Lecture12

EconomicGrowthEconomicGrowthExplainimprovementsinstandardsofliving(GDPpercapital)alongtimeExplaindifferencesacrosscountrieslearnhowourowngrowthrateisaffectedbyshocksandourgovernment’spoliciesSolowGrowthModelsomestatisticsInUganda,96%ofpeopleliveon

lessthan$2/day.(datalink)2.8billionpeopleliveonlessthan$2/day(1.1billionunder$1/day)GDPpercapitaChadin1960:$1212,in2000:$908Venezuelain1960:$7840,in2000:$6420Koreain1960:$1495,in2000:$15875H.K.in1960:$3090,in2000:$26698Hugeeffectsfromtinydifferences1,081.4%243.7%85.4%624.5%169.2%64.0%2.5%2.0%…100years…50years…25yearspercentageincreasein

standardoflivingafter…annualgrowthrateofincomepercapitaLongtermgrowtheffectRuleof72:1%growthrate,approximatelytakes72yearstodoubleGDPWhatwillhappenifChinakeeps10%growthrateandUSkeeps3%growthrate(USpercapitaGDP$42,000China$6800)WorldDistributionofIncome5WorldIncomeMap6Southvs.North78RealGDPpercapita,1975–20039LifeExpectancyandIncome(Preston,1976)1011HeightsofMalesandFemalesinChina12HappinessandIncome13TheSolowModelduetoRobertSolow,

wonNobelPrizeforcontributionsto

thestudyofeconomicgrowthamajorparadigm:widelyusedinpolicymakingbenchmarkagainstwhichmost

recentgrowththeoriesarecomparedlooksatthedeterminantsofeconomicgrowthandthestandardoflivinginthelongrunHowSolowmodelisdifferentfromChapter3’smodelKisnolongerfixed:

investmentcausesittogrow,

depreciationcausesittoshrink.Lisnolongerfixed:

populationgrowthcausesittogrow.Theconsumptionfunctionissimpler.NoGandTProductionInitiallyassumeconstantpopulation(L)andnotechnologychangeProductionofgoodsandservices:ConstantReturnstoScale:ProductionLettingz=1/L,wegettheproductionfunctioninpercapitaterms:

y=Y/L=outputperworker

k=K/L=capitalperworkerConstantReturnstoScalesizeoftheeconomydoesnotaffecttherelationshipbetweencapitalperworkerandoutputperworker

Production

DecreasingMPK:

Thisimpliesthefollowingshapefortheproductionfunction:Production MPKistheslopeofthiscurve.kyf(k)LowMPKHighMPKProductionCobb-Douglascase:DemandAssumeaclosedeconomywithnogovernment:NX=G=0Assumethatpeoplesaveafractionsoftheirincome(andthereforeconsume1–s),

DemandSubstituting:Inequilibrium:CapitalAccumulationTwoelementsdeterminehowthecapitalstockchangesovertime:Investment:additionofnewplantsandequipment(makescapitalstockrise)Depreciation:wearingoutofexistingcapitalstock(makescapitalstockfall)CapitalAccumulationInotherwords:CapitalAccumulationkf(k)sf(k)ciyCapitalAccumulation

Investmenthigherthandepreciationcapitalstockincreases

DepreciationhigherthaninvestmentcapitalstockincreasesCapitalAccumulationSteady-statecapitalstock(k*):Steadystateoutput,consumption,investment:Determiningthecapital–laborratiointhesteadystate28CapitalAccumulation LowkhighMPKhighreturnsfrominvestmentcapitalstockgrows HighklowMPKlowreturnsfrominvestmentcapitalstockdecreases Inbothcases,theeconomyconvergestothesteadystate(long-runequilibrium)CapitalAccumulationCobb-Douglas:Insteadystate:IncreaseinSavingsRateks1f(k)ks2f(k)IncreaseinSavingsRateHighersmeansthatmoreresourceswillbededicatedtoinvestmenthighercapitalstockinsteadystateTherefore,outputpercapitawillbealsohigherGoldenRuleWhatistherelationshipbetweensteady-stateconsumptionandsavingsrate?Twoconflictingforces:Highershigheroutputhighertheamountofresourcesavailableforconsumptionc*Higherslowertheproportionofincomeallocatedtoconsumptionc*GoldenRuleForlowvaluesofs,c*increaseswithsForhighvaluesofs,c*decreaseswithsGoldenRule:capitalstockimpliedbythesavingsratesuchthatc*ismaximizedGoldenRuleMoreformally: Butinsteadystate:GoldenRule GoldenRule:findk*suchthatc*ismaximized

GoldenRulekkf(k)MPK=GoldenRule sg

isthesavingsratethatimplieskg*:kkf(k)MPK=sgf(k)Therelationshipofconsumptionperworkertothecapital–laborratiointhesteadystate39GoldenRule Cobb-Douglascase: GoldenRule:MPK=

GoldenRule Insteadystate:TransitiontoGoldenRuleCase1:

s

>sg,i.e.,steady-statecapitaltoohigh.Decreasesinordertoreachsgksgf(k)s2f(k)kTransitiontoGoldenRuletttkyck*kg*y*yg*c*cg*i*ig*tiTransitiontoGoldenRuleCase2:

s

<sg,i.e.,steady-statecapitaltoolow.Increasesinordertoreachsgksf(k)sgf(k)kTransitiontoGoldenRulettkyck*kg*y*yg*c*cg*i*ig*ittTransitiontoGoldenRuleIftheeconomybeginsabovethegoldenrule(stoohigh),consumptionincreasesinallfutureperiodsdecreaseinsleadstowelfareimprovementIftheeconomybeginsbelowthegoldenrule(stoolow),consumptionfallsduringtransitionthereisatradeoffbetweenconsumingtodayorinthefuture

InternationalEvidenceonInvestmentRatesandIncomeperPersonPopulationGrowthAssumethatthepopulation--andlaborforce--growatraten.(nisexogenous)EX:SupposeL=1000inyear1andthepopulationisgrowingat2%/year(n=0.02). ThenL=nL=0.021000=20,

soL=1020inyear2.Break-eveninvestment(

+

n)k=break-eveninvestment,

theamountofinvestmentnecessary

tokeepk

constant.Break-eveninvestmentincludes:

ktoreplacecapitalasitwearsoutn

ktoequipnewworkerswithcapital

(otherwise,kwouldfallastheexistingcapitalstockwouldbespreadmorethinlyoveralargerpopulationofworkers)TheequationofmotionforkWithpopulationgrowth,theequationofmotionforkis

k=s

f(k)

(

+

n)

k

break-eveninvestmentactualinvestmentTheSolowModeldiagramInvestment,break-eveninvestmentCapitalper

worker,k

sf(k)(

+

n

)

kk*

k

=

sf(k)

(+n)kTheimpactofpopulationgrowthInvestment,break-eveninvestmentCapitalper

worker,k

sf(k)(

+n1)

kk1*

(

+n2)

kk2*

Anincreaseinncausesanincreaseinbreak-eveninvestment,leadingtoalowersteady-statelevelofk.Prediction:Highern

lowerk*.Andsincey=f(k),

lowerk*lowery*.Thus,theSolowmodelpredictsthatcountrieswithhigherpopulationgrowthrateswillhavelowerlevelsofcapitalandincomeperworkerinthelongrun.InternationalEvidenceonPopulationGrowthandIncomeperPerson55Clark2005,p1308Fig1TheGoldenRulewithPopulationGrowthTofindtheGoldenRulecapitalstock,

weagainexpressc*intermsofk*: c* =y*

i* =f

(k*

)

(

+

n)

k*

c*ismaximizedwhen

MPK=

+n

orequivalently,

MPK

=nTechnologyProgressRewritetheproductionfunctiontoincorporatetechnologychange: E=efficiencyoflabor

E

L=effectiveworkersAssume:

Technologicalprogressislabor-augmenting:itincreaseslaborefficiencyattheexogenousrateg:

59TechnologyProgressAssumethatEgrowsatrategThereforeE

Lgrowsatraten+gRedefineallvariablesintermsofeffectiveworkers:

k=K/EL=capitalpereffectiveworker60TechnologyProgressTheny=Y/EL(=outputpereffectiveworker)isgivenby:Similarlyforconsumptionandinvestment:61TechnologyProgressTherefore,theequationsarethesameasbeforeTheonlychangeisinthelawofmotionfork.Capitalpereffectiveworker:IncreaseswithinvestmentDecreaseswithphysicaldepreciationAlsodecreasesbecausetherearemoreeffectiveworkerstosharetheexistingcapital(higherLandE)62TechnologyProgressThen:Insteady-state,capitalpereffectiveworkerisfixed:63TechnologyProgressksf(k)(+n+g)kk*k1k264TechnologyProgressInsteadystate,income,consumptionandinvestmentpereffectiveworkerarealsoconstantovertime:

65TechnologyProgressThereforecapital,income,consumptionandinvestmentperworkergrowattherateginsteady-state:

slide66Steady-StateGrowthRatesinthe

SolowModelwithTech.Progressn+gY=

y

ELTotaloutputg(Y/

L

)=

y

EOutputperworker0y=

Y/

(L

E)Outputpereffectiveworker0k=

K/

(L

E)CapitalpereffectiveworkerSteady-stategrowthrateSymbolVariable67TechnologyProgressThisfollowssincesteady-statevariablesareconstantandEisgrowingattherategTherefore,theinclusionoftechnologyprogressintheSolowmodelcangeneratesustainedlong-rungrowth68TechnologyProgressMoreover,totalcapital,output,consumptionandinvestmentgrowattheraten+ginsteadystate: Giventhatsteady-statevariablesareconstantandELisgrowingattheraten+g69Consumptionpereffectiveworkerinsteadystate:GoldenRule:findk*s.t.c*ismaximized:GoldenRuleGovernmentPoliciestoraisetherateofproductivitygrowthImprovinginfrastructureWouldincreasedinfrastructurespendingincreaseproductivity?Theremightbereversecausation:Richercountrieswithhigherproductivityspendmoreoninfrastructure,ratherthanviceversaInfrastructureinvestmentsbygovernmentmaybeinefficient,sincepolitics,noteconomicefficiency,isoftenthemaindeterminantGovernmentPoliciestoraisetherateofproductivitygrowthBuildinghumancapitalThere’sastrongconnectionbetweenproductivityandhumancapitalGovernmentcanencouragehumancapitalformationthrougheducationalpolicies,workertrainingandrelocationprograms,andhealthprogramsAnotherformofhumancapitalisentrepreneurialskillGovernmentcouldhelpbyremovingbarrierslikeredtapeEncouragingresearchanddevelopmentGovernmentcanencourageRandDthroughdirectaidtoresearchWhyistechnologicalbreakthroughsprogresssounequalacrosscountries?Whatdeterminedwhether/whennewtechnologyadopted?Geographyview:importanceofecology,climate,diseaseenvironment,geography,inshort,factorsoutsidehumancontrol.Institutionsview:importanceofman-madefactors;especiallyorganizationofsocietythatprovideincentivestoindividualsandfirms.History’saccidents:somecountriesareunluckyandtrappedinunderdevelopment.72TheGeographyFactor73TheInstitutionsFactor74InstitutionsandEconomicPerformances75InstitutionsandEconomicPerformances76Butinstitutionsarecomplicated:

identificationproblemGoodinstitutionsarecorrelatedwithmanyothergoodthings.Theoriesaboutinstitutionsarethusverydifficulttotest.Thestudyofthecausalroleofinstitutionsoneconomicgrowthisthereforecomplicatedbyconcernsaboutendogeneity.Forexample,theUnitedStatesisrich;ithasgoodinstitutions;ithashighlevelsofeducation;ithasacommonlawheritage;ithasatemperateclimate.Goodinstitutionsaredifficulttopindownprecisely.Wewanttobeverycarefultodisentangledifferentcausaleffectsandisolatetheeffectofinterest.77ButinstitutionsarealsoendogenousInstitutionscouldvarybecauseunderlyingfactorsdifferacrosscountries:Geography,ecology,climateMontesquieu’sstory: –Geographydetermines“humanattitudes” –Humanattitudesdeterminebotheconomicperformanceandpoliticalsystem. –Institutionspotentiallyinfluencedbythedeterminantsofincome7879FactorPricesSofar,wesolvedthemodelwithoutanyreferencetowagesandrentalrates(factorprices)Wejustfocusedonhowincomeisgenerated,butnotonhowitisdistributedAssumethatacompetitivefirmhirescapitalandlabortogenerateoutput80FactorPricesAssumingCobb-Douglastechnology:Thentheproblemforthisfirmisgivenby:81FactorPricesFirst-orderconditionforKimpliesthat:Insteady-state,therealrentalrateisfixed(sincekisfixed)82FactorPricesFirst-orderconditionforLimpliesthat:Insteady-state,therealwagesincreaseattherateg(sincekisfixedandEgrowsattherateg)83FactorPricesAssumethatcapitalisinitiallybelowthesteady-state.Thenkwillevolveaccordingtothefollowingpath:tkk*84FactorPricesRentalrate:initiallyhigh(lowkimplieshighMPK)decreasesovertimeascapitalaccumulatesandMPKdecreasestR/P85FactorPricesDefinewageintermsofefficiencyunitsas:Then:initiallylow(lowkimplieslowMPLlaborabundantrelativetocapital)increasesovertimeascapitalaccumulatesandMPLincreasesconstantinsteadystate86FactorPricesThismeansthatrealwages(w/P):GrowfasterthangduringthetransitionGrowattherateginsteady-statetGrowthAccountingWanttobeabletoexplainwhyandhowcountriesgrowTherearemanysourcesofgrowthFirststepistodecomposeaggregategrowthintoitscomponents:GrowthinthelaborforceGrowthincapitalGrowthinproductivity8788SourcesofEconomicGrowthAssumeCobb-DouglasProductionFunctionTakeloganddifferentiatingComputingTFPz:TotalFactorProductivity(TFP)or“SolowResidual”YisGDP,Kisaggregatecapital,NisnumberofworkersNeedtoknowα8990Whatis“z”HumanCapital(Education)TechnologicalProgressExternality:environmentalIssuesInstitutionalEffectFirmOrganizationPatentProtectionCorruptionsLaborShareintheCobb-DouglasProductionFunctionFirmoptimization:First-orderconditionwithrespecttoN:LaborshareiswN/Y.Here:91ResultCanuseaveragelaborshareasmeasureofLaborshare(totalwagesdividedbyGDP)intheU.S.isabout64%Estimateα

tobe0.36CannowcomputeTFPas:92TotalFactorProductivityintheU.S.93DecomposingGrowthRatesTakinglogsofproductionfunction:Thesameappliestologdifferences:Logdifferencesareapproximatelyequaltopercentagechanges:94GrowthDecompositionfortheU.S.95GrowthDecompositionfortheAsianTigers96GrowthAccountingforChinaHumanCapitalinChina98HumanCapitalinChina99InnovationNewGoodsPatentsTechnologyi