The amplifying effect of capitalization rates on housing supply

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Journal of Urban Economics

journalhomepage:www.elsevier.com/locate/jue

The amplifying effect of capitalization rates on housing supply ^✩

Simon Büchler

, Maximilian v. Ehrlich

, Olivier Schöni

aMIT Center for Real Estate

bCenter for Regional Economic Development (CRED), Department of Economics, University of Bern

cDepartment of Finance, Insurance and Real Estate, Laval University

a r t i c le i n f o

JEL classification:

R 1 R 3 R 5 Keywords:

Housing supply Capitalization rate Land use regulation Geographic constraints

a b s t r a ct

Weprovideempiricalevidencethatincreasesinhousingrentalincomeleadtoalargersupplyresponsethanprice increasesofthesamepercentagevalue.Werationalizethisdifferentialinsupplyresponsivenesswithanampli- ficationmechanismarisingfromadownwardrevisionofcapitalizationratesfollowingarentalincomeincrease.

Wedocumentthattheamplificationofthehousingsupplypriceelasticityislesspronouncedingeographically constrainedandtightlyregulatedneighborhoodsandareashavingmoresophisticatedinvestors.Ourfindings holdvaluablelessonsforpublicpoliciesaffectingthehousingrentalincome,suchasrentcontrolandhousing subsidies.

1. Introduction

Existingresearchemphasizestheimportanceofhousingsupplyprice elasticityfora varietyof economicoutcomes.Theresponsivenessof housingsupplyaffects,amongotherthings,housingcycles,theallo- cationoflaboracrossspace,andthedegreeofcapitalizationofpublic policiessuchasplace-basedsubsidies.¹However,todate,weknowrel- ativelylittleabouttheresponsivenessof housingsupplywithrespect tochangesinrents.Thisissurprising,asurbaneconomictheorytypi- callyfocusesonperiodichousingcosts,andmanypublicpoliciessuch asrentcontrolandhousingsubsidiesdirectlyactontherentalincome generatedbyrealestateproperties.Inthispaper,weinvestigateunder whichcircumstancesthehousingsupplyresponsivenesstochangesin rentsdiffersfromthesupplyresponsivenesstopricechangesandwhy theratioofrentandpriceelasticitiesvariesacrossregions.

Westartbydevelopingapartialequilibriumframeworkfeaturing housingsupplyanddemandaswellasrealestateinvestors.Thethe-

✩ WearegratefultoBrentAmbrose,PaulAnglin,NathanielBaum-Snow,AymoBrunetti,GuillaumeChapelle,DavidGeltner,LuHan,ChristianHilber,Albert Saiz,AlexvandeMinne,AnnieKinsellaThompson,BillWheaton,PaulWillen,Jeff Zabelandtwoanonymousrefereesforveryhelpfuladviceandsuggestions.We benefitedfromnumerouscommentsbytheparticipantsoftheBostonFEDUrbanandRealEstateSeminar,theUniversityofSt.GallenResearchSeminar,2019UEA inPhiladelphia,2018UEAinNewYork,2018SSES,MITCREResearchSeminar,SRERCZurich2017,CREDResearchSeminar,aswellasfromthemonitoringgroup atSECOandBWO.WethankMeta-Sys,Comparis,SwissFederalStatisticalOffice,SwisscantonalofficesandComparisforgenerouslysharingtheirdata.Ehrlichand SchöniacknowledgefundingfromtheSwissNationalScienceFoundation(grantnumber162589).

∗Correspondingauthorat:DepartmentofFinance,InsuranceandRealEstate,LavalUniversity,2325RuedelaTerrasse,G1V0A6,Québec.

E-mailaddresses:buechler@mit.edu(S.Büchler),maximilian.vonehrlich@vwi.unibe.ch(M.v.Ehrlich),olivier.schoni@fsa.ulaval.ca(O.Schöni).

1 Forinstance,Glaeseretal.(2008)investigatetheroleofhousingsupplyelasticitiesforpricedynamics,Diamond(2017)linksthedegreetowhichlocalgovern- mentscanextractrentstohousingsupplyelasticities,KlineandMoretti(2014)emphasizetheimportanceofhousingsupplyelasticityforthedistributionaleffects ofplace-basedpolicies,andHsiehandMoretti(2019)focusontheimplicationsofhousingsupplyconstraintsforthespatialmisallocationoflabor.SeeGlaeserand Gyourko(2018)andHilber(2017)forasynthesis.

oreticalframeworkservestwopurposes.First,itguidesourempirical analysisand, inparticular,motivates theidentificationstrategyused toestimatehousingsupplyelasticities.Second,itallowsustorational- izedifferencesintheestimatedsupplyresponsivenesstorentandprice dynamics.Weshowthatlocalchangesininvestors’expectationsabout rentalincomegrowthandriskpremiaaredecisivetoexplainsupplydif- ferences.Specifically,thehousingsupplyresponsetochangesinprices andrentsisidenticalifcapitalizationratesdonotadjusttochangesin rents.Ifcapitalizationratesdoadjust,housingsupplypriceelasticities areeitheramplifiedordampenedbythisadjustment.

Next,webringthetheoreticalframeworktothedataandestimate theaverageresponsivenessofhousingsupplywithrespecttopriceand rentchangesattheneighborhoodlevel.Todoso,weusedetailedgeoref- erenceddataonadvertisedresidentialpropertiesandbuildingstockfor Switzerlandcoveringtheperiod2005–2015.Wefindthatanincrease in rentsleadstoanaboutthriceaslargesupplyincreasethananin- creaseofpricesofthesamepercentagevalue:Thesupplyresponsefol-

https://doi.org/10.1016/j.jue.2021.103370

Received29February2020;Receivedinrevisedform14June2021 Availableonline3July2021

0094-1190/© 2021TheAuthors.PublishedbyElsevierInc.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/)

lowingatenpercentincreaseinsquaremeterrents(prices)isapprox- imately14percent(fourpercent).Accordingtoourframework,these resultssuggestthat,onaverage,realestateinvestorsrevisecapitaliza- tionratesdownwardfollowingapositivedemandshock.Thisrevision, inturn,amplifiesthesupplyresponsetopricechanges.Wedocument thatthesupplyamplification,andthecorrespondingadjustmentofex- pectations,areheterogeneousacrossspace.Geographicallyconstrained andtightlyregulatedmarkets– i.e.,majorurbanareasandalpinetourist areas– andneighborhoodshavingmoresophisticatedbuyersasproxied bylandlords,institutionalinvestors,orsecond-homeinvestorsdisplay loweramplificationvalues.

Switzerlandisanexcellentlaboratorytoinvestigatehousingsupply duetosubstantialheterogeneityinthelocalfactorsinfluencingit.The decentralizedformofgovernmentgrantslow-tier politicalunits(mu- nicipalities)large autonomyin landuse planningandfiscalpolicies.

Geographicfeaturesofthelandscape,suchaselevation,slope,andter- rainruggedness,alsovaryconsiderablyacrossspace.Thesecharacter- isticsofthecountrymakethereactionofhousingsupplycontingenton localizedfactors.Importantly,theowner-occupiedandrentalmarkets areapproximateofequalsizeinSwitzerland,whichfacilitatesthees- timationofrentalandpricesupplyelasticitiesthroughoutthecountry, therebyallowingustostudytheroleofcapitalizationratesforhousing supply.²Finally,theexistenceofdetailedinformationonproperty-level housingcharacteristicsallowsustoruleoutthatdifferentattributes– i.e.,aqualitygap– betweenpropertiesdrivethedifferencesinsupply elasticities.

Ourpaperbridgestwostrandsoftheliterature.Thefirststrandfo- cusesontheestimationoflocalhousingsupplypriceelasticities.Despite theimportanceofhousingsupplyelasticity,papersquantifyingitremain scarce.GyourkoandMolloy(2015)provideacomprehensivereviewof theliteratureinvestigatingtheestimationanddeterminantsofhousing supply.Inhisseminalarticle,Saiz(2010)estimateshousingsupplyelas- ticitiesacrossU.S.MetropolitanStatisticalAreas(MSAs)asafunctionof geographicandregulatoryconstraints.UsingaVectorErrorCorrection Model,Wheatonetal.(2014)alsoestimatehousingsupplyelasticities forU.S.MSA’s,obtainingestimatesinlinewiththoseofSaiz (2010). Baum-Snow andHan, 2021adopt a structural approachto quantify cross-andwithin-cityhousingsupplyelasticitiesforU.S.metropolitan areas,showingthathousingsupplyelasticitiesincreasemonotonically withthedistancetocitycenters.WhilerelyingonSaiz(2010)empirical specificationforestimatinginversehousingsupplyelasticities,wefol- lowasimilaridentificationstrategyasinBaum-SnowandHan,2021. Specifically,weidentifyhousingsupplyelasticitiesusinglocaldemand shockstriggeredbythehistoricspatialdistributionofsectoralemploy- mentsharesandtheconnectivityofaneighborhoodwithlocallabor markets.Asacomplementaryshift-shareinstrument,weusethehistor- icaldistributionof languagesharesacross Swissneighborhoodscom- binedwiththegrowthoflanguagegroupsataggregatelevels.

Thesecond strandof theliteraturefocuses onhowinvestors’ ex- pectations impact market dynamics. Time variation in expectations – as captured by price to rent ratios dynamics – have been used byCase andShiller(2003)toidentifybubble-like behavior.Bycon- structing a user cost model incorporating economic fundamentals, Himmelberget al.(2005) show that expectedhouse price apprecia- tionplaysanimportantrolein explaininglocal U.S.pricedynamics.

FocusingontheU.S.housingboomintheearly2000s,Ben-Davidetal., 2019showthatagentsinvest invacanthomesiftheyexpectfurther priceincreases.Kaplanetal.(2020)highlighttheroleofexpectations forhousepriceandrentmovementsaroundtheGreatRecession.

Theimportanceof expectationsformarketdynamics hassparked interest in the way individuals form expectations. Mayer and Sinai (2007) investigate theeffect of backward-looking expectations

2 Similarhomeownershipratesareobservede.g.,inAustria,Germany,and SouthKorea.

inhousepricebooms.Sivitanidesetal.(2010)findthatcapitalization rates behavesimilarlytoprice/earningsratios,witheconomicagents formingpricegrowthexpectationsbasedonpastdynamics.Glaeserand Nathanson,2017constructamodelwherebuyersarenotentirelyratio- nalinpredictingfuturepricedynamics,whichexplainsobservedprice correlationovertime.KuchlerandZafar(2019)showthatindividuals formexpectationsabouthousepricedynamicsfromrecentpersonalex- periences.Thefactthatinvestorsaremyopic,orbackward-looking,isin linewithourfindings,whichsuggestthatinvestorsexpectfurtherrent growthinlocationsthathaveexperienceddemandincreasesinthere- centpast.Usingspatialvariation,weshowthatpartofthelocalhousing supplyresponsetodemandshocksisaffectedbychangesininvestors’

expectations.

Wealsorelatetotheliteratureonlocalgeographicandregulatory constraints(e.g.,AuraandDavidoff,2008,HilberandVermeulen,2016, andLutzandSand,2019)andshowthatpricesupplyelasticitiesarede- terminednotonlybyregulationandgeographicconstraintsbutalsoby adjustingcapitalizationrates.³HilberandMense(2021)showthatla- bordemandshocksinconjunctionwithsupplyconstraintsexplainmost oftheincreaseintheprice-to-rentratioinGreaterLondonoverthelast twodecades.

Ourcontributiontotheliteratureisthreefold.First,weempirically establishalinkbetween housingsupplyresponsivenessandinvestors expectations.Thislinkisessential,aspublicpoliciesaffectingrentalin- comemightleadtounanticipatedconsequencesinthesupplyofhousing duetochangesinexpectations.Second,ourempiricalanalysisquantifies thespatialdynamicsoflocalexpectations.Specifically,weprovidenovel evidencethattheadaptationofinvestorsexpectationsoccursatthelocal levelandthatsuchadjustmentisconsistentwithapath-dependentview ofspatialdevelopment.Investorsexpectthatplacesthathavegainedin attractiveness(i.e.,experiencedapositivedemandshock)willcontinue todoso,asreflectedbyadecreaseincapitalizationrates,leadingtoad- ditionalhousingdevelopment.Third,weshowthatthehousingsupply elasticityvariesconsiderablywithinandacrossurbanareasduetothe fine-scaleimpactofgeographicandregulatoryconstraints.Thisvaria- tionleadstoaspatiallyheterogeneouscapitalizationofglobaldemand shocksthatcannotbeobservedwhenestimatingthehousingsupplyelas- ticityattheurbanarealevel,asdonebypreviousresearch.

Theremainderof thepaperisstructuredasfollows.Section2in- troduces the conceptual framework motivating our empirical analysis. Section 3 explains our empirical identification strategy.

Section4presents thedataandprovidesdescriptivestatistics forthe Swisshousingmarket.WediscusstheresultsinSection5andprovide severalrobustnesschecksinSection6.Section7concludes.

2. Conceptualframework

Thefollowingpartialequilibriumframeworkallowsustoformal- izetheidentificationassumptionsunderlyingtheempiricalanalysisand rationalizecorrespondingfindings.Wespecifythesupplyanddemand sideofthehousingmarketandoutlinetheroleplayedbyrealestate investors.⁴

2.1. Housingdevelopers

AsinGlaeser(2008),ineachneighborhood𝑛,housingdevelopers choosetheamountofhousingspacetodevelop.Tobuildhousing,de- velopersmustpaytheprice 𝑃_𝑛^{𝑙𝑎𝑛𝑑} toacquireland,andthelocalcon- structioncost𝑐_𝑛 topurchasebuildingmaterialsandremuneratelabor.

3Relatedly,Solé-Ollé andViladecans-Marsal(2012)analyzetheroleofpo- liticalcompetitionforresidentialdevelopment.LinandWachter,2020docu- mentspillovereffectsoflocalregulatoryconstraintsonneighboringlocalities, Cosmanetal.(2018)analyzehousingappreciationandmarginallandsupplyin adynamicframework.

4OnlineAppendixApresentsamoredetailedderivationofthemodel.

Withoutlossofgenerality,wecapturebothlocalproductivityofthecon- structionsector,aswellastheunitcostofinputs,in𝑐_𝑛.Thedevelopers profitoptimizationproblemisgivenby

maxℎ (𝑃_𝑛ℎ𝑙−𝑐_𝑛ℎ^{𝛿𝑖𝑛𝑡𝑛+1}𝑙−𝑃_𝑛^{𝑙𝑎𝑛𝑑}𝑙), (1)

where𝑃_𝑛isthelocalpriceofhousingperunitoflivingspace,𝑙denotes theamountoflandandℎthebuildingheight.Weassumethatthecost component𝑐_𝑛ℎ^{𝛿𝑛𝑖𝑛𝑡+1}𝑙isconvexwithrespecttobuildingheight(𝛿_𝑛^𝑖𝑛𝑡>0), describingthefactthattheconstructionoftallerbuildingbecomespro- gressivelycostlierduetogeographicandregulatoryconstraintslimiting residentialdevelopmentontheintensivemargin.⁵

Developerschoosetheoptimalintensityofdevelopmentforeachho- mogeneousunitoflandintheneighborhood.Thezero-profitcondition ismetandgovernstheequilibriumpriceofland𝑃_𝑛^{𝑙𝑎𝑛𝑑}.Totalhousing supplyis givenbytheproductofoptimalbuildingheightℎ^∗_𝑛 andthe amountofdevelopableland𝐿_𝑛availableintheneighborhood.Weas- sumethatthequantityoflandavailableforresidentialdevelopmentin theneighborhoodrespondsendogenouslytohousingpricesaccording to𝐿_𝑛= ̄𝐿_𝑛𝑃

1 𝛿𝑒𝑥𝑡𝑛 + ¹

𝛿𝑖𝑛𝑡𝑛 𝛿𝑒𝑥𝑡𝑛

𝑛 ,where ̄𝐿_𝑛 capturescharacteristicsoflocations shiftinglandsupply,andtheparameter𝛿^𝑒𝑥𝑡_𝑛 governsthe(inverse)re- sponsivenessofresidentiallandavailability(seeOnlineAppendixA).

Totalhousingsupplyinaneighborhoodisthengivenby 𝑄^𝑠_𝑛=ℎ^∗_𝑛𝐿𝑛=

( 𝑃_𝑛 (𝛿^𝑖𝑛𝑡_𝑛 +1)𝑐_𝑛

) ¹

𝛿𝑖𝑛𝑡𝑛 ̄𝐿_𝑛𝑃

1 𝛿𝑒𝑥𝑡𝑛 + ¹

𝛿𝑖𝑛𝑡𝑛 𝛿𝑒𝑥𝑡𝑛

𝑛 =𝑆𝑛𝑃𝑛^{𝜖𝑛𝑄,𝑃}, (2)

where 𝑆_𝑛=𝑆_𝑛(̄𝐿_𝑛,𝑐_𝑛,𝛿^𝑖𝑛𝑡_𝑛 ) summarizes exogenous housing supply shifters.Thestructuralparameter𝜖^𝑄,𝑃_𝑛 = ¹

𝛿_𝑛^𝑖𝑛𝑡+ ¹

𝛿_𝑛^𝑒𝑥𝑡+ ¹

𝛿_𝑛^𝑖𝑛𝑡𝛿^𝑒𝑥𝑡_𝑛 ≥0corre- spondstothelocalhousingsupplyprice-elasticity,whichdependson thelocalresponsivenessofresidentialdevelopmentontheintensive(𝛿^𝑖𝑛𝑡) andextensive(𝛿^𝑒𝑥𝑡)margin.⁶

2.2. Realestateinvestors

We build on the framework proposed by DiPasquale and Wheaton(1992)andassumethatinvestorsarewillingtopayasquare meterprice𝑃_𝑛forapropertygeneratingaperiodicrentalincome𝑅_𝑛in neighborhood𝑛.Investorsthusmediatebetweentheproperty market -inwhichhouseholdsconsumehousingservices-andhousingdevel- opers.⁷Weassumethattheelasticityofbuildingtenurewithregardto capitalizationratedifferencesbetweenowner-occupiedandrentalprop- ertiesisinfinite.Putdifferently,investorsoptimallychoosewhetherto sellor rentoutaproperty,whichimpliesthatthecapitalizationrate ofrentalandsellingpropertiesisthesame.Ifitwerenotso,arbitrage opportunitieswouldarise,leadinginvestorstoshifttheirdemandfrom onerealestateassettotheother.⁸

Wedepartfromtheliteraturebyassumingthatinvestorsformex- pectationsendogenouslyaboutlocalrisk-adjustedreturns𝑟_𝑛 andrent growth 𝑔_𝑛 according to observed contemporaneous rents and prices,

5 Tallandhigh-risebuildingstypicallyrequirespecificbuildingmaterialsand specializedworkers,suchasarchitectsandengineers,thatensurethestabilityof itsstructure.Additionally,geographicandregulatoryconstraintsbecomemore binding,astheyaremorelikelytohinderverticaldevelopment.

6 Itiscommonintheliteraturetorepresenthousingsupplyelasticitywith asinglestructuralparameter𝜖enteringahousingsupplyfunctionoftheform 𝑄^𝑠=𝑆𝑃^𝜖,seee.g.,HsiehandMoretti(2019),Baum-SnowandHan,2021,and LinandWachter,2020.

7 Inthecaseofowner-occupancy,theinvestorrentsouttherealestateasset toherself.

8 Weassumethatrentalandsellingunitsare,onaverage,identicalwithina givenneighborhood,suchthatinvestors’expectationsarethesameduetothe no-arbitragecondition.InSection3.1,wethuspartialoutpotentialqualitydif- ferencesfromrentandpricedynamics.Theno-arbitrageassumptionisatthe coreofthestandardusercostapproachemployedbyHendershottandSlem- rod(1983),Poterba(1984),andMayerandSinai(2007).

i.e., 𝑟_𝑛=𝑟_𝑛(𝑅_𝑛,𝑃_𝑛) and𝑔_𝑛=𝑔_𝑛(𝑅_𝑛,𝑃_𝑛). Across periods, investors up- datetheirexpectationsbasedon thecapitalinvestmentthey haveto makeandthecorrespondingrentalincometheycouldpotentiallyearn at that time, thus leadingto heterogeneousexpectation adjustments across neighborhoods.Thisleads totheformula𝑃_𝑛= ^𝑅𝑛

𝑖𝑛(𝑅𝑛,𝑃𝑛), where 𝑖𝑛=𝑟𝑛(𝑅𝑛,𝑃𝑛)−𝑔𝑛(𝑅𝑛,𝑃𝑛)isthelocalcapitalizationrate.

Using thissimple framework,we can analyzethe propagationof rentalincomechangestothesupplyof housing.Therelativerespon- sivenessofhousingsupplytorentchangesisgivenby

𝜖_𝑛^𝑄,𝑅= 𝑅𝑛

𝑄^𝑠_𝑛 𝑑𝑄^𝑠_𝑛 𝑑𝑅_𝑛 = 𝑃𝑛

𝑄^𝑠_𝑛 𝑑𝑄^𝑠_𝑛 𝑑𝑃_𝑛

𝑅𝑛

𝑃_𝑛 𝑑𝑃𝑛

𝑑𝑅_𝑛 =𝜖_𝑛^𝑄,𝑃𝜖^{𝑃 ,𝑅}_𝑛 , (3) where𝜖^𝑄,𝑃_𝑛 isthestandardhousingsupplypriceelasticityinEq.(2),and 𝜖_𝑛^{𝑃 ,𝑅}isanamplificationcoefficientthatcorrespondstothepriceelasticity withrespecttorentchanges.Thislatterisdeterminedbytheresponsive- nessofthelocalcapitalizationratetorentchanges,i.e.,𝜖_𝑛^{𝑃 ,𝑅}=1−𝜖^𝑖,𝑅_𝑛 (seeOnlineAppendixA).Eq.(3)tellsusthathousingsupplyresponses torent andprice changesdifferwhentheelasticityofpricestorent changesisnotunitary.Ifthevaluationoflocalrealestateassetsisvery sensitivetolocalrentchanges,i.e.,𝜖_𝑛^{𝑃 ,𝑅}>1,thehousingsupplywill respondmorestronglytorentchangesthantopricechanges.Investors adjustmentofgrowthexpectationsandlocalriskcapturedbythecap- italizationratedeterminetheelasticityoflocalpricestolocalrents.If these factorswereindependentof rentdynamics, weshould observe identicalsupplyresponsestorentandpricechanges,whichisacentral hypothesiswetestempirically.⁹

Aparametrizationoflocalcapitalizationratesisinstructivetopro- videanintuitionaboutthewaywedifferfromtheliteratureandtoun- derstandtheidentificationassumptionsexposedinthenextsection.Let usassumethat𝑖_𝑛=𝑖0𝑅^𝛾_𝑛^𝑛𝑅𝑃_𝑛^𝛾𝑃𝑛,where𝑖0isthe“standard” capitalization rate,whichtheliteratureusuallyassumestobeexogenouslydetermined bycapitalmarkets.¹⁰Theparameters𝛾_𝑛^𝑅and𝛾_𝑛^𝑃representthelocalelas- ticityofcapitalizationrateswithrespecttorentandpriceshocks.Itis easytoshowthattheamplificationcoefficientispinneddownbythese twoparametersviatheequation𝜖𝑛^{𝑃 ,𝑅}=^{1−𝛾𝑛𝑅}

1+𝛾_𝑛^𝑃.Thisparametrizationpar- simoniouslyendogenizescapitalizationrateswhileallowingforspatial differencesintheinvestors’discountratewhenevaluatingrealestate assets.Ifweset𝛾_𝑛^𝑅=𝛾_𝑛^𝑃 =0,weobtainthestandardGordongrowth model.Empirically,wetestwhetherthisspatialgeneralizationof the Gordongrowthmodelismeaningful.¹¹

2.3. Residents

The economyis endowed witha continuous measure of 𝑁 indi- vidualsdistributedacrossneighborhoods.Buildingonrecentworkby Monteetal.(2018),eachindividualworkinginindustry𝑘decidesin whichneighborhood𝑛toliveandinwhicharea𝑖towork.Theidiosyn- craticindirectutility𝑈_𝑛𝑖^𝑘 ofindividual𝜔isgivenby

𝑈_𝑛𝑖^𝑘(𝜔)=𝑏^𝑘_𝑛𝑖(𝜔)𝑊̃_𝑛𝑖^𝑘

𝑅^𝛼_𝑛 , (4)

9NotethatEq.(3)isvalidforanysupplyfunctionwhosepriceelasticityis describedbyasingleparameter.ThestructureimposedbyEq.(2)onlyservesthe purposeofillustratingtheidentificationassumptionsunderlyingtheempirical estimation.

10Ourresultsgeneralizetoaparametrizationthatallowsforlocalexogenous capitalizationrates𝑖0𝑛.InSection6,wechecktherobustnessofourresultswhen 𝑖0𝑛includeslocalmeasuresofliquidityrisksanduncertaintyintherevenuegen- eratedbytheproperty.

11Theexistingliteratureoncapitalizationratesempiricallydocumentsastrong heterogeneityincapitalizationratesacrossspace,withurbanandhigh-amenity areastypicallydisplayinglowercapitalizationrates.However,theexistingur- banliteraturelargelyneglectssuchdifferences.Ourparametrizationaccommo- datessuchfeatures.

wherewe setthepriceof thetradablenuméraireequaltounityand assumethatindividualsspendashare𝛼onhousing.Thevariable𝑊̃_𝑛𝑖^𝑘 denotestheindustry-specificwageofworkerslivingin𝑛andcommuting to𝑖.

Theutilitycomponent𝑏^𝑘_𝑛𝑖capturesidiosyncraticpreferencesthatdo notdependonmarketfundamentalsbut,rather,ontheexogenoustastes ofworkersforagivenplaceofresidence/placeofworkcombination.We assumesuchpreferencestobei.i.d.realizationsofaFréchet-distributed randomvariablewithscaleparameter𝐵_𝑛𝑖^𝑘 andshapeparameter𝜀^𝑘>1. Thegreaterthevalueof𝜀^𝑘,thelessheterogeneousarelocationalpref- erencesofworkersinagivenindustry,thusimplyinggreatermobility acrossspace.

Wemodel𝑊̃_𝑛𝑖^𝑘aswagepereffectiveunitsoflabor𝑊_𝑛𝑖^𝑘dividedby commutingcosts𝑚_𝑛𝑖,implyingthatworkersreducelaborsupplywhen commutingfromdistantlocations.Ourfocusbeingonhousingmarkets, wedonotexplicitlymodelthedemandsideoflabormarkets,andcon- siderwages𝑊_𝑛𝑖^𝑘asanexogenousvariable.¹²

Givenhouseholdshomotheticpreferences,totalhousingdemand𝑄^𝑑_𝑛 inneighborhood𝑛isgivenby

𝑄^𝑑_𝑛 =𝛼𝑊̄𝑛

𝑅_𝑛𝑁_𝑛=𝛼 1 𝑅^𝛼𝑛^(1+𝜖𝑘)

𝑁 Φ

∑

𝑖,𝑘𝐵^𝑘_𝑛𝑖 (𝑊_𝑛𝑖^𝑘

𝑚_𝑛𝑖 )𝜖^𝑘+1

, (5)

where𝑊̄𝑛= _𝑁¹

𝑛

∑𝑖,𝑘𝑊_𝑛𝑖^𝑘

𝑚_𝑛𝑖𝑁_𝑛𝑖^𝑘 istheweightedaverageincomeearnedin neighborhood𝑛,𝑁_𝑛=∑

𝑖,𝑘𝑁_𝑛𝑖^𝑘 isthetotalnumberofhouseholdsliving in𝑛,andΦisacompositetermreflectingtheattractivenessofallother possiblepairsofresidence𝑟andemployment𝑠.¹³Eq.(5)providestwo insightsthatproveusefulwhenconstructinghousingdemandshifters.

Specifically,weshouldexpecthigherhousingdemandinneighborhoods thatarei)betterconnectedtoproductiveareas,andii)attractivealong oneofthedimensionscapturedbyidiosyncratictastes𝐵^𝑘_𝑛𝑖.InSection3, wederivetwoinstrumentsthatcaptureshiftsinhousingdemandtrig- geredbythesetwodimensionswhileremainingexogenouswithrespect tohousingsupplychanges.

2.4. Demandshocks,expectations,andhousingsupply

Inthissection,weoutlinecomparativestaticresultsonhowanex- ogenousdemandshockinformsusaboutchangesinhousingsupplyand adjustmentsofexpectations.Ininterestofparsimony,letusdenoteby 𝜃anylocalshockexclusivelyaffectingthedemandsideofthehousing marketasdescribedbyEq.(5),andassume thattheperiodiccostof housingservices– equilibriumrents– increasefollowingthisdemand shock,i.e.^𝜕𝑅_𝜕𝜃^𝑛

𝑛 >0.

UsingEq.(2),thehousingsupplyresponsetoademandshock is givenby

𝜕𝑄^𝑠_𝑛

𝜕𝜃𝑛 = 𝑆_𝑛𝜖^𝑄,𝑃 𝑖𝑛 𝑃_𝑛^{𝜖𝑄,𝑃−1}

(𝜕𝑅_𝑛

𝜕𝜃𝑛 −𝑃_𝑛𝜕𝑖_𝑛

𝜕𝜃𝑛

)

. (6)

Theterm𝑃_𝑛𝜕𝜃^𝜕𝑖𝑛

𝑛isresponsiblefortheamplificationofhousingsupply viachangesincapitalizationratesfollowingapositivedemandshock.¹⁴ Wearguethattheresponseoflocalcapitalizationrates toapositive demandshockisunequivocallynegative,i.e.^𝜕𝑖𝑛

𝜕𝜃𝑛 <0,thusincreasingthe supplyofhousingwithrespecttothestandardGordonGrowthmodelin whichcapitalizationratesareexogenouslyfixedandonlythefirstterm inparenthesesremains.

12 Indeed,theidentificationstrategyexposedinSection3reliesonexogenous changesinlocallabordemand.Forthisreason,werefraintomodellaborde- mandendogenously.

13 SeeOnlineAppendixAforadetailedderivationofEq.(5).

14 Tokeepthenotationassimpleandgeneralaspossible,herewerefrainfrom explicitlyformalizingtheendogenousrelationshipbetweencapitalizationrates 𝑖_𝑛andrents𝑅_𝑛– whichareaffectedbythedemandshock– andsimplywrite

𝜕𝑖𝑛

𝜕𝜃𝑛.

This negativerelationshiparisesbecause,followingapositive de- mandshock,i)theperceptionoflocalrisklikelydecreases(^𝜕𝑟𝑛

𝜕𝜃𝑛 <0), and/orii)rentgrowthexpectationsincrease(^𝜕𝑔𝑛

𝜕𝜃𝑛>0).¹⁵Forexample, anunexpecteddemandshock𝜃capturingimprovementsoflocalameni- ties,orarelocationofasufficientlylargecompany,leadstochangesin localhousingdemandandthusalterinvestors’expectations.

Expectations arelikely to be formedaccording topastdynamics (see e.g.DiPasqualeandWheaton,1995). Our resultsare consistent with myopic expectation as documented for real estate markets by KuchlerandZafar(2019).Begleyetal.(2019)documentthathetero- geneousexpectationsaboutlocalpopulationgrowthleadtodifferences inlocalprice-rentratiosintheUS.Aslongasthelocaldemandincrease hassome unexpectedelement, myopicinvestors willadjusttheir ex- pectationsaboutthegrowthratesofrentsupwardsandthusdecrease capitalizationrates.

Theequilibriumfeatureofrentgrowthratesmakesitextremelydif- ficulttopredictthem,evenwheninvestorshavestrongpredictivecapa- bilitiesregardingfuturedemandchanges.First,housingsupplyreacts endogenouslyatthelocalleveltothedemandshock.Second,evenif ademandshockisinitiallylocalizedtoagivenneighborhood,itwill spreadthroughoutthecountryduetothespatialequilibriumcondition.

Thismakesitverydifficulttocorrectlypredictthe“final” effectofade- mandchangebasedonpastdynamics,anditrationalizestheadjustment ofexpectationsaftertherealizationofademandchange.¹⁶

Wenotethattheextenttowhichcapitalizationratesadjustfollow- ingapositivedemandshockarguablydependsontheinvestors’idiosyn- craticcharacteristicaffectingtheirabilitytobuildexpectations.Wein- vestigatethismatterinmoredetailinSection5.3.

3. Empiricalframework

Basedontheaboveframework,wederiveempiricalspecifications toestimatehousingsupplyelasticities𝜖^𝑄,𝑃𝑛 and𝜖^𝑄,𝑅𝑛 ,anddiscussthe corresponding identificationassumptions.Westartbyimposingaver- agesupplyelasticities𝜖^𝑄,𝑃 and𝜖^𝑄,𝑅commontoallneighborhoods.In thenextstep,weprovideaparametrizationallowingustoestimatehet- erogeneoushousingsupplyresponsivenessattheneighborhoodlevel.

3.1. Partiallingoutqualitydifferences

TheconceptualframeworkexposedinSection2implicitlyassumes thatthequalityofhousinggoodsishomogeneouswithinthesameneigh- borhoodandacrossrentalandsellingproperties.Therelativelysmall neighborhoodsinourprincipalempiricalanalysisjustifythisassump- tiontoacertainextent,aspropertiessharingsimilarhousingcharacter- isticstendtoclustertogether.

Yet,withinaneighborhood,differencesinthequalityandtypeof housinggoodsmayremain.Topreventpotentialqualitybias,inwhat follows,weremoveallpriceandrentvariationacrosslocationsthatorig- inatefromdifferencesinobservablehousingcharacteristics.Tothisend, weconstructlocal(log)priceandrentindicesfromhedonicregressions.

Specifically,ineachperiodweseparatelyestimate

ln𝜏_𝑗𝑛𝑡=𝛾_𝑛𝑡^𝜏 +𝛽_𝑡^𝜏𝐀_𝑗𝑛𝑡+𝜖^𝜏_𝑗𝑛𝑡, 𝜏=𝑅,𝑃 (7) where𝜏_𝑗𝑛denoteseitherthepriceorrentofproperty𝑗inneighborhood 𝑛attime𝑡.Thevector𝐀_𝑗𝑛𝑡includesacomprehensivesetofattributes suchashousingsurface,theaveragenumberofrooms,age,agesquared, andanindicatorforsingle-familyvs.multi-familyhouses.𝜖^𝜏_𝑗𝑛𝑡denotes theerrorterm.

15Giventhatrentexpectations entercapitalizationratesnegatively,anin- creaseinexpectedrentalgrowthdecreaseslocalcapitalizationrates.

16Fortheinstrumentsusedbelow,wefindthatpastdynamicsexplainonlyvery littleofthevariationsuchthatdemandchangescannotbeperfectlyanticipated basedonpastdynamics.

Weusetheestimatedneighborhood-timefixed-effects𝛾_𝑛𝑡^𝜏 asquality- adjustedlog-prices(log-rents)ln𝑃_𝑛𝑡(ln𝑅_𝑛𝑡).¹⁷Notethatthecoefficients 𝛽_𝑡^𝜏aretime-variant,suchthatthevaluationofhousingcharacteristics canflexiblychangefromperiodtoperiod.

3.2. Model-informedidentificationofaveragesupplyelasticities

Log-linearizing supplyEq. (2), expressing prices asa functionof quantities,andfirstdifferencing,in equilibrium¹⁸ weobtainthefol- lowingempiricalspecification

Δ ln𝑃𝑛=𝛼^𝑃+ 1

𝜖^𝑄,𝑃Δ ln𝑄𝑛+Δ ln𝑆_𝑛^𝑃, (8) where_{𝜖𝑄,𝑃}¹ istheaverageinversehousingsupplyelasticitycommonto allneighborhoodsandΔdenotesatimedifferencebetween2005and 2015.Theterm𝛼^𝑃 denotestheaveragevalueofchangesinobserved supplyshifterscommontoallneighborhoodsand,inaslightabuseof notation,Δ ln𝑆_𝑛^𝑃representsthecorrespondingmean-centeredvariable.

Time-invariantcomponentsarepartialledoutfromΔ ln𝑆_𝑛^𝑃 byfirstdif- ferencing,suchthatonlydynamicsupplyshiftersenterEq.(8).

EstimatingEq.(8)byOLSlikelyleadstobiasedestimatesofthepa- rameterofinterestduetotheendogeneityofΔ ln𝑄_𝑛 viathedemand side.This isapparentfromEq.(5)whenwriting changesinhousing demandas

Δ ln𝑄_𝑛=Δ ln𝑊̄_𝑛+Δ ln𝑁_𝑛−Δ ln𝑅_𝑛. (9) Therefore,estimatesof ¹

𝜖^𝑄,𝑃 inEq.(8)arepotentiallybiasedduetoi) acorrelationofthecomponentsof housingdemand changessuchas changesinaveragewagesandnumberofresidentswithchangesofun- observedsupplyshiftersinΔ ln𝑆_𝑛^𝑃 (omittedvariablebias),andii)the impactofhousingpricesviachangesinrentsonhousingdemand(re- versecausality).

AccordingtoEq.(2)(seeOnlineAppendixA),Δ ln𝑆_𝑛^𝑃 includes,in additiontoexogenoussupplyshifters,changesinlocalconstructioncost.

Changesinthepriceofconstructionmaterialsandthecosttomakeland availableforresidentialdevelopmentareunlikelytodifferacrossspace, mostlyduetothesmallcountrysize.Onthecontrary,shiftsinhousing demandmightaffectconstructioncostsviawages.

Topartiallyaddressdifferencesinconstructioncostsacrossneigh- borhoods,wecontrol,inafirststep,forseveralsupplyshiftersinEq.(8). Let𝐗_𝑛 denotethevectorcontainingsuchcontrols.¹⁹Inparticular,𝐗_𝑛 includesconstructioncostindicesi.e.,changes inlabor andmaterial costsdefinedforthemainnationalconstructionmarkets,theintensity ofhistoricaldevelopmentasmeasuredbydevelopmentdensityin1980 andterrainruggedness.AccordingtoHilberandRobert-Nicoud(2013), thehistoriclevelofhousingdevelopmentproxiesforthefactthathigh- amenityareasdevelopfirstandtendtoadoptmorestringentland-use regulationsovertime.Controllingforterrainruggednesstakesintoac- countthatplotsoflandfeaturinggeographiccharacteristicsfavorable todevelopmentsuchasflatandnon-rockysurfacesarelikelydeveloped beforethoseshowingadversegeographiccharacteristics.Therefore,we expectunfavorablegeographicfeaturestoincreaserentsandpricesover time,asdevelopersfacehigherconstructioncostsforprovidingaddi- tionalhousingunitsontheextensivemarginofexistingdevelopment.

Similarly,wecontrolfortheelevationoftheland.Wefurthercontrolfor thedistancetothenearestcentralbusinessdistrictstocapturepotential

17 Notethatallourresultsarerobusttoallowingforregion-specificvaluations ofhousingattributes,i.e.,theinclusionof𝛽_𝑟𝑡 whereregions𝑟aredefinedas cantonsorcommutingzonescontainingasufficientnumberoflocations𝑛.

18 Inequilibrium𝑄^𝑑_𝑛=𝑄^𝑠_𝑛=𝑄_𝑛holds,suchthatweomitsupplyanddemand superscriptsinwhatfollows.

19 Notethatsuchcontrolsmightalsopartialoutqualitydifferencesnotfully capturedbyhedonicindices.

timetrenddifferentialsinthelaborsupply(anddemand)acrossspace.

Thesevariablesmightalsocapturechangesintransportationcosts.²⁰ Despite controlling for several supply shifters, omitted variables and reverse causality may still bias the estimation of Eq. (8). To solve this issue, we proposean instrumental variableapproach that aimstoexclusivelyshifthousingdemandwhileleavinghousingsup- plyunchanged.Specifically,werequireaninstrument,denotedΔ ln𝑍𝑛, whichisrelevantforhousingdemandchangeswhileremainingexoge- noustosupplychangesconditionalonthesetof controlsin 𝐗_𝑛,i.e., 𝐸(Δ ln𝑍_𝑛Δ ln𝑆_𝑛^𝑃|𝐗_𝑛)=0.

AsapparentfromEq.(9),wecannotuseobservedchangesin the componentsofthehousingdemand,asinequilibriumtheyareaffected bytensionforcesbetweenhousingdemandandsupply.Followingthere- centworkbyBaum-SnowandHan,2021,weisolateexogenouschanges inlabordemandgiventhespatiallinkages(commutingcost)ofaneigh- borhoodwithemploymentcenters.Wedefine

Δ ln𝑍_𝑛=∑

𝑖,𝑘

𝟏(𝑚_{𝑛𝑖𝑡0}<1hour)

𝑚_{𝑛𝑖𝑡0} 𝑓_𝑛𝑡^𝑘₀Δ ln𝐹_𝐶^𝑘_(𝑛), (10) wheretheindicatorfunction𝟏(𝑚𝑛𝑖𝑡0<1hour)equalsoneforneighbor- hoods𝑖thatarelocatedatmostat60minutestraveltimefromneigh- borhood𝑛,andzerootherwise.²¹Thequantity𝑓_𝑛𝑡^𝑘₀representstheshare ofemploymentbelongingtosector𝑘inneighborhood𝑛attime𝑡0.The termΔ ln𝐹_𝐶(^𝑘_𝑛)isthecorrespondingaggregategrowthrateofemploy- mentinindustry𝑘over[𝑡,𝑡0]inregion𝐶inwhichneighborhood𝑛is located.²²

The intuition behind Eq. (10) is straightforward.We computea weightedemploymentgrowthofthepredeterminedsectoralcomposi- tionintheproximityofagivenneighborhoodbyimposingacommon industrygrowthequaltotheonethatoccurredintheregion𝐶inwhich theneighborhoodislocated.Takingintoaccounttheproximityinterms ofcommutingtimetootherneighborhoodsisofparticularrelevancein thecaseofsmallspatialunits,e.g.,neighborhoods,asmostindividuals likelydonotworkinthesameneighborhoodwheretheylive.Weuse aone-hourradiusforthemaximumcommutingdistanceinthebench- markanalysis,asthisleadstothestrongestpredictivepowerofthein- strument.

Two features in thewaywe computeΔ ln𝑍_𝑛 support exogeneity claimswithrespecttounobservedsupplydynamics.First,inlinewith Bartik(1991),weexcludeneighborhood𝑛itselffromthecomputation ofΔ ln𝐹_𝐶^𝑘_(𝑛).Second,weexcludeallsectorsrelatedtoconstructionand realestatefrom𝑓_𝑛𝑡^𝑘₀andΔ ln𝐹_𝐶^𝑘_(𝑛).Therefore,theinstrumentcaptures weightedchangesinlabordemandthatarenotrelatedtotheconstruc- tionsector.

TheinstrumentdefinedbyEq.(10)isashift-shareinstrumentinline withBartik(1991).²³Recently,Adãoetal.,2019,Borusyaketal.,2021, andGoldsmith-Pinkhametal., 2020investigatedtheeconometricas- sumptionsnecessaryforthevalidityofshift-shareinstruments.These instrumentsarevalidifeitherinitialsharesareindependentandran- domlyassignedacrossobservationsorgrowthshocksoccurrandomly acrossregions.Inoursetting,wearguethatinitialsectoralsharesare exogenouswithrespecttochangesinunobservedsupplyshiftersandlo- calrentandpricedynamics.Thesectoraldistributionofemploymentis highlypersistentandlargelydeterminedbynaturalamenitiesandmar- ketaccess,suchthatthehistoricsectoraldistributionisunlikelytobe

20Ofcourse,thesecontrolvariablesalsoaffecthousingdemand.Inthiscase, includingtheminthesupplyfunctionisevenmoreimportantastheyreduce endogeneityissuesarisingfromchangesinhousingdemandaccordingtoEq.(9).

21Wesettraveltimewithinthesamemunicipalityto1minute.

22Inourbaselineresults,weuseCantonsasaggregateregion𝐶,whichrepre- sent26upper-tieradministrativeunits.Ourresultsarerobustusinglowertier regions,suchasdistricts(Bezirke).

23GrahamandMakridis,2021introducearelatedidentificationstrategycom- biningvariationintheinitialdistributionofhousingcharacteristicstogether withanationaldemandshiftforthesecharacteristics.

correlatedwithrecentchangesoflocalhousingsupplyshiftersΔ ln𝑆^𝑃. FollowingGoldsmith-Pinkhametal.,2020,inSection6,weassestheva- lidityoftheidentifyingvariationbycomputingtheRotembergweights foreachsector.

WefurthersupportexogeneityclaimsregardingΔ ln𝑍_𝑛bycompar- ingourresultswiththoseobtainedusinganalternativeshift-sharein- strumentbasedonthedistributionoflanguageshares.²⁴Specifically,for eachneighborhoodwecomputethehistoricalshareoflanguageshares andinteractthemwiththecantonalgrowthoftherespectivelanguage group.²⁵Assumingthattheidiosyncraticutilityshiftercanbedecom- posedas𝐵^𝑘_𝑛𝑖=𝐵𝑛𝐵_𝑖^𝑘inEq.(5),wecaninterpretthisinstrumentaspre- dictingdemandchangesviaashiftintheidiosyncraticpreferences𝐵_𝑛 toliveinaneighborhood𝑛.

Theno-arbitrageconditionforinvestorspurchasingrealestateassets preventsthatthedemandshockscapturedbyourtwoinstrumentsare tenurespecific(seeSection2.2).Evenifoneofthedemandshockswere morerelevanttoaspecificpartofthepopulationthatismoreinclined torentorown,itwouldpropagateacrosstenuresduetochangesinat- tractivenessofinvestments.InthecontextofSwitzerland,thecloselink betweentherentalandowner-occupiedmarketsisreflectedinahousing marketthatisapproximatelyequallysplitbetweenrenters(56%)and owner-occupiers(44%).Thecloselinkbetweendifferenthousingmar- ketsegmentsissupportedbyrecentworkofMense(2020)forGermany, acountrydisplayingsimilarhousingmarketconditionsasSwitzerland.

Specifically,theauthorshowsthatthelocalconstructionofhigh-quality housingunitslowersrentsthroughouttherentdistributionshortlyafter thenewunitsarecompleted.

Theestimationofthesupplyelasticitywithrespecttorentchanges 𝜖^𝑄,𝑅_𝑛 followsthesamelogicasbefore.Bysubstitutingtherelationship betweenpricesandrentsarisingfromtheparametrizationofcapitaliza- tionratesintoEq.(8),andisolating𝑅_𝑛,weobtain

Δ ln𝑅_𝑛=𝛼^𝑅+ 1

𝜖^𝑄,𝑅Δ ln𝑄_𝑛+Δ ln𝑆_𝑛^𝑅 (11) where_{𝜖𝑄,𝑅}¹ =_{𝜖𝑄,𝑃}¹_{𝜖𝑃 ,𝑅},andweassumethatthevector𝐗_𝑛capturingthe observablesupplyshiftersdiscussedaboveiscontrolledfor.Thenew errortermisΔ ln𝑆_𝑛^𝑅= ¹

𝜖^{𝑃 ,𝑅}Δ ln𝑆_𝑛^𝑃.Becausethisnewerrortermequals theoneofEq.(8)timesaconstantstructuralparameter,theprevious discussionoftheidentificationassumptionsstillholds.²⁶

Weconcludethissectionbynotingthataveragehousingsupplyprice andrentelasticityestimatescanunambiguouslyberecoveredfromin- versesupplyequations(8)and(11)simplybytakingtheinverseofthe estimatedvaluefor_{𝜖𝑄,𝑃}¹ and_{𝜖𝑄,𝑅}¹ ,respectively.²⁷

Housingsupplyelasticityestimatesallowus,inturn,toestimateelas- ticityparameters𝜖^{𝑃 ,𝑅}and𝜖^𝑖,𝑅.²⁸

Estimatingtheinversesupplyfunction,ratherthanthedirectone,is acommonapproachintheliterature(e.g.Saiz,2010)thatoffersseveral advantages.First,usingasdependentvariablesquality-adjustedprices andrentsresultingfromahedonicregressiondoesnotrequireadditional

24 Saiz(2007)usesasimilarapproachbycomputingashift-shareinstrument basedonthenumberofimmigrantsmovingintoU.S.cities.

25 SeeOnlineAppendixCforaformaldefinitionoftheinstrument.

26 Theexogenouscomponentofthecapitalizationrate𝑖0iscapturedbythe rent-specificconstant𝛼^𝑅inEq.(11).Ifweassumetheparametrizationoflocal capitalizationratesexposedinSection2andallowforlocation-specificcapital- izationrates𝑖0𝑛,theerrorterminEq.(11)becomesΔ ln𝑆_𝑛^𝑅+_{𝜖𝑃 ,𝑅}¹ ₁₊¹_𝛾𝑃

𝑛Δ ln𝑖0𝑛. Thus,theexogeneityoftheinstrumentmustalsoholdwithrespecttolocation- specificexogenouscapitalizationrates.InSection6,weshowthatincluding severalcontrolsproxyingforΔ ln𝑖0𝑛doesnotaffectourresults.

27 Thisrelationshipbetweeninversesupplyequationsandhousingsupplyelas- ticityparameterestimatesispurelymechanicalanddoesnothingeonadditional identificationassumptions.Weobtainidenticalpointestimateswhenestimating non-invertedsupplyequations.

28 Assumingthattheidentificationassumptionsunderlyingthe2SLSestima- tionof𝜖^𝑄,𝑃 and𝜖^𝑄,𝑅hold,accordingto(3)wecanestimate ̂𝜖^{𝑃 ,𝑅}= ^̂𝜖_̂𝜖^𝑄,𝑅_𝑄,𝑃 and

̂𝜖^𝑖,𝑅=1−̂𝜖^{𝑃 ,𝑅}.

statisticaltreatment.Thisisnotthecaseifquality-adjustedprices(and rents)areusedasregressors,astheirstandarderrorsarenotvalidand needtobebootstrapped.Second,instrumentalvariablestendtobemore relevantforquantitychangesthanforpriceones,therebyimprovingthe precisionof theestimates.Third, estimatinginversesupplyfunctions allowsustoinstrumentthesamevariable(i.e.,Δ ln𝑄_𝑛)torecoverthe responsivenessofhousingsupplytopriceandrentchanges.This,inturn, facilitatesthecomparisonofthecoefficientsacrossspecifications.

3.3. Localsupplyresponsivenessandtheroleofgeographicandregulatory constraints

Eqs.(8)and(11)assumethatinversesupplyelasticitieswithrespect topricesandrentsareconstantacrosslocations.However,ourconcep- tualframeworksuggeststhathousingsupplyelasticityvariesatthelocal level,bothattheintensiveandextensivemarginofresidentialdevelop- ment.Ontheintensivemargin,theempiricalliteraturepointsoutthat supplyelasticitymightvary considerablyaccordingtoregulatoryre- strictions– suchasheightrestriction,floortoarearatios,etc.– adopted bylocalgovernments.AccordingtoHilberandRobert-Nicoud(2013), attractiveplacesarehistoricallymoredevelopedand,asanoutcomeof thepoliticalgamebetweenlanddevelopersandownersofdeveloped land,moreregulated.Ontheextensivemargin,Saiz(2010)pointsout thatsuchconstraintsareempiricallyrelevantonlywhenthereisenough development tomakethembinding.²⁹ Toimplementsuchconsidera- tionsempirically,wethusfollowSaiz(2010)andusethefollowingap- proximation

1

𝜖_𝑛^𝑄,𝜏 ≈𝛽^{𝑎𝑣𝑔,𝜏}+𝛽^{ℎ𝑖𝑠𝑡,𝜏}×𝑄¹⁹⁸⁰_𝑛 +𝛽^{𝑐𝑜𝑛𝑠𝑡𝑟,𝜏}× Λ_𝑛×𝑄¹⁹⁸⁰_𝑛 , 𝜏=𝑅,𝑃, (12) wheretheobservedhistoricstockin1980𝑄¹⁹⁸⁰_𝑛 proxiesforregulation constraintson theintensivemargin,accordingtoHilberandRobert- Nicoud(2013).ThevariableΛ_𝑛isameasuresummarizingthemostim- portantgeographicandregulatoryconstraintsontheextensivemargin.

InsertingsuchapproximationinEqs.(8)and(11),wethenestimatethe followingequation

Δln(𝜏_𝑛)=𝛼^𝜏+𝛽^{𝑎𝑣𝑔,𝜏}Δln(𝑄_𝑛)+𝛽^{ℎ𝑖𝑠𝑡,𝜏}Δln(𝑄_𝑛)×𝑄¹⁹⁸⁰_𝑛

+𝛽^{𝑐𝑜𝑛𝑠𝑡𝑟,𝜏}Δln(𝑄_𝑛)× Λ_𝑛×𝑄¹⁹⁸⁰_𝑛 +Δ ln𝑆_𝑛^𝜏, 𝜏=𝑅,𝑃, (13) wherewecontrolagainfor𝐗_𝑛 (whichincludeshistoricdevelopment 𝑄¹⁹⁸⁰_𝑛 )aswellasforthemaineffectofextensivemarginconstraintsΛ_𝑛. Tworemarksareworthnoting.First,Λ_𝑛 isinteractedwiththehistoric stock level 𝑄¹⁹⁸⁰_𝑛 , thusallowing theimpact ofregulatory constraints tobecomemorebindinginmore-developedplaces.Havingestimated the parameters 𝛽^{𝑎𝑣𝑔,𝜏},𝛽^{ℎ𝑖𝑠𝑡,𝜏},and𝛽^{𝑐𝑜𝑛𝑠𝑡𝑟,𝜏}, we thenrecover 𝜖^𝑄,𝜏_𝑛 using Eq.(12).Second,theidentificationassumptionsofthepriceandrent equationinEq.(13)arethesameasinEqs.(8)and(11)provided𝑄¹⁹⁸⁰_𝑛 andΛ_𝑛areexogenouswithrespecttoΔ ln𝑆^𝜏.

4. Dataanddescriptivestatistics

Theempiricalanalysisreliesonseveraldatasources.Furtherinfor- mationisavailableinOnlineAppendixB.

4.1. Datasources

HousingdataWeusegeo-referenceddataonadvertisedresidential propertiesprovidedbyMeta-Sys.Thedatasetcontainsapproximately 2.1millionpostingsofrentalpropertiesandabout0.8millionpostings ofsellingresidencesforthewholeofSwitzerlandfrom2004to2016.

Inadditiontoaskingrentsandprices,thedatasetincludescompre- hensive informationon housingcharacteristics.The FederalRegister

29Forexample,protectedforestlikelyhinderresidentialdevelopmentonlyif noothertypeofdevelopablelandisavailableintheneighborhood.

ofBuildingsandHabitationspublishedbytheSwissFederalStatistical Office(FSO)providesacensusoftheresidentialhousingstockofthe country.Changesinthehousingstockaremeasuredeveryfiveyears, providingthreetimeperiods2005,2010,and2015thatoverlapwith ouradvertisementdata.Upto2015,theregistercontainsapproximately 4.8millionhousingunitsforthewholeofSwitzerland,11.5percentof whichwerebuiltbetween2005and2015.The2000BuildingCensus (publishedbytheFSO)providesinformationonwhetheradwellingis aprimaryorsecondaryresidenceinthatyear.

Socio-demographicandeconomicdataWeusetheFederalPopu- lationCensusof2000(publishedbytheFSO)aswellasthePopulation andHouseholdsSurveyfrom2010to2015(publishedbytheFSO)to infergeo-referencedhomeownershipratesandtoobtaininformationon predeterminedlevelsandchangesinthelocalsocio-demographiccom- positioni.e.,nationalityandlanguageofresidentslivinginagivenarea.

The2000FederalPopulationCensusprovidesinformationonthetype of buildingowner,suchaslandlords andinstitutional investors.The FSOpublishesaconstructionindextrackingthecostevolutionofmate- rialandlaborintheconstructionsectorforsevenstatisticalareas.We obtaineddetailedinformationaboutthespatialdistributionofemploy- mentandfirmsbysectorfromtheStructuralBusinessStatistics(STA- TENT).WeusetheNOGA1sectorclassification,whichcomprises16 differentsectorsinthecaseofSwitzerland.³⁰ Wecombinethis infor- mationwithdataaboutroadtraveltimeprovidedbywww.search.chto constructalocalmeasurelabormarketaccess.

RegulatoryandgeographicdataTheLandUseStatisticsofSwitzer- land(publishedbytheFSO)providessatellite-basedlandcoverdata, allowingustoidentifygeographicconstraints,suchaslakes,rocks,and glaciers,andareassubjecttoparticularregulations.Informationabout regulationsontheextensivemarginandprotectedareasinparticular isobtainedfromCantonalofficesof spatialplanningandtheFederal OfficefortheEnvironment(FOEN).

OtherdataWecomplementtheabovedatawithavarietyofdata onSwissadministrativeunitsandmetropolitanareas(publishedbythe FSO)andelevation(EuropeanEnvironmentAgency).Weidentifythe agglomerationsofthe15maincitiesinSwitzerland,asdefinedbythe FSO,andcomputethedistanceofeachneighborhoodtotheclosestcity center.

4.2. Datastructureanddescriptivestatistics

Westructurethedatabypartitioningthewholeterritoryofthecoun- tryintosmall squareneighborhoodsof2x2km.Weaggregate hous- ingstock,socio-demographicandeconomicdata,andgeographicand regulatoryconstraintswithinthese neighborhoods.³¹ Weassigneach neighborhoodtooneof2324municipalities,whichrepresentthelow- estgovernmentaltierinSwitzerlandandhaveaninfluenceonlanduse regulation.

From2005to2015,rentshaveincreasedbyapproximately14per- centwhileprices haveincreasedbyapproximately35percent atthe countrylevel.³²Overthesameperiod,thehousingstockgrewbyap- proximately11percent.Despitethesegeneraltrends,stock,rent,and pricedynamicsareheterogeneousacrossspace,asillustratedinFig.1. Specifically,Fig.1shows stock,rent,andpriceindex growthin ma- jorcities(PanelA)andthecountryside(PanelB)from2005to2015, using2005asthebaseyear(=100).Overtheconsideredperiod,hous- ingstockgrewalmosttwiceasmuchinthecountrysideareasthanin cities.Thissuggeststhatincitiesalackofdevelopablelandinconjunc-

30 ThisclassificationcorrespondstothemajorSICindustrygroupsintheU.S.

31 Ourresultsarerobusttoalternativeneighborhoodsizes,asdiscussedin Section6.

32 FornewtenancyagreementsmarketrentsapplyinSwitzerland.Toprevent abusiveincreases,propertyownerscanadjustrentsforexistingtenancyagree- mentsonlyifsomeformalcriteriaaremet.However,severalexceptionsinthe regulationallowlandlordstoadjustrentstolocalmarketlevels.

Fig.1. Rent,price,andstockdynamicsNotes:Citiesinclude2x2kmneigh- borhoodslocatedinoneofthe15mainmunicipalitiesofthecorresponding biggesturbanareasaccordingto2015boundaries.Thetwopanelsshowindex growthfrom2005to2015oftheconsideredvariables,using2005asthebase year(=100).Stockismeasuredasthetotalnumberofdwellings,andrentsand pricesaremeasuredasadvertisedaveragerentsandpricespersquaremeter.

SeeOnlineAppendixB.2foradefinitionofmajorSwissagglomerations.

tionwithgeographicandregulatoryconstraintshindersfurtherdevel- opment.Giventhiscomparativelylowerresponsivenessofhousingde- velopmentincities,itisnotsurprisingthatrentsandpricesgrewmore intheseareasthaninthecountryside.Interestingly,from2007onward, rentsandpricedynamicshavestartedtodivergeconsiderably-with pricesrisingatafasterpace-whichimpliesthatcapitalizationrates havebeenreviseddownwardintheselocations.

InFig.2,weshow themostimportantgeographicandregulatory constraintsfor housingdevelopment inSwitzerland. Geographic fea- tures preventingany form of development areanimportantcompo- nent of the Swisslandscape. Similarlyto Saiz (2010) andLutz and Sand(2019),wedefineundevelopablelandaslandthatislocatedabove 2000 m andwhose landcover corresponds to unproductive vegeta- tion,vegetation-freeareas,orrocks,andglaciers.³³ Waterbodiessig- nificantlyreduce theamountofdevelopablelandintheproximityof majoragglomerations,asvirtuallyallmajorCBDsareadjacenttoalake orriver.³⁴

Inadditiontogeographicconstraints,therearesignificantregula- toryrestrictionsinplacethatpreventorhinderdevelopmentinspecific areas.We refertomeasuresthatprevent newconstructiononunde- velopedlandasregulationsontheextensivemargin.Regulationsonthe extensivemarginincludeforests³⁵,UNESCOculturalornaturalheritage sites,parks,andotherhigh-valuenaturalamenityareas.Theserestric- tionsaccountforapproximately49.1percentoftheSwissterritory.Total restrictedareasobtainedbyoverlappinggeographicandregulatorycon- straintsattheextensivemarginamounttoapproximately67.3percent ofthecountry’ssurface.Theremaining32.7percentofthecountry’ssur- face(whiteareainFig.2)isavailablefordevelopmentunderdifferent

33Ourdataallowsustocompilethismeasureatevenfinerscalethanprevious literature.

34Thisismainlyduetothecompetitiveadvantageofareasintheproximityof waterbodiesduringtheIndustrialRevolutionandthesubsequenturbanization ofSwitzerland.

35Inresponsetothegrowingindustrializationofthecountry,in1876,Switzer- landpassedafederallawprohibitingfurtherdeforestation,defactofreezing forestareastothelevelobservedatthattime.Thelawhasremainedmainlyun- changedtothepresentday.Asaconsequence,forestareasinhighlypopulated regionshaveremainedpracticallyunchangedsince1876.

Fig.2.ConstraintstodevelopmentNotes:Wedefinegeographicconstraintsasundevelopableland,whichcorrespondstoaplotoflandlocatedabove2000m,or whoselanduseclassificationcorrespondstounproductivevegetation,vegetation-freeareas,orrocksandglaciers.Exceptforforests,redareassummarizeregulatory constraintsontheextensivemargin.Swissforestsareprotectedareassince1876.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderis referredtothewebversionofthisarticle.)

Table1

Inversehousingsupplyelasticity– averageestimates.

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

ΔLog P ΔLog R ΔLog P ΔLog R ΔLog P ΔLog R

ΔLog Q 2.367 ^∗∗∗ 0.694 ^∗∗ 2.004 ^∗∗∗ 0.747 ^∗∗∗ 2.084 ^∗∗∗ 0.735 ^∗∗∗

(0.442) (0.287) (0.342) (0.215) (0.316) (0.191)

Amplification 𝜖^{𝑃 ,𝑅} 3.411 2.683 2.835

Instruments I I L L I & L I & L

Observations 2,498 2,498 2,498 2,498 2,498 2,498

Kleibergen-Paap F 15.61 15.61 71.39 71.39 42.76 42.76

Overidentification - - - - 0.40 0.87

Notes:Standarderrorsinparentheses^∗𝑝<.10,^∗∗𝑝<.05,^∗∗∗𝑝<.01.Standarderrorsareclusteredatthemunicipalitylevel.Thesamplecoverstheperiod2005–2015.

TheAdãoetal.,2019standarderrorsforcolumns(1),(2),(3),and(4)are0.100,0.048,0.386,and0.198,respectively.Theunitsofobservationsareobtained bypartitioningSwitzerlandin2x2kmneighborhoods.Logrentsandlogpricesarequality-adjustedwithrespecttothelivingsurface,thenumberofrooms,age, agesquared,andbuildingtype.Allregressionscontrolforsupplyshifters,whichincludeelevation,elevationstandarddeviation,log-distancetothenearestCBD, log-housingstockin1980,totalrestrictedareas,andchange(2005–2015)inconstructioncosts.SeeOnlineAppendixEfordetailedestimationresultsandfirststages.

ChangesinhousingstockΔLogQ,areinstrumentedusingashift-shareinstrumentforindustriesIincolumns(1)and(2),ashift-shareinstrumentformainspoken languagesLincolumns(3)and(4),andboththeseinstrumentsI&Lincolumns(5)and(6).

regulatorymeasuresdeterminingtheintensityandtypeofresidential development.

5. Results

5.1. Supplyelasticityestimatesandamplificationmechanism

Table1summarizesaveragesupplyelasticityestimateswithrespect toprice(columns1,3,and5)andrent(columns2,4,and6)changes,re- spectively.Columns1and2reportestimatesbasedontheshift-sharein- strumentΔ ln𝑍_𝑛derivedfromhistoricindustryshares(usedasabench- mark).Columns3and4reportthecorrespondingeffectsfortheshift-

shareinstrumentderivedfromhistoriclanguageshares.Columns5and 6showtheresultswhenusingthetwoinstrumentssimultaneously.Since ourmodelframeworkinSection2establisheslabormarketshocksasa source ofshiftsin housingdemand,we refertotheresults basedon industrysharesasourbaselineestimates.

Responsivenessestimatesbasedontheindustryinstrumentareequal to𝜖^𝑄,𝑅= ¹

0.694 =1.44forrentand𝜖^𝑄,𝑃= ¹

2.367 =0.42forpricechanges.

These results show that, on average,the housingsupplyin Switzer- landisrelativelyelastictorentchanges,butlesssotopricechanges.

Thecorrespondingamplificationeffectis𝜖^{𝑃 ,𝑅}=^{𝜖𝑄,𝑅}

𝜖^𝑄,𝑃 =3.43.Thecoun- try’saverage responseoflocal capitalizationratestorent changesis thus𝜖^𝑖,𝑅=1−𝜖^{𝑃 ,𝑅}=−2.43,suggestingthatinvestorsreviselocalrent