曼昆第10版讲义mankiw10e-irm-ch09

|CHAPTER9 EconomicGrowthII:Technology,Empirics,andPolicy

LectureNotes|

CHAPTER9

EconomicGrowthII:Technology,Empirics,andPolicy

NotestotheInstructor

ChapterSummary

ThischaptercontinuesthepresentationoftheSolowgrowthmodelstartedinChapter8.Thechapterbeginsbyaddinglabor-augmentingtechnologicalprogresstothemodel.ThisadditioncompletestheSolowgrowthmodel.Oncethecompletemodelisdeveloped,itisusedtoaddresshowpublicpolicyaffectsgrowthanddevelopment.ThelastsectionofthechapterexaminessomeoftheweaknessesoftheSolowgrowthmodelandintroducesthestudenttoendogenousgrowththeory.Inaddition,thereisanappendixongrowthaccountingbasedontheSolowgrowthmodel.

BuildingonthelessonsofChapter8,thischapterteachesthefollowinglessons:

Technologicalprogressisthesoledeterminantofgrowthinlivingstandardsinthelongrun.

Policymakerswouldliketoincreasesavingandtechnologicalprogress,butthesegoalsarenoteasytoachieve.Inaddition,theproductivityslowdownofthepasttwodecadespresentsoneofthemostimportantandperplexingproblemscurrentlyfacingeconomistsandpolicymakers.

AweaknessoftheSolowgrowthmodelisitsfailuretoexplainwhatdrivestechnologicalprogress.Endogenousgrowththeoryattemptstoincorporatethesourceoftechnologicalprogressintoagrowthmodel.

Comments

ThischapterexpandstheSolowgrowthmodelofChapter8toexplainsustainedgrowthinoutputpercapitaandthustheongoingriseinthestandardofliving.Thechapteralsodiscussesendogenousgrowthmodelsthat,unliketheSolowmodel,allowforendogenoustechnologicalprogress.Supplement9-7continuestheinformalpresentationofthemodelstartedinSupplement8-9.

AsnotedinthecommentsonChapter8,economicgrowthisoneofthemoredifficulttopicscoveredinthetextbook.ThefollowingisalistofcommondifficultiesencounteredwiththeSolowgrowthmaterialpresentedinthischapterandwaystoovercomethem.

1. TheMeaningofEffectiveWorker

Theanalysisofpopulationgrowthoftenseemseasytostudents,whilethatoftechnologicalprogressseemsdifficult.Sincetheyareanalyticallyidentical,themainproblemapparentlycomesinunderstandingwhatwemeanbyeffectiveworker.Supplement3-2,“WhatIsCapital?”whichdiscusseshumancapital,maybehelpful;seealsotheintuitivepresentationinSupplement9-7,“TheSolowGrowthModel:AnIntuitiveApproach––PartII.”

2. WhyDoesTechnologicalProgressReducek?

Studentsfinditcounterintuitivethattechnologicalprogressreducesthecapital–laborratio,probablybecauseofthedifficultyofinterpretingtheconceptofeffectiveworker.Toemphasizethat,thelowerkdoesnotmeanthattechnologicalprogressisbad;onecanexplainthethoughtexperimentofintroducingtechnologicalprogressintoaneconomyoriginallyinsteadystatewithg=0.Themostimportantobservationisthatoutput,andhencelivingstandards,startstoimproveimmediately.Thecapitalstockincreasesasoutputincreasesbutinitiallyataslowerratethantherateoftechnologicalprogress,socapitalpereffectiveworkerdeclines.

3. ConfusionAmongaNumberofSimilarGraphsandVariantsoftheModel

Thefollowingaresuggestionstocorrectsuchconfusion:

Makesomeorallofthediscussionintuitiveratherthanmathematical;seeSupplements8-9and9-7.

Stressthatthereisultimatelyjustonemodelwithanumberofspecialcases.TheentireSolowmodelcanbereducedtoasinglegraphshowingf(k),sf(k),and(n+δ+g)k;ifstudentsunderstandthis,theyunderstandthemodel.ThesummarytableintheLectureNotesforSection8-1mayalsohelp.

Whenpresentingthetwo-sectorendogenousgrowthmodel,explainhowthisworksliketheSolowgrowthmodelifuisheldconstant,wheresdeterminesthesteady-statecapitalstockandudeterminesthegrowthofknowledge.

4. DifficultiesRelatingtheModeltotheRealWorld

TheSolowmodelcanberoughlycalibratedtotheU.S.economy.AsdiscussedinChapter9ofthetextbook,ifdepreciationis10percentofGDP,andthecapitalstockis2.5timesoneyear’sGDP,wecancomputethedepreciationratebydividingk=0.1ybyk=2.5ytoobtain:

k/k=(0.1y)/(2.5y),

=0.04.

RealGDPgrowsatabout3percentperyear,son+g=0.03.Todeterminethesavingratethatensurestheeconomyisatasteadystate,setsy=(n+g+δ)kandsolvefors:

s=(n+g+δ)(k/y).

Substitutingfor(n+g)=0.03,δ=0.04,and(k/y)=2.5,weobtain

s=(n+g+δ)(k/y)

=(0.04+0.03)×2.5=0.175.

Theeconomywillbeinasteadystatewhens=0.175.ThiscalibrationcouldbeusedtostudythedeclineinsavingintheUnitedStatesduringthe1980sandearly1990s,theslowdowningrowthfollowingtheoilshocksoftheearly1970s,andthepickupingrowthduringthelasthalfofthe1990s.Theweb-basedMacroeconomicsModelsmayalsobeusefulforsuchanalysis.

UseoftheEWebsite

GototheEwebsiteanddownloaddatafortotalbusinessfixedinvestmentandinvestmentininformationtechnologyandsoftwareoverthepast40years.Computetheratioofinvestmentininformationtechnologyandsoftwaretototalbusinessfixedinvestment.Howhasthisratiochangedovertime?Discusswhetherthedataareconsistentwiththepickupintrendproductivitygrowthduringthelate1990s.

ChapterSupplements

Thischaptercontainsthefollowingsupplements:

9-1 MoreontheConvergenceHypothesis

9-2 ConvergenceofIncomeAcrosstheUnitedStates

9-3 TheEconomicsofIdeas

9-4 GreenGrowth

9-5 CorruptionandGrowth

9-6 IncomeInequalityandGrowth

9-7 TheSolowGrowthModel:AnIntuitiveApproach—PartII

9-8 MoreontheProductivitySlowdown(CaseStudy)

9-9 MoreontheNewEconomy(CaseStudy)

9-10 AdditionalReadings

LectureNotes

Introduction

TheSolowgrowthmodelasdevelopedinChapter8showedhowchangesinthecapitalstockandpopulationgrowthaffectthelong-runlevelofoutputoftheeconomy.Thischapteraddschangesintechnologytocompletethemodel.ThecompleteSolowgrowthmodelcanthenbeusedtoexaminehowpublicpoliciesinfluencesavingandinvestmentandthusaffectlong-runeconomicgrowth.

WhiletheSolowmodelisausefultoolforunderstandingeconomicgrowth,itisnotwithoutweaknesses.Macroeconomistshaveattemptedtoaddresssomeoftheseweaknessestobetterunderstandtheprocessofeconomicgrowth.

9-1 TechnologicalProgressintheSolowModel

Chapter8providedanexplanationofpersistentlyrisingoutput,butwehavenotyetexplainedrisinglivingstandards.Todoso,weincorporatetechnologicalprogress,meaningthatweareabletoproducemoreoutputwithagivenamountofcapitalandlabor.

TheEfficiencyofLabor

Technologicalprogressisaslightlytrickierprocesstoincorporateintothemodel.Thereasonisthatitcanentertheproductionfunctionindifferentways;itmayincreasetheproductivityofcapitalorlabor.Thesimplestformtoanalyzeislabor-augmentingtechnologicalprogress.Returntotheproductionfunctionandamenditsothat

Y=F(K,L×E).

Here,Emeasurestheefficiencyoflabor.ThebiggerEis,themoreoutputcanbeproducedwithagivenamountoflabor.Wesupposethattechnologicalprogresscomesaboutfromincreasesintheefficiencyoflaborovertime.

Thisassumptionmakesanalysissimplesinceincreasesintheproductivityoflabornowlookjustlikeincreasesinpopulation.IfeitherLorEincreases,outputisaffectedinjustthesameway.Forthisreason,wecallL×Ethenumberofeffectiveworkers.Inotherwords,labor-augmentingtechnologicalprogressworksasifwearegettingmoreworkers.Ifwehaveprogressattherateg=0.02,then100workerscanproducethisyearwhatitwouldhavetaken102workerstoproducelastyear.IfLgrowsattheratenandEgrowsattherateg,thenL×Egrowsattheraten+g.

TheSteadyStatewithTechnologicalProgress

Figure9-1

Nowredefinektobecapitalpereffectiveworker(k=K/LE),andlikewise,y=Y/LE.Theanalysisoftechnologicalprogressisnowexactlyanalogoustothatofpopulationgrowth.Theeconomywillbeinsteadystatewithkconstantwhen

∆k=sf(k)–(n+δ+g)k=0

or

sf(k)=(n+g+δ)k.

TheEffectsofTechnologicalProgress

Table9-1

Insteadystate,output,capital,andconsumptionperworkerareallgrowingattherateg.Themodelcannowexplainrisinglivingstandards.AccordingtotheSolowmodel,technologicalprogressistheonlysourceofrisinglivingstandardsovertime.TheanalysisoftheGoldenRuleisagainalteredwhenwehavetechnologicalprogress.Theconditionformaximumconsumptionpereffectiveworkeris

MPK–δ=n+g.

Tosummarize:

PopulationGrowth=0

PopulationGrowth=n

PopulationGrowth=n;TechnologicalProgress=g

Lisconstant

Lgrowsatraten

Lgrowsatraten

LEgrowsatraten+g

Kisconstant

Kgrowsatraten

Kgrowsatraten+g

k=K/Lisconstant

k=K/Lisconstant

k=K/(LE)isconstant

K/Lgrowsatrateg

Yisconstant

Ygrowsatraten

Ygrowsatraten+g

y=Y/Lisconstant

y=Y/Lisconstant

y=Y/(LE)isconstant

Y/Lgrowsatrateg

9-2 FromGrowthTheorytoGrowthEmpirics

Thusfar,wehaveusedtheSolowmodeltohelpunderstandhowpolicymightinfluenceeconomicgrowth.Wenowturntothequestionofhowwellthemodelfitstheempiricalfacts.

BalancedGrowth

DatafortheUnitedStatesbearoutthepredictionsoftheSolowmodelfortechnologicalprogressreasonablywell.Aspredictedbythemodel,outputperworker-hourandcapitalperworker-hourhavetendedtogrowatroughlythesamerate(2percent).Also,astheSolowmodelpredicts(seeend-of-chapterProblem3),therealwagehastendedtogrowatthisrate,whiletherealrentalpriceofcapitalhasstayedapproximatelyconstant.

Convergence

Thedifferencesinlivingstandardsaroundtheworldarestaggering.YettheSolowmodelsuggeststhateconomiesarelikelytoconvergetowardthesamesteadystate—atleastiftheypossesssimilartechnologiesandhavesimilarratesofsavingandpopulationgrowth.Ifthedifferencesbetweenrichandpoorcountriesarejustduetothefactthatrichcountrieshavemorecapital,thenwewouldexpectpoorcountriestoaccumulatecapitalfasterandsoeventuallycatchupwithricherones.

Supplement9-1,“MoreontheConvergenceHypothesis”

Supplement9-2,“ConvergenceofIncomeAcrosstheUnitedStates”

AlthoughtheSolowmodelpredictsconvergence,othertheoriesofgrowth(seeSection9-4onendogenousgrowththeories)suggestthattherearecircumstancesunderwhichconvergencewillnotoccur.Economistsarenotfullyagreedonwhetherornotcountriesareinfactconvergingtosimilarstandardsofliving.Butthedataprovidesomesupportfortheviewthatoncewetakeaccountofdifferencesinsavingrates,populationgrowth,andeducation,countriesareconverging.Inotherwords,countriesexhibitconditionalconvergence,reflectingmovementtowardindividualsteadystatesthatdependonsavingrates,populationgrowth,andeducation.

FactorAccumulationVersusProductionEfficiency

Cross-countrydifferencesinincomeperpersonariseeitherbecauseofdifferencesincapitalperperson(physicalcapitalandhumancapital)orbecauseofdifferencesintheefficiencywithwhichfactorsareemployed.Althoughresultsvaryfromstudytostudy,researchhasshownthatbothfactoraccumulationandproductiveefficiencyareimportantindeterminingdifferencesinincomeperperson.Decidingwhichismoreimportant,however,isdifficult,becausecountriesthathavehighlyefficienteconomiestendalsotoaccumulatealotofcapital(andviceversa),blurringcauseandeffect.

Furthermore,itispossiblethatbothfactoraccumulationandproductiveefficiencyaredeterminedbyacommonfactor,perhapsthequalityofanation’slegalandpoliticalinstitutions.Socountrieswith“good”institutionsarealsoonesthatexperiencegreaterfactoraccumulationand/ormorerapidgainsinproductiveefficiency.

CaseStudy:GoodManagementasaSourceofProductivity

Differencesinincomesacrossnationsoccurinpartbecauseofdifferencesinproductionefficiency.Thesameistrueaboutbusinesses.Onepossiblereasonisdifferencesinmanagementpractices.AninfluentialstudyfindssignificantvariationinmanagementpracticesacrossfirmsintheUnitedStates,theUnitedKingdom,France,andGermany.Ineachcountry,somefirmsareefficientlymanagedandothersarepoorlymanaged.Butthedistributionofmanagementqualityvariessharplyacrossthesecountries.FirmsintheUnitedStateshavethehighestaveragequality,followedbyGermany,thenFrance,andfinallytheUnitedKingdom.Twopossiblereasonsforwhyfirmsdon’talwaysadoptthebestmanagementpracticesarealackofcompetitionandatraditionofpromotingfamilymembersinfamily-ownedfirms.Whenfirmsdon’tfacecompetitioninthemarket,theirmanagerscanperformbadly,yetthefirmcanstillsurvive.WhentheeldestsonistheheirapparenttobecomeCEO,hehaslessincentivetoacquiretheskillsneededtobecomeagoodmanager.Thestudyconcludesthatdifferencesinmanagementpracticescanhelpexplainwhysomecountrieshavehigherproductivityandhigherincomesthanothers.

9-3 PoliciestoPromoteGrowth

WhatarethepolicyimplicationsoftheSolowgrowthmodel?

EvaluatingtheRateofSaving

AnaturalstartingpointforevaluatingthesavingrateistoseeiftheU.S.economyisabovetheGoldenRule,sinceweknowthatpolicymakerscouldthenmakeeverybodybetteroffbydiscouragingsaving.Weneedtocomparethegrowthrate(n+g)withthereturntocapitalnetofdepreciation(MPK–δ).

ThefollowingaretruefortheU.S.economy:

1. K≅(2.5)Y.

2. ∆K≅(0.1)Y.

3. Capital’sshareofoutput≅0.3.

From(1)and(2),wecancalculateδ=0.04.Recallalsothatcapital’sshareofoutput=(MPK×K/Y)iffactorsarepaidtheirmarginalproduct.WeknowfromthatK/Y=2.5,sowecaninferfrom(1)and(3)thatMPK≅0.12.SoMPK–δ=0.08.ThegrowthratefortheU.S.economy,however,isabout3percentperyear.Thus,themarginalproductofcapitalnetofdepreciationexceedsthegrowthrate,indicatingthatthecapital–laborratioisconsiderablybelowtheGoldenRule.Increasingthesavingratewouldpermithigherconsumptioninthelongrun(though,aswenotedbefore,atthecostofdecreasedconsumptioninthepresent).

ChangingtheRateofSaving

AlthoughtheSolowmodelassetouthereexcludedthegovernmentforsimplicity,weknowfromtheanalysisoftheclassicalmodelthatnationalsavingdependsonbothprivatesavingandgovernmentsaving.Oneway,therefore,forpolicymakerstochangethesavingrateisbyincreasingpublicsaving—runninggovernmentsurplusesratherthangovernmentdeficits.Recallfromtheanalysisoftheclassicalmodelthatdecreasesinpublicsavingleadtocrowdingoutofinvestment.Thelong-runconsequenceofthis,astheSolowgrowthmodelshows,isalowercapitalstock.Policymakerscanalsoenactpoliciestoaffectprivatesavingdecisions—forexample,taxexemptionsforIndividualRetirementAccounts(IRAs)aredesignedtoencourageprivatesaving.Economistsremaindividedovertheeffectivenessofpoliciestopromoteincreasesinprivatesaving.

AllocatingtheEconomy’sInvestment

AlthoughtheSolowmodelassumesasinglecapitalgood,itishelpfultodistinguishthreedifferenttypesofcapital.First,thereisprivatephysicalcapital—thatis,thefactories,machinery,andthelikefirmsusetoproducegoods.Second,thereispublicphysicalcapital—thatis,capitalgoods,suchastheinterstatehighwaysystem,thatthegovernmentprovides.Suchgoodsareoftenknownasinfrastructure.Andthird,thereishumancapital—ortheknowledgeandskillsofpeopleintheeconomy.

Supplement3-2,“WhatIsCapital?”

Recentworkoneconomicgrowthhasfocusedmuchattentionontheroleofinfrastructureandhumancapital.Mosteconomistsnowagreethataccumulationofhumancapitalisasimportantacontributortoeconomicgrowthasphysicalcapital,andsomearguethatthegovernmentshouldencourageinvestmentinhumancapital.Someeconomistsalsoarguethatincreasedinvestmentininfrastructureisdesirable.

CaseStudy:IndustrialPolicyinPractice

Along-standingdebateineconomicsrevolvesaroundwhethergovernmentsshouldpromotecertainindustriesorfirmsbecauseoftheirimportancetotheeconomy.ThisdebateintheUnitedStatesgoesbacktotheearlydaysofthecountryandtheTariffof1789,whichwasintendedtohelpdevelopdomesticmanufacturing.OneexamplesupportersofindustrialpolicyoftenpointtoisthesuccessoftheInternet—agovernment-sponsoreddefenseprojectthat,byallestimation,hashadlargeeffectsonproductivity.Butcriticspointtootherinstanceswheregovernmentinterventionhinderedadvancesorsubsidizedventuresthatultimatelyprovedunsuccessful.EvenJapan’sMinistryofInternationalTradeandIndustry(MITI),oftenlookedatasasuccessfularchitectofindustrialpolicy,initiallyopposedHonda’sexpansionfromproducingmotorcyclestoproducingautomobiles.Thecompanymovedaheadanywayandbecameoneofthemostsuccessfulautoproducersintheworld—althoughprobablylaterthanitotherwisewouldhave.

EstablishingtheRightInstitutions

Asnotedearlier,nationshavedifferencesinper-capitaincomebecauseofdifferencesinfactoraccumulationanddifferencesinproductionefficiency.Inturn,nationsmayhavedifferentlevelsofproductionefficiencybecausetheyhavedifferentpoliticalandlegalinstitutionsthataffecttheallocationofscarceresources.Forexample,theextentoflegalprotectionaffordedshareholdersandcreditorsmayinfluencethefunctioningofcapitalmarketsandthustheallocationofcapitalintheeconomy.Moregenerally,the“quality”ofthegovernmentmayplayanimportantroleinprotectingpropertyrights,enforcingcontracts,preventingfraud,spurringcompetition,etc.,helpingensuregreatermarketefficiency.Innationswhereexpropriation,bribery,payoffs,andsucharethenorm,resourcesthatcouldincreaseper-capitaincomearesiphonedofftothebenefitthepowerfulattheexpenseofsociety.Theevidencesuggeststhatthelevelofcorruptioninanationisinverselyrelatedtoitsrateofeconomicgrowth.

AcomparisonoftheeconomicperformancebetweenNorthandSouthKoreahighlightswelltheimportanceofinstitutionsforeconomicsuccess.Bothnationssharedacommongovernment,economy,heritage,andcultureformanycenturies.AfterWorldWarII,KoreawassplitintoNorthandSouth.InNorthKorea,institutionsbasedontheSovietmodelofauthoritariangovernmentwereestablished.InSouthKorea,institutionsbasedontheAmericanmodelofdemocraticcapitalismwereestablished.Theoutcomecouldnothavebeenstarker:todayper-capitaincomeinNorthKoreaisone-tenththatinSouthKorea.NighttimesatellitephotosshowNorthKoreashroudedindarkness,whileSouthKoreaisablazewithlight.

CaseStudy:TheColonialOriginsofModernInstitutions

Anation’sgeographiclatitudeisstronglycorrelatedwithitsincomepercapita.Nationsneartheequatortypicallyhavealowerincomepercapitathannationsfartherawayfromtheequator.Thisfindingholdsforboththenorthernandsouthernhemispheres.Someeconomistsarguethatthiscorrelationisduetothedirecteffectoftropicalclimatesonproductivityinagricultureandindustry:hotclimatesareassociatedwithmorediseaseandgenerallypoorerresultsinagriculture.ResearchbyDaronAcemoglu,SimonJohnson,andJamesRobinsongoesbeyondthedirecteffectofclimateonproductivitytoconsidertheindirecteffectofclimateoninstitutions.TheseauthorsarguethatthepresenceoftropicaldiseasedissuadedEuropeansfromsettlingintropicalareasandoptinginsteadtoestablishpermanentsettlementsinmoretemperateclimates,e.g.,theAmericancolonies,Canada,andNewZealand.InregionswhereEuropeansestablishedpermanentsettlements,theyalsobroughtwiththemthepoliticalandlegalinstitutionsoftheirhomelands,whichprotectedpropertyrightsandlimitedthepowerofgovernment.Butwheretheycolonizedanddidnotsettle,theEuropeanssetupextractiveinstitutions,suchasauthoritariangovernmentsthatweredesignedtoexploitnaturalresourcesforexport.Theseinstitutionsmadethecolonizersrichbutdidnotdomuchtopromoteeconomicgrowth.Overthecenturies,ascolonialismfaded,theinstitutionsthatemergedweresimilarinstructuretothosethatwereoriginallyputinplaceduringthecolonialera.Thelegacycontinuestoday:tropicalnationsaremorelikelytohaveauthoritariangovernmentsrunbymodernelitesthanrepresentativegovernmentswithstronglegalinstitutions.Totheextentthatinstitutionalqualityhelpsdetermineeconomicsuccess,tropical-latitudenationswithlower-qualityinstitutions(corruptgovernments,weakerenforcementofpropertyrights,etc.)willbelessprosperousthantemperate-latitudenations.

SupportingaPro-GrowthCulture

Asociety’scultureincludesthevalues,attitudes,andbeliefsofitspeople.Theseaspectsofculturearehardtomeasurebutmayhelpexplaindifferencesinincomeacrosscountries.Culturalnormsthatkeepwomenpoorlyeducatedandoutoftheworkforceservetoreducethestandardofliving.Differencesinhowsocietiesvaluechildrencanaffectpopulationgrowthandtheaccumulationofhumancapital,and,inturn,income.Opennesstonewideascanallowsocietiestoadaptmorequicklytotechnologicaladvances,spurringmorerapidgainsinincome.Andthedegreetowhichpeopleinasocietytrustoneanothercaninfluencetheabilitytocoordinateeconomicactivities.Surveydatashowapositivecorrelationacrosscountriesbetweentheleveloftrustandincomepercapita.Trustisrelatedtosocialcapital,thenetworksofrelationshipsamongpeopleinasocietythatarisefromactivitiessuchastennisclubsandchurchgroups.Culturedevelopsfromhistorical,anthropological,andsociologicalforces,andisnoteasilyorquicklychangedbypublicpolicy.Butculturecanevolveovertime,andpolicycanplayarole.Lawsensuringeducationalopportunitiesforwomenandprotectingwomen’sworkplacerightshavesupportedchangingattitudestowardwomenintheUnitedStatesoverthepastcentury.

EncouragingTechnologicalProgress

HavinggonethroughtheSolowmodelinsomedetail,weareleftwithasomewhatdisturbingconclusionfromthepointofviewofourtheory.Explaininggrowinglivingstandardsmeansexplainingtechnologicalprogress,whichisexogenousinthemodel.Economistsdonotyethaveaverygoodunderstandingofthesourcesoftechnologicalprogress.Nonetheless,governmentpoliciesareoftendirectedtoencouragingtechnologicalprogress.Suchpoliciesincludetaxbreaksforresearchanddevelopmentandgovernmentfundingofbasicresearch.Morebroadly,governmentsubsidizationofeducation,byimprovingtheskillsoftheworkforce,mayincreasetheefficiencyoflabor.

CaseStudy:IsFreeTradeGoodforEconomicGrowth?

AsAdamSmithnoted,internationaltradeallowscountriestospecializeinproductiveactivitiesinwhichtheyhaveacomparativeadvantage.Soonemightexpectthatcountriesthatareopentotradewouldhavehigherlivingstandardsthancountriesthatareclosedtotrade.Theempiricalevidenceshowsthatcountriesthataremoreopentotradeindeeddoexperiencemorerapideconomicgrowththanthoseclosedtotrade.Inaddition,theevidenceshowsthataftercountriesopenuptotrade,theytypicallygrowmorerapidlythanbefore.Butthesecorrelationsbetweenopennessandgrowthdonotnecessarilyimplycausation,sinceitmaybethecasethatcountrieswithopen-tradepoliciestendalsotohaveothereconomicpoliciesandinstitutionsthatencouragegrowth.Onewaytosortoutwhethertradecausesgrowthistofindvariablesthatarecorrelatedwithtradebutarenotcorrelatedwithotherpolicyorinstitutionalvariables.JeffreyFrankelandDavidRomernotethatgeographicdistancefromothertradingpartnersandwhetheracountryislandlockedareimportantdeterminantsofhowmuchacountrytrades(i.e.,its“openness”)butareunlikelytobecorrelatedwithotherpolicyvariables.TheythenusethisinsightinapplyinginstrumentalvariabletechniquestothedataandfindthatincreasedtradeleadstohigherGDPperperson.

9-4 BeyondtheSolowModel:EndogenousGrowthTheory

Howdoweincorporatetheprocessoftechnologicalchangeintoagrowthmodel?

TheBasicModel

Startwithaproductionfunction

Y=AK,

whereAisaconstantmeasuringtheamountofoutputproducedforeachunitofcapital.ThisisknownasanAKmodel.Theproductionfunctiondoesnotexhibitdiminishingreturnstocapital.

Ifsisthefractionofincomesaved,then

∆K=sY–δK,

Supplement9-3,“TheEconomicsofIdeas”

Supplement9-4,“GreenGrowth”

Supplement9-5,“CorruptionandGrowth”

Supplement9-6,“IncomeandEqualityGrowth”

whichtogetherwiththeproductionfunctionimplies

∆YY=∆KK=sA-δ.

Thus,aslongassA>δ,theeconomygrowsforever.Notethatthisdoesnotrequiretheassumptionofexogenoustechnologicalprogress.

Doesitmakesensethatcapitaldoesnotexhibitdiminishingreturns?No,ifcapitalisdefinedasthestockofplantsandequipment.Yes,ifcapitalisbroadlyinterpretedtoincludethestockofknowledge.Someeconomistsarguethatthereareincreasingreturnstoknowledge.

ATwo-SectorModel

TheAKmodeldevelopedaboveisthesimplestexampleofanendogenousgrowthmodel.Amoresophisticatedversionincorporatestwosectors:amanufacturingsectorthatproducesgoodsandservicesforeitherconsumptionorinvestmentinphysicalcapitalKandaresearchsectorcomposedofuniversitiesthatproduceknowledge,E,whichisusedinbothsectors.

Theeconomycanbedescribedbythreeequations:

1. Y=F[K,(1–u)EL] theproductionfunctionofmanufacturingfirms,

2. ∆E=g(u)E theproductionfunctionforresearch,

3. ∆K=sY–δK capitalaccumulation.

Thefractionofthelaborforceworkinginresearchisu.Thestockofknowledge,E,determinestheefficiencyoflabor.Boththemanufacturingandtheresearchsectorsexhibitconstantreturnstoscale.

ThismodelissimilartothebasicAKmodelinthatcapitalexhibitsconstantreturnstoscalesincecapitalincludesbothphysicalcapitalandhumancapital(knowledge).Themode