©CopyrightJASSS

Jung-HunYangandDickEttema(2012)

ModellingtheEmergenceofSpatialPatternsofEconomicActivity

JournalofArtificialSocietiesandSocialSimulation 15(4)6<http://jasss.soc.surrey.ac.uk/15/4/6.html>

Received:09-Oct-2011Accepted:28-Aug-2012Published:31-Oct-2012

Abstract

Thispaperdescribesasimulationmodelofthespatialdevelopmentofeconomicactivitiesovertime.Thekeyprincipleaddressedishowspatialpatternsofeconomicactivityemergefromdecisionsofindividualfirms,whichareinturninfluencedbytheexistingspatialconfiguration.Astylizedsimulationispresented,inwhichtwotypesoffirmsgrowatdifferentrates,givingrisetosplitoffsandspatialrelocations.Theinfluenceofthespatialpatternonindividualfirms'decisionsisimplementedinvariousways,relatedtowell-knowneffectssuchasJacobsandMarshallexternalitiesdescribedintheeconomicliteratureandcongestioneffects.Wedemonstratethatdifferentassumptionsaboutthespatialscaleoftheseexternalitiesleadtodifferentspatialconfigurations.Functionconcentration(Marshalleffects)ismorelikelytoleadtotheemergenceofsubcentreswithaspecificspecialisation.However,thespatialscaleofthemarketandagglomerationeffectsmatters.Inparticular,ifMarshalladvantagesstretchoutoveralongerdistance,moresubcentresemerge.Somewhatsurprisingly,congestionseemstohaveaminorimpactontheemergingpatterns.Thesimulationoutcomesareintuitivelyplausible,suggestingthatmicro-simulationisapromisingtoolfordevelopingforecastingmodelstosupportspatialandeconomicpolicies.However,theyalsoarticulatetheneedforvalidationofthebehaviouraldecisionrules,inparticularbyinvestigatinghowgrowthratesandthespatialscaleofexternalitiesdiffersbetweendifferentindustrialsectors.

Keywords:FirmLocation,Externalities,SpatialPattern,Micro-Simulation

Introduction

1.1 Thespatialpatternofeconomicactivitiesisanimportantdeterminantofurbandevelopment.Locationsoffirmsinfluencewhereworkerswilllive,whereconsumerswillbuyproductsandwhereotherfirmsarelocated.Thelocationsoffirmsalsoimpactontransportationflows,sincetheyareimportantattractorsandproducersofbothpersonalandfreighttraffic.Finally,thespatialpatternoffirmsobviouslyhasaprofoundimpactontheeconomicviabilityandconditionsforeconomicgrowthinaregion.Throughthedecades,therefore,researchershavedevelopedmodelsthatdescribeandpredicthowspatialpatternsofeconomicactivityemerge.

1.2 Aratherrecentdevelopmentistheuseofmicro-simulationmodelsforthispurpose.Insuchmodels,individualfirmsratherthanthenumberoffirmsoremployeesinacertainspatialunitaremodelled.Theunderlyingideaofsuchapproachesisthatbymodellingindividualfirms,theprocessesthataretheoutcomeoftheaggregationofbehavioursofindividualfirms(e.g.spatialconcentration)canbebestunderstoodandmostreliablymodelled(Benensonetal.2004).Itisimportanttodistinguishatthisstagebetweenmicro-simulationmodelsandagent-basedmodels.Whereasmicro-simulationmodelsencompassallmodelsthatarebasedonrepresentingindividualdecision-makers(inthiscasefirms)inordertofindaggregateeffects,agent-basedmodelscanbeconsideredamorespecificclassofmodelsassigningspecificcharacteristicstotheindividualdecision-makersthataremodelledthatallowtoclassifythemasagents(Grimmetal.2006;MacalandNorth2010).Inparticular,agentsareassumedtobeself-directed,implyingthattheymakeindependentdecisionsinresponsetoinformationacquiredfromtheirenvironment.Inaddition,agentsareassumedtobesocial,inthesensethattheyinteractwithandexchangeinformationwithotheragentsandareabletorecognizecharacteristicsofotheragents.Agentsarealsoassumedtobeadaptive,meaningthattheyareabletolearnfromexperiencesandtheirenvironmentandconsequentlychangebehaviouralrules.Thesebehavioursaresupposedtoleadtogoalsandagents(inordertolearnandadapt)willcomparetheoutcomesoftheirbehaviourstotheirgoals.Finally,agentsaretypicallyheterogeneous,inthesensethattheydifferintermsofsalientcharacteristics.Totheauthors'knowledgeagent-basedmodelsofeconomicdevelopmentmeetingtheabovedefinitionarenotyetexisting.However,inlanduseandhousingmodels,variousexamplesexistofmodelsthatdescribehowaggregatepatternsoflanduseorpricelevelsemergefromthebehaviourofagentsasdefinedMacalandNorth(2010).Sinceadetaileddiscussionofthesemodelsisbeyondthescopeofthispaper,wereferhousingmarketandlandusemodels(Berger2001;Brownetal.2006;Diappietal.2008;Ettema2010;Ettema2011;Filatovaetal.2009;Maglioccaetal.2011;ParkerandFilatova2008)formoredetailsaboutthesevariousapproachesandlimitourdiscussiontomicro-simulationmodelsofspatialeconomicdevelopmentintheremainder.

1.3 Afirsttypeofmicro-simulationmodelsused(UrbanSim,SimFirms,ILUMASS)describestheevolutionofspatialeconomicsystemsasastochasticprocess,inwhicheventssuchasfirmgrowth,firmrelocation,spinoffsandtakeplacewithaprobabilitythatispredominantlyafunctionoffirmcharacteristics.InUrbanSim(Waddell2002),economicactivityisrepresentedintermsofindividualjobs,whicharetakenfromanindependenteconomicforecastingmodel,andareexogenoustothemodel.Thejobsaretreatedasindependententities(i.e.notorganisedinfirms),whicharedistributedacrossgridcells.ILUMASS(Moeckel2005)appliesamoreelaborateeconomiccomponent.Inparticular,itusesasyntheticdatabaseoffirms,whichmaytakedecisionsregardingrelocation,growthandclosure.Inaddition,newfirmsmayemergeataparticularbirthrate,whichisspecificpersectoranddependentongeneraleconomicgrowthrates.Oneofthemostelaboratemicro-simulationmodelsoffirms'developedtodateisSIMFIRMS(VanWissen2000).ThismodeldistinguishesthesameeventsasILUMASS(birth,growth,(re-)location,closure)butusesmoresophisticatedbehaviouralrules,accountingforsuchfactorsasmarketstress,spinoffsofexistingfirms,ageeffectsandspatialinertiainthecaseofrelocation.Marketstressisrelatedtotheconceptofcarryingcapacity,which,analogoustotheecologicalconcept,indicatesthemaximumnumberoffirmsthatanurbansystemcancontain.Carryingcapacityisoperationalisedasthedifferencebetweenmarketsupplyandmarketcapacity,whichisbasedonaggregateinput-outputmodels.Thus,themeasureistheoutcomeofaggregateconceptualisations,ratherthanonfirms'perceptionofdemandandsupply.Ingeneralthemicro-simulationapproachesareespeciallyinsightfultostudydemographicprocesses.Forinstance,theysufficetodescribewhatthedistributionacrosssectorsinaregionwillbegivensomeinitialsettingandgivenbirthrates,spin-offprobabilitiesetc.Anelementthatismuchlessdevelopedinthesemodelsistheroleofspatialproximity.Thefactthatfirmsclusterinordertoachieveagglomerationadvantagesisnotwellrepresented.Structuralchangesinspatialeconomicsstructures(e.g.theemergenceofneweconomiccentresduetochangesinindustries)arenotwellrepresented.Hence,itisconcludedthatexistingmodelsofeconomicdevelopmentcanberegardedasmicro-simulationmodels,inthesensethatforecastsareobtainedastheaggregationofindividualsimulatedfirmbehaviours.However,typicalelementsthatsetapartagent-basedapproaches,suchasagentsinteractingwithotheragents,changingtheirbehaviouralrulesandadapttheirbehaviourtochangedsituationsarelacking.

1.4 Asecondtypeofmodelsthathasrecentlyreceivedincreasedinterestadoptsamorestylisedapproachtomodellingtheemergenceofspatialpatternsofeconomicactivity.Itfocusesontheemergenceofhierarchiesofconcentrations(offirmsorpopulation)asaresultofsimplereproductionandmigrationrules.Simon(1955)showsthatbyassumingfixedreproductionratesandrelocationprobabilities,andassumingthatlargerconcentrationsattractmoremigrantsthanlowerconcentrations,ahierarchyofconcentrationsemergesthatfollowsapowerlawdistribution.Remarkably,suchpowerlawdistributionsmatchexistinghierarchiesineconomicconcentration(Frenkenetal.2007)andpopulationconcentrations(Pumain2006)verywell.Althoughapparentlythesesimplereproductionandmigrationrulestouchupongeneralprinciplesof

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spatialorganisation,thetheoreticalunderpinningofthemodelsissomewhatcumbersome(Krugman1996).Intheirmostbasicform,modelsassuggestedbySimonarenon-spatial.Thatistosay,therelativepositionofaconcentration(e.g.acityoracommercialarea)tootherconcentrationsdoesnotmatter,sincelocationalpreferencesofmigrantsonlydependonthesizeoftheconcentrationandnotonitssurroundings.Asaresult,abigcityonanisolatedplacewouldbeequallyattractiveasanequallybigcitysurroundedbyothercities.Thisassumptionisproblematicsinceitignorestheimpactofproximity.Forinstance,studiesinevolutionaryeconomics(Boschmaetal.2002)suggestthatproximitytootherfirmsmattersfortheirproductivityandinnovativecapacity,andthatthisproximityexceedsthepurelylocalscale.Inparticular,regionsplayanimportantroleinprocessesofeconomicinnovation,wherethesizeofaregiondiffersbetweentypesofindustries.Thus,althoughcorrectlyreproducingtheranksizedistributionofexistingeconomicandpopulationconcentrations,theSimonmodelfallsshortindescribingtheemergenceofclustersofeconomicdevelopmentonaregionallevel.

1.5 Fromtheabove,weconcludethatexistingmicro-simulationapproachestomodellingspatialeconomicdevelopmenthavesomeimportantlimitations.Mostimportantly,theroleofspatialproximitytootherfirmsisnotwellrepresentedinthesemodels.Yet,spatialproximityisregardedakeyfactorinstudiesofregionaleconomicdevelopment(Quigley1998;FujitaandThisse2002).AccordingtoFujitaandThisse(2002),McCannandVanOort(2009)andBeaudryandSchifauerova(2009),spatialproximityplaysakeyroleintheemergenceofsocalledagglomerationeffects,whichcanbeunderstoodasexternalitiesstemmingfromconcentrationoffirms,whichareunintentionalandnotrepresentedinmarketprices.Animportantdebatethathasbeenongoingoverthepastdecadesiswhetheragglomerationeffectsshouldbeunderstoodaslocalisationeconomies(Marshal1990)orurbanisationeconomies(Jacobs1969).Localisationeconomiesconcernintra-sectorexternalities,stemmingfromtheconcentrationofsimilarfirms.Suchexternalitiesmayconcernsharinginputs,relyingonalarger,specialisedlabourforce,exchangingspecialisedknowledge(throughcirculatingemployees)andreducingtransactionscosts(e.g.searchcostsforemployees)(seeDurantonandPuga2000;VanOortandMcCann2009).Urbanisationeconomies(Jacobs1969),incontrast,assumethatvarietyinskills,knowledgeandtypeoffirmsarekeytoeconomicdevelopment.Thesestemfromalargeraccumulationofeconomicactivityofanykind(acrosssectors).Itisarguedthatthewidervarietyoffirms/skillsmakesaregionmoreinnovativeandlessvulnerabletoeconomicsetbacks,sincenewproductsandservicesaremoreeasilydeveloped.Inaddition,alargeraccumulationoffirms,irrespectiveoftype,isassociatedwiththeexistenceoflargescaleurbanfacilitiessuchasuniversities,knowledgeinstitutes,tradeassociations,culturalorganisationsetc.,whichalsobolsterdevelopmentandexchangeofknowledgeandattractskilledworkers.Bothtypesofexternalitieshavebeentestedinempiricalsettings,andindicationsofbothhavefoundtoinfluenceregionaleconomicperformance.However,indicatorsandmeasurementscalesvarysignificantlyacrossstudiesandoutcomesofdifferentstudiesareofteninconsistent(BeaudryandSchifauerova2009).Apartfromtheseagglomerationeffects,whicharealsotermedcentripetalforces,firmsaresubjecttocentrifugalforces(FujitaandThisse2002).Centrifugalforcesincludecompetitionforfacilitiesandaccommodations,leadingtohigherprices,thespatialdispersionofdemandorcompetitionofworkers.

1.6 Despitethedebateandtheremainingunclarity,wefeelthatwhenmodellingeconomicdevelopmentinmicro-simulationmodels,thevariousformsofspatialexternalitiesshouldbeproperlytakenintoaccountonaconceptuallevel.Thispaperproposesastylisedmicro-simulationmodeloffirmdevelopmentandrelocationthatincludesbothMarshalandJacobseffectsaswellascompetitioneffects.Byvaryingtherelativeimportanceoftheeffectsandthespatialscaleatwhichtheywork,weaimatincreasingtheinsightintohowthesedifferentandpartlycounteractingeffectsallowdifferentaggregatepatternstoemerge.Suchinsightisregardedasanecessaryfirststepinthedevelopmentofmicro-simulationoragent-basedmodelsoffirmdevelopmentaspartof,forinstancelandusetransportinteraction(LUTI)models.Themodelthatisusedcanberegardedasamicro-simulationmodel,althoughtheindividualdecision-makingunitshavesomecharacteristicsthataretypicalforagents,asdefinedbyMacalandNorth(2010):thefirmscouldbetermedself-directedinthesensethattheyfindoptimallocationsbasedonautilitymaximisationruleandareheterogeneousintermsofbusinesstype,ageandsize.However,thefirmsarenotsocial,sincetheydonotinteractwithotherfirmsorobserveotherfirmsdirectly,andarenotadaptivesincetheydonotchangebehaviourrulesortacticsinresponsetochangesintheenvironment,inordertomeetamoreabstractgoal.Also,wedonotmodelcollectivesoffirms,byrepresentingthemassocialnetworks.Basedontheoutcomeswewilldrawconclusionsregardingthesensitivityofspatialeconomicdevelopmentontheassumptionsmadeabouttheexternalities.Specifically,atheoreticalframeworkisdevelopedinwhichmarketpotential,agglomerationbenefitsandcompetitionaffectlocationaldecisionsondifferentspatialscales.Themodeloflocationbehaviourisembeddedinademographicmodeloffirmgrowthandspin-offprocesses.

1.7 Thepaperisorganisedasfollows.Thesecondsection,ModelDescription,outlinesamodelthatdescribesthebehaviouralmechanismandtheimpactofdifferentformsofspatialproximity.Thethirdsection,StudyDesign,describestheapplicationofthemodelinaseriesofsimulations.Thefourthsection,SimulationResults,analysestheimpactsofspatialproximity,weightingeffectsandrelocationprobabilitiesontheemergingpatternsofeconomicactivity.Thepaperisconcludedwithconclusionsandsuggestionsforfurtherresearch.

ModelDescription

2.1 Inlinewiththemicro-simulationmodelsreviewedabove,ourmodeldescribesthespatialbehaviouroffirmsdynamicallyoveranumberoftimesteps.However,asfirmsmayconsistofmultipleestablishmentsanddivisions,thatmaytakeindividuallocationaldecisions,wetakethedivisionastheunitofanalysis.Wedefinedivisionsascoherentworkingunitswithaminimumandmaximumsize,dependentonthetypeoffirm.Firmsmaybeoftwoabstracttypes:'traditional'and'innovative'industries,whichhasimplicationsfortheirbehaviouralrules.Firmsarelocatedinalandscapeconsistingofsquarecells(alsotermedcities),definedbyauniformsizeandxandycoordinates,thatallowustocalculatedistancesbetweencells.Eachfirmislocatedinaparticularcell.Inaddition,eachcellhasasitscharacteristicsthenumberoffirmsofeachtypethatishosted,butalsomeasuresoftheproximityoffirmsofeachtypehostedbyothercells,aswillbediscussedintheremainder.

2.2 Thefirmbehavioursdescribedbythemodelaregrowth,spin-offandrelocation.Withrespecttointernalgrowth,weassumethatdivisionsinacertainsectorgrowuniformlywithafixedamountperyear.Inreality,growthrateswilldifferbetweenfirmsduetofactorssuchasqualityofmanagement,positioninanetworkoffirmsandgeographicalposition.Althoughwerecognisetheexistenceofsuchheterogeneity(Quigley1998),wewillnotincludeitinthisstudy,sincetheemphasisisontheimpactofproximityeffectsonrelocationdecisions.

2.3 Inparticular,weassumethatdivisionsizeSt+1inyeart+1equals:

(1)

2.4 Thisimpliesaconstantgrowthofoneunitperyear.Thus,growthspeedisinourmodelgivenexogenouslyandisnotinfluencedbystatevariablesoffirmsorcellsinourmodelsystem.Wefurtherassumethatdivisionshaveamaximumsizeδandthatgrowthbeyondthismaximumresultsinlesseffectivefunctioningofdivisions,e.g.throughincreasingoverheads.Hence,weassumethatifthemaximumsizeisreachedthedivisionwillsplit,resultinginanewdivision(spin-off).Toreflectdevelopmentsinproductandsectorlifecyclesaspin-offdoesnotnecessarilyresultinadivisionofthesametypeastheparentdivision.Forinstance,aspin-offofanindustrialdivisionmaybeadivisioninservicesorhigh-tech.Thisreflectsongoingshiftsineconomiesfromtraditionalindustriestohigh-techandfrommanufacturingtoservices.Inthestylisedmodelstestedinthisstudywewillassumetheexistenceofatraditionalandaninnovativeindustry.Theruleforoccurrenceofspin-offsis:

(2)

2.5 Thus,ifthemaximumsizeofatraditionaldivisionisreachedwithprobabilityφ,thespin-offisthenewtype.Thesizeofaspinoffis0bydefinition.Apartfromsuchdemographicprocesses,themodeldescribesfirms'relocationbehaviour.Relocationoffirmsmaytakeplaceformanyreasons,whichareusuallyconcernedwithinternalprocesses,suchasgrowthorsuitabilityofthebuilding(Lloydetal.1977;VanDijketal.2000).Insuchcases,therelocationislikelytotakeplacewithinthesame

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municipalityorregion,withoutstructurallychangingthespatialstructureoftheeconomy.Inthisstudy,however,weareparticularlyinterestedinthemorestrategicrelocation,inwhichdivisionsseektoimprovetheiraccesstomarketsandresourcesbymovingtoanothergeographiclocation.Inthisrespect,weassumethateachdivisionhasacertainprobabilitytoevaluateitscurrentgeographicalpositionagainstalternativepositionstotestwhetherrelocationresultsinanimprovementofitsconditions.Twooptionsaredistinguishedinthecaseofrelocation.First,adivisionmayinvestigaterelocationtoanexistingcity(definedasanexistingconcentrationoffirms),inanattempttoprofitfromproximitytofirmsofthesametype(Marshallexternalities)orfromotherfirmsingeneral(Jacobsexternalities).Second,afirmmayseekanewplacewithoutacurrentconcentrationoffirms.Inthatcase,immediateproximitytootherfirmsisnotthemotivation,butafirmmaylookforastrategiclocationthatmaximisesaccesstomarkets,suppliersetc.reachablewithinalargerbutstillacceptabledistance.Itisnoted,though,thatsuchstrategicconsiderationsmayalsoplayarolewhenchoosinganexistingcity.Inourstylisedmodel,citieswillbeequivalenttogridcellsinaplane.Weassumethattheprobabilitiesofnotexploringrelocationλ1,investigatingrelocationtoanexistingcityλ2andtoanewcityλ3are0.9,0.09and0.01respectively.Itisrecognisedthatdifferentprobabilitiesofrelocationmayresultindifferentspatialpatternsanddifferentdevelopmentspeeds.However,sincethefocusofourstudyisontheroleofspatialproximityintheemergenceofspatialpatterns,weusetheabovevalues,whichprovedtoworkwellinotherstudies(Krugman1996;Simon1955).

2.6 Incaseaspinofflooksforalocationinanother(existing)oranewcity,alocationisselectedbasedontheevaluationofalternativelocationsandrelocationtakesplaceasfollows.Afirmwillevaluatealllocationstofindthelocationwiththehighestutility.Ifthismaximumutilityishigherthantheutilityofthecurrentlocation,thedivisionwillmovetothisnewlocation,otherwise,itwillstayinitscurrentplace.

2.7 Thecentralissuewhendiscussingtheimpactofspatialproximityishowutilityisdefined.Inanon-spatialmodel,utilityofeachlocationwouldbeequal,suggestingarandomspatialprocess.Thespatialsensitivityofthemodelisimprovedifthelocationalpreferencedependsonthesize(numberofdivisions)inthedestination.Inthiscaseutilityisdefinedas:

(3)

whereUiistheutilityofareaiandNiisthenumberofdivisioninanareai.Inessence,thisisthemodelproposedbySimon,whichleadstothewellknownpowerlawdistributionofconcentrations.However,theSimonmodelislocalintermsofitsutilityfunction,sinceitonlyaccountsforfirmsinacertainlocation,andthesurroundingsarenottakenintoaccount,ignoringthefactthattravelallowsforinteractionbetweenfirmsthatarenotinthesamelocation.Theagglomerationeffectsreferredtointheintroduction(MarshallandJacobsexternalities)arelikelytooccuroverlargerdistancesthanforinstancewithin-municipalitydistance,providedthataccessibilitytootherplacesissufficient.Inthisrespect,thisstudyproposesandtestsutilityformulationsthatnotonlytakeintoaccountlocationalcharacteristics,butalsocharacteristicsofthesurroundings,suchastheproximitytootherfirms.Lookingatlocationalcharacteristicsoffirms,theliteraturesuggestsvariousfactorsrelatingtoproximityoffirmsthatclearlyexceedthepurelylocallevel.

2.8 Afirstfactorconcernsthe"Jacobs"potential.Asnotedbeforethisreferstotheproximitytoanykindoffirms,whichhasadvantagesintermsofdiversityofskills,innovativecapacityandprovidingacriticalmass(Ball2004;Garreau1992)forknowledgeinstitutesandtradeorganisationsandotherfacilities.Inaddition,proximitytofirmsingeneralserveasaproxyformarketpotential(Harris1954).Firmsmakeprofitsfromsellingproductsofservicestootherfirmsortoindividuals.Theshorterthetraveldistancetotheseclients,thelowerthecostsandthehighertheprofit.Inaddition,themoreclientscanbereachedwithinacceptabletraveldistancefromalocation,thelargerthemarketpotentialandthemoreattractivethelocationistosettle.Inthisrespect,thesensitivitytodistanceisthefactordeterminingthespatialconfiguration.Forcommongoods,suchasgroceries,willingnesstotravelislow.Formorespecialisedgoods/services,thewillingnesstotravelandthemarketareawillbelarger.Suchdifferencesindistancedecaywillhavealargeimpactontheemergingspatialpatternsofeconomicactivity.Takingtheaboveintoaccount,Jacobspotential(JP)canbedefinedas:

(4)

whereJPiistheJacobspotentialinareaiandNjispopulation(numberofdivisions)incityj.α1isaparameterforcontrollingthedistancedecayanddijisdistancebetweenareaiandcityj.AsecondfactorrelatedtospatialproximityistheMarshallexternalities.Manystudiessuggestthatfirmsbenefitfromproximitytosimilarfirms.Onereasonisthattheymayprofitfromsharedfacilitiesandsuppliers.Inaddition,somefirmsmaybebetterabletoattractclientsandemployeesjointlythanindividually.Anotherimportantissueisthatfirmsformnetworksinwhichknowledgeisexchanged,projectsarecarriedoutandmarketinformationisexchanged,inordertoachievecompetitiveadvantages.SuchMarshallexternalitiessuggestthatfirmswillprefertolocatenearotherfirmsfromthesamesector.Inequation,Marshalleffectsareexpressedas:

(5)

whereMPitypeistheMarshallpotentialofdivisionofspecifictypeinarea iandNj

typeisapopulationofdivisionsofaspecifictypeincityj.α2isaparameterforcontrollingthedistanceeffectanddijisdistancebetweenareaiandcityj.Itisrecognisedthatagglomerationadvantagesfordifferentsectorsmaydifferinimportance,e.g.duetotherelativeimportanceofknowledgeandinnovationinasector.Alsothescaleofagglomerationadvantagesmaydiffer,duetothetypeofinteraction,e.g.havingsimilarconsumersasksforimmediatephysicalproximity,whereasexchangeofknowledgeviapersonalmeetingsallowsalongertraveltime.

2.9 Finally,havingnotedtheadvantagesofbeingclosetootherfirmsandclients,wenotethattherewillalsobedisadvantages.Increasingdensityleadstocongestionofinfrastructureandfacilities,butalsotohigherpricesandincreasingcompetitionforemployeesandotherresources.Notethatcongestionisnotsectorspecific,inthesensethatfirmssufferfromcongestioncausedbyallotherfirms.Inequations:

(6)

whereCPiisthecongestioneffectinareaiandNjispopulationincityj.α3isaparameterforcontrollingdistanceeffectanddijisdistancebetweenareaiandcityj.Again,wenotethatsensitivityofcongestionmaydifferbetweenfirmtypes,duetotheirneedforspaceandinfrastructureandtherequiredqualificationsoftheiremployees.However,alsotheadvantageofagglomerationwillbeweightedoffagainstthedisadvantageofcongestion.Asaresult,theSimonutilityofexpression3canbetransformedas:

(7)

(8)

whereUiistheutilityinanareaiandJPiisthemarket(Jacobs)potentialinanareai.MPitypeistheagglomeration(Marshall)potentialoftypetandCPiisthecongestion

effectintheareai.Therelocationprobabilitycanthenbedefinedas:

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(9)

wherePiistheprobabilityofareaiforrelocation.Thisfunctionisappliedbothformigrationtoexistingcitiesandformigrationtonewcities.

2.10 Tosummarise,ourmodelassumesthatgrowth,spin-offandrelocationaretheguidingbehavioursleadingtotheemergenceofaggregatepatternsofeconomicactivity.Theseaggregatepatterns,inturn,determinetheMarshall,Jacobsandcongestioneffectsthatinfluenceindividualfirms'relocationbehaviours.Thus,aniterativemulti-scaleprocessresults,asillustratedinFigure1.Whereasgrowthisauniformandautomatedprocess,thespin-offandrelocationprocessisstochasticinnature,implyingthatsimilarinitialsettingsmayleadtodifferentoutcomes.Althoughbothtypesoffirms(traditionalandinnovative)haveinessencethesamebehaviouralrules,theparametersforweightsofdifferenteffectsanddistancesensitivitydiffer.Wehypothesizethatthepreferencesoffirmswithrespecttoproximitywilldeterminethespatialconfigurationofeconomicactivities.Forinstance,agglomerationadvantagesonasmallscalewillleadtomultiplecentresofeconomicactivity,whereasagglomerationadvantagesonalargerscalemayleadtoasinglecentre.Intheremainderofthispaperwewilltesttowhatextentdifferencesinthespatialscalewillleadtodifferentspatialconfigurations.

Figure1.Multi-scaleprocessineachtimestep

StudyDesign

3.1 Althoughwerecognisethatmanyfactorsotherthandiscussedbefore(suchastheavailabilityoffacilities,pathdependencyetc.)impactonfirms'locationchoice,wewilluseastylisedsettinginwhichwewilltestsomefundamentalrelationshipsbetweenindividualpreferencesoffirmsontheonehand,andaggregatespatialpatternsontheotherhand.Inparticular,weassumethatfirmsoperateinalandscapethatishomogeneousintermsoftravelspeedsandqualityoflocations,andonlyvariesintermsofthepresenceofotherfirms.Thelandscapeconsistsofasquareof50×50cells.Initially,att=0,thelandscapeisfilledwith2500divisions(oneineachcell),whichineachtimestepwillgrow,reproducespin-offswithsomeprobabilityandwithsomeprobabilityrelocate.Thelikelihoodandeffectuationoftheseeventsisdeterminedbytheequationsdescribedintheabove.Theprocessisorganisedsuchthatprecedingeachtimestep,theMarshall,Jacobsandcongestionmeasureforeachcelliscalculated,basedonthespatialdistributionoffirmsatthatstage.Then,foreachfirm,growth,spin-offandrelocatedaresimulatedasdescribedabove,basedonthecalculatedJacobs,Marshallandcongestionmeasures.Thisleadstoachangeinthespatialconfiguration,necessitatingrecalculationoftheMarshall,Jacobsandcongestionmeasures,whichareinputtoanextstepoffirmsimulation.ThiscyclicprocessisdisplayedinFigure1.Totesttheimpactofdifferentpreferencesofspatialproximity,themodelwillberunwithdifferentparametersduring50timesteps,afterwhichtheresultingpatternisanalysed.Thisanalysiswillincludethreeelements.Sincewepresentastylizedmodel,timeanddistanceunitsdonothaveameaning,andwewillfocusondifferencesinemergentpatternsbasedondifferenceinthesensitivitytothisabstractdistance.

3.2 First,theresultingpatternswillbeinterpretedvisuallyintermsofthenumberandsizeofemergingclustersofeconomicactivity.Second,thedistributionofranksizeswillbeplotted,toseewhethertheresultingpatternsfollowthepowerlawdistributiontypicalforurbanandeconomicdistributions(Simon1955;Pumain2006).Third,thedegreeofclusteringisexpressedusingtheformula:

(10)

(11)

whereKextensionistheclusterdensityandNisthetotalnumberofdivisions.C(si,d)isacirclewithdistancedfromsi(Kosfeldetal.2011;Marconetal.2003).Thisindexhasahighervalueifmoredivisionsareclosertooneanother.Theindexiscalculatedwiththedistance10forthepurposeofourstudy.

Table1:BaseModel

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Model1 Model2 Model3 Model4 Model5 Model6 Model7

Parameter Type Empty OnlyJP JP+MP

JP+MP+CP

LargerJP LargerMP LargerJP+MP

JP α1 Traditional 0.6 0.6 0.6 0.6 0.6 0.6 0.6

Innovative 0.5 0.5 0.5 0.5 0.3 0.5 0.3MP α2 Traditional 0.6 0.6 0.6 0.6 0.6 0.6 0.6

Innovative 0.5 0.5 0.5 0.5 0.5 0.3 0.3CP α3 Traditional 0.6 0.6 0.6 0.6 0.6 0.6 0.6

Innovative 0.5 0.5 0.5 0.5 0.5 0.5 0.5JPeffect β1 Traditional 0 1 1 1 1 1 1

Innovative 0 1 1 1 1 1 1MPeffect β2 Traditional 0 0 0.5 0.5 0.5 0.5 0.5

Innovative 0 0 0.5 0.5 0.5 0.5 0.5CPeffect β3 Traditional 0 0 0 -1 -1 -1 -1

Innovative 0 0 0 -1 -1 -1 -1MaximumGrowth

δtrad Traditional 0 0 0 -1 -1 -1 -1

δinno Innovative 0 0 0 -1 -1 -1 -1

RelocationProbability

λ2 Traditional 0 0 0 -1 -1 -1 -1

λ3 Innovative 0 0 0 -1 -1 -1 -1

TimeStep 50 50 50 50 50 50 50Probabilityofturningintoinnovative

φ 0.01 0.01 0.01 0.01 0.01 0.01 0.01

3.3 Thestartingpointoftheanalysesisabasespecificationofthemodel,withparametersspecifiedasinTable1.Thistablefollowsthefollowinglogic.First,startingfromaSimon-typemodelwithoutlocationalpreferences(βarezero),variousspatialfactorsareaddedstepwise,toseehowthischangestheresultingpattern.Inaddition,amodelwithonlycongestioneffectsandamodelinwhichcongestionhasadoubleweightaretested.Second,theimpactofdifferentspatialfactorswillbevariedbychangingtheαparameter,inordertofindouthowthisrelativeimpactaffectsthespatialpatternofeconomicactivity.Theseanalysesarefollowedbytwoextensions.First,themodelsarerunwithvaryinginitialconditions:

1. 2500initialfirmsbeingrandomlyallocatedtocells2. 25initialfirmsbeingrandomlyallocatedtocells

3.4 Finally,basemodel4willberunwithvaryingvaluesfortheparameterslambda,toseehowthatinfluencestheresultingspatialpattern.Itisrecognisedthattheseanalysesdonotservetofind'true'orrealisticparametersettingsasabaseforsimulationsinmoreconcretesettings.However,byvaryingmodelparametersinasystematicwaywewanttoexplorehowarelativeemphasisonacertainfactor(Marshallexternalities,Jacobsexternalities,congestion)hasimplicationsforemergingaggregatepatterns.

SimulationResults

4.1 Asshowninfigure2(whichrepresentsModel4withJacobs,Marshallandcongestionpotential),theinitialstateofsimulationisthatthedivisionofoldtypeisequallydistributedacrossallregionswhichconsistsof2500cells(50by50).Adivisioninthetraditionalindustrygrowsineachtimestepleadingtoaspin-offorrelocation.Theutilityandprobabilityformigrationalsofollowtheexpressions8and9respectively.Thefigure2showsthatthespatialpatternoftraditionalindustrychangedfromanevenlydistributedpatternintoaclusteredspatialpattern.Concerningtheemergenceofainnovativeindustry,weassumeagrowthrateoftheinnovativeindustryisfivetimeshigherthanthatofthetraditionalindustry.Thedifferentparametersforthetraditionalandinnovativeindustryclearlyaffecttheirpatternofevolution.Theinnovativeindustryemergesbothinnewagglomerationsandinexistingagglomerations.Thiscanbeunderstoodfromthefactthattheinnovativeindustryprofitsfromagglomerationeconomiesofco-locationwithfirmsoftheownkind(whichexplainstheemergenceofnewagglomerationsespeciallyinthebeginningoftheprocess)aswellasfromproximitytodemand(explainingthegrowthoftheinnovativeindustryintheexistingagglomerations).Theresultingspatialpatternaftertheinnovativeindustryhasemerged,hasbecomemore"Zipf-like"(Zipf1949)inthesensethatwecanwitnesscitiesofdifferentsizeswiththefrequencyofparticularsizedecreasingwithincreasingsize(figure3).Ourmodelthusunderlinestheneedtounderstandthespatialstructureofaneconomyasahistoricalprocessofstructuralchangeleadingtoaprogressivediversificationoftheeconomy.

(celldensity:low-high )

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Figure2.Timeseriesforbasemodel4

Figure3.Ranksizedistributionforbasemodel4

Theimpactofspatialproximity

4.2 Thefirstmodel(model1)thatistestedisonlybasedongrowthandspin-offprocesses,lackingspatialpreferences.ThismodelisrathersimilartotheSimonmodel,exceptforthefactthatSimon'smodelassumesthatcellswithmoredivisionsaremorelikelytoattractnewcomers,whereasinourmodelallcellshaveequalprobability.Ascanbeseeninfigure4,thismodelresultsinapatternwithoutcentres,withdivisionsscatteredoutoverspaceandfilledallcells.

BaseModel1CDI=15.66

BaseModel2CDI=32.97

BaseModel3CDI=32.81

BaseModel4CDI=29.73

(celldensity:low-high )Figure4.Theimpactofspatialproximity

4.3 Thesecondmodel(model2)includestheproximitytobothtraditionalandinnovativeindustryfirms,representingJacobspotential.Thesecondpictureoffigure4suggeststhataddingmarketpowerresultsinamoreclusteredconfiguration,withonelargecentre.Intimestep50,asmallersubcentrehasemerged,whichmayintimedevelopintoanewcentre.Thus,theJacobseffectactsasacentripetalforceleadingtoahigherdegreeofconcentration(32.97against15.66formodel1).However,path

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dependencyallowsfortheemergenceofsubcentres.Notalsothatinnovativeindustriesaremoredispersedwithinthebiggeragglomeration,sincetheydonotspecificallylooktobeclosetofirmsoftheirowntype.Itisnotedthattheclustersarenotuniformintermsofdensity.Thisisduetodifferencesbetweencellsintheinitialconditions,whichcarryforwardtolaterstates.Thus,cellswithinaclusterthathavealreadyattractedmorefirms,aremorelikelytodosoinlaterstages,duetothefactthattheyresultinthehighestMarshallandJacobseffects.

4.4 Thethirdmodel(model3)includesJacobsandMarshalleffects.Thesimulationsuggeststhatthismodelalsoleadstoclusteringofdivisions,withonelargecentre.However,agglomerationmay,sinceitaddsMarshalleffectassimilarfirmtypes,moreeasilyresultinlocalclusters.Inthissimulationinnovativefirmsclustermorearoundalimitednumberofaxeswithinthecentralarea.Thedegreeofclustering(asexpressedbytheCDI)issimilartothecasewhereonlyJacobsexternalitiesaremodelled.

4.5 Model4,addingtheimpactofcongestiontothemodel,resultsinapatternwithonecentrelikethefourthpictureoffigure4.Overall,theeffectofcongestion,whichiscounteractingtheJacobsandMarshallexternalities,leadstoaslightlylowerdegreeofclustering,asexpected.Inparticular,theinnovativeindustries,whichareslightlymoreflexibleinlocation(sinceinitiallytheydonotexperienceMarshalleffects),locateinanadjacentsubcentrethatgrowsthroughpathdependency.

4.6 Finally,usingcongestionastheonlyspatialimpact(model4b)ordoublingitsimpact(model4c)leadstosimulationsinwhichcentripetalforcesaredominant.Themaindrivingforceisthatfirmsseektomaximisethespacebetweenthem,leadingtodispersedpatternsasinfigure5.Consequently,thedegreeofclusteringissignificantlylower.

Celldensity Potential Celldensity Potentialβ1=0,β2=0,β3=-1 β1=0,β2=0,β3=-2

BaseModel4b BaseModel4cCDI=12.35 CDI=12.54

(celldensity:low-high )(cellpotential:low-high )

Figure5.Theimpactofcongestion

Weightingeffects

4.7 InthissectionvariousmodelsinwhichthespatialreachimpactofJacobsandMarshalleffectsisvaried,arediscussed.Asseeninfigure6,Model5hasalowerα1fortheJacobspotentialimplyingalowerdistancedecayfunction(e.g.becausetransportcostsarelower).Thismodelresultsinaspatialpatternwithonelargecentre,whichismoreclustered(CDI=35.95)thanthebasemodel(model4)andthemodelswithoutcongestioneffects(models2and3).Apparently,thegeographicallylargerreachhastheeffectthatallrelocatingfirmsareattractedbythecentralarea.Also,innovativefirmsaremorespreadoutacrossthecentralarea.

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BaseModel5CDI=35.95

BaseModel6CDI=31.96

BaseModel7CDI=35.27

(celldensity:low-high )Figure6.Theimpactofweightingeffects

4.8 Model6increasesthespatialscaleofMarshalleffectsthroughalowerα2fortheagglomerationpotentialofinnovativeindustries.Thisresultsinapatternwithasub-centrefortheinnovativeindustries.Apparently,thelargerspatialreachincreasestheattractivenessoflessdensely'populated'areas,increasingalsotheprobabilityofsubcentresemerging.Inturn,ifaninnovativefirmsettlesintheperipherybychance,itwillbemorelikelytoattractothersinthevicinity,duetothelargerreach.Yet,theclusterindexhasahighvalue,suggestingthatwithinandaroundtheclustersaccessibilitytootherfirmsishigh.Thisisalsotheresultoftherelativeclosenessoftheclusters.

4.9 Model7,inwhichbothJacobsandMarshalleffectshavealargerspatialreachforinnovativefirms,clusteringdegreeishigh,asinmodel5.Apparently,theJacobseffectsexhibitastrongcentripetalforceonallinnovativefirms,duetothespatialreach.Thisleadstoahigherdegreeofclusteringoverall.

Theeffectofinitialconditions

4.10 Thesimulationsformodels1-7wererepeatedwithdifferentinitialsettings:

1. 2500initialfirmsbeingrandomlyallocatetocells2. 25initialfirmsbeingrandomlyallocatedtocells

Condition1representsanincreasedflexibilityofthesystemintheemergenceofcentres.Accidentalclustersintheinitialstagearelikelytodevelopintooverallcentres,duetoMarshallandJacobseffects.Condition2increasestheeffectofpathdependencyevenmore,sinceitstartsfrom25firms,suggestingthatonce2500firmsarereached,theirconfigurationissubjecttotheMarshall,Jacobsandcongestioneffectsasspecified.Althoughcareshouldbetakennottodrawgeneralconclusionsbasedonsinglesimulations,anoverallpatternseemstobethatthecentrallocationismuchlessdominant.Thisfollowslogicallyfromtheincreasedprobabilitythatlocalperipheralclustersgrowintomaincentresofeconomicactivitythroughaprocessofpathdependency.Inasimilarvein,theprobabilityofmultiplecentresincreases,sincetwoaccidentalclustersmayattractrelocatingfirmsatasimilarrate.Ifthishappens,thisresultsinalowerdegreeofclustering,asexpressedbytheCDI.Invariably,however,modelsinwhichbothJacobsandMarshalleffectsarepresent,leadtothehighestdegreeofclustering.

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BaseModel1CDI=15.39

BaseModel2CDI=26.12

BaseModel3CDI=31.92

BaseModel4CDI=29.70

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BaseModel5CDI=35.74

BaseModel6CDI=19.73

BaseModel7CDI=27.58

(celldensity:low-high )Figure7.2500initialfirmsbeingrandomlyallocatetocells

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BaseModel1CDI=13.14

BaseModel2CDI=29.90

BaseModel3CDI=31.14

BaseModel4CDI=30.58

BaseModel5CDI=21.86

BaseModel6CDI=28.67

BaseModel7CDI=30.24

(celldensity:low-high )Figure8.25initialfirmsbeingrandomlyallocatedtocells

Theimpactofrelocationprobabilities

4.11 Totesttheimpactofrelocationprobabilities,thevariablesλ2andλ3werevariedtorepresentahigherrelocationprobabilityofmovingtoanexistingcityingeneral(mostlydeterminedbyλ2)andahigherprobabilityofmovingtoanewcity(λ3).λ1isalwaysdefinedas1-(λ2+λ3).Foreachcombination,theemergingspatialpatternaswellastheclusterindexisdisplayed(figure9).VisualinspectionoftheemergingpatternsandtheCDIsuggeststhatwithhigherλ2,thedegreeofclusteringincreases,whereasitgoesdownwithincreasingλ3.Thus,ahigherprobabilitytomovetoanexistingcity(anoccupiedcellinourcase)increasestheprobabilitythatfirmsadheretocentripetalforces(MarshallandJacobseffects).Ahigherprobabilityofmovingtoanewcity(unoccupiedcell)asindicatedbyλ3maydiminishthiseffect,sinceunoccupiedcellsaremoreoftenlocatedintheperiphery.Itisnoted,though,thattherelativeeffectofvariationsinλ2andλ3ismuchlessthanchangingthepresence,sizeandspatialreachofMarshall,Jacobsandcompetitioneffects.

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(celldensity:low-high )Figure9.Variationofλbasedonbasemodel

ConclusionandDiscussion

5.1 Inthispaperwehavedemonstratedinastylisedsetting,howdifferencesinpreferenceswithrespecttospatialproximityleadtodifferentspatialpatternsofeconomicactivity.Inthisrespect,apreferencetoachieveahighlevelsofJacobsexternalitiesandtoprofitfromMarshallexternalitiesresultsinmorecentralisedsettings.Thesimulationssuggestatendencythatfunctionconcentration(Marshalleffects)ismorelikelytoleadtotheemergenceofsubcentreswithaspecificspecialisation.However,thespatialscaleofthemarketandagglomerationeffectsmatters.Inparticular,ifMarshalladvantagesstretchoutoveralongerdistance,moresubcentresemerge.Somewhatsurprisingly,congestionseemstohaveaminorimpactontheemergingpatterns.Althoughthesimulationoutcomesareintuitivelyplausible,theyalsoarticulatetheneedforvalidationofthebehaviouraldecisionrules.Ifoutcomesaredeterminedbythepresence(andpotentiallystrength,althoughnottestedinthispaper)andspatial

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reachofJacobspotential,Marshallandcongestioneffects,itisimportanttoinvestigatehowfirmsofdifferenttypesvaluatethesefactorsintheirlocationchoicebehaviour.Inparticular,itisimportanthowthevaluationofthesefactorsvarieswithfirmcharacteristicssuchastypeofactivities,size,historyandthepositionineconomicnetworks.Suchinformationwouldbenecessarytoapplytheaboveapproachinamorerealisticsettingasapolicysupporttool.Asecondconclusionthatcanbedrawnfromthesimulationsisthatrelocationprobabilitytoexistingandnewcitiesimpactsontheemergingpatterns.Thisfindingishighlypolicyrelevant,sinceitsuggeststhattheavailabilityoflocationswherefirms/divisionscanmovehasasignificantimpactonspatialpatternsofeconomicactivity.Ifthisisconfirmedbyvalidationstudies,itwouldsuggestthatspatialplanningisatoolthatcandirectlyimpactontheeconomicstructureofregionsandwillinfluencefirms'performanceandtherebyregionaleconomicdevelopment.

5.2 Althoughthisstudyprovidesfirstinsightsintotheemergenceofspatialpatternsofeconomicactivity,itisobviousthatmuchmoreresearchisneededtodevelopthisapproachintoatoolthatcanbereadilyusedforpolicyanalysis.Thisresearchshouldaddressthefollowingissues.First,thebehaviouralrulesappliedinthistestofconceptneedtobeverifiedandrefined.Inparticular,multivariateanalysesareneededthatrelatefirmcharacteristicstothedegreeandspatialreachofproximitypreferences.Thiswillrequirededicateddatatobecollectedfromindividualfirms.Second,itshouldberecognisedthatfirmsdonotoperateinisolation,butinteractwithhouseholdsandindividuals(asclientsandemployees),institutions(suchasgovernmentagencies,universities,schoolsetc.)andreacttothephysicalenvironment(landscape,qualityofresidentialenvironment,pollutionandnoise).Apropermodelforpolicyevaluationshouldincludearepresentationofhowproximityconcernsaretradedoffagainsttheseotherfactors.

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