EUROPEANCENTRALBANKEUROSYSTEMClémenceBerson,Pierre-PhilippeCombes,LaurentGobillon,AurélieSoturaTime-varyingagglomerationeconomiesandaggregatewagegrowthDisclaimer:ThispapershouldnotbereportedasrepresentingtheviewsoftheEuropeanCentralBank(ECB).TheviewsexpressedarethoseoftheauthorsanddonotnecessarilyreflectthoseoftheECB.Abstractfortyyears.First,wede?necitiesdynamicallytoaccountfortheirchangingfootprints.Our?ndingsshowthataggregatewagthansmalleronesorbypopulationshiftsacrosscities.Weestimateindividualwageporatingtime-varyingcityandindividual?xedefects,andanalysehowcitycharacteristics(employmentdensity,area,andmarketaccess)andthChangesinthevaluesofthesecharacteristicshaveminimalefect,butchangesintheirre-turnssigni?cantlyin丑uencewagearnings,supportingourempirical?ndings.JELCodes:R23,J31,J61ECBWorkingPaperSeriesNExecutivesummaryOurcontributionisthreefold.First,wedelineatecitieseveryyear,enablingustocapturedensity,landarea,andmarkin丑uencemigrationpatternsand?rmrelocationsbetweencities,which,inturn,afecttheredistributionofeconomicadensityeachyearonthebasisofCEREMAandBDTOPOdata,whichincludesthefootprint,mergers,andabsorptions,incontrasttostudiesthatviewcitieECBWorkingPaperSeriesNotovaryovertime.Our?ndingsshowthattheelasticityofwagagglomerationvariableswithhistoricalcitycharacteristicswagedisparities.Inparticular,weobservethatlargecitiesdisplayincreasingreturnstoscale,driverofwagegrowth,whileshiftsincitycharacteristicscontributelesssigni?cantly.speci?edasaCobb-Douglasfunctionofcitycharacteristics,inlinewithourempiricAlthoughthemodelcannotbesolgestthatwhilethedirectefectsaresubstantial,theindichangesincitydensityandlandarea—arerelativelysmall.Thisalignswithourempiricalob-afectnationalwagegrowthunlesstheysigni?cantlyalterreturnstocitycharacteristics.distributionsinFrance.Thisunderstandinghasimplicationsforurbanpolicy,suggestingthatefortstoimprovecityproductivityshouldfocusoratherthanmerelyexpandingcityboundaries.Largercitiesbene?tdisproportionateefectiveinshapingaproductiveandequitableECBWorkingPaperSeri1IntroductionOverthelast?ftyyears,citieshavegrownsteadilyworldwide,thoughatdiferentrates.ManyThisstudyaimstoquantifythesimultaneousroleofchangesincitycharacteristicsandtheirdata.Ourcontributionisfourfold.First,wedelineatecitiesannuallytoproperlyconsidertheareafectedbybothdirectefectsduetochangesinreturnstocitycharacteristicsandindirectAmericaandWesternbeforestabilizing.Giannone(2022)andEckertetal.(2022a)reconciletwiththespatialdifusionoftechnoloafectedlargecities.Wedepartfromthisliteraturebyconsideringasystemofcitieswithvary-fECBWorkingPaperSeriesNoandPietrostefani,2019;DurantonandPuga,2020).Inparticular,Combesetal.(2008)esti-observables.1TheirworkEckertetal.,2022b).Contributionsinahistoricalpersrivedfromawagespeci?cationthatalsoincludesindividual?xedefecCardetal.,2024).Thisindirectapproachmitigatesbiasesfromthesortingofindividualsintolosses(GlaeserandGottlieb,2008;KlineandMThereisanextensiveliteratureonsystemsofcitiesthatstudiestheirevolutionSeeMoretti(2013)andDiamond(2016)forframeworksinvolvingspatialsortingdependingoneducation,andDiamondandGaubert(2022)forasurveyanddiscussionofspatialsortinganditsevolutionovertime.2OurworksomehowcomplementsSteijnetal.(2022)whostudyhowspatialdeterminantsofindustryco-agglomerationpatternshaveseentheirefectsvaryoverthe1970-2014periodintheUS.ECBWorkingPaperSeriesNovariablesafectingtheproductivityofcitiesdiferentlydependingontheirsize.Anadvantageinformationonbuildingfootprint,heightandconstructionyearfromCEREMAandBDTOPOdata.Pixelsareclassi?edas“urban”iftheirbuilthanrandomwithinurbanareas.Citiesatime.Interestingly,weobservethatlargecitiescanhavediferenttrajectories.Inparticular,Lillewashistoricallyspecialisedinmining,textileandheavyindustries,andduringourstudyperiod.Thisisconsistentwithanincreasing2009).ECBWorkingPaperSeriesNo2varyovertime.Theelasticityofwageswithrespectt0.082,respectively).Theseestimatesaretocitydensityandlandareaattheequilibrium.Changesinthereturnstocitycharacteristicsofcitycharacteristicsconsistentwithourempiricalspeci?cation.Althoughthemodelcannotrnstoagglomerationvariables.ThisallowsustoffcitiesinvolvingagglomeraECBWorkingPaperSeriesNo2DelineatingcitiesovertimeTheattractivenessofcitiesforworkerschangeswwhichafectsbothtduringourstudyperiod.Wethusratherrelyondelineatio2.1Built-updataAsdescribedinAppendixA,wematchtwodatasourcestration(FichiersFonciers)anda3Dmodellingofbuildings(BDTOPO).Theresultingdataset2.2Algorithmtodelineatecitiesf3Forthesmoothingprocedure,weuseabi-squarekernelwitha2.1-kilometerbandwidth,suchthat,foreachpixel,smoothingtakesintoaccount10pixelsoneachofitssides.MoredetailsonbandwidthchoiceareprovidedinSection6ECBWorkingPaperSeriesNointhesamewayasthInthethirdstep,apixrandomlyredistributingbuilt-updensit95thpercentileofcounterfactuals.We?nallyname‘city’anurbanareathathasatleastoneipalitiesinmainlandFrance).Wethusneedtomodifyourde?nitionofcitiessothattheaggregatesofmunicipalities.Weconsideracitytoincoftheirbuilt-upareainthatcity,andmostpopulatedmunicipalityi2.3DescriptionofdelineatedcitiesTableB.1reportsdescriptivestaticitiesisfairlystableovertime,ataround290-310cities.The95thpercentileofcitypopulationParishasgrownsigni?cantthecaseforLyon(FiguresB.1.aandB.1.b)thathasabsorbednotonlyurbanareaswithouta4Non-buildablepixelsarede?nedaspixelsabovethe99thpercentileofelevation,slope,andshareofwaterofthepixelswherethereissomebuilt-up,consistentlywithdeBellefonetal.(2021).1.a:Paris,19761.b:Paris,2015Notes:Urbanareasobtainedfromourdelineationalgorithmseparatelyrunfor1976(Figure1.a)and2015(Figure1.b)usinga2.1kmbandwidth.Urbanareaswithcores(cities)areinblueandurbanareaswithoutacoreareinred.Bordersofmunicipalitiesincludingpartofacityareinblack,andtheareaofthemunicipalitiesnotcoveredbythedelineationbutthenconsideredaspartofthecitybecausecorrespondingtomorethan50%ofthemunicipalityareinbluestripes.1976and2015(FiguresB.1.candB.1.d).Itsareahasincreasedalotwiththeabsorptionofcities,urbanareaswithoutcores,andruralareas.Inparticular,MarseillesabsorbedtheratherlargecityofAix-en-Provencein1989.Finally,theareaofLillehasnotevolvedmuch(FiguresB.1.eandheavyandtextileindustrieswhichwer3Wagedataandcitycharacteristics3.1Individualwagepanelandlocaldatadailywage,occupation(1digits),industry(3digits)andlocationatthemunicipalitylevel.WedataconstructionaregiveninAppendixA.2.(Harris,1954),thecityitselfbeingexcludedfromthissum.Thedistancebetweentwocitiesisthatbetweenthegeographicbarycentre3.2Stylizedfactsovertime.Densityexhibitssmallvariationswithouttrend(Figure2.a).ThisisnotsurprisingcangobothwaysforagivencityandisingeneralfairlFigure3.athatrepresentstheevolstandingasanexception.DensityforLilleduringourstudyperiod.Marketaccessexhibitstimevariationswhichareconsistentwiththoseofdensityoverall(Figure2.c)andforthefourlargestcities(Figure3.c).Finally,wages(inconstanteuros)increaseovertimeatanypointofthecitydistributionFigure2:Momentsofcitydistributionsfordel4MedianEmploymentdensity19761981198619914MedianEmploymentdensity197619811986199119962001200620112016Year 25th75th90thArea0500010000150002000025000197619811986199119962001200620112016YearMedian 25th75thMedian90thMedianMarketPotentialMedianMarketPotential197619811986199119962001200620112016Year 25th75th90thDailywage4045505560657075197619811986199119962001200620112016YearMedian 25th75thMedian90thNotes:Employmentdensityiscomputedastheratiobetweenemploymentinourdatasetandarea(inkm2).SinceourdatasetincludesonlyindividualsborninOctoberofevenyears,densitiesshouldbemultipliedby24toobtain?guresthatareconsistentwithemploymentdensitiesinFrance.Marketaccessisthesumofemploymentdensitiesdividedbydistances,excludingthecityitself.Wageisinconstanteuros.Employmentdensity197619811986199119962001200620112016Year ParisLyonEmploymentdensity197619811986199119962001200620112016Year ParisLyonMarseilleLilleArea0100000200000300000400000197619811986199119962001200620112016Year ParisLyonMarseilleLilleMarketPotentialMarketPotential197619811986199119962001200620112016Year ParisLyonMarseilleLilleDailywage405060708090197619811986199119962001200620112016Year ParisLyonMarseilleLilleNotes:Employmentdensityiscomputedastheratiobetweenemploymentandarea(inkm2).Marketaccessisthesumofemploymentdensitiesdividedbydistances,excludingthecityitself.Wageisinconstanteuros.4Empiricalstrategyempiricalstrategy.First,weestimatealog-wagespeci?cationthatinvolvescity-yearefects,characteristicsacrosscities.4.1Speci?cationInourlog-wagespeci?cation,wedistinguish(C),urbanareaswithoutacore(U),andruralareasthatgatherremainingplaces(R).5Weintroducecity-year?xedefectforeachcity,butonlylocation-year?xedefectsforurbanareaslnwi,t=Xi,tβ+1{(i,t)∈C}γc(i,t),t+1{(i,t)∈U}γ+1{(i,t)∈R}γ+μs(i,t),t+ui+εi,t,(1)c(i,t)(resp.s(i,t))isthecity(resp.industry)whereindividualiworksinyeart(whenworkinginacity),γk,tisalocation-year?xedefect(whennotworkinginacity),Xi,taretime-varyingindividualvariables(inpractice,agesquared),μs,tisanindustry-year?xedefect,uiisanindividual?xedefectandεi,tisarandomcomponent.6γc,t=Zc,tθt+δt+ηc,t,(2)whereZc,tisavectoroftime-varyingcitycharacteristics,i.e.density,landareaandmarketaccess,θtaretheirtime-varyingefects,δtisayear?xedefectandηc,tisacityrandomcompo-5NotethatthethreesetsC,UandRchangeovertimeduringourstudyperiod.Forthesakeofsimplicity,wedonotindexthesethreesetsbyt.6Asthede?nitionofindustrieschangesovertimeduetoclassi?cationchangesin1993and2009,weusethreesetsof?xedefects{1,...S},{S+1,...,S+S1}and{S+S1+1,...,S+S1+S2}suchthats(i,t)isincludedinthe?rstsetbefore1993,inthesecondsetfrom1993to2008,andinthethirdsetafter2008.4.2Instrumentationfrompastcensusesinlinewistocksthatinducesinertiaoflocalpopulation.Atthesametime,weexpecttyearswiththeriseofservicesindutheEuropeanSoilDatabase(ESDB)compiledbytheEuropeanSoilDataCentrethatoriginallythusexplainthelocationof?rstsettlementswhichmighthaveturn7Weusetheseweightsfortworeasons.First,wehaveadoptedtheperspectiveofindividualsre-aggregatedatthecityandnationallevels.Wewanttheestimatedefectsofagglomerationvariablesto?tthisindividualperspective.Notethatthisisconsistentwiththeestimationattheindividual-yearlevelofequation(1)afterreplacingcity-year?xedefectswiththeirexpression(2).Wedidnotproceedthiswaybecauseestimatesarethenconsistentunderstrongerassumptions.Second,city-yearefectsusedasdependentvariableinthesecondstepareestimatedwithasamplingerrorsincetheyarerecoveredfromthe?rst-stepestimation.Ourweightsgivemoreimportancetocity-yearefectsoflargecitiesthatareestimatedmoreaccurately,andthismakesthesecond-stepestimatesmoreaccurate.Thisalsomeansthatwerecoverefectsofagglomerationvariablesusingvariationsforlargercitiesratherthanforthewholesetofcities.Fromaneconometricpointofview,thismeansestimatingtheefectsofagglomerationvariableslocally,atlargecitysizes.4.3Assessingtheroleofagglomerationeconomiesinwageevolutionincities,logwC;t-logwC;t-1.Denotebypc;ttheproportionamongcitiesofworkerslocatedinway:logwC;t-logwC;t-1=(pc;t-pc;t-1)logwc;t-1+pc;t(logwc;t-logwc;t-1)(4) -logwc;t=Xc;tβ+Zc;tθt+c;t+c;t+δt+ηc;t,(5) whereXc;t,uc;tandμc;tdenoterespectivelycity-yearaveragesofindividualvariables,indiv?xedefectsandindustryefects.Notethat,sincecity-year?xedefectsareintroducedinlogwc;t—logwc;t-1=(Mc;t—Mc;t-1)+Z;1(θt—θt-1)+(Z;t—Z;t-1)θt-1+(ηc;t—ηc;t-1),(6)whereZ;t=Zc;t—Z*withZ*thevaluesofcityvariablesforareferencecity,andMc;t=Xc;t+uc;t+μc;t+Z*θt+δtthecompositionefectforcitycinyeart.The?rstright-handsidetermstructure)andtimeefects.Itcannotbedecomposedfurtherbecauseindividual?xedefects,NotethattermstwoandthreeconstituteaOaxaca-BlinderdecoFinally,thefourthtermcorrespondstotheevolutionofcityunobservedefects.8oflogwC;tlogwC;t-1indecomposition(4).5Results5.1Localefectsandspatialsortingwithoutacore,γ,andinacity,γ三Σ1pc;tγc;t.Figure4graphsγ—γandγ—γasafunctionoftime.Urbanareaswithoutacorearecharacterizedbyyearlyefectsthatremainclosetothoseofruralareas.Thisisnotreallysur8Weintroduceareferencecitytomakeameaningfulassessmentoftheefectofchangesinreturnstoagglomer-ationvariables.Asthesevariablesareinlogarithmicform,changingtheirmeasurementunitchangestheirvaluesbutnottheirreturns.Consideringthediferencebetweencitiesandthereferencemakesthisissuedisappearssincelogarithmdiferencesareimmunetochangesofmeasurementunit.Forthereference,weconsidera?ctitiouscitywhichvaluesforalltheagglomerationvariablesaretheminimum.Thisway,diferencesofagglomerationvariableswiththereferencecityareallpositive,andtheefectofchangesinreturnstoagglomerationvariablescapturesefectsforcitieshavingagglomerationeconomiesthatarelargerthanfortheminimum.Forinstance,ifreturnstodensityareincreasingovertime,itcapturestheaverageefectofanincreaseinreturnswhenhavingadensitylargerthantheminimum.emerge.Bycontrast,yearlyefectsforcitiesareabovethoseforruralareasandthediferwithhigherunobservedskillsincitiesthatlargelydecFigure4:Yearlyefectsofworkinginanurbanareawithoutacoreoracityrelativelytotheruralarea0 0197619811986199119962001200620112016Year Cities-----UrbanareaswithoutcoreNotes:Diferencesbetweenyearlyefectsofbeinginanurbanareawithoutacoreorinacityandyearlyefectsofbeingintheruralarea.Yearlyefectsofbeinginacityareyearlyaveragesofcity-year?xedefectsweightedbytheyearlyshareofindividualsworkinginthecity.Therearenoyearlyefectsfor1981,1983and1990sincedataaremissingforthoseyears,andwethereforeconsiderinsteadtheaveragevalueofneighbouringyears.Wethenturntotheestimationagglomerationvariables(equation2),withtheconstraintintheliterature.ResultsdetailedinAppendixCareinlinewithpreviousstudies.Inparticular,Wheninstrumentingalltheagglomerationvariableswithbothhistoricalandsoilinstruments,fInterestingly,whenomittingindividual?xedefectsinthe?rststage(equation1),thepatternsarequitediferent(FiguresD.2.a,D.2.candD.2.e).Inparticular,thereisnoupwardtrendforspatialsortingofindividualsacrosstime.Weinvestigatethissortingfurthe?xedefectsandindividual?xedefectscomputedattheindividual-yearlevel.Interestingly,Fig-ureD.3.ashowsthatthisyearlycorraccessandindividual?xedefectsisratherstableuntil2002andthendecreases(FigureD.3.d).Theyearlycorrelationbetweendensity(resp.landarea)andindividual?xedefectsispositive,D.3.c).Sincetheyearlycorrelationsbetweendensity(resp.landarea)andindividual?xedefectstheyearlycorrelationbetweendensity(resp.landarea)andindividual?whenintroducingindividual?xedefects.Still,individual?xedefectscapturebothunobservedskillefectsandaverageageefects,9whichmattersfortheinterpretationofcorrelations.Inparticular,thereisatimepatternforthelabourmarketcloserto9Indeed,rememberthatthelinearefectofagecannotbeidenti?edseparatelyfromindividual?xedefectsandtimeefectscapturedbycity-yearandindustry-year?xedefects.ECBWorkingPaperSeri“netindividualefects”.Yearlycorrelationsbetweencityvariablesandnetindividualefectslarger.Inparticular,thecorrelationsinvolvingdensityandlandareaarestilldecreasingafterskills.105.cand5.e).10Onemayalsowonderwhetherimportantchangesinthepro?lesofestimatedcoe伍cientswhenintroducingindividual?xedefectscouldbeanartefactduetoperiodsinvolvedintheiridenti?cation.Indeed,in1976(resp.2015),onlyobservationsfrom1976onward(resp.2015downward)forindividualsparticipatetotheident?icationofthedensity,landareaandmarketaccesscoe伍cientsforyear1976(resp.2015).Foragivenyearτbetween1976and2015,coe伍cientsareidenti?edthankstoobservationsatyearτ,aswellasyearsbeforeandafterτ.Toinvestigatetheexistenceofapossiblebiasduetoedgeefects,were-estimateourspeci?cationwhenconsideringonlythe?rstfourobservationsforindividualsappearingatleastfourtimesinthepanel.Consideringshorttimespansforindividualsshouldlessenedgeefectsalthoughrestrictingtheestimationstoindividualsappearingatleastfourtimesinthepanelmayleadtosampleselection.Makingsuchrestrictionchangespro?lesofestimatedcoe伍cientsthatarenowratherdecreasingovertimewhenindividual?xedefectsarenotintroduced,especiallyfordensityandlandarea(FigureD.4.b,D.4.dandD.4.f),suggestingsampleselectioninourrobustnesscheck.Butpro?lesaremodi?edinthesamedirectionaswiththewholesamplewhenintroducingindividual?xedefects,asestimatedcoe伍cientsarethenincreasingovertimefordensityandmarketaccess,andratherstableforlandarea(FigureD.4.a,D.4.candD.4.e).ECBWorkingPaperSeriFigure5:Estimatedyearlycoe伍cientsofcityvariableswithindividualefectsinthe?rst-stagewithandwithoutinstrumentationwithhistoricalandgeologicalvariables5.b:Density,instrumentationLogdensity0015.b:Density,instrumentationLogdensity001020319761980198419881992199620002004200820122016Logdensity0Logdensity001020319761980198419881992199620002004200820122016.d:Landarea,instrumentationLogarea00050.d:Landarea,instrumentationLogarea000501019761980198419881992199620002004200820122016Logarea0005010Logarea0005010197619801984198819921996200020042008201220165.f:Marketaccess,instrumentationLogmarketpotential5.f:Marketaccess,instrumentationLogmarketpotential19761980198419881992199620002004200820122016LogmarketpotentialLogmarketpotential19761980198419881992199620002004200820122016Notes:Estimatedcoe伍cientsarerepresentedbybulletpointsandlinkedbyaplainline,andboundsofcon?denceintervalsarerepresentedbydots.Figuresb,dandf,historicalinstruments:logarithmsofpopulationdensitiesin1861,1931,1954and1856,andmarketaccessesforthesameyears;Soilinstruments:sharesofthecityareabylevelsofdepthtorock,soilerodability,hydrogeologicalclass,subsoilmineralogy,andtopsoilorganiccarboncontent.ECBWorkingPaperSeri5.2Decompositionsofwagegrowthlocationtypesandofthereallocarelatedtowageevolutionsfogrowthismostlydrivenbywageevolutionsinthediferentcities.Thereallocationofworkersfthecitiesinthefourthquartile,i.e.thelargestcities.ItisthegrowthinthoselocationsthatECBWorkingPaperSeri19761980198419881992199620002004200820122016 WagegrowthWagecontrib.Proportioncontrib.19761980198419881992199620002004200820122016 CitiesUrbanareaswithoutcoreRural