I NTRODUCTION Since Marshall 1920 economists have recognized the propensity for industries to agglomerate across space This effect is not an accidentspatial clustering results in increased returns and growth as a consequence of localized economies o ID: 54733
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aneffectiveagglomerationindex,ameasurementwhichidentiestheconcentrationofindustryandexplainstherelationshipbetweenrmlocationchoiceandindustryconcentration.Ithasprovenquitedifcult,however,tondsuchamesurement.Theproblemofmeasuringspatialconcentration,alone,isdifcult:DurantonandOverman(2002)arguedthatasatisfactoryspatialagglomerationmeasurementshould(1)becomparableacrossindustries,(2)controlforoverallagglomerationtrendsacrossindustries,(3)separatespatialconcentrationfromindustrialconcentration,(4)beunbiasedwithrespecttothedegreeofspatialaggregation,and(5)admitaclearstatisticalsignicancetest.Furthercomplicatingtheproblem,effectiveagglomerationindicesmust,forpracticalreasons,be(6)computableinclosed-formfromaccessibledata.Inaddition,anindexisalmostmeaninglessifitisnot(7)justiedbyasuitablemodel,asanindexwithoutasupportingmodeldoesnotgiverisetoarealisticinterpretation.Anindexsatisfyingallsevenoftheseconditionswouldalloweconomiststoeasilyandeffec-tivelycharacterizethedeterminantsofagglomerationacrossindustries,inturngivinginsightintotheeffectsbywhichaggmomerationdrivesrmproductivity.However,thedifcultiesinherentintheproblemhave,atpresent,provenprohibitive—noagglomerationindexintheliteraturesatisesalloftheconditions(1)-(7).Themostaxiomaticallycompleteindicesarethosewiththemostcomplicateddatarequirementsandweakestsupportinginterpretations.Thus,economistshavenotagreeduponwhichindicestouse.Sinceagglomerationstudieswhichuseinconsistentindicesare,asweshallsee,rarelycomparable,thisinconsistencypresentsaseriousproblemtothosehopingstudythedeterminantsanddynamicsofagglomeration.Inthispaper,wewilldiscussthecurrentbodyofagglomerationmeasurementliterature.InSec-tion2,wefocusourattentiononthevarietyofagglomerationindiceswhichhavebeendevelopedinresponsetoKrugman(1991).Weexplainandcritiqueboththediscreteandcontinuousagglom-erationmeasurementliterature.Wethen,inSection3,examinesomeofthestudieswhichhaveappliedandcomparedthedifferentagglomerationindices.Wealsodiscussthestudiesongeneralagglomerationdynamics,inSection3.2.Section4concludes.2.AGGLOMERATIONINDICESAstheeconomicgeographyliteraturehasevolved,therehasbeenadivergencebetweenmodel-basedandaxiomaticapproachestotheagglomerationmeasurementquestion.2 ofsuchforces.Thisestimateiseasilyinterpreted,astheprobabilitythatarmchoosingitslocationfollowsthepriorrmratherthanlocatingrandomly.Further, EGiseasilycomputed,asitonlydependsonspatial-unitlevelinformationabouttheplantdistributionsoftheindustry.TheEG-indexiscomparableacrossindustrieswithvaryingrminsize-distributionsandcontrolsforoverallagglomerationtrends.Also,theEG-indexseparatesspatialaggregationfromthemeasurementofagglomeration.6FollowingtheEllison-Glaeser(1997)framework,MaurelandS´edillot(1999)proposedamodi-cationoftheEG-indexanddevelopedanewsequentialmodelofrmlocationchoice.First,theysuggestedtheso-calledMS-indexofgeographicconcentration MS, MS=(PMi=1s2i�PMi=1x2i)=(1�PMi=1x2i)�H 1�H:Thisindexisbasedontheweightedestimator,whichweightsplantspillovermeasurementsineachindividuallocationibythesizesoftheplantsinlocationi.IthappensthatE( MS� EG)=0,sothatMaurelandS´edillot(1999)maypiggybackonEllisonandGlaeser(1997)'swell-denednessresultsandmodel,sothat MScanalsobeseenasameasurementofthedifferencebetweenrmdistributionacrossindustryandrandomchance.Unfortunately,thisfacetofthemodelisnotdevelopedfurther.Inthesecondhalfoftheirpaper,MaurelandS´edillot(1999)envisionaprocessinwhichrmsrststudythenaturaladvantagesandpotentialspilloverbenetsavailableandchoosearegionRinwhichtolocateandthenchooseamorespeciclocation`2Rwithineachregion,basedonaregion-levelspillovermodel.Fromthismodel,theyareabletocomputeweighted“second-stage”concentrationmeasurements,whichtheyndtoberobusttothe“rst-stage”concentrationmeasurements.7TheEG-indexandMS-indexgivesimilarresultsonindustryconcentration.8Thisisnotsurpris-ing,giventhesimilaritiesinthestructureofthetwoindices.TheEllison-Glaeser(1997)framework,however,isnotcommontoallindices;itisnotevenusedinallofthediscrete-spaceindicies.Anewerbreedofdiscrete-spaceindiceshasreliedoncarefullyselectedstatisticaltestsattheexpenseofunderlyingmodels. 6Withtheirindex,EllisonandGlaeser(1997)measuredtheconcentrationlevelsofthe459four-digitindustriesclas-siedintheCensusBureau's1987SICsystem.Theyfound,atthestate-levelofspatialanalysis,thatover97%ofUnitedStatesfour-digitindustriesareagglomerated.7Thatis,theagglomerationlevelrankingsoftheindustriesfoundwiththesecond-stageconcentrationmeasurementsarequitesimilartothosefoundusingtherst-stagemeasurements.8MaurelandS´edillot(1999)computebothindicesforFrenchindustriesandnotethattheindicesagree,ingeneral,onthelistof“mostlocalized”industries.Thereismorevariationbetweenthetwoindiceswithrespecttotheleast-localizedindustries,butthisisnotsurprisingwhenoneconsidersthesmallvarianceof -valuesassociatedwithlowagglomerationlevels.Devereux,Grifth,andSimpson(2003)comparetheMS-indicesforFrenchandUnitedKingdomindustrieswiththeEG-indicesofAmericanrmsandndresultswhichsupportthebasicndingsofMaurelandS´edillot(1999).4 notdireclyobservable,sothatanaturalsampleestimate^piofpimustbeused,^pi=Ni PMi=1Ni;D(^pjp0)=MXi=1^piln^pi p0iD(pjp0):Mori,Nishikimi,andSmith(2005)proposetomeasureagglmerationthroughacomparisonbetweentheD-indexforanindustryandareferencemodelofcompletespatialdispersion.Thisapproach'svaliditystemsfromthefactthattheD-indexisalimitingformofthelog-likelihoodratioforthehypothesispip0.Thismeasurementisattractivebecauseitisindependentofsamplesize,12althoughitstillsuffersfromtheregularproblemsofthediscrete-spatialregionindices.TheD-indexcan,further,bedecomposedtogiveinformationaboutagglomerationacrossandamongregionalbundles,therebygivingameasurementsimilartothatobtainedinthetwo-stagemodelofMaurelandS´edillot(1999).TheD-indexvalueswerecomputedforJapaneseindustriesinMori,Nishikimi,andSmith(2005)andwerethencomparedtotheassociatedGiniindexvalues.13WhiletheD-indexandGiniindexgenerallydifferonacase-by-casebasis,theyarehighlypositivelycorrelatedforJapaneseindustries.14Nonetheless,thedifferencesbetweentheirrespectivedenitionsofthespatialde-centralizationreferencecasemakeitespeciallydifculttomakeanyrealisticcomparisonbetweenthesetwoindices.15Alloftheseindicesreportsimilarconclusions,aswewillseeinSection3.1.Theybenetfrom(relatively)loosedatarequirements,andsomealsohaveclearinterpretationsderivedfromeco-nomicchoicemodels.However,theyall,aswehaveobserved,sufferfromthesamedeciency:theyaggregatermsacrossdiscretespatialunits.Thisassumptionofdiscreteness,asnotedbyMori,Nishikimi,andSmith(2005)andbyBertinelliandDecrop(2005),ignoresgeographicrela-tionshipsbetweenlocationsandisthereforeaseriousdisadvantage.2.2.ContinuousIndices.Wenowturn,then,toindiceswhichavoidthediscrete-spaceassump-tionandworkinsteadwithcontinuousspatialmodels.Thesemeasurementsweredevelopedin 12Notethatsamplesizedoes,however,playaroleinthecondenceboundsonthecomputedvaluesofD.13Mori,Nishikimi,andSmith(2005)wereunabletoobtaintheestablishmet-sizedataneededinordertorunacom-parisonbetweentheD-indexandtheEG-orMS-indices.Hence,theysettledforacomparisonoftheirindexandtheGiniindex,whichtheyarguediscloselycorrelatedwiththeEG-index.AquicklookatTable4ofEllisonandGlaeser(1997)showsthatthisisnotaterribleassumptionforhighlylocalizedindustriesbutthatmorecaremaybeneededwhenworkingwiththemoredispersedindustries.14Itissuggested,however,thatthisisasideeffectofthefactthatJapaneseindustriesarelikelytohavesmallemploy-mentshareswhenevertheyarelocalized(seeMori,Nishikimi,andSmith(2005)).ItwouldbeinterestingtodothesamecomparisonforacountrywithdimensionsmoreregularthanJapan's.15Intheirdiscussions,Mori,Nishikimi,andSmith(2005)suggestthatonemightcreateafewnewindices^G,^Dtobridgethedividebetweenthetwomethodologies,buttheirideasseemfanciful.Inparticular,theysuggestthatonemightobtainmeaningfulresultsbyeithercomputingtheGiniindexoftheirprobabilitymeasuresortheD-indexofthethespatialorganizationvariablesofEllisonandGlaeser(1997);itisnotclearhowwewouldinterpretsuchmeasurements.6 slightlyfromDurantonandOverman(2005)'sownK-function)tocomputetheirmeasurementofspatiallocalization.Thisframeworklacksasupportingmodel,althoughitmaybepossibletoadaptthemodelofDurantonandOverman(2005).AnicecomparisonwasgivenbetweentheL-functionresultsandtheK-functionresultsfoundbyDurantonandOverman(2005).WhileMarconandPuech(2003)madethesomewhatsillyargumentthatDurantonandOverman(2005)shouldnothaveattemptedtobuildatoolfromscratchwhenasuitabletoolexisted,theyalsogaveaneffectivecritiqueofthequanticationfailuresofDurantonandOverman(2005)'sK-function.20SeveraladvantagesofDurantonandOverman(2005)'sK-functionovertheL-functionwereidentied,aswell.21Thesetwocontinuousmeasurementsshareonecorestrength:theyarebasedonabsolutedis-tancemeasurementsandhenceareindependentofspatialunitsizechoice.Theyarenotpronetothespuriouscorrelationswhichariseduringtheaggregationprocessesinthediscretemodels.However,bothDurantonandOverman(2005)'sandMarconandPuech(2003)'sstudiesrequiredmassiveamountsofdata—theyneededtheexactspatialaddressesofeveryrmintheirsample.Thesemeasurementswerealsocomputationallyintensivetocalculate.Further,whileitiseasytotestthestatisticalsignicanceofthesecontinousmodelsusingMonteCarlomethods,suchmeth-odsmakesomeoftheresultsirreproducible.Finally,weturntotheverypromisingworkingpaperofGuillainandLeGallo(2007),whichcombineddiscrete-spaceandcontinuous-spacemodelsofspatialagglomeration.GuillainandLeGallo(2007)focusedonthedistinctionbetweenclustering,whichtheyarguedcanbeidentiedbythediscrete-spacemeasurements,andagglomeration,forwhichclusteringisanecessarybutnotsufcientcomponent.Owingtodecienciesintheirdata,GuillainandLeGallo(2007)wereonlyabletocomputetheGiniindexandtheMoran'sIcoefcient22ofaregion,ratherthananyofthemoreadvanceddiscrete-spacestatistics.23Theythenusedexploratoryspatialmeasurestolookforspatialautocor-relation,whichwouldbeindicative,theyclaim,ofactualagglomeration.Forthistask,GuillainandLeGallo(2007)employedbothMoranscatterplotsandLocalIndicatorsofSpatialAssocia-tions(LISAstatistics).Theseindicatorsdeterminethelevelsofspatialclusteringexhibitedintheregionsurroundinganobservationofconcentration. 20TheK-functiondoesnoteffectivelycharacterizelevelsofdispersion(seeMarconandPuech(2003)).21ThemostpertinentisthattheK-functioncanbemodiedtocontrolforrmsizeandindustrialconcentration.Also,theK-functionneednotbecorrectedforedge-effects.22Sincethissecondstatisticisdifculttoexplainandnotespeciallyrelevanttoourdiscussion,weomitthedenitionhere.SeeGuillainandLeGallo(2007)orCliffandOrd(1981)formoreinformation.23Theseissuesarenotsalient,however,acrossmostdatasetsavailable;weexpectthatthemethodologyofGuillainandLeGallo(2007)couldbeimprovedthroughtheuseofanyoftheadvancedmeasurementsdiscussedinSection2.1andthatsuchimprovementsarerealisticwiththetoolsathand.8 unfortunate,asthemeasurementtechniquesofMori,Nishikimi,andSmith(2005)arehighlyin-dependentfromtheotherindiceswehavediscussed.ThelackofotherAsianindustrystudiesforcomparisonexacerbatesthealreadygreatdifcultyofevaluatingthisindex'seffectiveness.26Thecontinuousmodelshavenotbeenwidelyapplied,asitisverydifculttoobtainthedatarequired.Indeed,BertinelliandDecrop(2005)remarkedthattheywouldprefertohaveusedacontinuousmeasurementfortheirstudybutwereunabletoobtainsufcientlydetaileddata.Thus,theempiricalliteratureoncontinuousmeasurementsofagglomerationcanonlydrawonthefoundationalpapers'computations.DurantonandOverman(2005)computedtheirK-indexforUnitedKingdomindustries,atvaryinglevelsofdetail.BothMarconandPuech(2003)andGuillainandLeGallo(2007)computedtheirindicesforFrenchindustries,centeringontheParisarea.WhileGuillainandLeGallo(2007)dociteMarconandPuech(2003),theydonotundertakeacomparisonbetweentheresults.Ourinspectionrevealsthattheindustryclassicationsinthetwopapersdifferstarkly.Further,GuillainandLeGallo(2007)tendtodisagreewithMarconandPuech(2003)alongseveralimportantdimensions,includingtherelativeagglomerationstatusofthetextileindustry.273.2.MeasuringAgglomerationDynamics.Withtherecentsurgeofagglomerationindexlitera-ture,attentionhasalsobeengiventothepotentialapplicationsofagglomerationmeasurements.Ingeneral,thesestudieshavereliedonthediscreteindiceswhichgiverisetoclearmodels.Anearlystudyinthisvein,AudretschandFeldman(1996),usedtheGiniindextoidentifylinksbetweenspatialagglomerationinmanufacturingindustriesandindustry-speciccharacteristics.Inparticular,knowledgespilloverswerefoundtobeespeciallyimportantindetermininglevelsofindustryagglomeration.EllisonandGlaeser(2002)appliedtheEG-indextoastudyoftheimportanceofnaturaladvan-tagetoindustrialagglomeration.Thisstudyconcludedthat20%ofmeasuredagglomerationlevelsarisethroughthenaturaladvantagepathway;EllisonandGlaeser(2002)conjecturedtheactualexplanatorypowerofnaturaladvantagetobecloserto50%.28Inacomprehensivestudy,RosenthalandStrange(2001)regressedtheEG-indexonaselectionofimportantindustrycharacteristics:knowledgespillovers,labormarketpooling,inputsharing, 26Recallthat,asmentionedinSection2.1,above,theD-indexofMori,Nishikimi,andSmith(2005)isgenerallyincomparabletotheotherindices.27GuillainandLeGallo(2007)seemtosuggestthatsometraditionalindustriesinFrancearenotasagglomeratedastheotherstudiesclaim.Thismightbeseentocastdoubtupontheircomputationalmethods,asitappearsthatmostoftheconfusionisarisingfromtheGiniindexvaluesfoundintheirstudy.28Thisstudysufferedfromseveraldeciencies,notablythesmallnumberofadvantagevariablesconsideredandthe(seeminglyunnecessary)restrictionofthestudytomanufacturingindustries.Amoresalient,methodologicalproblemwhichisbarelydiscussedbyEllisonandGlaeser(2002)istheignoranceofphysicalspatialcharacteristicsinherentinthediscretemodel;thisdistortionabstractsthenotionoflocalnaturalfeatures.10 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