美联储-CRE再开发方案和抵押贷款融资的使用（英）

FinanceandEconomicsDiscussionSeries

FederalReserveBoard,Washington,D.C.

ISSN1936-2854(Print)

ISSN2767-3898(Online)

CRERedevelopmentOptionsandtheUseofMortgageFinancing

DavidGlancy,RobertKurtzman,LaraLoewenstein

2024-046

Pleasecitethispaperas:

Glancy,David,RobertKurtzman,andLaraLoewenstein(2024).“CRERedevelop-mentOptionsandtheUseofMortgageFinancing,”FinanceandEconomicsDiscus-sionSeries2024-046.Washington:BoardofGovernorsoftheFederalReserveSystem,

/10.17016/FEDS.2024.046

.

NOTE:StafworkingpapersintheFinanceandEconomicsDiscussionSeries(FEDS)arepreliminarymaterialscirculatedtostimulatediscussionandcriticalcomment.TheanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstafortheBoardofGovernors.ReferencesinpublicationstotheFinanceandEconomicsDiscussionSeries(otherthanacknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.

CRERedevelopmentOptionsandtheUseofMortgage

Financing*

DavidGlancy†RobertKurtzman‡andLaraLoewenstein§2

1FederalReserveBoard

2FederalReserveBankofClevelandJune4,2024

Abstract

Asignificantshareofcommercialrealestate(CRE)investmentproperties—abouthalfbyourestimates—arepurchasedwithoutamortgage.UsingcomprehensivemicrodataontransactionsintheU.S.CREmarket,weanalyzewhichtypesofpropertiesarepurchasedwithoutamortgage,highlightingtheimportantroleofrenovationorredevelopmentoptions.Weshowthatmortgage-financedpropertiesarelesslikelytobesubsequentlyredeveloped,andthatownersanticipatetheseredevelopmentfrictionsandavoidmortgagefinancingforpropertieswithgreaterredevelopmentoptions.TheseeffectswereevenstrongerduringtheCOVID-19pandemic,whenuncertaintyincreasedredevelopmentoptionvalues.

Keywords:commercialrealestate,cashbuyers,redevelopmentJELClassification:G21,G22,G23,R33

*TheviewsexpressedinthispaperaresolelythoseoftheauthorsanddonotreflecttheopinionsoftheFederalReserveBoard,theFederalReserveBankofCleveland,ortheFederalReserveSystem.WethankparticipantsattheFederalReserveBankofClevelandandthe“ConferenceinSupportoftheSpecialIssueofRealEstateEconomicsonCommercialRealEstateFinanceandInvestment”fortheirusefulcommentsandsuggestions.

†FederalReserveBoardofGovernors,DivisionofMonetaryAffairs,20thStreetandConstitutionNW,Washington,D.C.20551;email:david.p.glancy@.

‡FederalReserveBoardofGovernors,DivisionofResearchandStatistics,20thStreetandConstitutionNW,Wash-ington,D.C.20551;email:robert.j.kurtzman@.

§FederalReserveBankofCleveland,1455East6thStreet,Cleveland,OH44114;email:

lara.loewenstein@.

2

1.INTRODUCTION

Thereissubstantialevidencethatcollateralplaysanimportantroleinmitigatingfinancialfrictions

(HartandMoore,

1994

).Realestateisespeciallywellsuitedascollateralforloans,givenitdepreciatesslowly(

RajanandWinton,

1995)andisrelativelyredeployable(Benmelechetal.,

2005

).Indeed,thecommercialrealestate(CRE)industryisgenerallyknownforoperatingwith

highleverage(Giacominietal.,

2017;

Glancyetal.,

2022)

.However,theuseofcollateralvariesdrasticallyacrossproperties;abouthalfofCREtransactionshavenomortgagesassociatedwiththem,wellabovetheshareofresidentialrealestate(RRE)transactionswithoutamortgage(

Han

andHong,

2020)

.CREisalsoalessleveredassetinaggregate,withCRE-secureddebtestimatedtobeabout15percentofthevalueofCREassets(comparedwith28percentforRRE)

.1

WhydosomanyCREinvestorspurchasepropertieswithoutamortgage?Theliteraturehasbroadlyemphasizedthedesiretomaintainfinancialflexibilityasmotivatingunsecuredborrowing(

Benm-

elechetal.,

2024)

.AnotherpotentialreasonmorespecifictoCREistomaintainflexibilitywithregardtopropertyoperationsandinvestment.Mortgagedebtcaninhibitinvestmentforseveralreasons.Perhapsmostimportantly,loancontractsfrequentlyprohibitborrowersfromengaginginmaterialalterationswithoutthelender’sconsentandprohibitborrowersfromtakingoutadditionalloanstocoverthecostsofalterations(

Mann,

1997

).Additionally,debtoverhangconsiderationsmaydiscourageinvestorsfromengagingincostlyinvestmentswhosebenefitswouldpartiallyac-cruetodebtholders(

Correaetal.,

2022;

DeFuscoetal.,

2023

),anddebtservicecostsmayin-troducefinancialconstraintsthatpreventpropertyownersfromundertakingprofitableinvestments

(Seltzer,

2021

).Understandinginvestorrenovationandredevelopmentdecisionsisespeciallyrel-evanttoday,astransitioningofficepropertiestoalternativeusescouldalleviatestrainsduetoover-supplyinthatmarket(

Guptaetal.,

2023)

.

Inthispaper,westudyhowfinancingdecisionsaffectredevelopmentoptionsusingcomprehen-

1Estimatesarefrom2023:Q3datareportedintheFinancialAccountsoftheUnitedStates.SeeFigure

A1

intheappendixfortime-seriesversionsofthesemeasuresandfordetailsonthedataconstruction.

3

sivemicrodataonU.S.CREtransactions.Weprovidetheoreticalandempiricalevidencethatanimportantmotivationforleavingapropertyunencumberedistomaintainthevalueoftheredevel-opmentoptionontheproperty.Toguideourempiricalanalysis,weestablishasimpletheoreticalframeworkwhereagingpropertieshavetheoptiontoberedevelopedatacost.Propertyownerschoosewhethertofinanceapropertywithamortgage,tradingoffthebenefitofsecuredfinancingagainstthehighercostofrenovationthatthemortgagecreates.Themodelshowsthatolderandlessproductivepropertieshavemorevaluableredevelopmentoptionsandarethus(1)morelikelytobepurchasedforimmediateredevelopmentand(2)lesslikelytobemortgagefinanced.

Guidedbyourtheoreticalframework,weconstructestimatesofredevelopmentoptionvaluesforthepropertiesinoursample.Weshowempiricallythatolder,lessproductivepropertiesaremorelikelytobepurchasedforredevelopmentorrenovation.Thefittedvaluesfromthisanalysis—namely,theestimatedprobabilityofalteration—mapdirectlyintooptionvaluesforpropertiesthatarenotpurchasedforimmediateredevelopment.Theseestimatedredevelopmentoptions,basedonpropertyageandquality,formthefoundationofouranalysisforhowsuchoptionsaffectfinancingdecisions.

Usingourproperty-levelredevelopmentoptionvalueestimates,weshowthatownersindeedstrate-gicallydecidewhethertousemortgagefinancingforpropertypurchaseswithrenovationoptionsinmind.Weidentifythiseffectusinganapproachinthespiritofadifference-in-differencesex-ercise:weestimatewhetherbuyersusemortgagefinancingbasedontheestimatedredevelopmentoptionandthepurchaser’sexperienceinrenovationorconstructionactivity(reflectingaspecificowner’scompetenceatundertakingarenovationproject).Buyerswithoutdevelopmentexperienceserveasacontrolforproperty-specificfactorsaffectingtheavailabilityofdebt(e.g.,lendersbeinghesitanttolendagainstquestionablecollateral),andtheinclusionofbuyerfixedeffectsaccountsforcross-borrowerdifferencesinfinancingneedsorbroadcreditavailability.Consequently,theeffectweidentifyshouldcapturetheextenttowhichaborrower’sdesiretopreservetherenovationoptionvalueaffectsfinancingdecisions.

4

Finally,wepresenttwopiecesofadditionalevidenceinfavorofredevelopmentoptionsaffecting

financingchoices.First,weshowdirectlythatwhenpropertiesarenotmortgagefinanced,theyaremorelikelytobesubsequentlyrenovatedorimproved.Second,weshowthatwegetsimilarfind-ingswhenweusetheCOVID-19pandemicasanalternativesourceofvariationinredevelopmentoptions.Byvirtueofproducingsignificantuncertaintyandinducingaflighttohigher-qualityprop-erties,thepandemicplausiblyincreasedtheshareofpropertyvaluesattributabletoredevelopmentoptions,particularlyforofficeproperties.Consistentwiththisidea,weshowthatbuyersreducedtheirusageofmortgagefinancingforofficesandforolderorlowerqualitypropertiesduringthepandemic.

Themostcloselyrelatedpapertoourownisthatof

Loewensteinetal.

(2021),whoshowthat

mortgagedpropertiesarelesslikelytoberedeployedtoanewuse.Weaddtothisworkintwoways.First,wedemonstratethatthepresenceofmortgagedebtnotonlyinhibitsredeploymentacrosspropertytypes,butalsoaffectssmallerrenovationsandpropertyimprovements.Second,weanalyzehowfrictionstorenovationaffectinvestors’ex-antefinancingdecisions.

Inaddition,wemakecontributionstothreestrandsoftheliterature.First,weprovideabroadsummaryofpatternsregardingthecharacteristicsofpropertiesthatareandarenotmortgagefi-nanced.Whilethereismuchworkanalyzing“allcash”purchasesintheresidentialrealestatemarket(see,forexample,

HanandHong

(2020)and

ReherandValkanov

(forthcoming

)),thereissignificantlylessworkonthistopicwithregardtocommercialproperties.

Conklinetal.

(2018)

alsousetransaction-leveldatatostudybuyers’decisiontotakeoutamortgage;however,theirsam-pleiscomposedentirelyofrealestateinvestmenttrusts(REITs),whichweshowdiffermarkedlyfromotherbuyersintermsoftheirusageofmortgagefinancing

.2

Consequently,weprovideamorecomprehensiveoverviewofpatternswithrespecttomortgageusageacrossdifferenttypesofCRE-owningentities.

2REITsareabouthalfaslikelyasotherborrowerstopurchasepropertieswithmortgagedebt.ThisdifferencecouldreflectagreateravailabilityofotherfundingsourcesortheneedforgreaterfinancialflexibilityinlightofREITs’limitedabilitytoretainnetincome.

5

Second,wecontributetoabroadliteratureonthebenefitsofcollateral.Theexistingworkdemon-

stratesthatpledgingcollateral(orhigher-qualitycollateral)canreduceborrowingcosts(

Benm-

elechetal.,

2022;

LuckandSantos,

2023),alleviatecreditrationing(

StiglitzandWeiss,

1981),

mitigateinformationasymmetries(

Bootetal.,

1991

),andincreaseborrowingcapacity(

Benm-

elechetal.,

2005;

Cerqueiroetal.,

2016)

.Nonetheless,theusageofsecureddebthasbeendeclin-ingovertime(

Benmelechetal.,

2024

),arguably,inpart,becauseofborrowers’desiretomaintainflexibilityintheusageoftheirassets.IntheCREliterature,unencumberedCREassetshavebeenshowntoprovidepropertyinvestorsasourceofliquidityviapotentialassetsalesorfuturesecured

borrowing(Conklinetal.,

2018;

Campelloetal.,

2022;

Demircietal.,

2023)

.However,unsecuredlendinggenerallycomeswithcovenantsthatmaylimitoveralldebtcapacity(

Giambonaetal.,

2018;

RiddioughandSteiner,

2020)

.Wecontributetothisliteraturebyanalyzinghowsecuredfinancingaffectsoperationalflexibilityforindividualproperties.Wefindthatunsecuredfinancinghelpsfirmsavoidrestrictionsfromrepositioningproperties

.3

Third,wecontributetotheliteratureonCREredevelopment.

MunnekeandWomack

(2020)and

Buchleretal.

(2023)useinformationonthelikelihoodofredevelopmenttoestimatethevalueof

redevelopmentoptions.Inasimilarspirit,weuseinformationonthelikelihoodoffinancingapurchasewithamortgageforpropertieswithdifferentredevelopmentoptionstoinfertheextenttowhichsecuredfinancinghindersthevalueoftheredevelopmentoption.Understandingthesefric-tionstoredevelopmentareespeciallysalientnow,giventhatshiftsinrealestatemarketspromptedbythepandemichavelikelydramaticallychangedthebestuseofspace(

Guptaetal.,

2023)

.

Theremainderofthepaperproceedsasfollows:inSection

2,wedescribethedataandprovide

descriptivestatisticsregardingwhichtransactionsaremortgagefinanced.InSection

3,wepresent

asimplemodelofhowredevelopmentoptionsaffectfinancingdecisions.InSection

4,wedescribe

ourempiricalapproachandprimaryfindings.InSection

5,weconclude

.

3Thisresultisalsoconsistentwith

Mann

(1997),whopresentsanecdotalevidencethatconcernsoverthelossof

operationalflexibilitycanmotivateunsecuredborrowing,andthemodelof

RampiniandViswanathan

(2020),which

postulatesareduced-fromcostofsecuredfinancingthatcounterbalancesthegreaterdebtcapacitythatcomesfromsecuredfinancing.

6

2.DATAANDDESCRIPTIVEANALYSIS

2.1.Data

OurprimarydatasourcecomesfromMSCIRealCapitalAnalytics(RCA).ThedatabaseprovidesinformationonpropertyandloancharacteristicsforCREtransactionssince2001forpropertiesabove$2.5millioninvalue.RCAsourcesinformationonmortgagesfrompublicrecordsdata,publicfilings,andindustrycontacts.

Afewfeaturesmakethesedataparticularlywellsuitedtothecurrentstudy.First,RCAidentifiesthe“truebuyer”inthetransaction,thusallowingustoknowtheactualentityacquiringapropertyratherthanthesubsidiary.Thisfeatureallowsustobetteranalyzewhethertheacquiringcompanyhadexperienceengaginginrenovationorredevelopmentprojects.Second,thedataincludeaqual-ityscore(Q-Score),reflectingthepricepersquarefootofapropertyrelativetopeerproperties.AlowQ-Scoreindicatesalowervaluerelativetowhatcouldlikelybeachievedafterrenovationandthusisindicativethatmoreofthevalueofthepropertycomesfromtheredevelopmentop-tion

.4

Third,thedatalinkpropertiesovertime.Consequently,wecanobservethecharacteristicsofprop-ertiesandloansthatareassociatedwithfuturerenovationandredevelopmentdecisions.Thisinfor-mationallowsustounderstandtheproperty-levelfactorsthatinfluencethelikelihoodofredevel-opmentandstudyhowtheexistenceofproperty-leveldebtcomplicatesthatredevelopment.

Weidentifytransactionsthatarenotmortgagefinanced(colloquiallyreferredtoas“cashpur-chases”)asthosewithoutanyloanorlenderinformation.ThisapproachwouldmisclassifysomemortgagedpurchasesascashtransactionsifRCAwasnotabletoobtainanyinformationonthemortgageloanorlenderoriftheywereunabletoprovidethatinformationintheirdata.How-ever,webelievethatthissourceofmisidentificationissmallfortworeasons.First,mortgagesare

4See

Cvijanovicetal.

(2022)foramoredetaileddescriptionofRCA’sQ-Scoremeasureaswellasavalidationof

RCA’scoverageandidentificationoftruebuyersbasedonREITdisclosures.

7

publicrecords,sowhileinformationaboutsomeloantermsorpropertycharacteristicsmightbe

unavailable,whetherthereisamortgageassociatedwithapropertyshouldbereliablyavailable.Itisrelevanttonotethatouranalysisonlyrequiresinformationonwhetheramortgageexists,notanyspecificloanterms.Thepublicrecordsshould,intheory,beacomprehensiveandcompleterecordofallliensonrealproperty.Whilealendercouldmakeamortgageloanwithoutrecordingitinapublicregistry,doingsowouldsignificantlyimpairtheirabilitytorecoupanylossesupononforeclosurebecauselackofapublicfilingwouldmeanthatotherpartiesorcreditorswouldnothavetorespectthepriorityoftheirlien

.5

Second,weverifythattheshareofcashtransactionsisconsistentwithtwootherdatasources.AppendixFigure

A1

showsthattheratioofCREdebttothecurrentmarketvalueofCREassetsintheU.S.averagesabout17percent.Thiscurrentleverageratioisaboutalignedwithwhatwouldbeexpectedgiventhecashsharesestimatedinthispaper,combinedwithnormalunderwritingterms

.6

Additionally,AppendixFigure

A2

showsthatcashsharesforinstitutionalinvestorsaresimilarinbothRCAanddatafromtheNationalCouncilofRealEstateInvestmentFiduciaries(NCREIF).AsNCREIFprovidesmoreuniformreportingofproperty-leveldebtthanRCA,thisfactgivesusconfidenceinRCA’scoverageofloanandlenderinformation

.7

Ourmainsampleislimitedtonon-portfoliopurchasetransactionsfrom2005through2022.Westartthesamplein2005becauseRCAexpandedcoveragethatyear.Estimatedcashshareswere

5Arelatedconcernmaybethatnotallpublicrecordsaredigitizedandaccessible,butgiventhatwelimitoursampleto2005onwardandthatRCAtransactionsareatleast$2.5millioninvalueandthereforelargelylocatedinmetropolitanareaswithdigitizedrecords,wedonotthinkthisisamajorconcern.

6Typicalat-originationLTVratiosforCREloansarearound60percent(see,forexample,

Glancyetal.

2022)

.Afteraccountingforamortizationandpropertyappreciation,theaveragecurrentLTVforoutstandingloans—i.e.,whatisbeingmeasuredintheFinancialAccounts—wouldbearound50.6percent(thiscalculationisbasedon2percentannualpriceappreciation,anaverageofa10-yearloanterm,and30-yearaverageamortizationschedules,anduniformlydistributedoriginationdates,whichwouldbebroadlyinlinewiththeaveragesofthesecharacteristicsacrossloansasrelayedin

Glancyetal.

(2022))

.Giventhatinvestmentpropertiesandowner-occupiedpropertieshavecashsharesof43percentand70percent,respectively(Figure

1),andabouttwo-thirdsofCREpropertiesareowner

-occupied(

Ghentetal.,

2019

),wewouldexpectabout61percentofthemarkettobecashfinanced.ThiswouldimplyacurrentLTVof50.6percent×.39≈20percent.Ifweoverestimatedtheportionofthemarketthatwascash-financed,wewouldexpectthisestimatetobebelow,ratherthanslightedabove,theestimatebasedonaggregateU.S.data.

7Additionally,thefactthatcashpurchasesaremostcommonforprivatebuyersandleastcommonforpubliconesisindicativethatcoverageisreliable.Ifmisclassificationswerecommon,wewouldexpecttoseehigherestimatedcashsharesforprivatebuyerssincetheirfundingismoreopaque.

8

higherbeforethisexpansion,raisingtheconcernthatloaninformationwaslesscompleteinthoseearlyyears.Weexcludeportfoliotransactions,asitislessfeasibleforthebuyertomakefinancingbasedontheredevelopmentpotentialofindividualproperties.

2.2.DescriptiveStatistics

Figure

1

showstheshareofpurchasetransactions(bynumber)withoutproperty-leveldebt(i.e.,thecashshareofpurchases),splitbybuyerobjective,buyertype,andpropertytype.Regardingbuyerobjectives,cashpurchasesaremostcommonforredevelopmentprojects,at75percent.Cashpurchasesarealsoonthehigherend,at59percent,forpurchasesbyintendedoccupiers,consistentwithhighlyfirm-specificassetsbeingmorelikelytobeownedthanrented(

SmithJr.

andWakeman,

1985

)andlesssuitedforusageascollateral(

Benmelechetal.,

2005

).Propertiespurchasedforinvestmenthavecashsharesaround46percent,whilecashsharesforrenovationsarelower,at31percent

.8

Regardingbuyertype,cashpurchasesarehighestforpublicbuyers(e.g.,REITs),at79percent,andlowestforprivatebuyers,at44percent.Regardingpropertytype,cashsharesarehighestfordevelopmentsites,at80percent;lowestforapartmentbuildings,at32percent;andbetween39and56percentfornonresidentialpropertytypes.Thesedifferencesincashpurchasesharesarereasonablystableovertime,asisshowninFigure

A3.

Thesedifferencesprovidesomehintsatmotivationsfordecidingagainstusingmortgagefinanc-ingtofundpurchases.First,differencesincreditavailabilityappeartoaffectcapitalstructuredecisions;publicbuyers,whichlikelyhavegreateraccesstounsecuredfinancing,aremuchlesslikelytousemortgagefinancingthanprivateborrowers.Additionally,mortgageusageishigh-estforapartmentbuildings,perhapsreflectinggreatercreditavailability,giventheinvolvementofthegovernment-sponsoredenterprisesinthesecondarymarket.Wewillaccountfordiffer-

8Thesepatternsarebroadlysimilarwhensharesareweightedbypropertyvalue(seeFigure

A4);onaweighted

basis,cashpurchasesarearound70percentofpurchasesforoccupancyorredevelopment,comparedwithabout43percentofpurchasesforinvestment.Figure

A5

alsoincludesthedistributionofobservationsacrossthecategories.

9

encesincreditavailabilityalongthesedimensionsintheempiricalresultsbyemployingbuyerand

property-typefixedeffects.

Second,theresultsareconsistentwiththehypothesisthatbuyersusecashfinancingtomaintainoperationalflexibilitytoengageinredevelopmentprojects.Namely,cashusageisparticularlyhighforredevelopmentprojectsordevelopmentsites.Inthenexttwosections,wewillfurtherdevelopandmoreformallytestthishypothesisbyanalyzingdifferencesinfinancingbehaviorbasedonproperties’redevelopmentoptionsandbuyers’redevelopmentexperience.

Table

1

providessomesummarystatisticsforthefullsampleofpropertysalesandforsamplesbrokenoutbywhetherthereisamortgageassociatedwiththetransaction.Sinceweareinter-estedinhowfinancingdecisionsaffectredevelopmentoptionsratherthanhowrenovationandredevelopmentprojectsarefunded,thissampleincludesonlypurchasetransactionsforthesakeofinvestment(asopposedtotheotherobjectiveslistedatthetopofFigure

1)

.Thelastcolumnpresentsthedifferenceinmeansforcash-andmortgage-financedpurchases.

Unconditionally,propertiesthatarecashfinancedhavemodestlyhigherQ-Scores,onaverage,butare1percentagepointmorelikelytohaveaQ-Scoreinthebottomquartile(“LowQ-Score”=1).Cash-financedpropertiesarealsomorelikelytobeyounger,andhaveloweraveragevaluationsbuthigherpricespersquarefoot.Additionally,transactionswithshorteraverageholdperiodsaremorelikelytobecashfinanced;thisresultisconsistentwith

Demircietal.

(2023),whodemonstratethat

REITsarelesslikelytosellencumberedproperties.

Regardingbuyercharacteristics,buyerswithdevelopmentexperience,definedasbuyersforwhichatleast25percentoftransactionsareflaggedasinvolvingrenovation,redevelopment,orconstruc-tion,aremorelikelytopurchasepropertiesallcash.Specifically,11.2percentofcashtransactionsareaccountedforbydevelopers,comparedwithonly10.7percentofmortgagedtransactions.Thefindingsaresimilarwhendevelopmentexperienceismeasuredcontinuously;theaveragecashbuyerhas16.5percentoftheirtransactionsinvolvingsomeformofdevelopment,comparedwith15.5percentformortgagedtransactions.Cash-financedpropertiesarealsomorelikelytobema-

10

teriallyimproved(i.e.,haveanatleast20-percentage-pointincreaseintheirQ-scoreinthenext

transaction),consistentwithagreaterlikelihoodofrenovation.Ofcourse,thesesummarystatis-ticsaresubjecttocompositioneffects,sowewillrequiremoreformalanalysistounderstandthesepatternsbetter.

3.MODELOFREDEVELOPMENTOPTIONSANDFINANCINGDECISIONS

Inthissection,wepresentasimplemodelofhowredevelopmentoptionsaffectfinancingdeci-sions.Inthefirstsubsection,wepresentamodelwhereCREinvestorsoptimallychoosewhentoredevelopproperties.Themodelestablishestheframeworkweuseforestimatingcross-sectionaldifferencesinthevalueofredevelopmentoptions.Inthesecondsubsection,weextendthemodeltoincludeleverageandderivehowfrictionstoredevelopingmortgagedpropertiesaffectoptionvaluesandfinancingdecisions.

3.1.Model

Supposethatanewlyrenovatedpropertyyieldsanetcashflowthatwenormalizeto1.Overtime,thiscashflowdepreciatesatrateδ.Ifpropertyinvestorsdiscountthefutureatrater,thenthevalueofapropertyaftertyearswillsatisfythepricingequation:

rV(t)=e—δt+VI(t).(1)

Supposethatownersareabletorenovateatcostctoreturnthepropertytothecashflowofanewlybuiltone.InAppendix

B,weshowthatequation(1)canthusbesolvedas

11

wheret*(c)istheoptimaltimeofrenovation,whichweshowtobemonotonicallyincreasinginc

.9

Thisexpressionsaysthattheincreaseinthevalueofthepropertyduetotherenovationoption—

definedin(2)asρ(

t;c)—isdecreasinginthetimeuntilrenovation(i.e,t*(c)-t).Highercostsofrenovationcauseownerstowaitlongertorenovateandreducethevalueoftheoption.Wecanthusderivethefirsthypothesiswetestinthedata.

Hypothesis1.Olderandlessproductive(highert)propertiesaremorelikelytobeimmediatelyredeveloped.

Thishypothesisfollowsdirectlyfromthefactthatρ(t;c)isdecreasinginthetimeuntilrenovation.Apurchaseriwouldacquireapropertyjforimmediateredevelopmentiftj-tj<0.IfweassumetjisobservableandtjisdistributedaccordingtothecumulativedistributionfunctionF,

thentheprobabilitythatapurchaseoccursforimmediateredevelopmentisF(tj).Thisprobabilityisincreasingintimesincerenovation(tj)anddecreasinginpropertyproductivity(sinceincomerelativetonewlyrenovatedproperties,e-δtj,isadecreasingfunctionoftime).

Inpractice,tjistypicallynotdirectlyobserved,sowhenweestimatethevalueofredevelopmentoptions,wewillinsteadestimateaprobitbasedonaflexiblefunctionofabuilding’sage(thetime

ithashadtodepreciate)andQ-Score(adirectmeasureoftheproperty’srelativeproductivity)tocapturetherenovationpotentialofaproperty.Specifically,weparameterizetj-tj,reflectingthe

valueoftherenovationoption,astj-tj=Xβ+σεi;j,whereXjisasetofvariablesmeasuring

theproperty’sageandquality,andεi;jfollowsastandardnormaldistribution.Wethenestimate

Pr(Renovation)=Φ(),whichprovidesameasureofthevalueoftherenovationoption

.10

9t*(c)isdefinedimplicitlybythevalue-matchingconditionthatV(t*)=V(0)-c.

10Moreformally,th