The Urbanization Process and Economic Growth

#2003KluwerAcademicPublishers.ManufacturedinTheNetherlands.

TheUrbanizationProcessandEconomicGrowth:TheSo-WhatQuestion*

VERNONHENDERSON

DepartmentofEconomics,BrownUniversity,Providence,RI02912

Thereisanextensiveliteratureontheurbanizationprocesslookingatbothurbanizationandurbanconcentration,askingwhetherandwhenthereisunderorover-urbanizationorunderoroverurbanconcentration.Writersarguethatnationalgovernmentpoliciesandnon-democraticinstitutionspromoteexcessiveconcentrationÐtheextenttowhichtheurbanpopulationofacountryisconcentratedinoneortwomajormetropolitanareasÐexceptinformerplannedeconomieswheremigrationrestrictionsareenforced.Theseliteraturesassumethatthereisanoptimallevelofurbanizationoranoptimallevelofurbanconcentration,butnoresearchtodatehasquantitativelyexaminedtheassumptionandaskedthebasic``so-what''questionÐhowgreataretheeconomiclossesfromsigni®cantdeviationsfromanyoptimaldegreesofurbanconcentrationorratesofurbanization?Thispapershowsthat(1)thereisabestdegreeofurbanconcentration,intermsofmaximizingproductivitygrowth(2)thatbestdegreevarieswiththelevelofdevelopmentandcountrysize,and(3)overorunder-concentrationcanbeverycostlyintermsofproductivitygrowth.Thepapershowsalsothatproductivitygrowthisnotstronglyaffectedbyurbanizationperse.Rapidurbanizationhasoftenoccurredinthefaceoflowornegativeeconomicgrowthoversomedecades.Moreover,urbanizationisatransitoryphenomenonwheremanycountriesarenowfullyurbanized.Keywords:growth,primacy,urbanizationJELclassi®cation:O0,R0

Thereisanenormousliteratureontheurbanizationprocessthatoccurswithdevelopment(seeDavisandHenderson,2003forareview).Therearetwokeyaspectstotheprocess.Oneisurbanizationitselfandtheotherisurbanconcentration,orthedegreetowhichurbanresourcesareconcentratedinoneortwolargecities,asopposedtospreadovermanycities.Partoftheinterestintheurbanizationprocessarisesbecauseurbanizationandgrowthseemsointerconnected.Inanyyear,thesimplecorrelationcoef®cientacrosscountriesbetweenthepercenturbanizedinacountryand,say,GDPpercapita(inlogs)isabout0.85.Thereasonisclear.Usuallyeconomicdevelopmentinvolvesthetransformationofacountryfromaruralagriculturalbasedeconomytoanindustrial-servicebasedeconomy(aswellasreleasinglaborfromagriculture,aslabor-savingtechnologiesareintroduced).Thattransformationinvolvesurbanization,as®rmsand

*SupportoftheWorldBankthrougharesearchgrantisgratefullyacknowledged,aswellassupportoftheNationalScienceFoundation.TheopinionsandconclusionsinthispaperarethoseoftheauthoranddonotnecessarilyrepresentthoseoftheWorldBankorofNSF.IthankZmarakShaliziformanyhelpfuldiscussions.JamesDavisexcelledasaRAontheproject.Ibene®tedfromadvicefromDavidWeilandAndrewFosteronaspectsofthepaperandinconceptualizingtheproblemfromearlydiscussionswithShaidYusuf.Ibene®tedfromcommentsonanearlierversionofthepaperbyDuncanBlack,JimDavis,Yannisloannides,DiegoPuga,andWilliamStrange.Earlyversionsofthepaperweretitled``How[Urbanizationand]UrbanConcentrationAffectEconomic[Productivity]Growth''.Finallytwoanonymousrefereesprovidedveryhelpfulcommentsusedinrevisingthepaper.

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workersclusterincitiestotakeadvantageofMarshall's(10)localizedexternaleconomiesofscaleinmanufacturingandservices(Henderson,1974;FujitaandOgawa,1982;HelsleyandStrange,1990;DurantonandPuga,2001).

Economistshavetendedtofocusontheissueofurbanconcentration,ratherthanurbanizationperse.Theliteraturethatdoesexistonurbanizationexaminesruralversusurbanbiasinthetransformationprocess.Governmentsmayfavortheurban-industrialsectorwithtradeprotectionpolicies,infrastructureinvestments,orcapitalmarketsubsidiesortheymaydiscriminateagainsttheruralsectorwithagriculturalpricecontrols(Renaud,1981;O,1993),bothleadingworkerstomigratetocities.Buttherecanbeabiastowardsinhibitingurbanization.Forexample,formerplannedeconomiestendtoexhibitaruralbias,inthesenseofdiscouragingrural-urbanmigration,butnotnecessarilyindustrialdevelopment(Ofer,1977;Fallenbuchl,1977).

Themoreextensiveliteratureonthedegreeofurbanconcentrationandchangesinthatdegreewhichoccursasurbanizationandgrowthproceedhasavarietyofstrands.Countriesandinternationalpolicyof®cialsworryaboutwhetherkeycitiesaretoobigortoosmall(Renaud,1981;UN,1993;WDR,2000)andovertheyearsvariouscountriessuchasEgypt,Brazil,Korea,Mexico,andChinahavepursuedmediumsizecityprogramsdesignedtoforestallthegrowthoflargercities(Henderson,1988;AdesandGlaeser,1995).Internationalagenciespresumethatmanyoftheworld'smega-citiesareover-populated,atconsiderablecosttothoseeconomies.TheUN(1993)askshowbad``thenegativefactorsassociatedwithverylargecities''needtoget``before[itisinthe]self-interestofthoseincontroltoencouragedevelopmentofalternativecenters.''Thesamereportwarnsof``unbalancedurbanhierarchies''andthecrime,congestionandsocialinequalityinmega-cities.TheWorldDevelopmentReport(2000)hasachapter(7)onthegrimlifeofpeopleinmega-citiesindevelopingcountries.AndtheEconomistinoneofitsspecialsurveyshasposedthequestiondirectly(July29,1995):Dothesplendorsoflargecitiesoutweightheirdarkside?

Howdowestarttoanalyzetheseissues?Intheeconomicdevelopmentliterature,thereistheWilliamson(1965)hypothesis,asadaptedtoanurbancontext(Hansen,1990),whichstatesthatahighdegreeofspatialorurbanconcentrationintheearlystagesofeconomicdevelopmentishelpful.Byspatiallyconcentratingindustrialization,oftenincoastalcities,theeconomyconserveson``economicinfrastructure''Ðphysicalinfrastructurecapital(transportandtelecommunications)andmanagerialresources.Suchspatialconcentrationalsoenhancesinformationspilloversandknowledgeaccumulationatatimewhentheeconomyis``informationde®cient''.Asdevelopmentproceeds,eventuallydeconcentra-tionoccursfortworeasons.Theeconomycanaffordtospreadeconomicinfrastructureandknowledgeresourcestohinterlandareas.Second,thecitiesofinitialhighconcentrationbecomehighcost,congestedlocationsthatarelessef®cientlocationsforproducersandconsumers.Indeed,anumberofauthors®ndthepatternof®rstincreasingandthendecreasingurbanconcentrationacrosscountriesasincomerises(El-Shakhs,1972;Alonso,1980;WheatonandShishido,1981;Junius,1999;DavisandHenderson,2003).Growthratesoftheverylargestcitiestendtoslow,whilethoseofmediumandlargesizecitiescontinueunabated(WDR2000,Chapter6,Table6).Thereisarelatedliteratureonregionalconvergencewithincountriesovertime(BarroandSala-I-Martin,1991,1992),whichmakesasimilarpoint.

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Anotherstrandoftheliteraturearguesthatpoliticalinstitutionsandpoliciesincountriesmayencourageover-concentration(Renaud,1981;Henderson,1988;AdesandGlaeser,1995;MoomawandShatter,1996;HendersonandBecker,2000;DavisandHenderson,2003).Theideaisthat,inmanycountries,thereisalackofalevelplaying®eldacrosscitieswiththenationalgovernmentfavoringoneormorecitiesoverothers.Suchcitiesmaybenationalcapitals(Bangkok,MexicoCity,Jakarta,orSeoul,nottomentionParis)or

ÄoPaulo).Thenationalgovernmentmayunderinvestintheseatofnationalelites(Sa

interregionaltransportandtelecommunications,whichfavorsproducersandinvestors(whomayincludenationalpoliticians)inthenationalcapitaloverthoseinhinterlandcities(Fujitaetal.1999).Favoritism,asinIndonesia(HendersonandKuncoro,1996;Kaiser,1999),caninvolverestrictionsincapitalmarkets,export/importmarkets,andlicensingofproductionrights,allfavoring®rmsthatlocateinthenationalcapital.Thisallowscentralbureaucratsandpoliticianstoextractrentsintheallocationofloansandlicenses,withoutcompetitionfromlowerrankedbureaucratsinotherlocations.Favoritismcaninvolvetheallocationoflocalpublicservicesinfavorofnationalcapitals,wheredecision-makerslive.Theseformsoffavoritismdisproportionatelydrawmigrantsintothenationalcapital.Whilethehypothesizedfavoritismmayapplyinmanysettings,over-concentrationdoesnotalwaysrise.Informerplannedeconomies,migrationrestrictionsworktolimiturbanagglomeration(seeAuandHenderson,2002,forthecaseofChina).Boththeurbanizationandurbanconcentrationliteraturesdescribeageographic-migrationprocessasaffectedbypolicy.Muchofthediscussioninthoseliteraturesispredicatedontheideathat,foragivenlevelofurbandevelopment,thereisanoptimallevelofurbanizationoranoptimallevelofurbanconcentration,witheconomiclossesfromdeviationsfromtheselevels.OrasauthorssuchasGallupetal.(1999)imply,urbanizationpersemaypromoteeconomicgrowth.However,noresearchtodatehasattemptedtodirectlyquantitativelyexaminewhetherurbanizationpromotesgrowthorwhetherthereareoptimaldegreesofurbanizationorurbanconcentration.Thispaperdoesso.Andthenitexaminesthebasic``so-what''questionÐhowgreataretheeconomiclossesfromsigni®cantdeviationsfromanyoptimaldegreesofurbanconcentrationorurbanization?

Inacross-countrypanelcontext,thepaperestimatestheeffectsofurbanizationandurbanconcentrationonproductivitygrowth.Inthegrowthliteraturethereisadebateabouttheformulationandrelevanceoftraditionalcross-countrygrowthregressions.AsarticulatedbyTemple(1999)anddiscussedtowardstheendofthispaper,differencesintechnologygrowthratesacrosscountriesandwithincountriesovertimethatmaydependinpartonthelevelofeachcountry'seconomicdevelopmentdonotreadily®tinthestructureofatraditionalcross-countrygrowthframework.Giventhisdebate,Iadoptthe``cleaner''approachofdirectlyestimatingthedeterminantsofnationalproductivitygrowth(e.g.,BehabibandSpiegel,1994;HallandJones,1999).

Thepapershowsthatproductivitygrowthisnotstronglyaffectedbyurbanizationperse,butitisstronglyaffectedbythedegreeofurbanconcentration.Onconcentration,the®ndingsare(1)thereisabestdegreeofurbanconcentration,intermsofmaximizingproductivitygrowth,(2)thatbestdegreevarieswiththelevelofdevelopmentandcountrysize,and(3)overorunder-concentrationcanbeverycostlyintermsofproductivitygrowth.Thestrengthandconsistencyofthe®ndingsareofsomesurpriseÐthepriorswere

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thatthedataaretoopoorandtheissuestoosubtletoshowupincross-countryproductivitystudies.Butthatisnotthecase.Thepaper®ndslittlesupportfortheideathaturbanizationpersedrivesgrowth.Urbanizationisa``by-product''ofthemoveoutofagricultureandtheeffectivedevelopmentofamodernmanufacturingsector,aseconomicdevelopmentproceeds,ratherthanagrowthstimulusperse.Neverthelessitmaybetruethat,forcountriesstillintheurbanizingstage,foranyincometheremayarguablybeabestdegreeofurbanizationwhichpromotesproductivitygrowth.However,quantifyingsucharelationshipprovesdif®culteconometrically.Partoftheproblemlieswiththefacts:inthedata,rapidurbanizationhasoftenoccurredinthefaceoflowornegativeeconomicgrowthoversomedecades(sub-SaharanAfrica).Anotherpartoftheproblemisthatthede®nitionofwhoisurbanvariessubstantiallyfromregiontoregion.Inaddition,theexerciseisofincreasinglylimitedrelevance.Urbanizationisatransitoryphenomenonsothat,in1990,onlyabout50percentofmybasesampleofcountriesarestillactivelyurbanizing.Ontheotherhand,Iwillarguethaturbanconcentration(aratio)isfairlywellmeasuredacrosscountriesanditsrolepersistsevenasmediumincomecountriesbecomefullyurbanized.TheEffectsofUrbanConcentrationonGrowthDevelopment

Inthissection,Iexaminetheeffectofurbanconcentrationonproductivitygrowth.Istartwithurbanconcentration,orprimacy,becausethatexaminationyieldsthekeyresults.Theexaminationalsodevelopsthemethodologythatisthenappliedtotheexaminationoftheeffectofurbanizationongrowth.The®rstissueishowtomeasureurbanconcentration.Therearethreemeasuresthatpeopleuse.First,WheatonandShishido(1981)andHenderson(1988)usethestandardHirschman±Her®ndahlindexofconcentrationwhichinanurbancontextisthesumofsquaredsharesofeverycityinacountryinnationalurbanpopulation.Second,RosenandResnick(1981)usetheParetoparameterlookingatthedistributionofcitysizeswithinacountry,whichmeasureshowquicklysizedeclinesaswemovefromtoptobottominthesizedistribution,ortheoveralldegreeofdisparityinthesizedistribution.Inthesepapers,bothmeasureswereconstructedforjustoneyearforalimitedsampleofmostlylargercountriesintheworld;theyarenotavailableforalargergroupofcountriesoverthetimespanthatwelookat,1960±1995.

ThethirdmeasureiswhatisavailableovertheyearsformanycountriesandwhatiscommonlyutilizedintheliteratureÐurbanprimacy(e.g.,Mutlu,19;AdesandGlaeser,1995;Junius,1999).Primacyismeasuredtypicallybytheshareofthelargestmetroareainnationalurbanpopulation.Isurbanprimacyasmeasuredbytheshareofthelargestcityinnationalurbanpopulationareasonablemeasure?Becausesuchsharesaretypicallyverylarge,primarymeasurestendtobecloselycorrelatedwithHirschman±Her®ndahlindices.SinceHirschman±Her®ndahlindicescontainsquaredshares,theyaredominatedbythelargestshareifthatisahighnumber(e.g.,over0.25).Averageprimacyinoursample,overcountriesandyearsis0.31.Similarly,RosenandResnick(1981)showahighdegreeof(negative)correlationbetweenprimacyandestimatedParetoparameters.Theideaofclosecorrelationissupportedconceptually,givenevidenceonZipf'sLaw(Gabaix,1999)inestimationoftheParetoparameterwherethecoef®cienttendstoÀ1.Then,within

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countrieswhenwerankcitiesfromlargest(rank1)tosmallest,ranktimespopulationsizeisapproximatelythesameconstantforallcities,atleastamongcitiesaboveacertainminimumsizecriterion.Ifthisisthecase,thesizeofthelargestcityinthecountrydelineatesallothercitysizesandissuf®cientinformationtocalculateanycomparativeindexofnationalurbanconcentration.

Itisimportanttonotethat,althoughprimacyrepresentstheshareofthelargestcityinnationalurbanpopulation,Iamnottryingtotalkaboutoptimalcitysizeperse(eventhoughtakenliterally,later,optimalprimacyresultsforacountrycouldbetranslatedintoresultsontheoptimalsize(withappropriateerrorbands)ofthelargestcity).Theissueinthispaperisnationalurbanconcentrationortheextenttypicallytowhichnationalurbanresourcesarerelativelyspatiallyconcentratedinmega-coastalcitiesversusspreadacrossavarietyofcitiesstretchingintothehinterlands.Sotheprimacymeasureistreatedassuf®cientinformationtomeasureoverallnationalurbanconcentration,ortherelativeresourceallocationbetweenbigandsmallcities.Forthatreason,concentrationisnotmeasuredbytheabsolutesizeofthelargestcity;wewantarelativemeasure.Questionsofoptimalcitysizepersearebetteranalyzedusingindividualcitydata,whereoptimalcitysizevarieswithlocalindustrial-servicecompositionandeffectiveleveloftechnologyinacomplexfashion(seeAuandHenderson,2002onChina).

Thenextissueishowtoestimatetheeffectofurbanizationprocessesongrowth.WelookdirectlyattheeffectongrowthandlevelsofrealGDPperworker.OutputinaneconomyisproducedaccordingtoaggregateCobb±Douglasfunctionoftheform

Yi󰀂t󰀃󰀄Ki󰀂t󰀃󰀂Ai󰀂t󰀃Ni󰀂t󰀃󰀃

a

1Àa

󰀂1󰀃

whereKi󰀂t󰀃iscapitalincountryiintimetandNi󰀂t󰀃isemployment.Rearranging(1),takinglogarithms,anddifferencingwehave

󰀁󰀂󰀁󰀂Yi󰀂t󰀃Yi󰀂tÀ1󰀃lnÀln

Ni󰀂t󰀃N󰀂tÀ1󰀃 󰀁󰀂i󰀁󰀂!

Ki󰀂t󰀃Ki󰀂tÀ1󰀃

󰀄aln󰀂2󰀃Àln󰀅󰀂1Àa󰀃󰀆lnAi󰀂t󰀃ÀlnAi󰀂tÀ1󰀃󰀇:

Ni󰀂t󰀃Ni󰀂tÀ1󰀃Equation(2)statesthatworkerproductivitygrowthisafunctionofchangesincapitalper

workerandintechnology.Iwillestimatethisequationasstructured,directlyestimatinga,afterspecifyingtheargumentsdetermininglnAi󰀂t󰀃ÀlnAi󰀂tÀ1󰀃.GiventheCobb±Douglasformin(1),workerproductivitygrowthduetochangesintechnologyisalsoequivalenttototalfactorproductivitygrowth.Changesintechnology,lnAi󰀂t󰀃ÀlnAi󰀂tÀ1󰀃,aremodeledinequation(3)belowasafunctionofbaseperiodcharacteristicssuchas(i)educationofthelaborforce,whichaffectstheabilitytoadoptnewtechnologies(NelsonandPhelps,1966;GrossmanandHelpman,1991;BehabibandSpiegel,1994;BarroandSala-i-Martin,1995;DurlaufandQuah,1998),and(ii)internalcountryconsiderationsaffectinggrowthinef®ciency,suchasopenness(again,theintroductionofnewtechnologies)orurbanizationorprimacy.Glaeseretal.(1992)formulateproductivitygrowthwithincitiesexactlyasin(2)and(3).WewillalsolookataformulationwherethesevariablesaffecttheleveloftechnologylnAi󰀂t󰀃,asopposedtoitsgrowth.Ofcourseiftherearegrowtheffects,insomesensetheremustbeleveleffects

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VERNONHENDERSON

sincelevelsareanaccumulationofgrowth.However,econometrically,aswewillsee,growtheffectsaremucheasiertoquantifythanleveleffects.

Thekeyquestioniswhyurbanconcentrationaffectsproductivitygrowth.Lossesfromexcessiveorde®cientprimacyinstaticurbanmodelscomefromGDPlossesfromresourcemisallocation,where,forexample,underexcessiveprimacywhereurbandevelopmentisconcentratedinjustoneortwoprimatecities,thesecitiesaresubjecttoexhaustedscaleeconomies,excessivecongestion,andexcessivepercapitainfrastructurecosts,whilesmallercitieshaveunexploitedscaleeconomiesandoftende®cientcapitalinvestment(e.g.,Tolleyetal.,1979;Fujita,19;HendersonandBecker,2000;AuandHenderson,2002).Inadynamiccontext,theissueisrephrasedandthein¯uencessomewhatdifferentlyarticulated.InBlackandHenderson(1999)buildingonLucas(1988),inanendogenousgrowthmodelofasystemofcities,citysizeaffectspositivelythedegreeoflocalinformationspillovers,whichinteractivelyaffectslocalknowledgeaccumulation,promotingproductivitygrowth.However,citiesofexcessivesizedrawresourcesawayfrominvestmentandinnovationinproductiveactivitytotrytomaintainqualityoflifeinacongestedlocalenvironment.Forfourdevelopingcountries,Richardson(1987)documentstheexceedinglyhighpercapitainfrastructureandhousinginvestmentcostsofpeopleresidingmegacities,drawinginvestmentoutofproductiveandinnovativeuses.He®ndsaminimumofathreefolddifferentialinpercapitainvestmentcostsoflocatingafamilyinamegaversussmallcity.Fromtheurbanliterature,therearepromisingmicro-foundationsfortheseideasinDurantonandPuga(2001).Inthatpaper,primatecitiesareurbanareasofexperimentation,inderivingappropriateproductdesigns.Relativelyunder-sizedprimatecitiesresultinenvironmentsthathavetoolittleexperimentation,affectingproductivitynationally.Relativelyover-sizedprimatecitieshavepeopledevotingexcessiveamountsoftimetocommutingandother``wasteful''activities,drawingresourcesawayfromexperimentalactivity.Inprinciple,onecouldadapttheDurantonandPugadynamicmodeltoagrowthcontextwhereunder-concentrationinaneconomyresultsinlowerknowledgeaccumulationduetolackofexperimentationandover-concentrationsiphonsresourcesawayfromexperimentalactivity,similarlyinhibitingproductivitygrowth.Thenprimacyaffectsgrowthinacontinuousnon-linearfashion.Butinthiscontext,giventheWilliamson(1965)hypothesis,wewouldexpecttheeffectofurbanconcentrationtodependonacountry'slevelofdevelopment,representingnationalscarcityofknowledgeaccumulationandeconomicinfrastructure.Allthesestatementscryoutforacomprehensivegrowthmodelthatcapturesthesespeci®cconsiderations,butthatissimplybeyondthescopeofthispaper.Whatevertheprecisemodel,theempiricswithcross-countrydataaregoingtocomedowntoaskingtheso-whatquestionÐtowhatextentdoesprimacyaffectgrowth?

Todeterminethis,Ihypothesizethatproductivitygrowthinequation(2)isafunctionofprimacy,nationalscalevariables,education,andbaseperiodoutputperworker,representingthelevelofdevelopment,or

lnAi󰀂t󰀃ÀlnAi󰀂tÀ1󰀃󰀄f󰀂primacyi󰀂tÀ1󰀃;nationalscalei󰀂tÀ1󰀃;󰀁󰀂Y󰀂tÀ1󰀃

;educationi󰀂tÀ1󰀃󰀃󰀅dt󰀅mi󰀅eit:ln

N󰀂tÀ1󰀃󰀂3󰀃

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53

Theerrorstructurediscussedbelowconsistsofdtcommonshocksacrossallnations,miacountry®xedeffectwheregeography,culture,andinstitutionsaffectproductivitygrowth,andeitacontemporaneouserrorterm.Here,Idiscussthevariablesin(3)andspeci®cfunctionalformsforf󰀂?󰀃.Educationisalwaysincludedasabasicdeterminantofproductivitygrowthintheliteratureasnotedabove.Thekeyistoestablishthatprimacyaffectsproductivitygrowth,andthat,inanycontext,thereisabestdegreeofprimacyanddeviationsfromthatdegreesigni®cantlyreduceproductivitygrowth.Forthegrowthformulationinequation(3),the``bestdegree''ofprimacywillbede®nedasonethatmaximizesproductivitygrowth,otherthingsbeingequal.Uncoveringabestdegreeofprimacyindicatesthatunderlyingpoliciesthatpromotetoolittleortoomuchprimacydetractfromproductivitygrowth.Tohaveabestdegreeofprimacy,apartfromtheeducationterm,thef󰀂?󰀃functionin(3)willbespeci®edasaquadraticinprimacy.Fora0primacy󰀅b0primacy2wherea0>0andb050,thebestdegreeofprimacyisthepeakpointÀa0=󰀂2b0󰀃.

Theliteraturesuggeststhatoptimalprimacyoughttoalsovarywiththelevelofdevelopmentandwithnationalscalevariables.First,wewouldexpectthebestlevelofprimacytodecreasewithbothnationalpopulationandland.Anycity'sshareofnationalurbanpopulationshoulddeclineasnationalurbanpopulationgrowsandmorecitiesform.Forthatreasonwemeasurecountrypopulationscalebyurbanpopulationratherthantotalpopulation.Itshouldalsodeclineasnationalgeographicsizeincreasesandnationalresourcesaremorespatiallydispersed.Second,thereistheissueofwhetherthisbestlevelofspatialconcentrationvarieswithoutputperworker,assuggestedbyWilliamson(1965).UnderWilliamsonhighspatialconcentrationattheearlieststagesofdevelopmentisimportantbutasdevelopmentproceedsdeconcentrationoccurs.Wethushypothesizethatoptimalprimacydeclinesasoutputperworkerrises.Insummary,wegivethef󰀂?󰀃functionin(3)theform󰀁󰀁󰀂󰀂

Y

primacy󰀅b0primacy2󰀅b1education:󰀂4󰀃a0󰀅a1ln󰀂nationalscale󰀃󰀅a2lnNTheworkinghypotheseswouldbethat(i)thecollectionoftermsmultiplyingprimacyispositive,whileb050;and(ii)a150anda250sothatthebestdegreeofprimacydeclinesasoutputperworkerornationalscaleincrease,wherebestprimacyisgivenby

ÀÀYÁÁÀa0󰀅a1ln󰀂nationalscale󰀃󰀅a2lnNprimacy󰀄:󰀂5󰀃

󰀂2b0󰀃Nationalscaleincludesbothurbanpopulationandlandsizemeasures,butitwillturnoutthatscaleeffectsarenotalwaysstatisticallysigni®cant.Thepaperwillfocusonthespeci®cationin(4),®rstwithoutnationalscalevariables(justprimacyandln󰀂Y=N󰀃variables)andthenwithscalevariables.Ineithercase,howeverequation(4)doesnottestamoresubtleversionofWilliamsonwherebestprimacymight®rstincreasefromverylowoutputperworkerlevels,peak,andthendeclineasoutputperworkerrises.Thatwouldrequiresomequadraticformtotheoutputperworkertermin(4)interactedwithprimacyvariables.Iwillexploresuchaspeci®cationlater.

Turningtoempiricalimplementation,estimationofaanoutputgrowthequationasin

VERNONHENDERSON

(2)requiresinformationoncapitalstock;IusetheDhareshwarandNehru(1993)dataforcapitalandtheircorrespondingoutputperworkermeasure,asdiscussedintheAppendix.Whilesamplecoverageislimitedininstrumentalvariablemodelsto69or70countries,thisisthecleanestformulationthatexaminesproductivitygrowth.Intheformulation,researchersoftenhesitatetoestimatethecapitalsharecoef®cientandinsteadassignitavalueandtakethetermtotheLHS,sotheLHSisTFPorTFPgrowthinadifferencedform(e.g.,HallandJones,1998).WhiletheDhareshwarandNehrucapitalstockmeasuresarecarefullydone,theypresumablysufferfrommeasurementerror.Underinstrumentalvariablesestimation(seelater)whichcandealwith(timeuncorrelated)measurementerrorIestimatetheproductionrelationshipinequation(2)directlygettinggoodresultsonthecapitalcoef®cient.ButIcheckinasectiononrobustnessandshowthatprimacyresultsarenotaffectedbydoingittheotherway.Intherobustnesssection,IwillalsoshowthatomittingcapitalstockmeasuresentirelyandproxyingchangesincapitalbyinvestmentratesandGDPlevelsinequation(2)willyieldsimilarresultsonprimacyeffects(seeespeciallynote9).DataandErrorStructure

ThedatacomefromavarietyofsourceslistedintheAppendixincludingthePennWorldTables,BarroandLee,DhareshwarandNehru,WorldBankandtheUnitedNations.Generally,theycovertheperiod1960±1995in®ve-yearintervals,althoughtheDareshwar±Nehrudataonlygoto1990andcoverabout70countriesforwhichIhavealsoprimacyandeducationmeasures.The®ve-yearintervalscenteredaroundthecensusandmid-censustimeperiodsinmostcountriesrepresentthebesttimestogetaccuratemetroareapopulationmeasures.TheDareshwar±Nehrucapitalstockmeasureisbasedonperpetualinventorymethodsandisinlocalcurrencyunits.Ialsousetheiroutputperworkermeasureinconstantlocalcurrencyunits.Given(seenext)theestimatingequation(2)willbedifferencedtoremovethecountry®xedeffectweareexamininginternalcountryproductivitygrowthwithconsistentLHSandRHSnumbers.Tohaveresultsincommonunits,all®guresareconvertedtoPPPnumbersforthe1987exchangerateandPPPconversion.

Inestimationofequations(2)and(3),theerrorstructureiscritical.Whilevariablessuchasprimacy,outputperworker,andurbanizationarecorrelated,wewanttoidentifythe``causal''effectofprimacyonproductivitygrowth.Inequation(3),asnotedearlier,thedtaretimeshocks/trendsacrosscountries.Themiarecountry®xedeffectsrepresentingunobservedcountrytimeinvariantfactorssuchasgeographyandculture.Thesewillaffectbothgrowthandcovariates,abasicprobleminidentifyingprimacyeffects.Thecontemporaneouseitshocksthataffectgrowthfrom󰀂tÀ1󰀃tot,suchasinternalcountryinnovationsandchangesinpoliticalorlegalregimes,Iassumeareexogenoustopredeterminedvaluesofcovariatesin󰀂tÀ2󰀃.Buteitdoaffectcovariatesintandevenpotentially󰀂tÀ1󰀃,suchasprimacyasdeterminedbymigrationtothedominantmetroareainthecountry;thatis,covariatesarenotstrictlyexogenous,whichbecomesrelevantintryingtoaccountfor®xedeffects.Todealwiththe®xedeffectmi,I®rstdifferenceequations(2)and(3)toeliminateit,yieldingasetofequation-years,

THEURBANIZATIONPROCESSANDECONOMICGROWTH

55

where󰀆ln󰀂Yi󰀂t󰀃=Ni󰀂t󰀃󰀃Àln󰀂Yi󰀂tÀ1󰀃=Ni󰀂tÀ1󰀃󰀃󰀇À󰀆ln󰀂Yi󰀂tÀ1󰀃=Ni󰀂tÀ1󰀃󰀃Àln󰀂Yi󰀂tÀ2󰀃=Ni󰀂tÀ2󰀃󰀃󰀇isafunctionofcovariates󰀂Xi󰀂tÀ1󰀃ÀXi󰀂tÀ2󰀃󰀃anderrorterms,󰀂eitÀeitÀ1󰀃and󰀂dtÀdtÀ1󰀃.Iestimatetheseequation-yearsjointlyconstrainingslopecoef®cientstobeequalacrossyearsforanunbalancedpanelofcountries.ForanequationyeartminustÀ1,ItheninstrumentwithlevelvaluesofcovariatesfromtÀ3andtÀ4becausecovariatesarenotexogenous.

Oneissueconcernstheviabilityofinstruments:whyshouldpastlevelsofvariablesbegoodinstrumentsforcurrentchanges?Partoftheanswerliesintheunderlyingnationaleconomicgrowthprocess,where,forexample,pastGDPperworkerisapredictoroffutureoutputperworkerchangesthroughthegrowthprocess.Anotherpartliesinfrictionsindomesticcapitalandlabormarkets(Rappaport,2000).Migrationfrictionsrelatecurrentprimacychangestopastprimacy,andcapitalmarketfrictionsandaccumulationprocessesrelatecurrentchangesincapitalstockorinvestmentratestopastlevelsorrates.Thesetofinstrumentsisstrongintermsof®rststagecorrelationsandF-tests;and,themodelsreadilypassspeci®cationtestsontheover-identifyingrestrictions,aswillbenoted.Generally,twoperiodsofpredeterminedvaluesofvariablesareusedasinstrumentsonthebasisthattheseunderlyingcomplexdynamicadjustmentsprocessesarebetterrepresentedwithtwo,ratherthanjustone,periodofpredeterminedvaluesofcovariates.Iwillnotebasicresultsifjustoneperiodofpredeterminedvaluesareusedasinstruments(seenote3).

Aconcernmightbewhether,withthisdifferencingtoeliminatemiinestimation,thereissuf®cientvariationincertain(differenced)covariatestoidentifyeffects.Forexample,forthoseunfamiliarwithmetroareapopulationdata,itmightseemthatprimacywouldnotvarymuchwithinacountryovertime.Infact,thisisnotthecase.Primacytendstochangefairlyquickly,astherural-urbanallocationofresourceschangeswithdevelopment,drivenbychangingrelativefactorreturnsindifferentsectors(whereequation(2)isameta-productionfunctionsubsumingthesesectorallocations).AsreportedinTableA2intheAppendix,fortheestimatingsample,theaverageabsoluterelativechangeinprimacy󰀂primacy󰀂t󰀃Àprimacy󰀂tÀ1󰀃=primacy󰀂tÀ1󰀃󰀃every®veyearsis0.18.Theonlyvariableswithalowpercentagerelativechangeareln(nationalurbanpopulation)andln󰀂Y=N󰀃.Theseenteronlyinteractivelywithprimacyintheestimatingequation,asdoes(unchanging)nationallandarea.Tosomeextentthen,heuristically,identi®cationofinteractiveeffectsreliesonthetimevariationinprimacy,whichmayplacepracticallimitsontotheextenttowhichcomplexinteractiveeffectscanbeidenti®ed.

The®nalissueconcernshowtoimplementIVestimation;thereareseveralpossibilities.Thereisbasic2SLS,usingtwoperiodsoflaggedcovariatesasinstruments.1Thereis3SLSwhichaccountsforserialcorrelationacrossequation-years(whichexistssincebyconstructioneitÀeitÀ1inoneequationyeariscorrelatedwitheitÀ1ÀeitÀ2inthepreviousequationyear).Finally,thereisGMMestimationwhichimproves3SLSestimatestoaccountforwithinyearheteroskedasticityincoef®cientestimation.Forthelasttwoprocedurestoaddanextraequation-year󰀂fln󰀆Y=N󰀂1975󰀃󰀇Àln󰀆Y=N󰀂1970󰀃󰀇gÀfln󰀆Y=N󰀂1970󰀃󰀇Àln󰀆Y=N󰀂1965󰀃󰀇g󰀃IinstrumentwithcovariatesfromjusttÀ3(1960)forthatoneequationyear,andtÀ3andtÀ4forallotheryears.Ingeneral,IrelyontheGMMformulation,usingtheDPD98Gaussprogramfor

56

VERNONHENDERSON

estimation(ArellanoandBond,1991;Casellietal.,1996).However,forkeysetsofresultsIwillpresentallthreeIVresults.2Withdifferencingandinstrumentingthereisalossofobservations.Forexample,ifinstrumentsarecovariatesfromtÀ3andtÀ4,foracountrytobeinanequation-yeartheremustbe®veperiodsofconsecutivedata󰀂ttotÀ4󰀃.Somecountriesfailtomeetthatstandard,socountrycoverageunderthisestimationprocedureislessthanforOLS.InallformulationsIalsoshowbaselineOLSresults.Results

Istartbypresentingresultsonthebasicproductivitymodelandthenturntotheresultsfromincorporatingprimacy.Fortheproductivitymodelthedataspan1960±1990in®ve-yearintervals.Givenequation(2)and(3)aredifferenced,ininstrumentalvariablesestimation,therearefourequationyears,with1960valuesneededasinstruments.Countrycoverageis69±81countriesdependingonthevariablesincluded.Table1presentsbaselineresults.Thedependentvariableasinequation(2)islistedasln󰀂Y󰀂t󰀃=N󰀂t󰀃󰀃Àln󰀂Y󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀃whichisthecaseunderOLS.ForIVestimationequation(2)isdifferencedsothedependentvariableasnotedaboveis

& ! !'& ! !'

Y󰀂t󰀃Y󰀂tÀ1󰀃Y󰀂tÀ1󰀃Y󰀂tÀ2󰀃lnÀlnÀlnÀln:N󰀂t󰀃N󰀂tÀ1󰀃N󰀂tÀ1󰀃N󰀂tÀ2󰀃OLS,®xedeffect,andinstrumentalvariablesresultsaregivenforthecasewheretheonly

argumentinthedlnAfunctioniseducation,asmeasuredbytheaverageyearsofsecondaryandaboveschoolingintheadultpopulation.2SLS,3SLS,andGMMresultsforinstrumentalvariablesarepresented.Thepointestimateofthecoef®cientoncapital,theCobb±Douglasshareparameter,startsat0.underOLSanddeclinesto0.405intheinstrumentalvariablesestimationunderGMM,whichincorporatesawithinperiodheteroskedasticstructure.Whilethatishigherthanthecapitalcoef®cientassumedintheliteraturesuchasHallandJones'(1999)0.33,theGMMestimateissimilartomicroworkindevelopingcountriessuchasHendersonetal.(2001)onKoreaandJeffersonandSingh(1999)onChina,wherebothstudies®ndacoef®cientof0.37±0.39forthetypicalindustry.Foreducation,theeffectunderGMMinstrumentalvariableestimationislarge.Aone-Table1.Abasicproductivitygrowthequation.(dependentvariable:ln󰀆Y󰀂t󰀃=N󰀂t󰀃󰀇Àln󰀆Y󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀇󰀃.

(1)OLS

Dln(capital/labor)Avg,yrs.hs&collegeofadults󰀂tÀ1󰀃

YeareffectsN[countries]AdjR2(within)Sarganp-value

(2)Fixedeffects(3)2SLS

(4)3SLS

G(5)MM

0.538**0.510**

(0.048)(0.0)0.012**0.0038(0.0052)(0.019)

YesYes482[82]482[82]0.3650.362

0.470**0.460**0.405**

(0.232)(0.121)(0.069)0.0250.0560.071**(0.0)(0.038)(0.019)

YesYesYes231313[81]313[81]0.144

0.386

Notes:**Signi®cantat5%level.

THEURBANIZATIONPROCESSANDECONOMICGROWTH

57

standarddeviationincrease(seeappendix)inbaseperiodnationaleducationleadstoa8percentgrowthinproductivity.However,thiseffectisnotrobust;otherinstrumentalvariableestimatesarelowerandinsigni®cant.Intheliterature,educationtypicallydoesnothaverobusteffects(Temple,1999).AuthorssuchasCasellietal.(1996)entermaleandfemaleeducationseparatelyincrosscountrygrowthregressionsgettingrespectivelynegativeandpositivecoef®cients.Ialsogetthatsameresultifmaleandfemaleeducationareenteredseparatelyalthoughbothcoef®cientsareinsigni®cant.Ichoosetorelyonthecombinedmeasure,recognizingthatitseffectisnotrobust.

AsinTable1,allGMMestimationsinthepaperpassSargantests,withresultsimprovingastheformulationincorporatesprimacyeffectsinlatertables.Sargantests,foracorrectlyspeci®edmodel,examinethevalidityoftheover-identifyingrestrictionsthatpresumeerrortermsareorthogonaltoinstruments.Secondallmodelsshow®rstdegreeserialcorrelation(given󰀂eitÀeitÀ1󰀃and󰀂eitÀ1ÀeitÀ2󰀃arecorrelatedbyconstruction)butnoseconddegreeserialcorrelationindicatingthattheeit'sinequation(3)themselvesarenotseriallycorrelated.Third,standarderrorsoncoef®cientsunderGMMarealwayslowerthanunder3SLS;anissueinArellanoandBond(1991)fromMonteCarlostudiesiswhetherGMMestimatedstandarderrorsinsmallsamplesareconsistentlytoolow.When3SLSresultsforamodelarenotreportedinatable,Iwillalwaysputtheminanote,soareadermaybothcomparecoef®cientsandhaveadifferentestimateofstandarderrors.BasicPrimacyResults

Withtheseresultsinmind,Inowturntotheprimacyvariable.Therawdatadonottellusmuch.Thereisamodestnegativecorrelationbetweeneitherdln󰀂Y=N󰀃andprimacyorddln󰀂Y=N󰀃anddprimacy.Controlsandanon-linearspeci®cationtotheeffectofprimacyareneededtosortoutwhatisgoingon.

ThebasiceconometricresultsareinTable2,columns(1)±(4)wherethereisaquadraticformtoprimacyanditisinteractedwithoutputperworkertoallowbestprimacytovarywithoutputperworker.Beforeanalyzingthoseresults,Inotethatasimplelinearprimacytermhasanegativecoef®cient.Second,incolumns(5)and(6)ofTable2,Ireportonasimplequadratic,tomakethepointthatthereisabestdegreeofprimacy.Incolumns(5)and(6)andinallotherreportedresultsinthepaper,OLSandinstrumentalvariableresultsonprimacydodiffer.OLStendstogivelowerbestprimacyvalueswithlesscurvaturetothef󰀂?󰀃function.Incolumn(5),underOLSthebestprimacyvalueis0.20,whileunderinstrumentalvariablesestimation(GMM)thebestdegreeprimacyhasahighpointestimateof0.46,withstrongandsigni®cantcoef®cients.Fromthebestlevelofprimacy,aone-standarddeviation(0.13)increaseinprimacyleadsproductivitygrowthtobe0.12lessover®veyears,ahugeeffect,albeitforalargechangeinprimacy.However,thebestdegreeofprimacyshouldvarywithlevelofdevelopment,undertheWilliamsonhypothesis.

Table2,columns(1)±(4)containthekeyresultsofthepaperalongwithresultsinTable3.Inthisspeci®cationinTable2,thereisaquadratictoprimacybutnowtheprimacytermisalsointeractedwithoutputperworker;orIamestimatingafunction󰀆a0󰀅a2ln󰀂Y=N󰀃󰀇primacy󰀅b0primacy2whereweexpecta0>0;b050anda250

58

VERNONHENDERSON

Table2.Productivitygrowthwithprimacy(dependentvariable:ln󰀆Y󰀂t󰀃/N󰀂t󰀃󰀇Àln󰀆Y󰀂tÀ1󰀃/N󰀂tÀ1󰀃󰀇).

Basicmodel

(1)OLS

Dln(capital/labor)Avg.yrs.hs&college󰀂tÀ1󰀃primacy󰀂tÀ1󰀃primacy2󰀂tÀ1󰀃primacy󰀂tÀ1󰀃*

ln󰀆Y󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀇YeareffectsN[countries]adj.R2

Sarganp-value

(2)2SLS

(3)3SLS

(4)GMM

Primacyalone(5)OLS

(6)GMM

0.563**0.493**0.447**0.4**0.556**0.514**(0.051)(0.248)(0.133)(0.071)(0.052)(0.044)0.022**0.0810.0490.047**0.00820.097**(0.0066)(0.068)(0.039)(0.017)(0.0053)(0.017)0.682**12.5**5.99**6.45**0.172*5.09**(0.194)(4.52)(3.01)(0.669)(0.0)(0.798)À0.184À3.90À3.67*À3.15**À0.431**À5.51**(0.187)(3.10)(2.15)(0.109)(0.109)0.808)À0.075**À1.29**À0.386À0.488**(0.028)(0.394)(0.2)(0.110)

YesYesYesYesYesYes417[69]199270[70]270[70]417[70]270[70]0.4470.4110.432

0.6630.415

Notes:**Signi®cantat5%level.*signi®cantat10%level.

3SLScoef®cients(andstandarderrors)forcolumn(6)areinorderofvariableslisted0.580(0.127),0.080(0.040),4.70(2.22),andÀ5.16(2.26).

buta0󰀅a2ln󰀂Y=N󰀃>0forrelevantY=N.FortherecordInotethataddingin(baseperiod)ln󰀂Y=N󰀃onitsowninthisformulationresultsinacompletelyinsigni®cantcoef®cient,withlittleimpactonothercoef®cientsorstandarderrors.Morecomplexformulationsarediscussedbelow.Underthecurrentformulation,wehypothesizethatbestprimacydeclinesasoutputperworkerrises.

InTable2,columns(2)±(4),theinstrumentalvariableresultsunderdifferentestimationmethodsonprimacyvariablesdodiffer,although3SLSandGMMresultsareverysimilar.Alsoatloweroutputperworkerlevels,bestprimacyresultsarequitesimilar.For2SLS,3SLS,andGMM,bestprimacyatln󰀂Y=N󰀃󰀄8($3,000)hasrespectivevaluesof0.28,0.40,and0.40.The2SLSresultsareinef®cient,notonlybecausetheydonotincorporateserialcorrelationandheteroskedasticity,butalsobecausetheyuseasmallersamplesize.Withtwoperiodsofinstrumentsforallyears,weloseoneequation-yearin2SLSestimationrelativeto3SLSorGMM(wherefortheearliestequationyearIuseonlyoneperiodofpredeterminedvaluesofvariablesasinstruments).Foref®ciencyreasons,myfocusisontheGMMresultsincolumn(4).3Intheresultsofchoiceincolumn(4),bestprimacydeclineslinearlywithoutputperworker.Atalowoutputperworkerof$1,100,bestprimacyis0.48,whileatmiddle($8,100)andhigh($36,000)outputperworkeritisrespectively0.32and0.21.Highconcentrationseemsveryimportanttogrowthatearlystageswheneconomicinfrastructureisscarceanddomesticknowledgeaccumulationislow.Butthenitsimportancedeclinesasgrowthprogresses.4Deviationsfrombestprimacyareverycostly:0.071growthpointsover5yearsorabout1.41percentayear,foraonestandarddeviation(0.15)increase[decrease]inprimacyabove[below]itsbestvalue.Inthislinearformulationofbestprimacy,thisgrowthlossamountdoesnotchangewithoutputperworker;anditseemstobeanotimplausiblevalue

THEURBANIZATIONPROCESSANDECONOMICGROWTH

59

Table3.Productivitygrowth:primacyeffectswithcountryscale(dependentvariable:ln󰀆Y󰀂t󰀃=N󰀂t󰀃󰀇Àln󰀆Y󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀇󰀃.

(1)OLS

Dln(capital/labor)

(2)Inst.Vars.

0.523**0.570**(0.057)(0.027)

Avg.yearsh.s.andcollege0.020**0.072**ofadults󰀂tÀ1󰀃(0.0066)(0.0081)primacy󰀂tÀ1󰀃0.557*14.9**

(0.303)(1.05)

2

primacy󰀂tÀ1󰀃0.065À3.26**

(0.187)(0.571)

primacy󰀂tÀ1󰀃*À0.094**À0.420**ln󰀆Y󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀇(0.031)(0.039)primacy󰀂tÀ1󰀃*0.052**À0.0**ln(nat.urb.pop󰀂tÀ1󰀃)(0.022)(0.028)primacy󰀂tÀ1󰀃*À0.020À0.075**ln(nat.landarea)(0.017)(0.070)YeareffectsYesYesN[countries]411[69]266[69]Adj.R2[within]0.457Sarganp-value0.818Notes:**Signi®cantat5%level.*Signi®cantat10%level.

3SLScoef®cients(andstandarderrors)forcolumn(2)variablesarerespectively0.572(0.106),0.069(0.045),13.9(7.11),À3.77(2.01),À0.387(0.174),À0.060(0.179),andÀ0.586(0.455).Notescaleeffectsarestatisticallyweak.

forsuchalargedeviationinprimacy.Notethatmeanprimacyis0.31soachangeof0.15isa50percentincreaseordecreasein``typical''primatecitysize,incontextswheretheprimatecitydominatestheurbanlandscape(hasahighvalueof0.31).Incontextswhereprimacyis,say,0.2,achangeof0.15becomesdif®culttoenvision.Ifwesegmentthesampleintocoarseoutputperworkerorcountrysizegroups,thestandarddeviationsofprimacydeclinetoaround0.1.Thenthegrowthlossfrombeing0.1abovebestorbelowprimacyfallstoabout0.03over®veyears,orabout0.6percentayear.Stilltheselossesareverylarge.Theyshouldanswertheso-whatquestion,indicatingthaturbanconcentrationisanimportantissueinthegrowthprocess.

Thenextissueconcernshowtoassesswhetherparticularcountrieshavetoolittleortoomuchprimacy.Sincecountrysizesvaryandbestprimacyshouldvarysubstantiallybycountrysizeforanyoutputperworkerlevel,weneedtocontrolforcountryscale,asinequation(4)Ðbothlandareaandpopulation.Withcountryscale,resultscanbestatisticallyweaker;andOLSestimation®tspoorly.ButtheIVresultsunderGMMforthebasicmodelarereasonableandarepresentedinTable3.There,incolumns(1)and(2)forOLSandGMM,IaddintermsinteractingtheprimacyvariablewithoutputperworkerandtwomeasuresofnationalscaleÐnationalurbanpopulationandnationallandarea.Thisgivesabestprimacylevelasinequation(5),onethatisalinearfunctionofoutputperworkerandnationalscale.FortheGMMresults,bestprimacydeclineswithoutputperworkerandwithnationalscale.Atanationalurbanpopulationof22m(󰀄10innatural

60

VERNONHENDERSON

Figure1.Optimalprimacybyoutputperworker.

logs,forpopulationinthousands)inanaveragelandareacountry(12.9),optimalprimacydeclinesfrom0.41atoutputperworkerof$1,100to0.19atanoutputperworkerof$36,300.TheresultisillustratedinFigure1,whereoutputperworkerrangesfromln(1100)󰀄7toln(36300)󰀄10.5.Asnationalurbanpopulationrises,bestprimacychangesverylittle,buttheeffectoflandareaisverylarge.Forthesamenationalurbanpopulation,theinterceptatanoutputperworkerof$1,100,shiftsdownfrom0.41to0.17ascountrysizeincreasesfromtheaveragelandarea(12.9)to1standarddeviationabovetheaverage(15.2),asillustratedinFigure1.

InTable4,resultssimilartoFigure1arecalculated,showinghowbestprimacydeclineswithincreasesinnationallandareaandoutputperworker.Thenegativepointestimateathighoutputperworkerinalargelandareacountry(e.g.,theUSA)willbediscussedbelow.Table4showsforeachpointestimateofbestprimacy,theassociatedstandarderrorcalculatedbythedeltamethod.Inthemiddlerangesofsizeandoutputperworker,standarderrorsareverysmallandthe®tistight.Standarderrorsaremuchlargeratthe

Table4.Bestprimacypoints[andtheirstandarderrors](mediumpopulationcountryof22murbanresidents).

Geographicarea

OutputperworkerLow($1,100PPPin1987)Medium($8,100)High($36,000)

Small

(ln(land)󰀄10.5)0.65[0.0]0.52[0.036]0.42[0.033]

Medium

(ln(land)󰀄12.8)0.41[0.014]0.28[0.029]0.19[0.052]

Large

(ln(land)󰀄15.2)0.16[0.048]0.034[0.077]À0.062[0.099]

THEURBANIZATIONPROCESSANDECONOMICGROWTH

61

extremessuchasverylargelandareacountrieswithmediumorhigherincome,orsmalllowoutputperworkercountries.

Intermsofwhethercountriesareaboveorbelowtheirbestprimacylevels,in1990,55percentareabove,41percentarebelow,andtherestnexttothebestlevel.Whatismoretellingarethecountrieswithlargedeviations.Countriesin1990withhighlyexcessiveprimacyarede®nedforillustrationashavinganactualprimacyvaluethatis(i)atleasttwicethebestpointestimate(forcountrieswithpositivepointestimates)and(ii)outsidethe95percenterrorband.ThelistcomprisesusualsuspectswithtraditionallyhighlycentralizedgovernmentsÐArgentina,Chile,Algeria,Mexico,Peru,andThailand.In1970,thelististhosesamecountriesplusIran,Mozambique,andVenezuela,whereallofthelastthreeexperiencedsharpdeclinesinprimacybetween1970and1990.5Countrieswithverylowprimacyde®nedasunder50percentofthepointestimateofbestprimacyandalsoasoutsidethe95percentcon®denceintervalareBelgium,WestGermany,Malaysia,Switzerland,andTheNetherlands.Notethe®rstthreecountriesarepeculiarinthesenseofrespectivelybeingadefactosplitcountry,beingadejuresplitcountryinthedata,andhavingtheprimatecity(Singapore)defecttobecomeitsowncountry(whichisnotinthesample).

NationalPoliciesAffectingPrimacy

Countrieswithexcessiveprimacyasnotedearliermayhaveexcessiveprimacyduetoinstitutionalarrangementsorduetonationalpoliciesconcerningtradeorde®cientinvestmentininter-regionaltransportinfrastructure.InDavisandHenderson(2003),weexamineddeterminantsofprimacysuchasopennessandtransportinfrastructure,withthelatterhavinglargeeffects.BothopennessandroaddensityintheproductivitygrowthequationsinTable2havenegativeandinsigni®cantcoef®cientsandhavelittleimpactonothercoef®cients.TheirimpactisindirectÐthroughtheireffectonprimacy.Forexample,inTable4,consideramiddleoutputperworkermiddlesizecountrythatisonestandarddeviation(0.15)aboveitsbestprimacyvalueof0.28(andhencealsooutsidethe95percentcon®denceintervalforbestprimacy),withanactualprimacyvalueof0.43.Ifthatcountryweretoincreaseeitheritsroaddensityoritswaterwaydensitybyonestandarddeviation,thatwouldlowerprimacyby0.02inDavisandHenderson(2003).Ignoringthecostofimplementingsuchachange,thatwouldraiseitsproductivitygrowthrateby0.018pointsover5years,oritspercentageannualgrowthratebyabout0.35percent,anoticeableeffect.

Ihavetwo®nalnotesontheresultssofar,beforeexaminingissuesofrobustnessandmodelspeci®cation.FirstFigure1andTable3showthelimitstoeconometricallymodelingbestpointsÐatextremevaluesofvariables,wecangetdegenerateresults.Athighoutputperworkerlevelsbestprimacybecomesnegative,althoughthe95percenterrorbandsstretchwellintopositivevalues.Thisproblemholdsinmostformulations.Forthespeci®cmodelincolumn(2)inTable3theproblemcanbeminimizedbyreplacingprimacy*ln󰀂land󰀃byprimacy=󰀂ln󰀂land󰀃󰀃,whichswitchesthesignofthecoef®cientbutforcestheeffectofincreasedlandtodiminishwithgreaterscale.Theresultsforthetwomodelsareverysimilar,exceptatthelargelandareaextreme.Ofthefourcountriesin

62

VERNONHENDERSON

1990withnegativepointestimatesforbestprimacy(Australia,Brazil,Canada,andUSA),allbutone(USA)becomepositive.6Howeverthelistofexcessiveandlowprimacycountriesisunaffected.

SecondtheformulationsinTable2imposeasimplestructureintermsofhowbestprimacyvarieswithoutputperworker.ThisallowsforthebasicideaoftheWilliamsonhypothesisthathighconcentrationisimportantatlowoutputperworkerlevelsandthenbestprimacydeclineswithdevelopment.However,itdoesnotallowbestprimacyto®rstincreasefromverylowoutputperworkerlevelsbeforepeakingandthendecliningwithfurthergrowth.Ifoundnoevidenceofthatbutgiventhelowtimevariationinln󰀂Y=N󰀃(butnotprimacy)theremaybealimittowhatinteractiveeffectscanbeidenti®ed.First,asimpleTaylorseriesinrelevantvariablesdoesnotyieldanysigni®cantresults.Second,justaddingaquadraticincometermintheprimacyexpressioninequations(4)and(5)

2

(thatis,addingprimacy*ln󰀂Y=N󰀃)topotentiallyrepresentaWilliamsoneffectresultsinaninsigni®cantrelationship,inallspeci®cations.Finally,Itriedaquadraticformulationinoutputperworkerwithinboththeprimacyandprimacysquaredterms.Thatis,thef󰀂?󰀃functiontakestheform

󰀁󰀁󰀂󰀁󰀂2󰀂

YY

a0󰀅a1ln󰀂nationalscale󰀃󰀅a2ln󰀅a3lnprimary

NN󰀁󰀁󰀂󰀁󰀂2󰀂

YY

󰀂6󰀃󰀅b0󰀅b1ln󰀅b2lnprimacy2:

NNThisformulationisquitegeneralandallowsforallkindsofpatterns.Estimatesofequation

7(6)arestatisticallyweak,especiallyunder3SLS.Intheresults,bestprimacydeclinesthroughoutanyrelevantoutputperworkerrangeformostcountries,especiallymediumandlargesizeones,justasinFigure2.Inthetailsofcountrysizeandoutputperworkervalues,otherpatternscanhold,butnottheWilliamsoneffectinrelevantoutputperworkerranges.

RobustnessandOtherSpeci®cations

Table2indicatestherobustnessofresultstoestimationmethod.Theotherissueisrobustnesstootherspeci®cationsandsamplechanges.The®rstproblemconcernsthecapitalmeasure.GivenmeasurementerroranalternativeprocedureusedintheTFPliteratureistoassigncapitalasharecoef®cientof,say,0.35andestimatethedeterminantsofTFPgrowthor

& ! !'& ! !'

Y󰀂t󰀃K󰀂t󰀃Y󰀂tÀ1󰀃K󰀂tÀ1󰀃lnÀ0:35lnÀlnÀ0:35ln;N󰀂t󰀃N󰀂t󰀃N󰀂tÀ1󰀃N󰀂tÀ1󰀃rearrangingequation(2).Ifweestimatethatmodel,here,againdifferencingoutthe®xed

effectandinstrumenting,GMMestimatesonprimacyvariablesaregiveninTable5correspondingtotheTable2,column(4)model.[Educationhasacoef®cient(andstandarderror)of0.049(0.018).]TheresultsarequitesimilartothoseinTable2.Forlowandmiddleoutputperworker($1,100and$8,100respectively)optimalprimacyundertheTFP

THEURBANIZATIONPROCESSANDECONOMICGROWTH

63

Table5.Primacyeffectsunderdifferentformulations:IV(GMM)results.

(1)TFP

󰀂fln󰀆Y󰀂t󰀃=N󰀂t󰀃󰀇

À0.35ln󰀆K󰀂t󰀃=N󰀂t󰀃󰀇gÀfln󰀆Y󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀇

À0.35ln󰀆K󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀇g󰀃

primacy󰀂tÀ1󰀃primacy2󰀂tÀ1󰀃primacy󰀂tÀ1󰀃*

ln󰀆Y󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀇OthercovariatesandyeareffectsSarganp-value

7.49**(1.09)À2.88**(1.42)À0.676**(0.138)

(3)Cross-countrygrowthmodel󰀂ln󰀆Y󰀂t󰀃=N󰀂t󰀃󰀇

Àln󰀆Y󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀇󰀃3.15**(1.04)À0.701(0.9)À0.350**(0.091)

(2)Levelsformulation󰀂ln󰀆Y󰀂t󰀃=N󰀂t󰀃󰀇󰀃2.24**(1.17)À1.06(1.25)

YesYesYes0.676

0.552

0.211

Notes:**Signi®cantat5%level.

Forcolumn(1),3SLScoef®cients(andstandarderrors)forvariableslistedare6.69(2.95),À3.52(2.24),andÀ0.493(0.241).Forcolumn(2),theyare2.83(1.80)andÀ2.07(1.83).Forcolumn(3),theyare3.15(1.04),À0.701(0.9),andÀ0.350(0.091).Noteincolumn(3),althoughthenotationNisused,Nreferstopopulationratherthannumberofworkers.

formulationis0.52and0.24respectively,comparedtotheproductionfunctionformulationinTable2of0.48and0.32.

Second,wehavehypothesizedthatprimacyaffectstherateofproductivitygrowthratherthanitslevel.Alevelproductionfunctionapproachestimatesequation(1)wherethedeterminantsofA󰀂t󰀃arenowleveleducation,primacyandothervariablesineithertortÀ1.NowitislessstraightforwardtointeractY󰀂t󰀃=N󰀂t󰀃orevenY󰀂tÀ1󰀃=N󰀂tÀ1󰀃withprimacyintheA󰀂t󰀃function.Inthebasespeci®cation,Ifollowcolumns(5)and(6)inTable2,whereargumentsofA󰀂t󰀃areeduc󰀂tÀ1󰀃,primacy󰀂tÀ1󰀃andprimacy2󰀂tÀ1󰀃,tosee,infact,whetherthereisanoptimalprimacyvalue.Inthemodelthecapitalandeducationcoef®cientsarehigh(0.662and0.168respectively,bothsigni®cant).Incolumn(2)ofTable5,thequadratictermonprimacyisinsigni®cant;resultsforprimacyvariablesfortvs.tÀ1arealmostidentical.Pointestimatesgiveabestprimacyvalueover1.0incolumn(2)formulation,whichmakesnosense.AddinginprimacytÀ1interactedwithln󰀂Y󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀃leavestheprimacyquadratictermnegativebutnearzero,andhasoptimalprimacyrisingwithincome.8Alevelsformulationdoesnotgiveplausibleresults.Oneissueforsuchaformulationisthatthetimevariationinthedependentvariableln󰀆Y󰀂t󰀃/N󰀂t󰀃󰀇fromTableA2ismodest(unlikethetimevariationindln󰀆Y󰀂t󰀃=N󰀂t󰀃󰀇󰀃.

Third,ourproductivityapproachislimitedinsamplesizeto69countriesunderinstrumentvariablesestimationandtheperiod1965±1990(for270observations)becauseofcountrycoverageoncapitalstockmeasuresintheDhareshwar±Nehrudata.AnalternativeapproachusedinHenderson(2000)istospecifyagrowthmodel,whichexpandsthecountrycoverageto79andthesampleto361(addinginanequationyearwithgrowthfrom1990to1995).Inagrowthmodelbasedontheproductionfunctionin(1),weareconvergingtoasteadystatevalueofYi=󰀂AiNi󰀃.Growthinobservedpercapitaincomeisgivenby(e.g.,DurlaufandQuah,1998)

VERNONHENDERSON

󰀁󰀂󰀁󰀂Yi󰀂t󰀃Yi󰀂tÀ1󰀃lnÀln

N󰀂t󰀃N󰀂tÀ1󰀃󰀁󰀂 i󰀁!󰀂

ÀÁY󰀂tÀ1󰀃as

ln󰀄1ÀeÀbtlniÀA0À

Ni󰀂tÀ1󰀃1Àad󰀅n󰀅gÀÁ󰀅gtÀeÀbt󰀂tÀ1󰀃

󰀂7󰀃

whereg,d,n,sandbareratesoftechnologicalchange,depreciation,populationgrowth,savings,andconvergence.tisthetimebetweentandtÀ1.Thesecondterminthesquarebracketsgivesthesteady-statevalueofYi=󰀂AiNi󰀃.Inimplementationinapanel(e.g.,Casellietal.1996),ratherthanhavingexogenoustechnologicalchangegandpopulationgrowthn,determinantsofpopulationchange(fertilityrate)andtechnologicalchangeareinserted,movingusbeyondthesimpleneo-classicalframework,asTemple(1999)andDurlaufandQuah(1998)emphasize.Technologicalchangeisnowrelatedtoendogenousenvolvingvariables(education,primacy);anysteadystatetowhichaneconomymightbeconvergingkeepsshifting;andtheequationtakesareducedform.HavingYi󰀂tÀ1󰀃=N󰀂tÀ1󰀃alsopotentiallyaffecttherateoftechnologicalchangeassayinteractedwithprimacy,furtherremovesusfromthestandardframework.Forthatreason,Iutilizetheconceptuallycleandirectproductivityapproachinthispaper.

NeverthelessinHenderson(2000),Iestimatedagrowthspeci®cation.Growthinoutputpercapitaispostulatedtobeareducedformfunctionofbaseperiodoutputpercapita,fertilityrate,investmentrate,averageyearsofhighschoolandcollege,andprimacyandnationalscalevariables.Itisalsopossibletointerpretthisformulationasanotherversionofequation(2)wherechangesincapitalstockareproxiedforbytheinvestmentrateandbaseperiodoutputpercapita.Forthisgrowthformulation,Ialsohavesigni®cantoptimalprimacy®ndingsandamoresubtleWilliameffectfromestimatingequation(6).Optimalprimacyappearsto®rstrisefromlowpercapitaincomelevelsintomiddleincomelevelsbeforedeclining.Ingeneral,optimalprimacylevelsarelowerthaninthispaperandmanymorecountriesappeartohaveexcessiveprimacy.However,theresultsarespeci®ctousinggrowthinincomepercapita,ratherthaninoutputperworkerastheoutcomemeasure.ThemoresubtleWilliamsoneffectsinequation(6)goawaywithoutputperworkerandoptimalprimacylevelsaremoreinlinewiththispaper.9ForasimpleprimacyformulationasinTable2column(4)theprimacyresultsareincolumn(3)inTable5.10Interestingly,theresultsarestatisticallyweakerandbyln󰀂Y=N󰀃󰀄9,anyprimacyeffectsarenegative.Thedirectproductivityformulationinthispaperhasmorecompellingandrobustresults.TheEffectofUrbanizationonGrowth

Examiningtheeffectofurbanizationonproductivityisdif®cult,inthesenseoftheabilitytoisolatemeaningfulresults.Istartbydiscussingthreereasonsforthisdif®culty.First,rapidurbanizationinAfricancountriesinparticularoverthelast30yearshasoccurredinthefaceofnegativeandlow-incomegrowth.Thisinitselfsuggestsurbanizationisaresultofavarietyoffactorsrelatedtochangesinnationaloutputcompositionandsocialconditions,notaforcepromotinggrowthperse.Second,urbanizationisatransitoryprocess,wherewitheconomicgrowthallcountrieseventually``fullyurbanize''.Atsome

THEURBANIZATIONPROCESSANDECONOMICGROWTH

65

middle-incomelevel,urbanizationtopsofforceaseswhenacountryisinthe65±85percenturbanizedcategory;andalmost50percentofourcountriesfallintoafullyurbanizedcategoryby1990.Finally,urbanizationde®nitionsvarywidelyacrosscountries,makingitverydif®culttoquantifyanybestdegreeofurbanization,sincethatwoulddependonhowthecountrycountsurban.

Focusingonthede®nitionofurbanizationforamoment,fullyurbanizedforSwitzerland,AustriaandFinlandmeans60±65percenturbanized;fortheUSAitisjustover70percent(withminusculefull-timeemploymentinagriculture);andforcountrieslikeArgentina,Chile,andBrazil,fullyurbanizedis80±85percenturbanized.Alotofthesedifferencesdependonhowlowdensitynon-agriculturalpopulationsaretreatedinde®ningurban,especiallyaroundthefringes,orex/peri-urbanareasofmetropolitanareas.Forexample,whileChinaisof®cially30percenturbanized,about70percentofitspopulationlivewithin``municipal''boundaries(jurisdictionofthecity).ThedebateaboutwhetherChinaisdefacto40±50percenturbanizedrevolvesinpartaroundwhomtocountasurbanamongthelowerdensitynon-agriculturalpopulationsintheex/peri-urbanareasoutsidethe``cityproper''(China'sof®cialurbanizedareaofthecity),butwithinmunicipalboundaries.Forprimacymeasures,de®nitionalissuesofurbanmaynotbesuchaproblemsinceitisaratiooftheurbanpopulationofonemetroarearelativetotheurbanpopulationsofallmetro,city,townandvillagelocationswithinacountry,allconsistentlyde®nedwithinacountry.11So,forChina,theproportionsofex-urbanpopulationsofitsmunicipalitiesdonotvaryconsistentlybysize.

Withtheseproblemsinmind,Ieconometricallyexploretherelationshipbetweengrowthandurbanization.Aswithprimacy,wehypothesizethatforanyincomelevel,thereisabestdegreeofurbanization.Evenif``urbanizationpromotesgrowth'',presumablynoonewouldarguethatlow-incomecountries,withhighdegreesofsemi-subsistencefarmingandhighilliteracyrates,shouldswitchtobeingfullyurbanizedovernight.Toexaminetheurbanization-growth,Iuseanf󰀂?󰀃functionoftheform

󰀂a0󰀅a1ln󰀂Y=N󰀃󰀅a2ln󰀂nationalscale󰀃󰀃shareurban󰀅b0shareurban2;correspondingtoequation(4)andcolumns(2)ofTable3,althoughthenationalscalevariableisunimportant.Inthisformulation,oranyother,therearenosigni®cantresultstothef󰀂?󰀃functionforthewholesample.Togetanyresultswithanoptimaldegreeofurbanization,itisnecessarytorestrictthesampletopotentiallyurbanizingcountries.HereIde®nethatasthesetofcountriesperiodbyperiodthatarelessthan70percenturbanized;analternativerestrictionistoeliminateallcountriesthatarehigh-incomein1965.Forthisrestrictedsample,OLSandinstrumentalvariable(GMM)resultsarereportedinTable6,columns(1)and(2).Theinstrumentalvariableresultssuggest(1)countrysizeisnotafactorindetermininganoptimaldegreeofurbanizationand(2)thatthereispotentiallyanoptimaldegreeofurbanization.Butbeyondthat,theresultsareperverse,inthesensethattheeffectofoutputperworkergrowthistoreducethe``bestdegree''ofurbanizationÐthatisa150.(Thisresultapplieswhethernationalscaleiscontrolledforornot.)Thatisthebestdegreeofurbanizationdeclines,asoutputperworkerrises,acompletelyimplausibleresult.Moreover,resultsdeterioratewhenIputurbanizationandprimacyinthesameestimatingequation.Forthatestimation,Iinteractnationalscalewithprimacybutnot

66

VERNONHENDERSON

Table6.Urbanizationandgrowth(dependentvariable:ln󰀆Y󰀂t󰀃=N󰀂t󰀃󰀇Àln󰀆Y󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀇󰀃.

OLS

Dln󰀂capital/labor󰀃

Avg.yearshsandcollege󰀂tÀ1󰀃Urbanshare󰀂tÀ1󰀃*ln󰀆Y󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀇Urbansharesquared󰀂tÀ1󰀃Urbanshare󰀂tÀ1󰀃*ln(nat.pop󰀂tÀ1󰀃)*ln(nat.landarea)primacy󰀂tÀ1󰀃*ln󰀆Y󰀂tÀ1󰀃=N󰀂tÀ1󰀃󰀇primacy2󰀂tÀ1󰀃primacy󰀂tÀ1󰀃

*ln(nat.pop󰀂tÀ1󰀃)*ln(nat.landarea)N[countries]adj.R2

Sarganp-value

3690.427

233[62]0.969

0.502**(0.610)0.073**(0.585)0.585**(0.417)À0.042(0.047)À0.527*(0.297)0.035**(0.018)À0.012(0.013)

GMM0.626**(0.043)0.185**(0.033)5.57**(1.16)À0.5**(0.084)À0.922**(0.367)0.022(0.102)0.028(0.081)

GMM0.8**(0.043)0.202**(0.034)6.66**(1.45)À0.737**(0.173)À0.073**(0.813)

13.8**(3.14)À0.328*(0.183)À4.42**(1.)À0.627**(0.140)À0.333(0.249)195[52]1.00

Notes:*Sampleisrestrictedtocountriesinanyyearwhereurbanshare 0.70.

Sampleisrestrictedtocountriesinanyyearwhereurbanshare 0.70.ThreeSLScoef®cients(andstandarderrors)forcolumn(2)variablesare0.624(0.106),0.165(0.066),7.67(2.31),À0.592(0.242),À1.42(1.20),0.105(0.232),andÀ0.135(0.210).Forcolumn(3)variablesare0.618(0.101),0.170(0.053),8.14(2.18),À0.837(0.288),À0.403(1.22),18.6(5.95),À0.262(0.211),À3.17(1.91),À0.676(0.201),andÀ0.779(0.345).

urbanizationgivenresultsincolumn(2)ofTable6andcolumn(2)ofTable3.Resultsareincolumn(3)ofTable6.Whilethebasicbestprimacypatternspersist,thenotionthatthereisabestdegreeofurbanizationevaporates,albeitinamuchmorelimitedsamplesizeinestimation(requiringforanyperiod-countryurbanization50.7andforprimacydatatobeavailable).Inthoseinstrumentalvariableresultsincolumn(3)ofTable6,infact,urbanizationwouldappeartohaveanegativeeffectongrowthovermostoutputperworkerranges.Insummary,theseresultssuggestthaturbanizationperse,atleastasmeasuredacrosscountries,doesnotdirectlyaffectproductivitygrowth.

THEURBANIZATIONPROCESSANDECONOMICGROWTH

67

Conclusion

Thispaperarguesthaturbanizationrepresentssectoralshiftswithinaneconomyasdevelopmentproceeds,butisnotagrowthstimulusperse.However,theformthaturbanizationtakes,orthedegreeofurbanconcentration,stronglyaffectsproductivitygrowth.Urbanconcentrationisaffectedbynationalpoliciesandinstitutions,re¯ectingtheextenttowhichaparticularcity(e.g.,anationalcapitalsuchasBangkokorMexicoCity)isfavored.Foranycountrysizeandlevelofdevelopment,thereisabestdegreeofurbanconcentration,whichbalancesthegainsfromenhancedconcentrationsuchaslocalknowledgeaccumulationagainstthelossessuchasresourcesdivertedtoshoringupthequalityoflifeincrowdedmega-cities.Thatbestdegreeofconcentrationdeclineswithcountrysizeandlevelofdevelopment.AppendixData

Thedataarefromavarietyofsources.12Thedatacover1960±1995in5-yearintervals.Dataonconstantdollarincomepercapita(Chainindex),outputperworker,andinvestmentshareofGDParefromthePennWorldTablesMark5.6.Dataonthetotalfertilityrate(childrenperwomen)arefromtheWorldBank'sWorldDevelopmentIndicators(WDI).Openness((exportsplusimports)/GNP)isfromtheWorldBankWDI.Dataonaverageyearsofhighschoolandcollegeeducationoftheadult(over25)populationarefromBarroandLee(1996).Populationdataontotalpopulation,urbanpopulationandprimacy(populationofthelargestmetroarea/nationalurbanpopulation)arefromtheUNWorldUrbanizationProspects,TablesA12,A.5andA.3.

TheNehrucapitalstockvariableisbasedonDhareshwarandNehru(1993).Theyestimateconstantlocalcurrencyvaluesofphysicalcapitalstocks,usingperpetualinventorymethodswitha4percentrateofdepreciation.InmodelsusingtheNehrucapitalstockvariable,Iusetheiroutputperworkermeasure,whichisalsoinconstantlocalcurrencyunits.Sincethisisaproductivitygrowthmodelandthebasicresultsrelyonadifferencedversionofthatequation,weareexamininginternalrealproductivitygrowthwithinacountrywithaconsistentsetofleft-andright-handsidenumbers,whichisappropriate.Inestimation,topresentgraphsandresultsincommonunits,all®gureswereconverted(i.e.,scaled)toPPPnumbersforthe1987exchangerateandPPPconversion,sotheyarein1987constantPPPvalues.Inprinciple,thisshouldhavenoimpactonestimates(althoughscalingdoesinpracticeaffectinstrumentalvariablesestimatesasinGMM).

Fortransport,(timeinvariant)kilometersofnavigablewaterwaysarefromtheCIAWorldFactbookandtimevaryingkilometersofroads(motorways,autobahns,highways,andmainnational,secondaryandregionalroads)arefromtheInternationalRoadFederationsupplementedbyCIAdata,for1967and1970±1995.Bothmeasuresaredividedbynationallandarea.Givencontrolfornationalurbanpopulationandgivenperpersonroadinvestmentsaremuchhigherinruralareas,Iampresumingthevariationin

68

VERNONHENDERSON

nationalroaddensitiesshouldcaptureinvestmentsininterregionalroadsystems.Ialsomeasuredtransportinfrastructurebyhighwaydensity,butthede®nitionofthisvariableismuchlessconsistentacrosscountries.MeansandstandarddeviationsofallvariablesaregiveninTablesA1andA2.Giventhe5-yearintervals,foranyyear(e.g.,1990),forinvestmentshare,openness,andfertilityrate,theXit1aretheannualaverageratesovert2À1tot1(e.g.,1990±1994for1995).ThePermWorldTablesonlygoto1992.Missingdatato1994or1995(including1995income)are®lledinusingtheWDInumbers.Forexample,1995incomepercapitaisprojectedbygrowingthePennWorldTablesconstant1992incomebyWDInumbersonannualincomegrowthfrom1992±1995.AmongstmissingobservationsaredataonCzechoslovakia,Yugoslavia,USSR,andWestGermanyfor1995,with1960±1990datade®nedforthesecountriesastheyexistedin1990.

TableA1.Descriptivestatistics.

Mean

ln(outputperworker,Nehru)ln(capital/labor,Nehru)Averageyearsofhighschoolandcollege,populationover25ln(PPPGDPpercapita)

PPPGDPpcgrowthrate(5years)Averageannualinvestmentrateln(averagefertilityrate)PrimacyUrbanshare

Log(nationalurbanpopulation)Openness

Log(nationallandarea)

Log(nationalwaterwaydensity)Log(nationalroaddensity)

8.9.711.177.970.11018.21.340.3050.4838.7762.712.90.0079À1.75

StandardDeviation0.9941.161.060.9620.1508.960.5270.10.2421.4536.81.0.0181.46

TableA2.Averageabsoluterelativechangeofdifferencedcovariates.

󰀁tSTt󰀄2Si󰀄1󰀂Xi󰀂t󰀃ÀXi󰀂tÀ1󰀃󰀃=Xi󰀂tÀ1󰀃󰀃

n

󰀂3.0

0.450.180.150.0530.0303.4

STt󰀄2nt

dln(capitalperworker)

Averageyearsofh.s.andcollegePrimacyUrbanshare

ln(urbanpopulation)ln(outputperworker)dln(outputperworker)

THEURBANIZATIONPROCESSANDECONOMICGROWTH

69

Notes

1.For2SLS,Iallowthefunctionalformforthe®rststageregressiontovarybyequationyear,toimproveef®ciency.Firststageregressionsareareducedformapproximationforhow,inunderlyingdynamicadjustmentprocesses,pastlevelvariablespredictfuturechanges.Thereisnoreasontoexpectthatineachperiodweareatthesameoverallpointinthedynamicadjustmentprocessorevenoperatingunderthesameprocess,andhencewantthesameapproximation.

2.Technicallyfor3SLSresultsIuse®rststepestimatesinGMMfromtheDPD98program.Computationallythereisaslightdifferencebetween3SLSand®rststepDPD98estimates,althoughthetwoestimatesaresymptomaticallyidentical.

3.Incolumn(4),ifallequation-yearsarelimitedtohavingjustoneperiodofpredeterminedvaluesofvariablesasinstruments,coef®cientsareveryclosetothoseincolumn(4),takingvalues(withstandarderrors)inorderof0.487(0.098),0.052(0.029),6.13(2.45),À2.94(1.83)andÀ0.435(0.230).Withaweaker®rststageformulation,standarderrorsarelargerthanincolumn(4);theSargantestresultisthesame󰀂p-valueof0.678󰀃.

4.Theseresultsareimmunetoaddinginvariablesthatarecommonlycitedtoaffectgrowth,suchasopennessorgovernmentconsumption.SinceeveryonehastheirfavoriteadditionalconsiderationandIcouldnot®ndanythatstronglyimpacttheeffectofprimacy.Istickwithasparsespeci®cation.

5.MissingfromthelistisIndonesia.IndonesiaistheonlycountrywhereIthinkthesizeofthemetroareaisseriouslymisrepresented.Jakartaisde®nedasDKIJakarta,thejurisdictionalmetroarea,ratherthanthegreatermetroarea(Jabotabek).Todaythedifferenceisabouttwofold.6.Thecoef®cientsfollowingthelistinginTable3are0.522,0.063,À0.032,À3.62,À0.394,À0.079,and81.0,withthelastnowapplyingtotheprimacy/ln󰀂land󰀃term.Allexceptthealmostzerocoef®cientontheprimacytermaresigni®cant.

7.Coef®cientsforthefunctioninequation(6)arefora0À5.37,fora11forln(nat.urb.pop)À0.1,fora12forln(nat.land)À0.907,fora25.58,andtheninorderÀ0.381,55.1,À14.3and0.886.Allexceptthe®rstaresigni®cantinsteptwoestimateswhichadjustcoef®cientsforheteroscedasticity;however,theirstep-onet-statisticsareallunderoneexceptfortheln󰀂nat.land󰀃term.

8.Thecoef®cients(andstandarderrors)onprimacy󰀂tÀ1󰀃,primacy2󰀂tÀ1󰀃andprimacy󰀂tÀ1󰀃*ln󰀂Y(tÀ1󰀃/N󰀂tÀ1󰀃)areÀ3.77(1.14),À0.277(0.746)and0.631(0.124).Forthecapitalandeducationterms,wehave0.418(0.060)and0.107(0.021).

9.Foramediumsizecountry,forvaluesofln󰀂Y/N󰀃of7,7.5,8,9,9.5,and10,optimalprimacytakesvaluesof0.21,0.33,0.29,0.31,0.35and0.30,notacompellingpattern.Theprimacytermsare(À66.35À0.28lnnationalurbanpop.)À0.71ln(land)󰀅18.58ln󰀂Y=N󰀃À1.07(ln󰀂Y=N󰀃󰀃2)primacy󰀅(152.9±36.38ln󰀂Y=N󰀃󰀅2:11ln󰀂Y=N󰀃󰀃2primacy2.Allcoef®cientsaresigni®cantinbothMMand3SLS.Thisformulationalsobestapproximatesequation(2),whentheinvestmentrateandbaseperoutputperworkeraresubstitutedinforchangesincapitalperworker,toavoidusingcapitalstockdata.

10.Thecoef®cients(andstandarderrors)onlaggedoutputperworker,investmentrate,fertilityandeducationare

À0.158(0.046),0.0069(0.0016),0.157(0.056),and0.045(0.016).Variablesarede®nedintheAppendix.11.Thatis,thede®nitionofwhoisurbanornoturbanisappliedconsistentlytotheprimatecity(numerator)and

allpotentiallyurbanlocations(denominator).Heuristically,ifroughlythesameproportionisexcludedacrossthenationalpopulationlocationswithinacountry,thenevenifthatproportionvariesacrosscountriesitwillnotaffecttheprimacymeasure.

12.Barro,R.J.,andJ.W.Lee,InternationalMeasuresofSchoolingYearsandSchoolingQualityonlinedata,

WorldBankEconomicGrowthResearchGroup,WashingtonDC:WorldBank,1996;CentralIntelligenceAgency(CIA),WorldFactbook,WashingtonDC:USGovernmentPrintingOf®ce,variousyears;FreedomHouse,FreedomintheWorld,NewYork:FreedomHouse,variousyears;InternationalRoadFederation(IRF),WorldRoadStatistics,WashingtonDC:InternationalRoadFederation,variousyears;Summers,R.,andA.Heston,PennWorldTableMark5.6versionofSummersandHeston(1991)onlinedata,ComputingintheHumanitiesandSocialSciences(CHASS),Toronto:UniversityofToronto,1995;UnitedNations,WorldUrbanizationProspects:The1996Revision,UnitedNationsPopulationDivision,DepartmentforEconomicandSocialInformationandPolicyAnalysis,NewYork,1996;andWorldBank,WorldDevelopmentIndicators(WDI)onCD-Rom,WashingtonDC:WorldBank,1998.

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