Theindividualdecidestodedicatetimetoacquirehumancapital.Theindividualdecisionhasanexternaleffectthatproducesbenefitsforothersindividuals.Theydecidetheallocationoftheirowntime(u)accordingtotheirutilitynomatterthedecisionsofotheragents.Thefunctionbecomes:L(t)c(t)+∆K=A(t)K(t)β[u(t)h(t)L(t)]1-βhh(t)γ,wherethetermhh(t)γshowstheexternaleffectsoftheaccumulationofhumancapital.Thisdependsonaverageskillability(hh).Individualproducersconsiderthislevelasgiven,beingtheoutcomeofdecisionstakenbyothers.Intheproductiontechnologyreturnsareconstantglobally,butdecreasingindividually.Therelationshipbetweenthegrowthofhumancapitalandthetimeemployedtowardseducationisgivenbyalinearfunction:∆h/h=hδ(1-u).Humancapitalgrowsatamaximumrate(δ)ifallavailabletimegoestotheaccumulationofknowledge(u=0),whileifnotimeisdedicatedtoitthereisnogrowth(u=1).Inbetweenthesetwoextremes,thestockofhumancapital(h)increasesinproportiontotime(u)nomatterthelevelreached.Educationisnotsubjecttodecreasingreturns.Thenon-decreasingendogenousgrowthrate–duetotheaccumulationofhumancapitalproducedwithaportionofthetimeavailable–requiresthataccumulatedhumancapitalcanbetransmittedfromonegenerationtothenext.Inotherwords,theaccumulationofknowledgeisnotlostacrossgenerations.Thisredefinesthenatureofhumancapital:itisnotapurelyindividualchoice,butconsidersitsaccumulationa‘social’activity.Eventhoughitisanindividualdecision,educationsharesthecharacteristicsofapublicgood.Theallocationproblembetweenconsumption(c)andtimetodedicatetoproduction(u)issolvedbyequatingmarginallythevalueofconsumptionandinvestment.Asimilaroptimisationgivesthetimededicatedtoproductionortotheaccumulationofhumancapital.Thegrowthrateofhumancapital(ν)determinesgrowthinthismodel.Therearetwoextremecases:a)withoutexternalities(γ=0)physicalandhumancapitalincreaseatthesamerate(κ=ν);b)withexternalities(γ>0),physicalcapitalincreasesfasterthanhumancapital(κ>ν).Inthelattercase,theallocationproblemdiffersuponwhetheronetakesaprivateorsocialperspective.Theratiobetweenphysicalandhumancapitalintheabsenceofexternalitiesisdescribedbyastraightlinethatpassesbetweentheoriginoftheaxeswherethetwovariablesaremeasured.Ifthereareexternalities,thesamerelationisdescribedbyacurvethatisconcavetowardstheaxisonwhichhumancapitalismeasured.Itspositiondependsonthegrowthrateofphysicalcapital(κ)andtheallocationoftime(u).Therefore,anefficienteconomyontheoptimalgrowthpathwillhaveahigherlevelofhumancapitalforeachlevelofphysicalcapital.Letustakethegrowthrateofpopulationasgiven,andconsidertwotypesofcapital.Physicalcapitalisgovernedbyatechnologywithdecreasingreturns.Thegrowthofhumancapitalincreasestheproductivityofphysicalcapitalandlabour,andisthedrivingforcebehindgrowth.Previously,thisrolewastakenupbyexogenoustechnologicalprogress.Economiescharacterizedbythistypeofexternalitiesdonotnecessarilyreachasteadystategrowthrate.IntheSolowmodel,thisratewasequaltothesumofthegrowthrateofpopulation(n)andtherateoftechnologicalprogress(g).Theefficientgrowthpathdivergesfromthisequilibriumgrowthpath.

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1.2.3.GovernmentandpoliciestoboosteconomicgrowthNeoclassicalgrowthmodelsnaturallytendtotheequilibriumsteadystate.Growthisexplainedintermsofshiftsfromonesteadystatetoanother.Hence,thesemodelsgivenosuggestionshowtostartorsustaineconomicgrowth.Incontrast,endogenousgrowthmodelsdonotnecessarilyproduceanequilibriumnorasteadystate.Thisgivesmanymorepossibilitiesforgrowthpoliciestoinfluenceeconomicdevelopment.Externalitiesinducedbytheaccumulationofhumancapital,determinethecapacityofaneconomytocontinuegrowing.Externalitiescorrespondtoamarketfailuresincethedecentralisedequilibriumbasedontheprivateinterestofatomistagents–individualorfirms–isnotoptimal,butresultsinanincomelevelthatislowerthantheoptimalone.Thereasonisinsufficientinvestment:theexternalitiesrelatedtoknowledgearenotincorporatedinindividualdecisions.Theeffectofexternalities–andinparticulartheirroleingrowthdynamics–iscertainlynotlimitedtotheconsequencesontheaccumulationofhumancapital.Theexternalitiesproblemmayjustifyaroleforthepublicsectoringrowthmodels.Letusassumethatthepublicauthorityhasthepossibilitytointerveneintheprovisionofprivateandpublicgoodsaswellofgoodssubjecttocongestion(Barro,Sala-i-Martin,1992).Inthefirstcase,thepercapitaexpenseforprivategoods(g=G/L)offeredbythepublicsectorisincludedintheproductionfunctionthatbecomes:y=Ak1-αgα,where0<α<1.Thisfunctionisnotstructurallydifferentfromtheoneseeninpreviousmodelswhereitwascapital,bothhumanandphysical,thatincludedtheexternality.Therefore,thegrowthratenowdependsontheamountofgoodsandservicesproducedbythepublicsector.Anyindividualproducerconsidersthisasagiven,notdifferentlyfromthereactiontotheamountofcapitalsuppliedbyotherproducers.Thesourceoftheexternalityisthussimilar.However,governmentproductionalsoabsorbsresourcesfromtheeconomy.Taxation(τ=g/y)inducesadistortioninthegoodsmarket.Asaconsequence,privateincomeislowerthansocialincome.Thegrowthrateisstilllowerthantheoptimallevel.Inthesecondcase,itistheindivisiblepublicgoodGthatisincludedintheproductionfunction:y=Ak1-αGαwhereGhasthecharacteristicsofanon-rivalrousandnon-excludablegood.Apublicinterventiondoesnotchangetheresult.Itissub-optimalasfinancingthepolicyimposesadistortionarytaxontheeconomy.Theequilibriumcanbechangedifthefinancingoftheinterventionhappenswithalumpsumtax.Thesupplyofprivategoodsagainstanequivalentlumpsumtaxisnotdifferentfromprivateproduction.Suchapublicinterventionwouldnotmodifyprivatedecisions.Inthethirdcase,thepublicgoodissubjecttocompetitionbutnottoexclusion.Thecongestionlevelisshownbytheratiobetweenpublicspending(G)andthecapitalstock(K).Itenterstheproductionfunctionasy=Ak(G/K)α.Thedecisiontoincreasethecapital-labourratio(k)alsoincreasestheuseofthecongestiongood.Withoutatolltherewouldbeanexcessiveuseofthepublicgood.Privatereturnsofinvestmentarehigherthansocialreturns.Thepaymentofthetollinteriorisestheexternalityandtakestheeconomytotheoptimalgrowthrate.Theseresultsshowhowtheinterventionofthegovernmenthastobesubjecttoanaccurateevaluation.Policiestosustaintheformationofhumancapital–forexample,forworkersbyimplementingprogramsforfreepubliceducation,orforfirms,throughfundingortaxreductionsaimedatpromotingtrainingonthejob,ortopromoteresearchanddevelopmentbymakingiteasiertoappropriaterentsoninnovation–canproducevariedresults.Publicinterventioncanaffectallthedifferentareasinvolvedintheaccumulationofhumancapital.Butgovernmentpoliciesareneitherunlimitednorunambiguous.Themainsuggestion

23

wecantakefromthisanalysiswouldbetostartfromaprecisedefinitionofthetypeofproductionthatshouldbecarriedoutbythepublicsector.Thissupposesanevaluationonthetypologyofhumancapitalandthenatureoftheexternality.Humancapitaltheorywouldpreferpublicspendingoneducation.Thetheoryof‘learningbydoing’insteadwouldgiveprioritytokeepingproductionatahighlevelinordertoreinforceexperience.TheSchumpetermodelincontrastwouldsuggestacommitmenttoprotectpatentsandresearch.Thedesignofpolicies,oncetheoriginoftheexternalityhasbeenfound,isnotasecondaryissue.Unfortunately,economictheorygiveslittleinsightinthetrade-offsbetweenoptimalpolicies.Sincepubliceducationisacongestiongood(justthinkabouttheintroductionoflimitedplacesinmanyhigheducationinstitutions),itshouldbepaidforaccordingtoitsconsumption(likeatollonmotorways).Yet,thisassumesthattheincomedistributiondoesnotconditionindividualbehaviour.Thisassumption,implicitinthemodelofrepresentativeeconomicagentsandcommoningrowthmodels,imposesaconditionthatdoesnotclearlycorrespondtoreality.Thelevelofproductionconsistentwiththenatureofpublicgoodcouldbeobtained,forexample,bylimitingcompetitionbyforeignfirms.Thiswouldgiveanadvantagetodomesticfirmsandreinforcetheirpositionininternationalmarkets.Ifcompetitiondependsonexperience,andproduceseconomiesinternaltothefirm,theimplicitriskistoreinforcedomesticmonopolies.Aguaranteeonintellectualpropertyrightsraisestheproblemofreconcilingtheprivateinterestofthepatentdeveloperwiththesafeguardofcommoninterest.Publicpoliciesshouldencourageresearch,butnotfavourmonopolisticrents.Inaknowledgebasedeconomy,innovationisofcrucialimportance.Ontheonehand,lawsmeanttoprotectintellectualpropertyrightsruntheriskofexcessiveprotection.Thiswouldassigntotheinnovatorthemonopolyprofitsoveratoolongperiod.Ontheotherhand,thereisariskofinsufficientprotectionwhichwouldgivetoolittleincentivestoinvestininnovation.Grantingtherighttoexploitthemonopolisticpowertiedtoapatentneedsberegulatedinsuchwaysoastoconsidertheindividualincentiveintheresearcheffort,theneedsofsocietyforarapidspreadofitscontents.Thecompromisebetweentheindividualincentivesandthesocialtargetsshouldpreservestressingthesocialdimensionofgrowth,increasingcompetitionthroughimitation,avoidingduplicationofexpensesforresearchanddevelopmentandfavouringthecumulativeeffectsofinnovation.

1.2.4.GrowthinanopeneconomyThegrowthmodelsconsideredsofarshareafeature:theyallpresentgrowthasanaggregatephenomenon.Growthisexaminedinaclosedeconomywithonlyoneproductandjustoneortwoinputs.Thesemodelsareunsuitabletofullyanalysetherelationsbetweeneconomicgrowthandinternationaltrade.Thetheoryofeconomicgrowthisalmostcompletelyabsorbedbylookingforitsdeterminingfactors.Thereforeitdoesnotassignanimportantroletointernationaltrade,andwhenitaddressesthisaspect,itmainlyregardsempiricalissues.Theempiricalstudiescomparetheperformanceofdifferenteconomicsituationsratherthananalysingindepththecomplexinterrelationsbetweencountries.Inendogenousgrowthmodels,alsoknownasthe‘newgrowththeory’,thecontributionofGrossmanandHelpman(1991)isanexception.Theseauthorsexaminehowequilibriacanpossiblyexistbetweentwodifferentcountrieswithadifferentlevelofresearchactivity.ThetypicalexampleisthatofaninnovatingcountryintheNorthandanimitatingcountryintheSouth.Themodelfollowstheneo-Schumpeterianparadigm:growthistheconsequenceofanendogenousimprovementinthequalityofproducts(regardlesstheproductiontechnology).Themodelexplicitlyanalysesthepossiblecontributionofinternationaltradetogrowth.

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Thetwocountriesarecharacterizedbytheirabilityinresearchanddevelopmentactivities(R&D).Thecostsoflabourdiffersacrossthetwocountries,whichproducedifferentgoodsthatcanbeorderedaccordingtotheirdifferentquality.Eachimprovementinqualitykicksoutofthemarketthegoodswithlowerquality.Shouldthequalitybethesame,thecheapergoodsubstitutesthemoreexpensiveone.Consumersmaximizeanintertemporalutilityfunction,ownaportfolioofsecuritiesandassets,andsolvetheallocationissueinthemarketofgoodsbychoosing,foreachproduct,thehighestqualityatthelowestprice.Firmsissueshareswhosestockmarketlistingdependsonprofits.Firmsearnprofitsfromthesaleofproductsforwhichtheyhavesuccessfullyinvestedinresearch.Onlyonefirmcanbesuccessfulineachperiodandsector.Thismeansthatfirmsgetmonopolisticprofits.Profitsdryupwhenanotherfirmimprovestheproductorcopiesitsellingitatalowerprice.Firmsareactiveinthetwocountriesindifferentsectorsandaresubjecttodifferentprofitratesanddifferentrisks.Ineachperiod,gettingearningsdependsontheintensitythefirmemploysininnovating(γ)orimitating(μ).Ineachperiod,onlyonefirmissuccessfulandobtainsmonopolyprofitsbysellingitsproduction,whichisoneofthenpossiblegoods.Byinvestinginresearch,eachfirmcanobtainaprofit.Thisincreasesitsvaluethroughitssharesinthefinancialmarket.ThemorethefirminvestsresourcesinR&Dactivity,thehighertheprobabilityofsuccessinR&D.TheprobabilitythatinnovationoccursfollowsaPoissondistribution.AfirmintheNorththatinnovatesonthequalityofaproduct(thatlaterisimitatedintheSouth),maximisesitsprofitsbysellingitatapricemarginallyhigherthanthepreviousone.Inthisway,itremainstheonlysellerinthemarket.AfirmintheSouththatimitatesthenewproductmaximizesprofitsbysellingitatapricemarginallylowerthanthepriceintheNorth.Thismeansitwillbetheonlyseller.AfirmoftheNorthcompetingwithanotherfirmoftheNorthimprovesthequalityofitsproductandsellsitatapricethatismarginallyhigher.Itbecomestheleaderinthismarketanditsfollowersrelyuponatemporarilyinferiortechnology.TotalproductionisthesumofgoodsproducedintheNorth(nN)andintheSouth(nS)andrespectsthecondition:nNN+nNS+nS=1wherenNN+nNS=nN.WedenotebyEtheexpenseofconsumersfortheproduct,byλthepositivepricedifferentialbetweenNorthandSouthandbywthewagesthatreflectmarginalcosts.WagesarelowerintheSouth(wN>wS).Profitswilldependonthekindoffirm.Thelabourunits(a)necessaryforleaderfirms,followerfirmsandimitatingfirms(M)areweightedbytheintensityoftheireffort(γ)and(μ).ThetermnNthatappearsinthelabourdemandoftheSouthdenotesthesetofproductsoftheNorththatwillbeimitatedbytheSouth.ThetermnSthatappearsinlabourdemandoftheNorthshowsthesetofproductsoftheSouththatwillbeimitatedbyfirmsintheNorth.ThelaboursupplyofthetwocountriesisgivenandisdistributedoverinnovatingandimitatingfirmsthatareeitherintheNorthorintheSouth,andoverthemanufacturingfirmspresentinbothcountries.Inequilibrium,laboursupplyisequaltolabourdemandinthedifferentfirms:1. intheNorth,itismadeupbytheunitsoflabouroccupiedbytheleaders(aDΓγSnS),thefollowers(aDFγNnN)andmanufacturingfirms:aDFγNnN+aDΓγSnS+nNNE/λwN+nNSE/λwS=LN.2. intheSouth,itisgivenbythelabourunitsemployedintheimitationsector,andmanufacturingsectoremployment:aMμnN+nSE/wS=LS.Insteadystate,differentequilibriaarepossible.Thesteadystatesdependontheparametersthatreflectthecostofinnovationandimitation.Itispossiblethatthereisnoinnovationandimitationbecauseofthehighcostsofbothactivities.Thiswouldcancelgrowth.

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Innovationandimitationcanalsoreinforceeachother.ThiswouldimplythatNorthandSouthindifferentperiodsleadtheproductionofgoods.Thiscouldevenmeanthatfollowersareinvolvedinproductionaswelliftheadvantagethatleadersenjoyisnottoobig.Undercertainconditions,themodelcanhaveinsufficientincentivesforimitationandfirmscangetnoprofitsintheSouth.AnincreaseofresourcesallocatedtoR&DintheNorthincreasestherateofinnovationandasaconsequenceimitationintheSouth.AnincreaseinemploymentintheSouthincreaseslearningandintensifiesimitationwhichreducestheperiodoverwhichthefirmintheNorthcanenjoyprofits.GrowthalwaysoriginatesfromaninnovationintheNorthandexpandstotheSouththroughinternationaltradebetweenthetwocountries.Theflowoftradedependsontheprevalenceinvariousperiodsofinnovativeorimitatedproducts.Notethatthismodelstillreferstoabartereconomy.Thereisaroleforpublicinterventioninthissetting,butittakesaratherneo-mercantiliststance,justasithappensinstrategicinternationaltrademodels.Thetwocountriescanimprovegrowthbysubsidizinginnovationandimitation.AninnovationsubsidyintheNorthhasadoubleeffect.First,itincreasestheintensityofeffort(γ)andenlargestheperiodoverwhichtheproductcannotbeimitated.Second,itreducesthenumberofimitableproductsbytheSouthoverthesameperiod.AsubsidytoimitationintheSouthimprovesthelearningskillsofimitatingfirms,butprolongsthedurationoftheproductcycle.ThelatterslowstheinnovationabilityoftheNorthandthustheeconomicgrowthrate.Governmentsofthetwocountriescansustainresearchanddevelopmentreinforcingtheinnovationandimitationratesandchangethedurationoftheaverageproductcycle.Theresultsdependinlargepartonthewayinwhichthedifferentparametersarecombined.Hence,itishardtocomeupwithageneralconclusion.Theresultsareoftenuncertain.Sincepoliciespursuedinonecountryhavetheoppositeeffectintheothercountry,theyareunlikelytoleadtoParetianoutcomes.TheinteractionbetweenthegrowthprocessesofNorthandSoutharedeterminedbyincreases(anddifferences)intechnologicalcapitalanddifferencesininputsupply.Growthhaswinnersandlosers.Thisiscertainlyanewfeatureintheanalysisofthefactorsofgrowth.Thereasoningproposedbythemodeldoesnotexclusivelyapplytotraderelationshipsbetweentwodifferentcountries.Themodelcanalsobeusedtodescribetherelationsbetweentworegionsofthesamecountry:e.g.,aSouthernandaNorthernregionwithoutperfectmobilityofresources.TheanalysisofthismodelwithdifferentproductionfeaturesinaninternationalsettinghastheSchumpeteriancreativedestructionastheengineofgrowth.Investingresourcesininnovationisanecessaryconditionforeconomicgrowth(althoughnotsufficientone)becausethesuccessofresearchisuncertain.

1.2.5.Growthproducedbydemand:export-ledmodelsInneoclassicalgrowthmodels,demandhasnoroleatall.Thebasictheoreticalrelationistheproductiontechnologythatdeterminesthegrowthabilityofaneconomy.Theimplicitassumptionisthatproductiondeterminesthe(possible)exports.Inendogenousgrowthmodelswithmorethanonegooditispossibletostudytheroleofinternationaltrade.Inthesemodels,theexportsectorisusuallyassumedtohaveahigherlevelofproductivitybecauseitismoreexposedtointernationalcompetitionwhichintroducesanexternality.However,thenewendogenousgrowththeoryisalsoguidedbysupplyfactors.Inparticular,theavailabilityofinputs,firstofallhumancapital,iscrucial.Thedemandforproductionfactorsderivesfromthegrowthofoutputitself.

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Unlikethesemodels,Keynesianmodelsarguethataggregatedemandisabletopromoteeconomicgrowth.Inordertounderstandthefactorsbehindgrowthratesinthelongrunitisnecessarytodetailthedemandforexports.Foranopeneconomy,exportsrepresentaclearlyautonomouscomponentofdemand.Achievingasustainedgrowthratecanbehaltedbydemandconstraintslongbeforesupplyconstraintsemerge.Hence,outputgrowthisnotthecause,buttheconsequence,ofexportsgrowth(Thirlwall,2002).Anin-depthexaminationofagrowththeorybasedondemandrequiresananalysisoftherelationsbetweeneconomicvariablesdisaggregatedoverdifferentsectors.Thesemodelsstresshowtheexpansionoftotaloutputispulledbythegrowthofexports.SinceKaldor,thesectoralapproachtogrowthmakesadistinctionbetweenindustrialactivitieswithincreasingreturnsandthosewithdecreasingreturns.Thereasonforthisdifferenceisthepresenceofanon-reproduciblefactor,likeland.Itisusuallyobservedthatpercapitaincomeandthedegreeofindustrializationofaneconomyarestrictlyrelated.CountriestendtogrowfasteriftheindustrialproductionratiotoGDPgrowsfaster.OnecanthusrelatethegrowthrateofGDPtothegrowthinthesectorthathasstronggrowthcharacteristics,usuallythemanufacturingindustry.Thissectorcouldexpandifthereisanautonomousdemandforthegoodsitproduces.Itisbelievedthatsuchdemandcouldfirstcomefromtheagriculturalsectorintheinitialstagesofdevelopment.Lateron,suchdemandmightcomefromabroad.Theexpansionofthemanufacturingsectorwouldnotoccurattheexpenseofothersectorsthen.Decreasingreturns(andhencefallingproductivity)insomesectors(e.g.agriculture)permitthegradualtransferofresourcestotheexpanding(manufacturing)sector.Growthtendstoslowdownwhenthesectorswithincreasingreturnscannotfurtherabsorbresourcesfromthesectorswithdecreasingreturns.Theexpansionofdomesticincomeisgivenbytheweightedsumofgrowthinconsumption,investmentandnetexports.Itispossibletostartaprocessofgrowthinducedbyconsumption,investmentorpublicspendingforashorttime.Incontrast,exportsrepresentatrulyexogenouscomponentindemand.Exportsmoreoverallowthefundingoftheimportsofgoodsthatarenecessarytogrowth.Butatleastpartofthesecomponentsofdemandshouldcomefromabroad.Thereasonforimportingisclear.Importsenterintheproductionprocessandprofitablyreplacedomesticresourcesthatwouldotherwisebeusedinothersectorsorwouldbetoocostly.Importsarepartofthebasketoffinalconsumptiongoodsbecausetheyaremorecompetitivethandomesticproducts.Bysavingresources,importshaveacrucialroleinboostinggrowth.Moreover,theimportofcapitalandintermediategoodsisanimportantvehicletotransfertechnology.Suchtransferscanaffectproduction,aswestressedinthemodelswithleadersandfollowers(innovatorsandimitators).Therearealsocasesinwhichitisnotpossibletoperfectlysubstitutedomesticandforeignresources.Aneconomythatoverlyreliesonimportscanactuallysufferpoorgrowth.Thishappensinparticularindevelopingcountrieswherethemainconstraintonincomegrowthisgivenbytheinsufficientavailabilityofforeigncurrencyreserves.Thegrowthofexportsloosensthisconstraintandallowstheothercomponentsofdemandtogrow.i.e.,moreexportsallowmoreimports.Inthefollowingcapitalletterswillindicatethevariableslevel,lowercaselettersgrowthrates,andttime.Weassumethattheproductiongrowthrate(gt)andthatofexports(ext)areproportional,hence:gt=ζ(ext).Thedemandforexports(EXt)isafunctionofthecompetitivenessofaneconomywhichisrepresentedbytheratiobetweenthelevelofdomestic(Pdt)andforeignprices(Pft)measuredinacommoncurrency,andbyforeignincome(YWt).Exportsdemandisamultiplyingfunctionwithaconstantelasticity:[2] 21)/( ηη W

tftdtt YPPAEX = whereη1(withη1<0)istheelasticityofexportstorelativeprices:

27

[3])//()/(

/1

ftdtftdt PPPPEXEX

Δ

Δ=η

andη2(withη2>0)istheelasticityofexportstoforeignincome:

[4] Wt

Wt YYEXEX//

2 Δ

Δ=η

Wecanrewrite[2]intermsofchangeasfollows:[5] ( ) W

tdfdtt yppex 21 ηη +−= Thegrowthrateofforeignincomeandforeignpricesaretakenexogenous.Internalprices(Pdt)arebasedonthecostoflabourperunitofproductplusamarkup:(Pdt=(Wt/Rt)(Tt)whereWindicatesthemonetarywage,RtheaverageproductivityoflabourandTthemarkupcalculatedonthecostoflabour.Therelationthatdescribesthegrowthofdomesticpricesdependsonthechangesinwages,productivityandthemark-up:pdt=wt-rt+τt).Learningbydoingintheproductionprocesssuggestsacausalrelationbetweenthegrowthofproductionandproductivityduetotheexploitationofstaticanddynamiceconomiesofscale(Verdoornlaw).Thetrendofproductivityisrelatedatleastinparttothegrowthofproduction:rt=rat+λ(gt).ThetermratindicatestheautonomouscomponentofproductivityandλistheVerdoorncoefficient.Thelattershowshowmuchoftheincreaseofproductivityisduetotechnologicalprogressincludedincapitalandhowmuchisduetotheaccumulationofexperience.Thissetofrelationsshowshowitispossibletostartacycleofexport-ledgrowth.Anincreaseinthegrowthrateleadstoanincreaseinproductivitythatcausesthelabourcostperunitofproducttofall.Ascompetitivenessimproves,exportsincreaseandsustainproduction.Acompetitiveadvantageofthiskindtendstosustainincreasinggrowth.Inequilibriumthegrowthrateisgivenby:

[6]( ) ( )[ ]

λζη

ητηγ

1

21

1++−+−

=Wtfttatt

t

yprwg

Sincethedemandforexportsdependsnegativelyonitsprice(η1<0),theequilibriumgrowthrate(gt)increaseswhen:a)thegrowthrateofautonomousproductivity(rat)increases;b)foreignprices(pft)rise;c)thegrowthofdomesticwages(wt)ismoderate;andd)themarkup(τt)decreases.Sincethedemandforexportsdependspositivelyonforeignincome(η2>0),thegrowthrate(gt)increaseswhenworldincome(yWt),increases.LavingasidetheVerdoorneffectandsupposethatrelativepricesareconstanttheequilibriumsolutionbecomes:gt=ζη2(yWt).Inordertomaintainanequilibriumgrowthrate,thecoefficient(ζ)needsbethereciprocaloftheelasticityofimportsdemandwithrespecttoincome(ρ).Hence,ifwesubstituteζ=1/ρwehavethat:gt=η2(yWt)/ρ.Theequilibriumgrowthrate(gt)isanincreasingfunctionofforeignoutputgrowth(yWt)andoftheratiobetweenincomeelasticityofexports(η2)andimports(ρ).Inotherwords,wehavethat:gt/zt=η2/ρ.Thismeansthatinanexport-ledgrowthmodel,thegrowthrateofacountryrelativetogrowthinothercountriesisproportionaltotheratiooftheincomeelasticitiesofexportsandimports.Thisresultisnotincompatiblewithaneoclassicalview.Thecontroversyrathercomesfromdifferentopinionsontheelasticitiesusedinthemodel.Theneoclassicalmodelsthatanalyzegrowththroughtheproductionofasingleaggregategoodthatcanbeconsumedor

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reinvested,leaveasideforeigntradeanddonotattributearoletothepriceorincomeelasticitiesofexports.Thefactorsthatdetermineexports,suchasthesupplyofnaturalresourcesofacountry,thestructureofproductionandthefeaturesofgoods,arerarelyexplicitlyconsidered.Empirically,itishardtodistinguishbothmodels.ThestrongcorrelationobservedbetweenthegrowthrateofGDPandofexportsdoesnothaveaclearcausaldirection.Thetradeflowsthatdraggrowthintheexport-ledmodel,couldinsteadbetheconsequence,ratherthanthecauseofgrowth.Yet,thegrowthperspectivesofcountriesspecializedintheproductionofprimarygoodsarequitedifferentfromthoseofcountriesspecialisinginindustrialgoods.Fortheformergoods,theincomeelasticityofdemandisusuallylowerthanone.Forthelatter,itisoftenhigherthanone.Theexport-ledmodeldoesnotimplyarapidconvergenceininternationaldifferencesingrowthratesandincomelevels.Themodeldescribingexport-ledgrowthcanbeextendedtoincludetheforeigncountryandinthisway‘endogenise’itsdemandforimports.Weconsiderasituationofequilibriumonthebalanceofpayments.Thereasonisthatnocountrycangrowataratehigherthantherateconsistentwiththeequilibriumconstraintonthecurrentaccount.Ifnot,thiscountrywouldbeabletocontinuefinancinggrowingdeficits.Tosimplifymatters,welookatthecurrentaccountonlyandomittimeindices:PdEX=PfIMe.EXdenotesthequantityofexports,Pdthepriceofexportsindomesticcurrency,etheexchangerate(indirectquotation),IMtheamountofimportsandPfthepriceofimportsinforeigncurrency.Ifwewritethisintermsofgrowthrates,thecurrentaccountbecomes:pd+ex=pf+im+e.Asbefore,thegrowthofexportsisgivenby:ex=η1(pd-pf-e)+η2(yWt).Weaddatermindicatingthechangeintheexchangerate.Likewise,thedemandofimportsdependsonforeigncompetitivenessanddomesticincome,hence:IM=B(Pfe/Pd)ψYρ.Inthisexpression,(similartoelasticitiesη1<0andη2>0)ψ<0isthepriceelasticityofimportsandρ>0istheincomeelasticityofimports.Ingrowthrates,thisbecomes:im=ψ(pf+e-pd)+ρ(y).Wesubstitutetheexpressionsindicatingthetrendofimportsandexportsintheequilibriumequationdescribingtheforeignsector.Wethenobtainthegrowthrateofincomethatisconsistentwithequilibriuminthebalanceofpayments(yB).Thisisgivenby:yB=[(1-η1+ψ)(pd-pf-e)+η2(yWt)]/ρ.Fromthisexpressionfollowsthatinacountrythatimprovesitstermsoftrade(pd-pf-e)>0,thegrowthrateincreases.Thisisconsistentwithequilibriumintheforeigncountry(yB).Thecountrythatexperiencesanincreaseinprices,measuredinacommoncurrency,willquicklyreduceitsequilibriumgrowthrate(yB)ifthesumofpriceelasticitiesishigherthan1.Giventhatthoseelasticitiesarenegative,theconditionis(1-η1+ψ)<0.Moreover,thecurrencydepreciation(e>0)increasesthevalueoftheequilibriumgrowthrate(yB)ifthesumofelasticitiesofpriceishigherthan1,whichcorrespondstotheMarshall-Lernerconditionsbesatisfied:thebalanceofpaymentwillimproveafteracurrencydepreciation.Thepriceelasticityofexportsperformsacrucialroleinpredictingtherelativegrowthofcountries.Theinterdependencebetweentwocountriesisdescribedbytheequation(viaη2)betweentheirrespectivegrowthrates(yBandyW).Eventually,thegrowthratecompatiblewiththeforeignconstraint(yB)isinverselycorrelatedwiththeownincomeelasticityofimports(ρ).Inanopeneconomy,thismarginalpropensitytoimportissimilartothepropensitytoconsumeineconomicmodelswithaKeynesianmultiplier.Ifrelativepricesdonotchange,theexpressionisreducedtoyB=η2(yW)/ρ=ex/ρ.Theequilibriumgrowthratepresentsadirectrelationwiththegrowthrateofexportsandaninverserelationwiththepropensitytoimport.

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1.3. ConvergenceThepersistenceofgreatdifferencesinthelevelofpercapitaincomebetweencountriesrepresentsachallengethat‘onceonestartstothinkaboutthem,itishardtothinkaboutanythingelse’(Lucas,1988).Theconvergenceofpercapitaincomedoesnotneedtohappeninendogenousgrowthmodels.Recentempiricalevidencehasshownaslowdownofgrowthinsomeindustrializedcountriesandanaccelerationinsomedevelopingcountries.Suchtrendsareofextremeimportancetounderstandthedifferentcausesofeconomicexpansionacrosscountriesalsobecauseaninternationalcomparisoncanshedlightontheexplanatorypowerofdifferenttheories.Theissueofconvergencehasbeentakenupbybothschoolsofthoughtinrecentyears.Thisfieldofresearchisdrivenbyadesiretoempiricallyverifydifferenttheoreticalmodels,andprovideananalysisofeconomicgrowththatisconsistentwiththeempiricalevidenceonconvergence.Aplausibleanswertotheconvergenceproblemisimportanttoidentifythosemechanismsthatunderlietheprocessofgrowthwhichisoffundamentalimportanceforpolicyaswell.Sinceeachtheoreticalmodelprovidesadifferentpredictionforlong-termconvergence,somefundamentalquestionsareraised.Isitpossibletorecognizeanysinglemodelasuniversallyvalid?Orshouldadifferentmodelbeusedfordescribingeachsituation?Isitpossibletoadmitmultiplemechanismstodescribeeconomicrelationsthatfindtheirexplanationeachinadifferenttheoryofgrowth?Thevaluationoftheexplanatorypowerofthedifferenttheoriesalsoraisesanotherissue:canapluralityofexplanationscoexistforthesamephenomenon?Iftheanswerisyes,dowethenhaveamodelathandthatisabletoexplainthegrowthslowdownthataffectssomecountriesandtheaccelerationinvolvingothers,inbothcasesregardlessoftheincomeleveltheyreached?

1.3.1.NeoclassicalgrowthandabsoluteconvergenceTheneoclassicaltheoryofgrowth,followingtheSolowmodel,implicitlypredictsthatforagivencommontechnology,twocountrieswithsimilarpreferences–suchasthegrowthofpopulation(n)andthepropensitytosaving(s)-wouldconvergetowardsthesamesteadystate.Observabledifferencesingrowthrates,percapitaincomeorlabourproductivitycanbeassignedexclusivelytodifferencesintheendowmentofcapital.Twocountriesmaystartattwodifferentlevelsinthecapital-labourratio(k=K/L)butwillendupsharingthesamesteadystatevalues.Investmentdecisionstoequaliseactualinvestmentwithnecessaryinvestmentarebasedonthesamesavingrate,andleadtothesamecapital-labourratio(k=k*)thatdeterminesthesamevalueofpercapitaincome(y=y*).Inthetransitionperiodtothislong-runequilibrium,thecountrywiththelowercapital-labourratio(k)andalowerpercapitaincome(y)hasalsoahigherreturnoncapital.Asaconsequence,economicgrowthrateinthepoorercountrywillbehigherandleveloff,onceitreachesthelevelofpercapitaincomeintherichercountry.Inthelattercountry,thereturnofcapitalislowerduetodecreasingreturns.TheconceptofabsoluteconvergencecomesfromtheconvergenceoftheeconomytowardsthesteadystatedeterminedbytheexistingtechnologyintheSolowmodel.Itimpliestheinternationalconvergencebetweendifferenteconomiestothesamesteadystate.InFigure6,nexttothesteadystateequilibriuminpart(a)thetransitiontosuchequilibriumintermsofabsoluteconvergenceisshowninpart(b)fortwocountries:North(N)andSouth(S).Onthehorizontalaxis,theintensityofcapital(k)ismeasured.Theverticalaxismeasurespercapitaincomeandinvestmentpart(a)andmarginalcapitalproductivitypart(b).Thegrowthrateofcapital(Δk/k)isshownbyverticallinesandiscalculatedasthedifferencebetweenthegrowthrateofeffectiveandnecessaryinvestment,whichequalsthesumbetweenthedepreciationrateandthegrowthrateofpopulation,constantbyhypothesis.

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Part(b)showstherelationbetweenthedistanceofthecapital-labourratiofromsteadystate(k*-ki,withi=N,S)andthegrowthrateofcapital.Thefurtherawayfromsteadystate,thehigherthegrowthrateofcapital.Infact,itisusefultorecallthatinsteadystatethecapitalaccumulationiszero(Δk/k=0).Thisholdsifsf(k)/k=δ+n.Figure6.Absoluteconvergence

IftheNorthhasalargercapitalstockthantheSouth,thevalueofkNwillbehigherthanthevalueofkS.Sincethegrowthrateofincomeineachcountryisproportionaltothegrowthrateofcapital,differencesincapitalintensitycausedifferencesinpercapitaincome.However,duetothelowermarginalreturnofcapitalintheNorth,theaccumulationofcapitalisfasterintheSouththanintheNorth,asthegrowthrateintheSouthishigher.Thecountrywithlesscapitalcatchesuprealizingan‘absoluteconvergence’inpercapitaincome.Inthelongrun,countrieswithsimilarpreferencesandtechnologywouldeventuallyconvergetowardsidenticallevelsofincome.Giventhelackofobservedconvergenceinpercapitaincome,empiricalevidenceinsupportofthistheoryisnoteasytofind.Theneoclassicaltheory,thereforeresortstotheintroductionofanimportantdetailbyarguingthateconomiesconvergeconditionally.

1.3.2.NeoclassicalgrowthandconditionalconvergenceIfweallowtwocountriestodifferinsomeotheraspects(otherthanjustthecapital-labourratio,e.g.technology)absoluteconvergenceneednothappen.Thetheoreticalsettingofthemodelcanbepreservedasallcountriesstillconvergetoasteadystate.However,themodelisdeprivedofitsimplicitmeaningofinternationalconvergenceofpercapitaincome.Conditionalconvergencebetweeneconomies,whichinourexampledonotsharethesametecnology,correspondsinpracticetoalackofconvergence.Anotherexampleof‘conditionalconvergence’isgiveninFigure7wheretwocountrieshavedifferentsavingrates(withsS<sN),andadifferentintensityofcapital.Tosimplifymatters,thehypothesisofasingleproductiontechnologyiskeptinthediagram.Hence,thetwocountrieshaveincommonboththeproductionfunctionandtheinvestmentfunction.TheaccumulationofcapitalintheNorthisfasterthantheoneobservedintheSouth,eventhoughthecapitallabourratiointheNorthishigherthantheoneintheSouth(kN>kS).Thishappensbecausethetwocountriesdonotsharethesamesteadystate( SN kk ** ≠ ).Hence,eachcountryconverges

y=Y/L

y*

k=K/L k=K/L0 0

(δ+n)k

y=f(k)

i=sf(k)δ+n

kNk* k*kS

sf(k)/k

(a) (b)

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toitsownsteadystate.Part(a)ofFigure7showsthatthesteadystateintheSouthislowerincapital-labourintensityandinpercapitaoutput.Figure7.Conditionalconvergence

Theconceptofconditionalconvergenceimpliesdifferentandevencontrastingresultsonthebasisof:1. theshapeandpositionofthefunctionsthatdescribethetransitiondynamicstoequilibrium;2. theobservedcapital-labourratio.Conditionalconvergenceiscompatiblebothwithabsoluteconvergencebetweendifferentcountriesorthecompletelackofinternationalconvergence.Forthisreasontheneoclassicalinterpretationforexplainingdifferencesintheobservedpercapitaincomeisratherambiguous.Intheexamplejustgiven,therearedifferentlevelsofcapitalintensity,ofgrowthratesofcapitalandincomeinthetwocountries.Theonlyreasonallowingfortwodifferentsteadystatesisadifferentpreferenceforsaving.Asbothcountriessharethesametechnology,catchingupoftheSouthcouldbepossibleifthetwocountrieswouldsharethesamesavingrate.Itisnecessarytodistinguishbetweenapersistentdifferencebetweenthetwocountriesduetoadifferentintensityofcapitalreflectedinadifferentlevelofpercapitaincome,andatemporarydifferenceduetodifferentgrowthratesofincomeandcapital.Infact,thegrowthrateofincomeandtheaccumulationofcapitalcanbehigherintheNorththanintheSouthevenifinitiallevelsarehigherintheNorththanintheSouth.Withconditionalconvergence,highergrowthratesforpoorerregionsbecauseoftheirlowinitiallevelsofcapitalaccumulationandpercapitaincomecannotbetakenforgrantedanylonger.Theconclusionisthatdifferencesinpercapitaincomegrowthratescanbeovercome.Thepercapitaincomeof‘poor’countriescouldconvergetothatof‘rich’countriesifthepoorcountriesavoidunderinvestmentbyadoptingappropriatestrategiestoeliminatedifferencesinbasic‘features’oftheeconomy,ascomparedtorichareas.Thisisalsotheindicationforanactiveeconomicpolicy.

y=Y/L

sNf(k)/k

k=K/L k=K/L0 0

(δ+n)k

y=f(k)

i=sNf(k) δ+n

kNkS

(a) (b)

kN*kS*

sSf(k)/k

i=sSf(k)

kN*kS*

yS*

yN*

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1.3.3.EndogenousgrowthandthelackofconvergenceInendogenousgrowthmodels,theinvestmentactivity,inbothphysicalandhumancapital,generatespositiveexternalitiesallowingtheproductivityoffactorsremainconstant.Thegreaterthesupplyofcapital,themoretheproductivityoffirmsincreases.Thisowestothespreadofnewtechnologiesintheproductionstructure,andthelearningbydoingofworkers.Increasingreturnstoscaleandexternalitiescreatedbyinvestmentactivitybothhaveimplicationsforconvergence.Ascapital,labourandtechnologicalprogressexpand,theconstantratesofreturnmakethecapital-outputratioconstant.Hence,theaccumulationofcapitalisindependentfromtheratiok.Differentgrowthratesofcapitalimplydynamicgrowthpathsthataredifferentbetweenthetwocountries.Figure8repeatstheAKversionoftheSolowmodelinpart(a),andtheconstancyofthegrowthratesinpart(b).Figure8,AbsenceofconvergenceintheAkmodel

Endogenousgrowthmodelsdonotpredictasteadystateequilibriumfortheeconomy.Sincethereisnolimittoexpansionapriori,thereisnoconvergence.Theobserveddifferencesinincomelevelsandgrowthratesareattributedtodifferentlevelsoftechnology,atermencompassingawidevarietyofdirectaswellasindirectinputs.Thisistheconsequenceofadifferentaccumulationofhumancapitalwithdifferentfeatures.Iftheroleofknowledgeispredominant,thelackofconvergenceisassignedtotheinsufficientaccumulationofhumancapital.

1.3.4.EndogenousgrowthanddivergenceThepolicyimplicationsaredifferentfromthoseinamodelofexogenousgrowth.Inpriciple,eachcountrycangrowataratethatdivergesfromthatinothercountriesinthelongrun.Infact,atdifferent(albeitconstant)growthratesofcapitalaccumulation,thegapinpercapitaincomecanincreaseifitisthepoorercountrythatexperienceslowergrowthrates.WeclarifythiswithanexampleinFigure9.Weplotonthehorizontalaxisthecapitalstockofthecurrentperiod(Kt)andontheverticalaxisthecapitalstockofthenextperiod(Kt+1).RecalltheequationdescribingtheaccumulationofcapitalintheAKmodel,thestockoffuturecapitalcanbeexpressedinrelationtothecurrentcapitalstockasfollows:Kt+1=[sA-(δ+n)+1]Kt.

y=Y/L

δ+n

k=K/L k=K/L0 0

(δ+n)k

yN=Ak

sNf(k)=sNA(a) (b)

sSf(k)/k

sNf(k)/ksSf(k)=sSA

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Weplotthislinearfunctioninthediagramtogetherwiththe45-degreeline,wheretheequalityKt=Kt+1holds.Thediagramshowstheinstabilityoftheequilibrium.Agrowthprocessstartsiftheeconomygetsoutoftheinitialequilibrium.Byfeedingintoevenmoregrowth,economicgrowthdoesnotcomebacktosteadystate.Thisstressestheimportanceofdifferencesingrowthratesinmodelswhereaccumulationisunlimited.Inthiscase,differencesininitialconditionsarenolongerimportant.Part(a)ofFigure9showsthegrowthpathsoftwocountriesthatdifferonlyintheirinitialcapitalstock:KNt0>KSt0butsharethesamesavingsrateandsothesamecapitalaccumulationequation:Kt+1=[sA-(δ+n)+1]Kt.Thediagramshowsthatthecountrythathasalargercapitalstock(theNorth,whosepathisshowedbythehatchedline)wouldneverbeovertakenbythecountrythatstartsfromarelativelylowerposition.Noconvergenceispossible:thecountrywithlesscapitalfollowstheothercountrywithsomedelay.AlthoughtheSouthisabletogrowatthesamerate,itfollowstheNorthwithadelayformorethanoneperiod.Inpart(b)instead,thetwocountrieshavethesameinitalcapitalendowmentandonlydifferintheaccumulationofcapitalduetoadifferentsavingrate:sN>sS.Thecountrywithahighersavingrateaccumulatesmorecapital,andthusexperienceshighergrowth.Thetwocountriesfollowdivergentpaths.IttakestheSouthinitiallytwoperiodstoreachthesamelevelofaccumulationobtainedbytheNorthinoneperiod.TheSouthneedssevenperiodstoarriveatapositionthattheNorthhadachievedinonlythreeperiodsFigure9.Absenceofconvergenceanddivergence

Thelackofconvergenceintheincomelevelmaybeduetodifferentinitialconditions.Butdivergencehappenseveniftwocountriessharethesameinitialconditions.Itisclearthatthesetwoexamplesdonotcoverallpossiblecases.Theneoclassicalmodeldoesnotassociateunfavourableinitialconditionswithreducedgrowthrates.Unfavourableinitialconditionsleadtohighergrowthrates.Themechanismsinaprocessofendogenousgrowthproduceincreasingreturns.Increasingreturnsandpositiveexternalitiesmakethatmarketcompetitiondoesnotequilibratetheeconomy.Thepresenceofincreasingreturnsproducesdivergenceofpercapitaincomeinamarketeconomy.Asaresult,someeconomiesmaybecaughtinapovertytrap.

45°45°

kt+1=[sA-(δ+n)+1]kt kt=kt+1

kt+1=fN(kt)

kt+1

kt+1

kt=kt+1

kt kt0 0

(a) (b)

kSt0.kNt0 kSt0.=kNt0

kt+1=fS(kt)

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Fromthesebriefobservationsontherelationbetweengrowthmodelsandtheanalysisofconvergence,weunderstandhowdifferentinterpretationsofgrowthandlevelsofincomecanco-exist.Therefore,intheanalysisofconvergence,weneedtodistinguishthelackofconvergenceinincomelevels,growthrates,orboth.Under‘absoluteconvergence’,differencesoccuronlyduringthetransitionfromoneuniquesteadystateequilibriumtoanother.Thedifferenceinincomelevelsisduetotheinvestmenttoadjustthecapitalstock.Differencesingrowthratesareexplainedbythedistancetothesteadystateequilibrium.Under‘conditionalconvergence’thedifferencesinincomelevelcanpersist.Growthratescanconverge,however.Appropriatepoliciesinthepoorerareamayeliminatethedifferencesininstitutional,economicandtechnologicalfactorscomparedtothericherarea.Inthisway,thepoorcountrycouldpursueaneconomicexpansion.Withoutsuchpolicies,conditionalconvergencedoesnotpredictareductioninincomegaps.Inendogenousgrowthmodels,therearenotheoreticalpriorsthatpredictatrendtowardsconvergence,divergenceortheconstancyofincomedifferences.Sincetheeconomicexpansionisnotconstrainedbyanyconvergencepathtothesteadystate,convergenceanddivergenceareequallypossible.Positiveexternalitiesareprobablylargerinindustrializedeconomiesthankstotheirmoredynamicfeatures.ProductivityoffactorsstayconstantintheNorth,andboostsitsgrowthrate.ThisperpetuatestheadvantageouspositionoftheNorthrelativetotheSouth.Theincreasinginterconnectionbetweenmarketsassignstogovernmentsof‘rich’countriesandtomultinationalfirmsanincreasinginfluence.Theincreasingstrengthofrichcountriesmayreducetheroleofinternationalorganizations,suchastheIMF,inpromotingthedevelopmentof‘poor’countries(Stiglitz,2002).Thelackofinternationalinstitutionsofgovernancetocoordinatedevelopmentinaneutralwayisdangerousgiventhemonopolisticinterestsininternationalmarkets.

1.3.5L’impostazionedeimodellielaverificaempiricaAtthebeginningofthe1980stwoimportantdatabaseweremadeavailabletoresearchers:one(Maddison,1982)collectedinformationaboutOECDcountriessince1870,theother(SummerseHeston,1984)hadshortertimeseries(1950-1980)butawiderscopeinspace,encompassingahighernumberofcountries.Thiscircumstancemadeitpossibletocheckonempiricalgroundswhetheranypatternemergedaboutincomeregularitiesacrosscountriesandthegrowththeoriescouldbesupportedbysoundevidence.Incomeconvergenceislikelytohavebeenthemainrealmwheregrowththeorieshavebeenputunderscrutiny.Yet,oneshouldnotforgetthattheveryaimoftheexerciseimpliesthatthequantitativeanalysisneedsbesetintoaframeworksuitabletofindoutwhygrowthrateaswellasincomelevelsdifferacrosscountries.Twopathshavebeenfollowed:

1. thegrowthratesneedbeexplainedstartingfromthetheoreticalmodelandtheempiricaltestismeanttoprovethetheory,sothatresultssuchasparametherestimatesmustbesensiblefirstontheoreticalgrounds

2. thegrowthratesareexplainedbyeconometricmodelsgroundedonempiricalevidenceandthereforeallowingforahighersetofindependentvariableswiththeirmainrequirementrelyingontheirexplanatorypower.

Whilethefirstpath,relyingontheory,mayimposeconstraintstotheestimatesespeciallyintermsofgrowthaccounting,thesecond,resortingtoasortofinformalmodelmaybeintractableontheoreticalgrounds.Theobviouswayoutistoabandonauniquesteadystateandadmitthatcountrieshaveownsteadystates,charaterizredbyownpreferencesandtechnology,andgrowmorethefurtherawaytheyarefromit.

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Theinterpretationshouldreconcilehighpopulationgrowthrateswiththelowerincomesharethatinpoorcountriesgoestolabour,whileinterestratesarenotconsiderablyhigher.Withinformalmodels(path1)thecontributionofinputstooutputgrowthhasbeenstudiedbyawideliteratureaddressingtheissueoftotalfactorproductivity(TFP)sotoempiricallyestimateSolow’sresidual.Theseresultshavebeenchallengedbecauseitisstllunclearwhethertheirinterpretationreliesuponabsoluteorconditionalconvergence.Itshouldbeclearwhethertheaimoftheresearchistoestablishwhygrowthratesdifferorwhyincomelevelsdiffer.Theanswertothisquestionbringsinthetheoreticalmodelaccordingtowhichdifferencesinpercapitaincomelevelsshouldbeduetodifferenceseitherintechnologyorincapitalaccumulation.Differencesinthecnologyimplydifferentsteadystates,differencesincapitalaccumulationgiverisetodifferentgrowthrates.Still,tojustifydifferencesinpercapitaincomelevelsacrosscountriesintermsofdifferentcapitalaccumulationoneshouldobservedifferentsavingrates,too.Empiricalevidence,however,doesnotsupportthisaspect.Alternatively,onecanincludehumancapitalwithintheeconomicgrowthdeterminants,butalsointhiswaymigrationshouldflowinadirectionoppositetotheoneweactuallyobserve.Tobeconsistentwiththemodel,differencesintechnologyneedhavearesidualcharacteristicsuchastheTFPhassinceitisnotafactoraprioriaseasytomeasureaseitherlabourorcapital.Yet,thesedifferencesmaybeeitherimposedorestimatedbytheempiricalmodel.IfdifferencesacrosscountriesareemployedinordertobetterunderstandtheTFPbyimposingvaluesempiricallyobserved,oneshouldnotfocustheanalysisontheregularityofthedatathatrefertoaveragebehaviour.Ifthetechnologycontributionstemsfromthegrowthequationestimatestheresult–beingaverage-mightnotbefullyrepresentativeofthevariabilityonecanobserveacrosscountriesandsolosetoomuchinformation.Inbothsituationsthesolutioncannotentirelyfitthetheoreticalmodelwiththeempiricalevidence.Withininformalmodels(path2)thegrowthdeterminantsarenotbasedonamodelbutemergefromempiricalobservationsthroughexplanatoryindependentvariables.Empiricalopenendedmodelsaresubjecttothecritiquethatmanyinterpretationsarepossibleandtheycannotexcludeeachother.Intheabsenceofapre-settheoreticalframeworktheoutcomemayendupbeingmainlydescriptiveandlackinganalyticalinterpretation.Acomprehensivelistofexplanatoryvariables,whichhavebeenusedbyopenendedmodelstoexplaineconomicgrowth,countsaveryhighnumberofcandidates.Morethanonehundredvariableshavebeensuccessfullyemployedbyvariousauthorstoexplainthegrowthrateofvariouscountriesorregionsinvariousperiodsyieldingstatisticalsignificance.Still,thisisexactlythemostlikelyoutcomeonecanexpectwhenanyreferencetoaformalmodelhasbeenabandoned.Astrongassociationofgrowthrateswiththeopennessoftheeconomydoesnotexcludeanothernolessstrongassociationwithshareofpublicexpenditure–eithergeneralortargetedtoinvestment–ontheGDP,orevenwithpoliticalinstability(Barroemployesthenumberofpoliticalmurdersannuallyobservedasaproxyforthisvariable).Leavingasidethesignificanceoftheestimates,whichmaybegood,manyofthesevariableshavetheunwelcomecharacteristictoallowacausaldirectioninbothways,sothatitisneversurethatwhatisthoughttobethecauseonthecontrarymayactuallybetheeffect.Moreover,manyofthesevariablesarenotindependentfroeachother:statisticsignificanceandrobustnessmayalsodependupontheparticularsetofexplanatoryvariablesonecanfindinthegrowthequations.Sinceopenendedmodelsdonotworryaboutbeingconsistentwithatheoreticalgrowthmodel,itispossibletocomeupwithineachcountrygrowthstemsfromdifferentcauses.Aresultwhichisunnusefulintermofdevisingageneralpolicytowardsanygrowthpolicy.

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Theinquiryabouttheexistenceofconvergenceinpercapitaincomeinthelongrunhasbeenmainlybeenpursuedbycheckingtherelatioshipbetweengrowthratesandpercapitaincomelevels.Crosssectionaldata,collectinginformationaboutcountriesorregionsduringagivenperiod,helpfindingwhetheranegativerelatioshipmayemerge.Arelationship,abletoconnectlowerpercapitaGDPlevelswithhigherpercapitaGDPgrowthratesandatthesametimebeingstatisticallysignificant,wouldgivestrengthtothegrowththeorysupportingconvergence.Empiricalestimateshavefollowedastandardmethodologyseekingtoidentifytheso-calledbetaconvergencebymeansofaregressionanalysisofpercapitaGDPaveragegrowthratesonalongperiodonitsinitialvalues.Theequationtobeestimatedforabsoluteconvergenceislinearinlogs:

y*i,tT=α+βlogyi,t0+uitwherey*i,tTindicatesthepercapitaGDPgrowthrateofcountryiduringtheperiodstartingint=0andendingint=Tandyi,t0indicatedthepercapitaGDPofcountryiinthefirstyear(t=0);theregressionestimatestheconstantαandthecoefficientβanduitindicatestheerror.Thehypothesisofconvergenceofpercapitaincomesissupportediftheestimateoftheβcoefficientisnegative(β<0).Anegativeβalsoindicatesthespeedofthecatchingup.:thehigheritsabsolutevalue,thesteepertheline,thequickerthecatchingup.Thereforethroughtheβestimateaforecastofhowmanyyearsareneededtoabackwardeconomyforthecatchinguptothesteadystateispossible.Forconditionalconvergence,moreexplicatoryvariablesareaddedontherightsideoftheequation.Informalmodelsthesevariablesincludemeasuresofhumancapitaland/orphysicalcapital,whileinformalmodelsallowalsovariableswhichmaybeverydifficulttofitintoagrowthaccountingexercise.