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Shopping externalities and retail concentration

Koster, Hans R.A.; Pasidis, Ilias; van Ommeren, Jos

published in

Journal of Urban Economics

2019

DOI (link to publisher)

10.1016/j.jue.2019.103194

document version

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Article 25fa Dutch Copyright Act

Link to publication in VU Research Portal

citation for published version (APA)

Koster, H. R. A., Pasidis, I., & van Ommeren, J. (2019). Shopping externalities and retail concentration:

Evidence from dutch shopping streets. Journal of Urban Economics, 114, 1-29. [103194].

https://doi.org/10.1016/j.jue.2019.103194

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ContentslistsavailableatScienceDirect

Journal

of

Urban

Economics

journalhomepage:www.elsevier.com/locate/jue

Shopping

externalities

and

retail

concentration:

Evidence

from

dutch

shopping

streets

☆

Hans

R.A.

Koster

a,1,∗

_,

_Ilias

_Pasidis

b

_,

_Jos

_van

_Ommeren

a,2

a Department of Spatial Economics, Vrije Universiteit Amsterdam, De Boelelaan 1105, HV 1081 Amsterdam, the Netherlands b Barcelona Institute of Economics, John Maynard Keynes, 1-11, 08034, Barcelona, Spain

a

r

t

i

c

l

e

i

n

f

o

JEL classiﬁcation: R30 R33 L81 Keywords: Retail Shopping externalities Rents Vacancies Agglomeration economies Footfall

a

b

s

t

r

a

c

t

Whydoshopsclusterinshoppingstreets?Wearguethatretailfirmsbenefitfromshoppingexternalities.We identifytheseexternalitiesforthemainDutchshoppingstreetsbyestimatingtheeffectoffootfall– thenumber ofpedestriansthatpassby– andthenumberofshopsinthevicinityonstoreowners’rentalincome.Weaddress endogeneityissuesbyexploitingspatialvariationwithinshoppingstreetscombinedwithhistoriclong-lagged instruments.Ourestimatesimplyanelasticityofrentalincomewithrespecttofootfallaswellasnumberofshops inthevicinityof(atleast)0.25.Weshowthattheseshoppingexternalitiesareunlikelytobeinternalised.Itfollows thatsubstantialsubsidiestoshopownersarewelfareimproving,seeminglyjustifyingcurrentpolicies.Finally, wefindlimitedevidenceforheterogeneitybetweenretailfirmslocatedinshoppingstreetsintheirwillingness topayforshoppingexternalities.

1. Introduction

Oneofthemainreasonsthatpeoplechoosetoliveinthecityisthe presenceofarichvarietyofconsumergoodsandservicesoﬀeredbythe retailsector(Glaeseretal.,2001).Shopstendtobeconcentratedeither inpedestrianshoppingstreetsandshoppingdistricts,oftenlocatedin citycentres,orinshoppingmallsinthesuburbs.InEurope,shopsare mostlyconcentratedinpedestrianstreets.Walkinginthosestreetsisso importantthatthemajorityofallpedestrianmovements occurwhile shopping.3

☆_We_thank_Locatus_and_HISGIS_for_providing_data._The_editor_Stuart_Rosenthal,

twoanonymousreferees,SergejGubin,JordiJofre-Monseny,AlbertSollé-Ollé, Jacques-FrançoisThisseandElisabetViladecans-Marsalarethankedforuseful commentsonearlierversionsofthispaper,aswellasparticipantsofseminars attheBalticInternationalCentreforEconomicPolicyStudiesinRiga,the Uni-versityofBarcelona,theAutonomousUniversityofBarcelona,IDE-JETROin Chiba(Japan),theLondonSchoolofEconomicsandparticipantsoftheUrban EconomicsAssociationconferencesinCopenhagenandVienna.Thispaperhas beenpreparedwithintheframeworkoftheHSEUniversityBasicResearch Pro-gramandfundedbytheRussianAcademicExcellenceProject‘5-100’.

∗_{Corresponding}_author.

E-mail addresses: h.koster@vu.nl(H.R.A.Koster),ipasidis@gmail.com(I. Pa-sidis),jos.van.ommeren@vu.nl(J.vanOmmeren).

1 _Hans_is_also_research_fellow_at_the_HSE_University_in_The_Russian_Federation,

theTinbergenInstituteandtheCentreforEconomicPolicyResearch.

2 _Jos_is_also_research_fellow_at_the_Tinbergen_Institute.

3 _This_is_based_on_data_from_Statistics_Netherlands._We_exclude_hiking_and

recreationalwalkingactivities.

Arguably,themostimportantreasonforretailfirmstoclusteristhe presenceofpositiveshoppingexternalities,whicharegeneratedby con-sumers’‘trip-chaining’behaviour.Shoppingexternalitieshaveasimple logic.Inretailmarketswherecustomershavetovisitstores, transporta-tioncostsarepaidbycustomersandincurredonashoppingtripbasis (Claycombe,1991).Consumerswhovisitseveralshopsbenefitfrom re-ductionsintransportandsearchcosts.Inthecontextofshoppingstreets, aretailfirm’sproductivityfunctiondependsonlocalfootfall– the num-berofpedestriansthatpassbyashop.Footfalltendstobehigherin ar-easwithmoreshops,sincepedestriansareattractedtoareaswithmany shops.Hence,theassociatedreductionsincostsforconsumersimplya positiveshoppingexternalityforretailfirms,whichisenhancedwhen multipleretailfirmsarelocatedincloseproximity(EatonandLipsey, 1982;Claycombe,1991;SchulzandStahl,1996).Similartoother ag-glomeration advantages,these shoppingexternalitiesareexpectedto capitaliseintostoreowners’rentalincome.4

Intheempiricalliterature,however,littleattentionhasbeengivento theimportanceofshoppingexternalities.Thefewstudiesthatmeasure shoppingexternalitiesfocusonU.S.shoppingmalls(seePashigianand Gould,1998).However,retailactivityinEuropeancitiesismainly

con-4_In_retail_markets,_{agglomeration}_economies_occur_locally,_so_{capitalisation}

intoemployees’wagesishardlyrelevant.Incontrast,innon-retailmarkets, ag-glomerationadvantagesaremoredispersedandmainlycapitaliseintowages (seee.g. ArzaghiandHenderson,2008).

https://doi.org/10.1016/j.jue.2019.103194

Received20February2018;Receivedinrevisedform5August2019 Availableonline28September2019

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centratedinshoppingstreetswhileshoppingmallsarefarlesscommon.5 Tothebestofourknowledge,thisistheﬁrstpaperthatquantiﬁes shop-pingexternalitiesinshoppingstreets.

Shoppingstreetsarecharacterisedbyadiﬀerentformofretail or-ganisationthanshoppingmalls.Incontrasttoshoppingmalls,wewill showthatpropertyownershipinshoppingstreetsishighlyfragmented andthateachshopisonlyaminorplayerlocally.Asaconsequence, internalisationofshoppingexternalitiesisunlikelytooccurinshopping streets.6 Thus,publicpoliciesthatfosterretailconcentrationby provid-ingsubsidiesarepotentiallywelfareimproving.7

Wefocusonthefullpopulationofmainshoppingstreetsinone coun-try:theNetherlands.Animportantfeatureofshoppingstreetsisthat theyaredominatedbyclothingstores(30%),cafés/restaurants(16%) andfoodstores(10%).Themainstrategyfollowedbytheretailfirmsin thesesectorsistodifferentiatethemselvesbysupplyingheterogeneous products.Thisis insharpcontrasttootherretailsectorsthatare ex-aminedintheeconomicliterature,whichofferhomogeneousproducts andwherespatialdifferentiationisthemainstrategy(e.g.gasstations, movie theatres,or videoretailers, seeNetzandTaylor,2002;Davis, 2006;Seim,2006,respectively).

Wecontributetotheliteratureinthreeways.First,weemploytwo measuresofshoppingexternalities.Ourﬁrstmeasure,footfall,isnovel intheagglomerationliterature.8 Wewillarguethatfootfallcaptures shoppingexternalitiesratherprecisely,alsobecausemeasuresoffootfall predominantlyincludeshopperswhovisit severalshops.Asasecond measureofshoppingexternalitiesweuse thenumberofshopsinthe vicinity.Thelatter is amorestandardproxy forexternalities, which isinlinewithalarge literatureonagglomerationeconomies(seee.g Combesetal.,2008;Meloetal.,2009).

Asecondcontributionofthepaperliesinanexplicittreatmentof het-erogeneity.Onemaysuspectthatthereisheterogeneityinthebenefits ofshoppingexternalities.Forexample,shopsthatarepartofachainare morelikelytolocateinstreetswithhighlevelsoffootfall.Using semi-parametricregressiontechniquesweshowthatheterogeneitybetween firmsintermsofmarginalwillingnesstopayforfootfallislimited.For example,shopsbelongtochainsandothershopshaveroughlythesame marginalwillingnesstopayforfootfall.Notethatthissuggeststhatstore ownerscannot,ordonot,discriminatebetweendifferenttypesofretail firmsinsettingtherent.

Thethird,andmain,contributionofthecurrentpaperisthe identifi-cationofshoppingexternalitiesbyestimatingthecausaleffectoffootfall ontherentalincomeofstoreowners,whichwederivebyestimating thecausaleffectsoffootfallontherentpaidbytenantsaswellason theprobabilitythataretailpropertyliesempty.Wewilladdressseveral sourcesofendogeneitybyexploitingspatialvariationwithinshopping streets,combinedwiththeuseofarangeofcontrolvariables(e.g.,size ofproperty,shoppingchainfixedeffects)andaninstrumentalvariable approach.

5 _Shopping_mall_ﬂoor_space_per_person_is_more_than_tenfold_in_the_U.S.

com-paredtoEurope(2150m2_per₁₀₀₀_people_in_the_U.S._compared_to₁₈₂_m2_per

1000peopleinEuropein2011,seeCushman&Cushman,2011).

6 _In_shopping_malls,_store_owners_set_the_rent_based_on_retail_ﬁrms’_revenues

andthus,shoppingexternalitiesareinternalised.Morespeciﬁcally,shopping mallrealestatemanagerschargelowerrentstofootfall-generatingshops(or ‘anchorstores’),whichcouldberegardedasaﬁrst-bestsubsidy.Hence,thereis noroomforpublicpolicytoimprovewelfare(Brueckner,1993;Pashigianand Gould,1998;KonishiandSandfort,2003).

7 _Many_examples_of_such_subsidies_can_be_given,_although_these_subsidies_tend

tobeimplicit.Forexample,inmanyEuropeancountries,inparticularGermany, policieshavecreatedpedestrianareas.Thelatterimpliesimplicitsubsidiesto localstoreowners,astheadvantagesarelocal,whereasthedisadvantagesof prohibitingcaruseintheseareasfallonotheragents.Subsidiestoparkingclose toshoppingclusters,andsubsidiestopark-and-ridefacilities,includingfree pub-lictransporttowardscitycentres,areotherrelevantexamples.

8 _In_the_retail_industry,_footfall_is_a_standard_measure_to_explain_the

attrac-tivenessofashoppinglocation.

Tobemorespecific,asemphasisedintheagglomerationliterature, bothourmeasuresofshoppingexternalities,i.e.footfallandnumberof shopsinthevicinity,areessentiallymeasuresofspatialconcentration thatmaybeendogenousbecausetheytendtobepositivelycorrelated tounobservedattractivelocationcharacteristics.Weaddressthisissue byfocusingonshopsthatarelocatedwithinthesameshoppingstreet andarethereforeclosetoeachother.9 Thisstrategylargelyaddresses theissuethatfootfallandnumberofshopsinthevicinityaregenerated bylocalamenitiesandaccessibility.Wefurthercontrolforawiderange ofshopandstreetcharacteristics,aswellaslocalamenitiesthatmay generate footfallthatisnot relatedtoshopping,suchasthenumber ofschools,publicbuildingsandreligiousbuildings.Furthermore,using web-scrapeddatafrom FlickR,we controlforthenumberofpictures takenbytouristsandresidentsintheshoppingstreet,whichproxyfor difficult-to-capturedifferencesinamenitiesandattractivenesswithina street(Gaigné etal.,2018).

Nevertheless,itisplausiblethatendogeneityissuesarestillpresent for both measuresof shopping externalitiesdue tomeasurement er-rorandreversecausation issues,whichwouldyieldanunderestimate of shopping externalities. We believethere are three reasons which maycausereversecausation.First,attractive,andthereforeexpensive, streetsdisproportionallyattractshopswithhigh-endbrands(e.g.Louis Vitton, GiorgioArmani). These shopsgenerate little footfall,so that there isadownward biasoftheestimatedfootfallcoefficient.Inthe Dutchcontext,themainexampleistheP.C.HooftstraatinAmsterdam, butoneobservesthesamephenomenoninwell-knownshoppingstreets in othercountries(NewBondStreet,London; Champs-Élysées,Paris; ViaMonteNapoleone,Milan;Bahnhofstrasse,Zurich).Second,aretail firmthatsignsacontracttopayhighfixedrentsmaybemorelikelyto ‘workhard’togeneratefootfall(and,therefore,sales) inorderto en-surethatitcanaffordtheserents.Third,onemayarguethatthereisa simultaneityproblem(whichusuallydoesnotoccurinahedonicprice setting),becauseweconsidertheaggregatenumberofshops(and foot-fall)inalocation,whichwouldfallwithrents,asinastandardtextbook supply-demandsettingwithahomogeneousgood.10

Endogeneityissuesalsoplayarolewhenfocusingontheeﬀectson vacancies.Forexample,ahigherlevelofvacanciesinastreetwilllikely inducelessfoottraﬃcand,mechanically,reducethesmallnumberof non-vacantstoresinthevicinity.

Toaddresstheseendogeneityissues,wewillemployan instrumen-talvariablesapproachusingtheexactlocationofcinemasin1930. Be-causethereisahighautocorrelationofretaillocations,itappearsthat thenumberofcinemasin1930hasastrongeﬀectonfootfallandon numberofshopsinthevicinity.Thisisnottoosurprising:forexample, themaimshoppingstreetinAmsterdamnowadays,deKalverstraat,has beenoneofthemainshoppingstreetsforalmost300years.Notethat weidentifytheseeﬀectswithinshoppingstreetsandcontrolforthe cur-rentlocationofcinemas,henceourinstrumentplausiblyaddressesthe variousendogeneityconcerns.

Wealsomakesurethatourresultsdonotdependonthis particu-larchoiceofinstrumentsbygoingbackevenfurtherintime.Wewill usethenumberofshopsin1832asaninstrument.Thisinstrumentis particularlyconvincingbecauseweshow,usingdataonlandvaluesin 1832,thatpastattractivelocationsdonotcommandhigherretailrents nowadays.Weareabletoshowthatthelocationofshopsin 1832is astronginstrument(forfootfallandnumberofshops),evenwhenwe controlforthenumberofbuildingsin1832.Wediscusstheassumptions underlyingouridentiﬁcationstrategyatlengthinthepaper.

Ourresults showthatfootfallandnumberofshopshaveastrong positiveeﬀectonrentalincomewithanelasticityrangingfrom0.25–

9_Shopping_streets_tend_to_be_short;_in_our_data,_the_median_length_is_only

182m.

10_We_would_like_to_thank_an_anonymous_referee_for_mentioning_the_latter_two

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0.50.Wheninstrumenting,theestimatesforbothfootfallandnumberof shopsaresomewhathigher.Thus,therearesubstantialexternalbeneﬁts fromfosteringfootfallandretailconcentration.

Basedontheseestimates,theoptimallevelofsubsidytostoreowners appearstobesubstantial,whichpotentiallyjustifiesarangeofcurrent policiesthatareespeciallybeneficialtoshoppingstreets.Current poli-cieseithersubsidiseshopowners,e.g.throughpedestrianisationof pop-ularshoppingstreets,orsubsidiseshopperseitherthroughtheprovision of(subsidised,andsometimesevenfree)publictransporttoshopping districtsorparking.Zoningpolicieswhichconcentratesshoppinginto shoppingstreets(e.g.attheexpenseofresidentialhousing),mayalsobe beneficial.

Relatedliterature.Ourpaperlinksandcontributestothreestrands

of literature.First, itrelatesto theliterature on spatialcompetition andproduct differentiation (D’Aspremontet al., 1979; Osborne and Pitchik,1987).Davis(2006)focusesonmovietheatres,andevaluates consumers’transportcosts,theeffectofgeographicdifferentiation,and theextentofmarketpower.Seim(2006)showsthattherearesignificant returnstoproduct(orspatial)differentiationandillustratesthatmarkets withmorescopefordifferentiationsupportgreaterentry.Jia(2008)and Arcidiaconoetal.(2016)studytheimpactofWal-Martontheretail marketonincumbent(discount)supermarketsandsmallgrocerystores. Clappetal.(2016) focusonopenings andclosingsof multi-line de-partmentstoresandfindevidenceforstrongnegativecompetitive ef-fects withinthe ownbranch.Zhou (2014)shows that multi-product search,whichisimportantwhenconsumersbuymultipleproductsin oneshoppingtrip,cansignificantlyinfluenceretailfirms’pricing de-cisions.JohansenandNilssen(2016)investigatetheconditionsunder whichone-stopshoppingcausestheformationofbigstores.However, thesepapersignorethatmanyshopsbenefitfromeachotherwhen lo-catedclosetoeachother.

Ourpaperalsorelatestoasecondliteraturethatexplicitlyfocuses onthebenefitsofagglomerationforfirms.Thereisampleevidencethat firmsthatlocateclosetogetherbenefitthroughinput-andoutput shar-ing,labourmarketpoolingandknowledgespillovers(Marshall,1890). Currentevidencesuggeststhatthe elasticityof productivitywith re-specttodensityisaround0.05(seee.g.themeta-analysisbyMeloetal., 2009).This literature typicallyfocuses on the manufacturing indus-try. Compared to that literature, we find substantial agglomeration elasticities, which are(at least) 5times larger. This is in line with Kosteretal.(2014),whoshowthatagglomerationeconomiesaremuch moreimportantforretailfirms.Teulingsetal.(2017)usea monocen-tricmodelwherecustomersarriveinacentrallocationandhavetowalk toshopsaroundthislocation.Locationsthatarefurtherawayfromthe centrearethereforeexpectedtobelessprofitable.Theirempirical evi-denceindicatesthatrentsinshoppingdistrictsareindeedhigherclose tothecentre.11

Our findings also contribute toa more policy-oriented literature studyingtheeffectivenessofretailpolicies,inparticulartowardsthe effectsoftheopeningoflarge‘big-box’retailersneartheurbanfringe (Sanchez-Vidal,2016).Somestudiesdemonstratethatthewelfare ef-fectsofcurrentplanningpoliciesthathinderentryinretailmarkets,and particularlyoflargeretailers,arenegative.Severalstudieshaveshown thatregulationpoliciesreduceretailproductivityandjobgrowthand in-creasemarketpowerofincumbentstores(BertrandandKramarz,2002; SchivardiandViviano,2011;HaskelandSadun,2012;Cheshireetal., 2015).Bycontrast,ourstudyshowsthatcurrentpoliciesthat implic-itlysubsidisestoreownersinshoppingstreetsarepotentiallywelfare improving,astheymakeitmoreattractivetoopenadditionalstoresin denseareas.Thisconclusionisconsistentwiththeshoppingmall litera-ture,whichshowsthattheprovisionofsubstantialrentdiscountsto ‘an-chor’storesinUSshoppingmallstointernaliseexternalitiesiscommon

11 _To_capture_this_phenomenon,_we_control_for_walking_time_to_the_centre_of_a

shoppingdistrict(i.e. thelocationwiththehighestfootfall).

practice(PashigianandGould,1998;Gouldetal.,2005).Shopping ex-ternalitiesmayjustifypublicpoliciesthatpedestrianiseshoppingstreets inordertoeﬀectivelyclustershopsandinternaliseexternalbeneﬁts.

Theremainderofthispaperisstructuredasfollows.InSection2we discuss the theoretical framework that guides the empirical results. Section3introducesthedataandreportsdescriptivestatistics,followed byadiscussionoftheeconometricframeworkinSection4.InSection5, wepresentanddiscussourresults,includingtheestimatesofthe op-timalsubsidy.Section6discussesanextensionwhereweallowfora heterogeneousversionofourmodel.Alsothemainsensitivityanalyses arediscussed.ThelatteraredescribedinmoredetailinAppendixD.We drawconclusionsinSection7.

2. Theoreticalframework

2.1. Rentalincome,rentsandvacancies

Weaimtomeasurethepresenceofshoppingexternalitiesby esti-matingtheeﬀectoffootfallornumberofshopson(expected)rental incomeofshopi,denotedbyIi.12 Footfallisdeﬁnedasthenumberof

pedestriansthatpassashop(perunitoftime).Weassumethat pedestri-answalkthroughoneshoppingstreetandpassallshopsinthisstreet.13 Let𝑠={𝑓,𝑁}denoteshoppingexternalities,wherefreferstofootfall andNtothenumberofshopsintheshoppingstreet.14 Inwhatfollows, wemakeadistinctionbetweenstoreownersthatownshopsandretail firmsthatrentshops.Shopscanbeeitheroccupiedbyretailfirmsor vacant.Storeownersofvacantshopsneedadvertisingservicestofind anewtenant,whichiscostly.Givenrentpiandvacancyratev,rental

incomeofashopisgivenby:

𝐼𝑖=𝑝𝑖(1−𝑣)−𝑐𝑖𝑣, (1)

where𝑝_𝑖(1−𝑣)isrentalincomewhenthepropertyislettoaretailﬁrm andc_ivistheadvertisingcosts.Itseemsreasonabletoassumethat,at leastinthelongrun,theadvertisingcostsci areproportionaltopi,so

𝑐𝑖=𝜅𝑝_𝑖,where𝜅 >0.Becausevacancyratestendtobesmall(usually smallerthan10%inourdata),log(1−(1+𝜅)𝑣)≈ −(1+𝜅)𝑣.Hence,the logofrentalincomeisthen(approximately)equaltolog𝑝_𝑖−(1+𝜅)𝑣.

Ifshoppingexternalitieshaveaneffectontherentandvacancyrate, itfollowsthattheeffectoflogshoppingexternalitiesonlogrental in-comecanbewrittenasthesumofthemarginaleffectoflogshopping externalitiesonthelogarithmofrentandthemarginaleffectoflog shop-pingexternalitiesonthelevelofthevacancyrate:

𝜕log𝐼_𝑖 𝜕log𝑠 ≈ 𝜕log𝑝_𝑖 𝜕log𝑠 −(1+𝜅) 𝜕𝑣 𝜕log𝑠. (2)

Note that a standard hedonic model cannot be used to predict 𝜕logIi/𝜕logsbecausevacanciesarenotincorporatedinsucha

frame-work. InAppendixA.1 wetherefore setup asearch andbargaining framework,wherestoreownershavetodecideonthelevelof advertis-ingwhichisnecessarytofindretailfirmssearchingforretailspace. Con-sequently,inthissetup,vacancyratesareendogenouslydetermined. Furthermore,itisassumedthatownerswithvacantpropertiesandretail firmssearchingforretailspacebargainabouttherentlevelwhenthey makecontactwitheachother,whilebothareuncertainhowmuchtime ittakestomakeanothercontact.Wethenshowthat,inequilibrium,

12_As_an_alternative,_one_may_estimate_the_eﬀect_on_transaction_prices_of_shops.

Therearetworeasonsweprefertofocusonrentalincome.First,transaction pricesreﬂectexpectationsaboutfuturerentsandthereforefuturelevelsof shop-pingexternalities.Second,salestransactionsarerarerelativetorent transac-tions.Inourdata,only10%oftheobservationsrefertosalestransactions.

13_This_assumption_is_made_for_convenience_only,_as_it_is_plausible_that_shoppers

usuallywalkthroughseveralshoppingstreets.

14_In_our_empirical_application,_we_take_into_account_that_shoppers_usually

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𝜕logpi/𝜕logs>0and𝜕v/𝜕logs<0.15 Hence,in equilibrium,shopping

externalitiesnotonlyincreaserents,butalsoincreasevacancyrates.If weassumethat𝜅 =0,wegetthelowerboundestimateoftheeffectof footfallonlogrentalincome.Wewillmakethatassumptionbutalso calculatetheeffectoffootfallonrentalincomefordifferentvaluesof𝜅 (basedontheadvertisingcostsforDutchretailproperties).

2.2. Welfareandretailpolicies

Letusnowfocusonwelfareeffectsofretailpolicies.Intuition sug-geststhatretailpolicycanbewelfareimproving,becauseretailfirms generatefootfall,andpoliciesmayinfluencethespatialconcentration ofretailfilms.Toinvestigatethis,wewillassumeherethattheeffect ofshoppingexternalitiesisentirelydrivenbytheeffectoffootfallon rentalincome.Theeffectofnumberofshopsisonlyindirect,asit af-fectsfootfall,butnotrentalincomedirectly.Hence,moreformally,we assumethatforashopitherentalincomeis:

𝐼𝑖(𝑓,𝑁)=𝐼𝑖(𝑓(𝑁))=𝑝𝑖(𝑓(𝑁))(1−𝑣(𝑓(𝑁)))−𝑐𝑖𝑣(𝑓(𝑁)). (3)

Storeownersmaydecidetoincreasethesupplyofstoresinastreet (ex-tensivemargin)or/andreduceexistingvacancies(intensivemargin).16 Hence,thenumberofshops,aswellasthenumberofvacantshopsina shoppingstreet,isendogenous.Bothdecisionsimplyanexternality be-causefootfalldependspositivelyonthenumberofshopsandnegatively onthevacancyrate.Hereweinvestigatethewelfareeﬀectofincreasing thenumberofoccupiedshops.17 Combinedwiththeassumptionthatwe focusonacompetitivemarket,thisimpliesthatitisnotnecessaryto distinguishbetweenshopownersandretailﬁrms.

Thenumberofoccupiedshops,N,inashoppingstreetis endoge-nouslydetermined.Fornowletusassumethatshopsarehomogeneous. Theper-periodmarginalconstructionandmaintenancecostsofNshops areequaltoC(N),whichisincreasinginN.Footfallinastreet,f,isan increasingfunctionofthenumberofshopsintheshoppingstreet,so 𝜕f/𝜕N>0,aswellasthefootfallgeneratedperindividualshop,denoted by𝑓̃𝑖,so𝜕𝑓∕𝜕𝑓̃𝑖>0.Theshop’scostsofgeneratingfootfallareequalto

𝑞𝑖(𝑓̃𝑖),whichisanincreasingandconvexfunctionof𝑓̃𝑖.Forexample,

shopsmaygeneratefootfallbyadvertising,whichiscostly.Welfarein theshoppingstreetisnowdeﬁnedby:

∫ 𝑁 0 𝐼𝑖(𝑓(𝑁,𝑓̃𝑖))d𝑖−𝐶(𝑁)−_∫ 𝑁 0 𝑞𝑖(𝑓̃𝑖)d𝑖. (4)

Thewelfare-optimalnumberofshopsisthendeterminedbythe follow-ingequation:

𝐼𝑖+𝑁_𝜕𝑁𝜕𝐼𝑖 =𝐶′(𝑁)+𝑞𝑖(𝑓̃𝑖), (5) 15 _Another_issue_is_that_footfall_depends_on_the_number_of_vacancies,_as_vacant

shopswillattractfewercustomers.WeaddressthisissueinAppendixA.2where weendogenisefootfallsothatitisdependentonvacancyrates.Weshowthat themainconsequenceofignoringthisendogenousrelationshipforourempirical investigationisthatoneunderestimatestheeﬀectoffootfallonrentalincome. WecomebacktothisissueinSection4.

16 _The_supply_of_shops_can_be_increased_by_building_new_properties_for_retail

activityorbyconvertingexistingspacetoretailuse.Existingvacanciesmaybe reducede.g. byincreasingthesearcheﬀort.

17 _The_welfare_eﬀect_of_ﬁlling_an_existing_vacancy_and_increasing_the_supply_of

shopsisequivalentgiventwoconditions.Thefirstisthatfillinganvacancyand increasingthesupplyofshopshasanidenticaleffectonfootfall,whichseems reasonable.Thesecondconditionisthat,intheabsenceofafootfallexternality, thedecisiontofillavacancyissociallyoptimal,implyingthattherearenoother externalities.Notethatstoreownerswithvacanciesmayincreasetheir advertis-ingexpenditure,whichincreasestheprobabilitytofindatenant.That,inturn, mayincreasefootfallforothershops.Itisingeneralnotclearwhetherstore ownerswithvacancieschoosethesociallyoptimaladvertisingexpenditure be-causeofnegativecongestionandpositivesearchexternalities.See,forexample, Hosios(1990)forananalysisofoptimaladvertisingexpenditureinthelabour market.Weleavethisissueforfurtherresearch.

where𝑖=𝑁.Theaboveequationstatesthatthemarginalexpected in-comeofNisequaltothesumofthemarginalcostofopeningan addi-tionalstoreandthecostofgeneratingfootfall.Notethatthemarginal benefitofopeningashop– i.e.theleft-handsideoftheaboveequation – isanincreasingfunctionofN.Thisisintuitive,becauseeachshopthat opensupintheshoppingstreetbenefitsfromthefootfallgeneratedby nearbyretailfirms.Thisimpliesthatthecostofopeningashop(C(N)) mustbestronglyconvex,sothatthesecond-orderconditionholds.18

Tocalculatetheoptimalsubsidytostoreownersisstraightforward. ThemarginalstoreownerwillignorethetermN(𝜕Ii/𝜕N)when

consid-eringtoincrease(ordecrease)thesupplyofshops.Hence,themarginal externalbeneﬁtofopeningupanewshopisequalto:

𝑁_𝜕𝑁𝜕𝐼𝑖 =𝐼_𝑖⋅ 𝜀_𝐼,𝑁(𝑖)>0, (6) where𝜀I,N(i)denotestheelasticityofrentalincomeofshopiwithrespect

tothenumberofshops.Inourempiricalapplicationwewillestimate theelasticity𝜀I,N(i).

Importantly, wewill assume thatthis shoppingexternalityis not internalised bystoreowners.Thisseemsareasonableassumptionfor shoppingstreetsduetothefragmentedownershipofshops,whichis, aswewillshow,supportedbyourdata.19 Giventhisassumption,the Pigouviansubsidytothemarginalstoreownerintheﬁrst-bestoptimum is𝜀I,N(i)timestherentalincomeofashop.Inourempiricalanalysis,we

areabletocalculatethissubsidyaswewillobserverentalincomeand estimate𝜀I,N(i).

We willnow determinethewelfare-optimallevel of footfallin a street,whichistheresultoftheself-chosenfootfalllevelbyanindividual ﬁrm.Thewelfare-optimallevelatthestreetlevel,f,canthenbederived bymaximisingwelfarewithrespecttotheindividualleveloffootfall,

̃

𝑓𝑖.Itcanbederivedbyanequation,whichstatesthatthemarginal

ex-pectedincomeof individualfootfall, 𝑓̃𝑖,isequaltoitsmarginalcost:

𝜕𝐼𝑖 𝜕𝑓 𝜕𝑓 𝜕𝑓̃𝑖 =𝑞′ 𝑖(𝑓̃𝑖). (7)

Wewillnowassumethatshopsarehomogeneous.Thisimpliesthat𝑓̃𝑖=

̃

𝑓,𝐼𝑖=𝐼,𝑞𝑖(𝑓̃𝑖)=𝑞(𝑓̃)and𝜀𝐼,𝑁(𝑖)=𝜀𝐼,𝑁.Itfollowsthat𝑓=𝑁𝑓̃and

Eq.(7)canbewrittenas: 𝜕𝐼

𝜕𝑓𝑁=𝑞′(𝑓̃). (8)

Theleft-handsideofthisequationdepictsthemarginalbenefitof foot-falltosocietygeneratedbyanindividualshop.Themarginalbenefitof footfalltoashopisequalto𝜕I/𝜕f(astheshopignoresthatothershops inthesamestreetbenefitfromthefootfall).Giventhatthenumberof shopsisusuallylargeinastreet(andfaraboveone),theexternalbenefit offootfall,andhencethewelfare-optimalsubsidy,isequalto:20

𝜕𝐼

𝜕𝑓𝑁=𝑁𝑓⋅ 𝐼𝜀𝐼,𝑓>0, (9)

18_The_latter_is_likely_true_because_in_shopping_streets,_shops_almost_always

occupythegroundﬂoorofabuilding(seeLiuetal.,2016),whichimpliesthat thenumberofshopsisrestrictedbythelengthofthestreet.

19_In_contrast,_in_shopping_malls,_developers_will_internalise_these_{externalities}

bydeterminingtheoptimalnumberofstoresandbycharginglowerrentsto footfall-generatingshops(or‘anchorstores’)(Brueckner,1993;Pashigianand Gould,1998;KonishiandSandfort,2003)Therefore,inashoppingmall,the developerisabletoprovideﬁrst-bestsubsidies,basedontheamountoffootfall generatedbyeachstore,andmaximizeashoppingmall’swelfare.

20_To_evaluate_the_exact_{general-equilibrium}_welfare_improvements_associated

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where𝜀I,fdenotestheelasticityofrentalincomewithrespecttofootfall.

Inourempiricalapplicationwewillalsoestimatetheelasticity𝜀I,f.We

willshowthatinourdata𝜀𝐼,𝑓=𝜀𝐼,𝑁(whichisinlinewithour

assump-tionthatfootfallisproportionaltothenumberofshopsinthestreet). Wepreviouslyassumedthatretailfirmsarehomogeneous.Itisclear howeverthatretailfirmsmaydifferintheextentthattheybenefitfrom thepresenceofothershops,i.e.footfall.Hence,wewillallow𝜀I,Nand

𝜀I,f toberetailﬁrm-speciﬁc.Wewillsee howeverthatheterogeneity

ofretailﬁrmswithrespecttothemarginalwillingnesstopayfor foot-fallgeneratedbyothershopsisquitelimitedinshoppingstreets,which suggeststhatmodernshoppingstreetsattractrelativelysimilarshops. InSection6wewillinvestigatethisfurther.

3. Dataanddescriptives

3.1. Data

Webaseourempiricalanalysisonvariousdatasets.Thefirstoneis obtainedfromStrabo,aconsultancyfirmthatgatherscommercial prop-ertydata.Itcomprisestransactionsofcommercialpropertiesprovided byrealestateagentsfrom2003to2015. Thedatasetcontains infor-mationaboutannualrents(reportedatthemomentthatthecontract hasbeensigned)andrentalpropertyattributes,suchasaddress,size (grossfloorareainm2₎_and_whether_the_building_is_newly_constructed orrenovated.Inourdata,allrentsareindependentofretailrevenues inlinewithcommonpracticefortheNetherlands.21 FromtheStrabo dataset,weexcludeobservationsforwhichnorentisreported(27.8% ofallshopsinthedataset).22 Therentaltransactionsarethenmatchedto datafromtheBuildingRegistry(BAG),whichprovidestheexactlocation andconstructionyearforallbuildingsintheNetherlands.Usinga25m distancethreshold,wematchedalmostallof theStraboshops.Based ontheListedBuildingRegister,wehaveaddedinformationonwhether therentalpropertyisinanareathatisassignedasahistoricdistrict. Thelatterisrelevantsincehistoricdistrictsmayattracttouriststhatare notinterestedinshopping(CarlinoandSaiz,2008).Thedatasetisalso mergedwithdetailedlandusedatafromStatisticsNetherlands.Thelatter dataenablethecalculationofdistancetothenearestrailwaystation. Todetermineamenitiesandaccessibility oftheshop,wefirstgather datafromDuoonthelocationsofkindergartens,primaryandsecondary schoolsinthestreet.FromImergisweusethelocationofpublic build-ings(townhalls,policeandfirestations)andreligiousbuildings.Using OpenStreetMapwealsodeterminethenumberofbusstopsina shop-pingstreet.Itishardtocontrolforallrelevantamenities.Wetherefore gatherdatafromEricFisher’sGeotagger’sWorldAtlas,whichcontainall thegeocodedpicturesonthewebsiteFlickr.Thesepicturesshouldbea reasonableproxyforalocation’sattractiveness(seeGaigné etal.,2018). Theothermaindataset isa retaildatasetobtained from Locatus, whichcontainstheentirepopulationofshops.Foreachestablishment, weknowwhetherashopisvacantoroccupiedanditsretailsector(when occupied),andwhetheraretailfirmoccupyingashopispartofachain. Furthermore,weknowthe8-digitretailsector,whichprovidesvery de-tailedinformation.Forexample,wedonotonlyknowwhetheraretail firmsellsapparel,butalsowhetherittargetedatkids,womenormen.

writtenas 𝐼 1_{⋅ 𝜀}1

𝐼,𝑁−𝐼 2⋅ 𝜀2𝐼,𝑁.Nowsupposethatstreet1containsmoreshops

thanstreet2.Thisequationshowsthatlargershoppingstreetsmustreceive largersubsidiesaslongastheelasticityofrentalincomewithrespecttonumber ofshopsispositive(implyingI 1_>_I0₎_and_{non-decreasing}_in_the_number_of_shops

(so,𝜀 1

𝐼,𝑁≥𝜀 2𝐼,𝑁).Wewillseethatbothconditionsarefulﬁlled.Thisimpliesthat

subsidiestostoreownersinlargeshoppingstreetsmustexceedthoseinsmall shoppingstreets.

21 _Moreover,_our_{identification}_strategy_will_address_the_issue_of_‘percent_rents’. 22 _We_do_not_find_evidence_for_differences_between_the_transactions_with_and

withoutinformationonrents,althoughthelatterseemtorefertosomewhat largerrentalproperties.

TheLocatusdatasetalsoprovides3936annualcountsoffootfallin allmainshoppingstreetsoftheNetherlandsfrom2003to2015,sothat wehavemorethan50thousandfootfallcountsoverthewholestudy pe-riod.Themeasurementpointsarenottheshopsthemselves,butselected pointsinpedestrianstreetsoratsidewalkswithanaveragedistanceof 45mbetweenthem.Themainshoppingstreetscontainabout13.4% ofallshopsintheNetherlands.Theannualfootfalldata,providedby Locatus, isbasedonfootfallmeasurementscollected onfour‘regular’ Saturdays(twoinSpringandtwoinAutumn)atfourdiﬀerenthours oftheday.Usingthese16measurements,Locatuscalculatesthe aver-agefootfallperday.Thefootfalldataarematchedtoallshopsinthe previously-deﬁned shoppingstreets.Withineach shoppingstreet,the averagedistancebetweenfootfallmeasuresisapproximately45m.

Formostobservations(about90%)in theStrabo datasetwehave detailedinformationonthenameoftheretailﬁrmrentingthestore. WehavematchedeachrenttransactionintheStrabodatasettoashop intheLocatusdatasetinordertorecoverthe8-digitsectorandwhether theﬁrmispartofachain.

Wehavedefined ashoppingstreetasacontinuousstraightstreet (orslightlycurvedstreet)basedonmanuallycreatedGISpolylinesfor allstreetsforwhichthereisatleastonelocationwherefootfalldatais available.Usingthisdefinition,basedontheabove-discussedBuilding Registrydataset,wedefine1253uniqueshoppingstreets.Themedian lengthofthesestreetsis182m,sostreetsareshort.Themedianwidth ofastreetis12m.Thisunderlinesthatwefocusonshoppingstreets withinEuropeancitieswithshortandnarrowstreets,ratherthan,for example,U.S.cities,whichusuallyhavelongerandwiderstreets.

WeillustratethedatainFig.1basedonasampleofourdatafor thecitycentreof Amsterdam,whichcontains twoshoppingdistricts includingthecitycentre.Thisareaisthebusiestshoppingdistrictofthe Netherlandswiththehighestlevelofdailyfootfall.Itshowsthatthere is substantialspatialvariationin theannualaverageof footfallboth withinshoppingstreetsandbetweenshoppingdistricts.Moreover,rent transactions(thestarsinthemap)arenumerousandcoveralmostthe wholeshoppingdistrict.Thecentreofshoppingdistrictsisdetermined bytakingthelocationwiththehighestfootfallwithinthedistrict.

Forouridentiﬁcationstrategy,explainedlateron,wewillalsorely onhistoricdatagoingbackto1930oreven1832.Wegathered infor-mationon theexactlocationofcinemasin1930,aswellasin 2010 (in1930therewere315cinemas,whilein2010thishasbeenreduced to180)fromSpinLab.Formapsanddescriptivestatistics,wereferthe readertoAppendixB.1.

We furtheruse datafrom HISGIS, whichprovides geocodeddata of the ﬁrst Dutchcensusof 1830. Itis the oldest nationwide regis-trationsystemofpropertyandlandownership.Wehaveinformation on thefootprintsizeofeach building.Moreover, foreach parcelwe knowtheownerandtheowner’soccupation.Basedontheoccupation andwhethertherewasabuildinglocatedontheparcel,wedetermine whetherabuildingwasusedasashop.Weexplainthisin more de-tailinAppendixB.1.Foreachparcelwealsohaveinformationonthe so-calledCadastralIncome,whichisaproxyforthelandvalue,asland taxeswerebasedonthisvalue.Again,wereportdescriptivesandmaps inAppendixB.1.

3.2. Descriptives

Inthissection,wepresentthedescriptivestatisticsforthemain vari-ablesthatweincludeinouranalysis.Ourmaindependentvariableis theannualrentalprice.Table 1summarisesthedescriptivestatistics fortheStrabodataset.Wehave4738rentaltransactionslocatedin131 shoppingdistricts.Themeanrentalpriceisequalto€ 51,449.Footfall exhibitssubstantialvariationrangingfrom100to71,000pedestrians passingbyeachday.Meandailyfootfallis13,328withastandard de-viationof8935.

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Fig.1. SamplemapfortheAmsterdamcitycentre.

Table1

DescriptivestatisticsfortheStrabodataset.

(1) (2) (3) (4)

mean sd min max

Rent (in €) 51,234 83,227 3400 2,700,000

Footfall (number of shoppers per day) 13,328 8935 100 71,000

Number of shops, < 200 m 132.2 68.89 0 406

In pedestrianised street 0.862 0.345 0 1

Size of property (in m 2 ) _201.2 _{268.2 19} ₇₂₀₀

Building – new 0.0112 0.105 0 1

Building – renovated 0.00708 0.0839 0 1

Construction year 1933 85.30 1325 2016

In historic district 0.474 0.499 0 1

Number of photos in street, < 200 m 283.4 451.3 0 5181 Religious buildings in street, < 200 m 0.714 1.058 0 6

Bus stops in street, < 200 m 0.861 1.478 0 10

Public buildings in street, < 200 m 0.0955 0.302 0 2 Schools, kindergartens in street, < 200 m 0.153 0.515 0 4

Railway stations, < 200 m 0.0247 0.155 0 1

Notes :Thenumberofobservationsis4378.

whowalkthroughseveralstreets.Therefore,wewillmeasurethe num-berofshopswithinaradiusof200mfromeachshoplocation(butwe willalsoexperimentwithotherthresholds).Theareadeﬁnedbya200m radiusmaycontainseveralshoppingstreets.Thereareonaverage132 shopswithin200m,hencethenumberofshopswithinthevicinityis veryhigh.Moreover,thelargemajorityofshopsaresmall,withamean of201m2_._One_implication_of_this_is_that_individual_shops_usually con-tributelittletooverallfootfall,whichmakesitveryunlikelythatshop ownerswithinshoppingstreetshavemarketpowerandsuggeststhat theretailrealestatemarketishighlycompetitive.

Thecorrelationbetweenfootfallandnumberofshopsinthevicinity ismoderate(𝜌 =0.375).About1%ofshopsareeitherneworrenovated

whentherentaltransactiontookplace.About6%oftheshopsisbuilt before1832,whileabouthalfoftheshopsarebuiltbeforetheSecond WorldWar.Therefore,almosthalfoftheobservationsisinhistoric dis-tricts.InTable1wealsoprovideinformationaboutpedestrianstreets. Wedonotcontrolforpedestrianstreetsintheanalysis (pedestrianisa-tionmightbeendogenous),butnotethatthelargemajorityofshops, about85%,arelocatedinstreetsthatarepedestrianised.

Inourdata,wewilldistinguishbetween153shoppingdistricts(a shoppingdistrictcontainsabout260shops,onaverage).Asubstantial proportionof shoppingdistricts(about45%)arenotwithin 5kmof thecentreof acity.Hence,intermsofshoppingdistricts,wehavea goodrepresentationofshoppingdistrictsthatareoutofthecitycentre. However,theproportionofshopsnotwithin5kmofthecentreofacity is muchsmallerandonlyabout25%(assuburbanshopping districts tendtobesmaller).

InTable2,wereportdescriptivestatisticsforshopsintheLocatus dataset.Wehave410,544observationsofshopsin133shopping dis-trictsand1243shoppingstreets.About6%oftheshopsarevacant.23 Thedescriptivestatisticsofthelocationvariablesarecomparabletothe descriptivestatisticsfortheLocatusdata.

Wefocusonshopsinshoppingstreetsthatpresumablyaimtobeneﬁt fromfootfall,henceoursampleofshopsisfarfromarandomsample ofshops.Thisisparticularlythecaseforclothing.Clothingstoresare themostcommonbranch(30%ofshops)– almost4timeshigherthan thenationalaverage.However,thisisnotthecaseforrestaurantsand

23_The_Strabo_dataset_contains_a_considerably_higher_share_of_shops_in_older

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Table2

DescriptivestatisticsfortheLocatusdataset.

(1) (2) (3) (4)

mean sd min max

Shop is vacant 0.0610 0.239 0 1

Footfall (number of shoppers per day) 12,379 10,732 100 102,600

Number of shops, < 200 m 129.0 62.77 0 439

In pedestrianised street 0.843 0.364 0 1

Building size (in m 2 ) _179.9 ₁₀₈₉ ₂₅ _27,694

Construction year 1967 35.83 1445 2012

In historic district 0.403 0.490 0 1

Number of photos in street, < 200 m 280.5 560.7 0 5493 Religious buildings in street, < 200 m 0.755 1.096 0 7

Bus stops in street, < 200 m 0.705 1.338 0 10

Public buildings in street, < 200 m 0.0951 0.301 0 2 Schools, kindergartens in street, < 200 m 0.185 0.552 0 4

Railway stations, < 200 m 0.0193 0.138 0 1

Notes :Thenumberofobservationsis410,544.

cafés:theshareofrestaurantsandcafés(16%)isexactlyequaltothe nationalaverage.Inbothbranchesthedegreeofproductdiﬀerentiation isextremelyhigh.

InEurope,shoppingdistrictsusuallyexhibitapatternofmixedland uses.ThisisalsothecaseintheNetherlands.Usinginformationfromthe BuildingRegistryonbuildingswithin25mofashoppingstreet,itappears thatasmallminority,onlyaboutonequarter,ofthepropertiesisused forshopping,whereasalmosthalfofthepropertiesisresidential,and theotherquarterisusedforotherpurposes(e.g.oﬃces,publicservices). Theobservationthatshopsaretypicallysmallsuggeststhatthe re-tailrealestatemarketishighlycompetitive,butthisisonlytruewhen storeownership(andthereforelandownership)withinshoppingstreets ishighlyfragmented.Thisappearstobethecase.Thisclaimisbased ontheStrabodatasetforwhich storeowner typeandregularlyeven owner’snameisreported(weknowthestoreownertypeforabouttwo thirdsoftheobservationsandstoreowner’snameforaboutonethird oftheobservations).Usinginformationaboutnames,itappearsthaton averageonly28%oftheshopswithinashoppingstreetbelongtoastore ownerwhoownsmorethanoneshopinthesameshoppingstreet.24 On average,storeownerspossess1.32shopsperstreet,whichisalow num-bergiventhatthereareonaverage55shopsperstreet.Thisindicates thatitishighlyunlikelythattheshoppingexternalitythatwemeasure isinternalised.

Wealso useinformationabout owner typethat distinguishes be-tweenprivate-storeowners, realestateagencies,pension funds, con-structioncompaniesetc.Only34%ofshopsareownedbyrealestate investors.Thus,thelarge majorityofshopsareownedbyindividual privateinvestors,whichfurthersupportsourclaimthatownershipof shopswithinshoppingstreetsishighlyfragmented.Wealsogathered in-formationfromMenger(2014)onlocalisedshopassociations,inwhich externalitiesmaybeinternalised (butwhich maynotengagein anti-competitiveactivities).Theseshopassociationsarearea-basedand or-ganisee.g.collectivemarketingandprovidepublicgoodssuchas Christ-maslightning.Onaverage14%oftheretailﬁrmsarepartofsuch asso-ciations.

4. Econometricframework

4.1. Rents

Wefirstfocusontheestimationoftheeffectofshoppingexternalities onrentsofretailestablishments.Letpijtbetherentpaidbyretailfirmi

inshoppingstreetjinyeart.Weusetwoproxiesforshopping

external-24 _Given_that_this_dataset_only_contains_rental_{transactions,}_it_is_likely_that_the

shareofmulti-storeownersisoverrepresentedinoursample,becausethisshare islikelylowerforownedshops.

ities𝑠_𝑖𝑗𝑡={𝑓_𝑖𝑗𝑡,𝑁_𝑖𝑗𝑡}:footfallandthenumberofshopsinthevicinity. Furthermore,letx_ijtbeothershopandlocationcharacteristics(e.g.shop size,constructionyear,historicdistrictetc.).Thebasicequationtobe estimatedyields:

log𝑝_𝑖𝑗𝑡=𝛼 log𝑠_𝑖𝑗𝑡+𝛽𝑥_𝑖𝑗𝑡+𝜃_𝑡+𝜖_𝑖𝑗𝑡, (10) where𝛼 and𝛽 areparameterstobeestimated,𝜃tareyearﬁxedeﬀects

and𝜖ijtisarandomerrorterm.

Thereareanumberofconcernswhenusingfootfallasaproxyfor shoppingexternalities.Onemaybeworriedthatnon-shoppersand one-stopshoppersmaybeincludedinfootfall.Arguably,thisisaminorissue becauseourmeasureoffootfallpredominantlyincludesshopperswho visitseveralshops.25

Anotherconcernismeasurementerror.Measurementerrorislikely presentforarangeofreasons.First,forfootfall,weonlyhavemeasures onspecificSaturdays,whichmaynotberepresentativefortheaverage Saturday,orforotherdaysoftheweek.Webelievethattheextentof measurementerrorhereisnottooserious.Second,thenumberofshops inthevicinitymayhavesubstantialmeasurementerror,becauseshops differsubstantiallyinsize.Inspecificationswithstreetfixedeffects,the biascausedbymeasurementerrorwithinthesamestreetmaybecome morepronounced.Mostlikely,wewillgetunderestimatesbecauseof measurementerror.Totakemeasurementerrorintoaccount,wewill useanIVapproach,asexplainedlateron.

Amoreseriousconcernispotentialsimultaneity.Rentsofshopsmay determinethetypeofshop,whereasshopsvaryintheextentoffootfall theygenerate;hencethereispotentiallyaneffectofrentsonfootfall. Furthermore,thelevelofrentmaydeterminethesizeofshopsand there-fore,thenumberofshopsinvicinity.Hence,thenumberofshopsmay alsobeendogenous.Moreover,theremaybeunobservedstoreand loca-tioncharacteristicsthatarecorrelatedwithfootfallandthenumberof shopsinthevicinity.Forexample,astore’sbuildingqualitymaybe im-portantforprofits.Whenbuildingqualityisnon-randomlydistributed overspace(e.g.nicerbuildingsinareaswithmorefootfallandshops) andcustomersvaluebuildingquality,anaïvehedonicregressionwould sufferfromomittedvariablebias.

Tomaketheidentificationofacausaleffectofshoppingexternalities moreplausible,wetakeanumberofsteps.First,weincludeshopping districtfixedeffects,implyingthatweidentifythedifferencesin foot-fallwithintheshoppingdistrict.Thisapproachmitigatestheproblem ofunobservedendowments,butmaynotsolvetheproblementirely be-causeshoppingdistrictsmaybequitelarge.Wethereforealsopropose anotheridentificationstrategyusingspatialvariationinlocalfootfall withinshoppingstreets.Wewillalsocontrolforweb-scrapeddataon picturestakenbyresidentsandtouristsandcountthenumberofpictures ineachshoppingstreet.Theideaisthatlocationswithanabundant sup-plyofaestheticamenitiesmayhaveahighpicturedensityandahigh numberofnon-shoppersorone-stopshoppers.26

Second,tomitigatetheissuethatspecificretailfirmsthatgenerate alotoffootfallmaynegotiatelowerrents,weuseinformationonthe 8-digitretailsectorandwhethertheretailfirmispartofachain.𝜓i∈kis

thenaﬁxedeﬀectforeachretailsectorbychaincombination,denoted byk.Wethenestimate:

log𝑝_𝑖𝑗𝑡=𝛼 log𝑠_𝑖𝑗𝑡+𝛽𝑥_𝑖𝑗𝑡+𝜑_𝑗+𝜓_𝑖∈𝑘+𝜃𝑡+𝜖𝑖𝑗𝑡, (11)

25_Since_the_probability_that_a_shopper_is_included_in_our_measure_of_footfall

is(approximately)proportionaltothenumberofshopsvisited,theshareof non-shoppersorone-stopshoppersshouldbemuchsmallerthantheshareof multi-stopshoppers.Forexample,if25%offootfallwereone-stopshoppers, andtheother75%visitfourshops,thentheproportionofone-stopshoppers wouldbeonly7.8%.

26_Ahlfeldt₍₂₀₁₆₎_and_{Gaigné et}_al.₍₂₀₁₈₎_show_that_there_is_a_strong_positive

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where𝜑jareshoppingstreetﬁxedeﬀects.

Weimproveonthisspecificationbyestimatingspecificationswhere (i)weincluderetailfirmfixedeffectstofurthercontrolforunobserved retailfirm characteristics,(ii) onlyfocusonsmall shops,whereitis unlikelythattheretailfirmwillcontributesubstantiallytofootfall,and (iii)focusonfirmsthatarenotpartofalargerretailchain,whichare morelikelytoadvertiseandthereforetogeneratefootfall.Wealsoshow that(iv)whenflexiblycontrollingforthewalkingtimetothecitycentre, theresultsareessentiallyunaffected.

Still,onemaynotbefullyconvincedthatEq.(11)fullyaddressesthe issueofunobservedstoreandlocationalcharacteristics.Furthermore,it isplausiblethatreversecausationstillplaysarole.

Inordertoaddresssuchconcerns,wewill alsopursuean instru-mentalvariablesstrategy.Wewilluselocallylong-laggedinstruments, whichdonotaffectdirectlytoday’srents,butdeterminecontemporary concentrationofshopsand,therefore,footfall.Morespecifically, condi-tionalonshoppingstreetfixedeffects,wewillfirstusethenumberof cinemasin1930inthevicinityasaninstrumentforthecurrentnumber ofshopsinthevicinityandfootfall.

Weusecinemasin1930asaproxyforhistoricshops,becausewedo nothavehistoricdataonthelocationofshops.Historicshopswouldbe apreferredinstrument,becauseonemayarguethatchanginghistorical buildingsfordiﬀerentuse(e.g.fromretailintoresidentialortheother wayaround)isacostlyprocessandrequireschangingzoningplans.Asa result,currentretailoutletstendtobelocatedinbuildingswhereretail was1930evenwithinthesamestreet.

Historically,mostcinemasweresmall, withonescreen only,and werelocatedinshoppingstreets(thosewhohavesurvivedtendtobe relativelylarge).Thebuildingscontainingsuchcinemasarenot very diﬀerentfromthesurroundingbuildingstypicallyusedforshops.One maybe concernedthatcinemasthemselvescreatefootfall,while this doesnotnecessarilyimplyshoppingexternalities(aspeoplemayonly visitthecinemaandnotvisitothershops).Hence,wecontrolforthe numberofcinemasinthevicinityin2010.27 Thebuildingsoftheclosed cinemasnowadaysarefrequentlyusedasshops,butalsoattractother businesses.

Themainidentifyingassumptionwhenrelyingonlong-lagged in-strumentsisthatpastunobservablecharacteristicsofeitherstoresor locationsareuncorrelatedtocurrentunobservables (whichaffect de-mand).Thisassumptionisoftencriticisedbecausethelocationsofcities aredeterminedlongago,e.g.duetonaturaladvantages.However,we identifytheeffectwithinshoppingstreets,making theidentifying as-sumptionmorecredible.28 Themostobviousthreattoidentificationis thatpastbuildingandlocationqualityarecorrelatedtoshopping exter-nalities.Wethereforecontrolforconstructionperioddummiesincluding adummywhethertheshopshasbeenbuiltbefore1930.Wealsoinclude adummyindicatingwhetherthepropertyisinahistoricdistrictto con-trolforthequalityof(historic)buildingsinthesurroundings.

Wealsoconstructanalternativeinstrumentbasedondataofthe ex-actlocationsofallbuildingsin1832,whichisavailableforabout50% ofourdata.Basedonoccupationalcensusoflandowners,wedetermine whetheracertainbuildingwasashop.Wethencalculatethenumber ofshopsin1832inthevicinity.Thecensusfrom1832alsoprovides informationontheso-calledCadastralIncome,whichwasataxbased ontheassessedvalueofeachparcelofthebuildingandthe

surround-27 _In_the_shopping_streets_we_focus_on,_there_are_currently₁₈₀_cinemas,_but

in1930therewereabout60%more(315cinemas).Wecontrolforcurrent cin-emas,sovariationincinemascomesfromthepresenceofclosed,andlikely smaller,cinemas.

28 _{Gaigné et}_al.₍₂₀₁₈₎_argue_that_for_Dutch_cities,_the_amenity_distribution

withincitieshasconsiderablychanged.Forexample,aroundthe1930s,open wateranddenselybuilt-upareaswerenotnecessarilyconsideredamenities.It wasalsobeforethetimewhencarsbecamethedominantmodeoftransport. Peopleusuallywalkedtotheirworkingplace,andthuscommutingdistances wereveryshort.

ingland.Wewillthereforecontrolforthevalueoflandin1832,which shouldaddresstheissuethatpastunobservablesarecorrelatedto cur-rentunobservables.Tofurthercontrolforthefactthatalocationisin ahistoricallydenserpartofthestreet(e.g.closertothecitycentre),we controlforthenumberofbuildingsin1832inthevicinity.

Hence,ouridentiﬁcationstrategyexploitsthatthereisareasonably strongautocorrelationofshoplocationsovertime.Thisautocorrelation ofretaillocationsisalsoinlinewithanecdotalevidence.Forexample, Amsterdam’scurrentmainshoppingstreet,theKalverstraat,hasbeenan importantshoppingstreetformorethan300years.29 Weemphasisehere thattheunobservedfactorswhichmakeshoplocationsattractivenow, arelikelyverydiﬀerentfromthe(economic)forceswhichinducedshops tosettleat certainlocationshistorically:up toa hundredyearsago, shopperswalkedtothesestreets,andshopworkers,whowerealsoshop owners,frequentlylivedabovetheirshops.Nowadays,duetochanges in transporttechnology,shoppersdonot walktotheshoppingstreet (butonlywithin),whereasshopworkers,whoareemployeesandnot shopownersany more,come fromfarawayusingmoderntransport technologies(motorvehicles,publictransport,bicycle).

Theﬁrststageofourestimationprocedureentails:

log𝑠_𝑖𝑗𝑡=̃𝛿 log𝑧_𝑖𝑗+ ̃𝛽𝑥_𝑖𝑗𝑡+̃𝛾ℎ_𝑖𝑗+𝜑̃_𝑗+ ̃𝜓_𝑖∈𝑗+ ̃𝜃𝑡+𝜉𝑖𝑗𝑡, (12)

wherethe ∼ refer toﬁrst-stagecoeﬃcients, z_ij iseither thenumber ofcinemasin1930orthenumberofshopsin1832inthevicinity.hij

arecontrolvariablesrelatedtothehistoricinstruments(e.g.numberof cinemasin2010,CadastralIncomein1832).Thesecond-stageisgiven by:

log𝑝_𝑖𝑗𝑡=𝛼 loĝ𝑠_𝑖𝑡+𝛽𝑥_𝑖𝑗𝑡+𝛾ℎ_𝑖𝑗+𝜑_𝑗+𝜓_𝑖∈𝑗+𝜃𝑡+𝜖𝑖𝑗𝑡, (13)

where loĝ𝑠_𝑖𝑗𝑡={log𝑓̂_𝑖𝑗𝑡,log𝑁̂_𝑖𝑗𝑡} represents the predicted footfall or numberofshopsfromtheﬁrststage.

4.2. Vacancies

Wewillalsoestimatetheeffectoflogfootfalaswellasthelog num-berofshopsinthevicinity,onwhethertheshopisvacant,indicatedby thedummyvariablev_ijt.Onceagain,wewilluseshoppingstreetfixed effectsandexploit thevariationin footfallandtheprobabilitytobe vacantwithinshoppingstreets.Forthesamereasonsthatfootfallmay beendogenouswithrespecttorent,itispossiblethatfootfallis endoge-nouswithrespectofvacancies.Furthermore,theremaybeadirectform ofreversecausation,becauseoneexpectsfootfalltodecreasewhen va-canciesincrease.Wewilluseagainlong-laggedhistoricinstrumentsto dealwithendogeneityissues,asitisimpossiblethatcurrentvacancies directlyimpactthenumberofcinemasin1930orthenumberofshops in1832.

5. Results

Theresultssectionisstructuredasfollows.Wefirstdiscusstheeffects offootfallandthenumberofshopsintheshoppingstreetonrents.In thesecondpart,wefocusontheeffectsoffootfallandthenumberof shopsontheprobabilityofashoptobevacant.Wetaketheseresults togethertoestimatetheeffectsoffootfallandnumberofshopsonrental income.Weclosethissectionbydiscussingthewelfareimplicationsand derivingthePigouviansubsidy.

5.1. Shoppingexternalitiesandrents

Table3reportstheresultsofourbaselineregressions.The specifica-tionincolumn(1)isanordinaryleastsquares(OLS)regressionofthe logrentalpriceonlogfootfall,logsizeoftheshop,building character-istics,andshoppingdistrictfixedeffects.Theelasticityoffootfallwith

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Table3

Resultsforretailrents.

(Dependent variable: log of rent per m 2 )

Footfall Number of shops

(1) (2) (3) (4) (5) (6)

OLS OLS OLS OLS OLS OLS

Footfall (log) 0.3737 ∗∗∗ _0.3181∗∗∗ _0.2609∗∗∗ (0.0149) (0.0203) (0.0181)

Number of shops, < 200 m (log) 0.1786 ∗∗∗ _0.2066∗∗∗ _0.1513∗∗∗

(0.0214) (0.0359) (0.0324) Size of property (log) 0.6376 ∗∗∗ _0.6267∗∗∗ _0.5929∗∗∗ _0.6323∗∗∗ _0.6283∗∗∗ _0.5938∗∗∗ (0.0119) (0.0121) (0.0136) (0.0131) (0.0126) (0.0141)

Building – new 0.1341 0.0844 0.0877 0.0980 0.0684 0.0671

(0.0948) (0.0790) (0.0795) (0.0843) (0.0805) (0.0816) Building – renovated 0.4123 ∗∗∗ _0.3715∗∗∗ _0.3148∗∗∗ _0.3256∗∗∗ _0.3391∗∗∗ _0.2908∗∗∗ (0.1162) (0.0830) (0.0842) (0.0928) (0.0880) (0.0847)

Construction year dummies Yes Yes Yes Yes Yes Yes

Location characteristics No Yes Yes No Yes Yes

Year ﬁxed effects Yes Yes Yes Yes Yes Yes

Shopping district ﬁxed effects Yes Yes Yes Yes Yes Yes

Shopping street ﬁxed effects No Yes Yes No Yes Yes

Retail sector × chain ﬁxed effects No No Yes No No Yes

Number of observations 4378 4378 4378 4378 4378 4378

R2 _0.682 _0.782 _0.821 _0.604 _0.760 _0.807

Notes :Footfallismeasuredasthenumberofshoppersperday.Theconstructionyeardummiesarecategorisedas follows:< 1832,1832–1930,1931–1950,1951–1960,1961–1970,1971–1980,1981–1990,1991–2000, > 2000. Locationcharacteristicsincludewhetherthepropertyisinahistoricdistrict,andthenumberofgeocodedpictures

< 200m,religiousbuildings< 200m,busstops < 200m,publicbuildings< 200m,schools,andrailwaystations

< 200m.Robuststandarderrorsareclusteredatthepostcodeandinparentheses.∗∗∗_p_<_0.01,∗∗_p_<_0.05,∗

p < 0.10

respecttorentalpriceis0.37.Thecontrolvariableshaveplausiblesigns, withlargerandrenovatedpropertiesbeingmoreexpensive.30

Thespecificationincolumn(1)mightsufferfromomittedvariable bias due to theomission of unobserved features of a shop location thatarecorrelatedwithfootfall.Forexample,someshoppingareasare moreattractivedue totheirproximitytoabusstop,schoolorother neighbourhood-specificamenities.Apartialsolutiontothisproblemis theinclusionofshoppingstreetfixedeffectsandlocationcharacteristics incolumn(2),whichmaymitigatethisendogeneityissue.Thishardly affectstheresults.

Onemaystillbeconcernedthatrentsarepartlydependentonthe amountoffootfallashopgenerates– sothatreversecausalityisanissue. Tomitigatethisissue,wewillincluderetailsector×chainfixedeffects. Thatis,weincludeadummyforwhetheraretailfirmispartofachain ineach retailsector,whichshould absorbmost oftheheterogeneity inexpectedsalesbetweenretailfirms.Thecoefficientincolumn(3)is somewhatsmallerandnowequals0.26.Thus,a10%increaseinfootfall isassociatedwitharentincreaseof2.6%.

Columns(4)–(6)inTable3focusesonanotherproxyforshopping externalities:thenumberofshopswithin200m.Whenusingshopping districtfixedeffects,theelasticityis0.179(seecolumn(4)).This elastic-ityisslightlyhigherwhenusingshoppingstreetfixedeffectsincolumn (5).Whencontrollingforretailsector×chainfixedeffects,the elastic-ityis0.151.Hence,a10%increaseinthenumberofshopsleadstoan increaseinrentsof1.5%.Thelatterelasticityisabout40%lowerthan theelasticitywithrespecttofootfall.However,thenumberofshopsin thevicinityasaproxyforshoppingexternalitiesmaybemeasuredwith error,e.g.becausewedonotknowtheexactrelevantspatialscaleof shoppingexternalities.Wewillthereforeinvestigatewhetherthis con-clusionstillholdswhenusinginstrumentalvariables.

Table4furtherinvestigateswhetherthepreviousresultsmakesense. Wefirstfocusonfootfall.Incolumn(1)weincluderetailfirmfixed

ef-30 _Note_that_the_dummy_variable_indicating_whether_the_property_is_new_is

conditionalontheconstructionyear,sopartoftheeﬀectofbeinginanewer buildingisabsorbedbytheconstructiondecadedummies.

fects,implyingthatweincludedummiesforeachandeveryretailchain andindependentretailfirm.Thisimpliesthatwecomparerentand foot-falldifferencesofidenticalfirmswithinthesameshoppingstreet.The resultsstillindicateasizeableeffectoffootfall:a10%increasein foot-fallisassociatedwitha1.8%increaseinrents.Notsurprisingly,because ofthelargenumberoffixedeffects,theestimateislesspreciseandonly statisticallysignificantatthe5%level.Giventhestandarderror,the es-timateisnotstatisticallysignificantlydifferentfromthepreferred spec-ificationincolumn(3),Table3.

Incolumn(2)ofTable4,wecontrolflexibly(usinga5th-order poly-nomial)forthewalkingtimetothecentreoftheshoppingdistrict,by includingafifth-orderpolynomialofwalkingtimetothecentre.When one-stopshoppersareimportant,theymayaccessshoppingdistrictson onelocation(e.g.thecentreortheedgeofacitycentre)andthenwalk tothe intendedshop in thecentre,while passing manyother shops (Teulingsetal.,2017).Ontheotherhand,controllingforwalkingtime tothecentremayalsopartly absorbshoppingexternalities. Reassur-ingly,thefootfallcoefficientishardlyaffected.

Onemaystillbeworriedthatfootfallisinfluencedbytherentthat retailfirmshavetopay(e.g.duetorentspaidasafunctionofexpected retailrevenuesorexpectedgeneratedfootfall).Incolumns(3)and(4) we thereforeonlyincluderetailfirmsthatareunlikelytocontribute (substantially)tolocalfootfall.Column(3)onlyincludesshopsthatare smallerthan90m2_(the_25th_percentile)._The_estimate_is_virtually iden-ticaltothepreferredspecification.Alsowhenweonlyfocusonretail firmsthatarenotpartofachain,theestimateisessentiallythesame. Thisseemstosuggestthattheissueofreversecausalityislimited. Impor-tantly,italsostronglysuggeststhattheelasticityofrentswithrespect tofootfalldoesnotvarybetweentypesoffirms,i.e.heterogeneityofthe estimatesisabsent,atleastwhenwedistinguishbetweendifferentsizes offirmsorwhetherretailfirmsarepartofachain.Wecomebackto thisissuelateron.

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ap-Table4

Footfallandretailrents:extensions.

(Dependent variable: log of rent per m 2 )

Retailer Walking time Small No chain Historic instruments: Historic instruments:

ﬁxed eﬀects to the centre shops shops cinemas in 1930 shops in 1832

(1) (2) (3) (4) (5) (6) (7) (8) (9)

OLS OLS OLS OLS 2SLS 2SLS 2SLS 2SLS 2SLS

Footfall (log) 0.1820 ∗∗ _0.2032∗∗∗ _0.2556∗∗∗ _0.2435∗∗∗ _0.4563∗∗∗ _0.4348∗∗∗ _0.4034∗∗∗ _0.3740∗∗∗ _0.4799∗∗ (0.0724) (0.0189) (0.0553) (0.0228) (0.1061) (0.0982) (0.1131) (0.1105) (0.2203)

Number of cinemas in 2010, < 200 m (std) 0.0107

(0.0115)

Cadastral income (log) − 0.0177 − 0.0213

(0.0236) (0.0256)

Cadastral income is zero in 1832 − 0.1822 − 0.2700

(0.2659) (0.3240)

Number of buildings in 1832, < 200 m (std) − 0.0461

(0.0868)

Shop characteristics Yes Yes Yes Yes Yes Yes Yes Yes Yes

Location characteristics Yes Yes Yes Yes Yes Yes Yes Yes Yes

Walking time to centre, f (·) No Yes No No No No No No No

Shopping street ﬁxed effects Yes Yes Yes Yes Yes Yes Yes Yes Yes

Retail ﬁrm ﬁxed effects Yes No No No No No No No No

Retail sector × chain ﬁxed effects Yes Yes Yes Yes Yes Yes Yes Yes Yes

Year ﬁxed effects Yes Yes Yes Yes Yes Yes Yes Yes Yes

Number of observations 4378 4378 987 2932 4378 4378 2496 2496 2496

R2 _0.969 _0.826 _0.873 _0.792

Kleibergen-Paap F -statistic 42.65 48.68 31.46 32.67 17.95

Endogeneity test 4.858 4.426 0.790 0.795 1.153

𝜉2 (2) p -value _0.0275 _0.0354 _0.374 _0.373 _0.283

Notes :Footfallismeasuredasthenumberofshoppersperday.Shopcharacteristicsincludepropertysize,whetherthebuildingisneworrenovatedandconstruction yeardummies,whicharecategorisedasfollows:< 1832,1832–1930,1931–1950,1951–1960,1961–1970,1971–1980,1981–1990,1991–2000,> 2000.Location characteristicsincludewhetherthepropertyisinahistoricdistrict,andthenumberofgeocodedpictures < 200m,religiousbuildings < 200m,busstops < 200m, publicbuildings< 200m,schools,andrailwaystations< 200m.Robuststandarderrorsareclusteredatthepostcodeandinparentheses.∗∗∗_p_<_0.01,∗∗_p_<_0.05,∗

p < 0.10

pearstobestrongandmeaningful:astandarddeviationincreaseinthe numberofcinemasin1930increasescurrentfootfallby12%.31 The ef-fectoffootfallisnowsomewhatstronger(0.456),whichisstatistically differentfromthebaselineestimateusingaHausman-test,reportedat thebottomofthetable.32 Onemaybeworriedthatcinemasmostly at-tractone-stopshoppers.Wethereforecontrolforthenumberofcinemas in2010incolumn(6).Itcanimmediatelybeseenthatthecoefficient offootfallishardlyaffected.Moreover,thecurrentlocationofcinemas donotseemtogeneratehigherrents.

Columns(7)–(9)useanalternativesetofinstruments,byrelyingon datafromthe1832census.Becausethesedataareonlyavailablefor about50%of theNetherlands, ournumberofobservationsis lower. Column(7)indicatesastrongfirststage:astandarddeviationincrease inthenumberofshopsin1832increasesfootfallby35%.Thefirststage isagainstrong,albeitlessstrongthanwhenusingcinemasin1930asan instrument.Forthisspecification,theIVestimateisnotstatistically sig-nificantlyhigherthanthebaselineOLSestimate(theendogeneitytest hasap-valueof0.374).Themainadvantageofthe1832dataisthat wehaveinformationontheCadastralIncome,whichisagoodproxyof thevalueofpropertyin1832.Ofcourse,thereisafairshare(20%)of missingvalues,eitherbecauselandwasnot(commercially)owned(e.g. becauseitwasnotyetreclaimedfromthesea),oritwasmissing.We thereforeincludeadummyindicatingwhethertheCadastralIncomeis missing.Inanycase,controllingfortheCadastralIncomedoesnotmake

31 _The_ﬁrst-stage_results_are_reported_in_Appendix_D.1_.

32 _We_have_also_re-estimated_the_model_by_redeﬁning_the_instrument_into_a

dummyvariable(wethenuseabinaryvariablefortheproximitytoacinema). WiththedummyinstrumenttheIVestimatesaresomewhatlower,andbased onaHausmantest,notstatisticallysigniﬁcantfromtheOLSestimates. Conse-quently,followingargumentsdevelopedbySargan(1958),andmorerecently emphasisedbyYoung(2019),onemayprefertheOLSestimates,asthesehave beenmorepreciselyestimated.

anydifference,astheCadastralIncomedoesnotseemtoberelatedto currentrentsofretailproperties.33 Hence,theassumptionthat unob-servedendowmentswithinshoppingstreetsofthepastareuncorrelated tocurrentunobservedstoreandlocationcharacteristics,isevenmore plausible.Inthefinalspecificationwealsocontrolforthenumberof buildingswithin200m,tomakesurethatwedonotjustmeasurethat certainshopsareinlocations thataredenser(e.g.citycentres). Col-umn(9)showsthatitisindeedthelocationsshopsin1832thatmatter forcurrentfootfall,astheeffectofnumberofbuildingsisstatistically insignificant.Thecoefficientalsobecomessomewhatstronger,but be-causeofthewideconfidencebands,itisnotstatisticallysignificantly differentfromthebaselineOLSestimate.

InTable5werepeatthesamesetofspecifications,butnowusing theothermeasureforshoppingexternalities:thenumberof shopsin thevicinity.Whenusingretailfirmfixedeffects,orwhencontrolling flexiblyforthewalkingtimetothecentreoftheshoppingdistrict,the estimatesareabout50%lower(respectivelycolumns(1)and(2)). How-ever,whenfocusingonsmallstoresorwhenonlyincludingchainstores, theelasticitiesarecomparabletothebaselineestimates(respectively columns(3)and(4)).Again,theresultsstronglysuggestanabsenceof between-firmheterogeneityintheelasticityofrentwithrespectto shop-pingexternalities.

Incolumns(5)–(9)weusehistoricinstruments.Inallspecifications, theimpactofnumberofshopsismuchhigherwhenusingIVthanwhen using OLS.Inmostspecifications,endogeneitytestsindicate thatthe estimatesusinginstrumentsaresignificantlyhigher.Animportant ob-servationisthattheIVestimatesfortheelasticityofnumberofshopsare verycomparabletoIVestimatesfortheelasticityofrentwithrespectto

33_Furthermore,_the_{unconditional}_correlation_between_log_price_and_log