CRE Redevelopment Options and the Use of Mortgage Financing

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) CRE Redevelopment Options and the Use of Mortgage Financing David Glancy, Robert Kurtzman, Lara Loewenstein 2024-046 Please cite this paper as: Glancy, David, Robert Kurtzman, and Lara Loewenstein (2024). “CRE Redevelopment Options and the Use of Mortgage Financing,” Finance and Economics Discussion Series 2024-046. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2024.046. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

CRE Redevelopment Options and the Use of Mortgage Financing∗ David Glancy†,1 Robert Kurtzman‡,1 and Lara Loewenstein§2 1Federal Reserve Board 2Federal Reserve Bank of Cleveland June 4, 2024 Abstract A significant share of commercial real estate (CRE) investment properties—about half by our estimates—are purchased without a mortgage. Using comprehensive microdata on transactions in the U.S. CRE market, we analyze which types of properties are purchased without a mortgage, highlighting the important role of renovation or redevelopment options. We show that mortgage-financed properties are less likely to be subsequently redeveloped, and that owners anticipate these redevelopment frictions and avoid mortgage financing for properties with greater redevelopment options. These effects were even stronger during the COVID-19pandemic,whenuncertaintyincreasedredevelopmentoptionvalues. Keywords: commercialrealestate,cashbuyers,redevelopment JELClassification: G21,G22,G23,R33 ∗The views expressed in this paper are solely those of the authors and do not reflect the opinions of the Federal ReserveBoard,theFederalReserveBankofCleveland,ortheFederalReserveSystem. Wethankparticipantsatthe FederalReserveBankofClevelandandthe“ConferenceinSupportoftheSpecialIssueofRealEstateEconomicson CommercialRealEstateFinanceandInvestment”fortheirusefulcommentsandsuggestions. †FederalReserveBoardofGovernors,DivisionofMonetaryAffairs,20thStreetandConstitutionNW,Washington, D.C.20551;email: david.p.glancy@frb.gov. ‡FederalReserveBoardofGovernors,DivisionofResearchandStatistics,20thStreetandConstitutionNW,Washington,D.C.20551;email: robert.j.kurtzman@frb.gov. §Federal Reserve Bank of Cleveland, 1455 East 6th Street, Cleveland, OH 44114; email: lara.loewenstein@clev.frb.org.

1. INTRODUCTION Thereissubstantialevidencethatcollateralplaysanimportantroleinmitigatingfinancialfrictions (Hart and Moore, 1994). Real estate is especially well suited as collateral for loans, given it depreciates slowly (Rajan and Winton, 1995) and is relatively redeployable (Benmelech et al., 2005). Indeed, the commercial real estate (CRE) industry is generally known for operating with high leverage (Giacomini et al., 2017; Glancy et al., 2022). However, the use of collateral varies drastically across properties; about half of CRE transactions have no mortgages associated with them, well above the share of residential real estate (RRE) transactions without a mortgage (Han and Hong, 2020). CRE is also a less levered asset in aggregate, with CRE-secured debt estimated tobeabout15percentofthevalueofCREassets(comparedwith28percentforRRE).1 WhydosomanyCREinvestorspurchasepropertieswithoutamortgage? Theliteraturehasbroadly emphasized the desire to maintain financial flexibility as motivating unsecured borrowing (Benmelech et al., 2024). Another potential reason more specific to CRE is to maintain flexibility with regard to property operations and investment. Mortgage debt can inhibit investment for several reasons. Perhaps most importantly, loan contracts frequently prohibit borrowers from engaging in materialalterationswithoutthelender’sconsentandprohibitborrowersfromtakingoutadditional loans to cover the costs of alterations (Mann, 1997). Additionally, debt overhang considerations may discourage investors from engaging in costly investments whose benefits would partially accrue to debt holders (Correa et al., 2022; DeFusco et al., 2023), and debt service costs may introducefinancialconstraintsthatpreventpropertyownersfromundertakingprofitableinvestments (Seltzer, 2021). Understanding investor renovation and redevelopment decisions is especially relevanttoday,astransitioningofficepropertiestoalternativeusescouldalleviatestrainsduetooversupplyinthatmarket(Guptaetal.,2023). In this paper, we study how financing decisions affect redevelopment options using comprehen- 1Estimatesarefrom2023:Q3datareportedintheFinancialAccountsoftheUnitedStates. SeeFigureA1inthe appendixfortime-seriesversionsofthesemeasuresandfordetailsonthedataconstruction. 2

sive microdata on U.S. CRE transactions. We provide theoretical and empirical evidence that an important motivation for leaving a property unencumbered is to maintain the value of the redevelopment option on the property. To guide our empirical analysis, we establish a simple theoretical framework where aging properties have the option to be redeveloped at a cost. Property owners choose whether to finance a property with a mortgage, trading off the benefit of secured financing against the higher cost of renovation that the mortgage creates. The model shows that older and less productive properties have more valuable redevelopment options and are thus (1) more likely tobepurchasedforimmediateredevelopmentand(2)lesslikelytobemortgagefinanced. Guided by our theoretical framework, we construct estimates of redevelopment option values for the properties in our sample. We show empirically that older, less productive properties are more likely to be purchased for redevelopment or renovation. The fitted values from this analysis— namely,theestimatedprobabilityofalteration—mapdirectlyintooptionvaluesforpropertiesthat arenotpurchasedforimmediateredevelopment. Theseestimatedredevelopmentoptions,basedon propertyageandquality,formthefoundationofouranalysisforhowsuchoptionsaffectfinancing decisions. Usingourproperty-levelredevelopmentoptionvalueestimates,weshowthatownersindeedstrategically decide whether to use mortgage financing for property purchases with renovation options in mind. We identify this effect using an approach in the spirit of a difference-in-differences exercise: we estimate whether buyers use mortgage financing based on the estimated redevelopment option and the purchaser’s experience in renovation or construction activity (reflecting a specific owner’scompetenceatundertakingarenovationproject). Buyerswithoutdevelopmentexperience serveasacontrolforproperty-specificfactorsaffectingtheavailabilityofdebt(e.g.,lendersbeing hesitant to lend against questionable collateral), and the inclusion of buyer fixed effects accounts for cross-borrower differences in financing needs or broad credit availability. Consequently, the effectweidentifyshouldcapturetheextenttowhichaborrower’sdesiretopreservetherenovation optionvalueaffectsfinancingdecisions. 3

Finally, we present two pieces of additional evidence in favor of redevelopment options affecting financingchoices. First,weshowdirectlythatwhenpropertiesarenotmortgagefinanced,theyare more likely to be subsequently renovated or improved. Second, we show that we get similar findings when we use the COVID-19 pandemic as an alternative source of variation in redevelopment options. Byvirtueofproducingsignificantuncertaintyandinducingaflighttohigher-qualityproperties,thepandemicplausiblyincreasedtheshareofpropertyvaluesattributabletoredevelopment options, particularly for office properties. Consistent with this idea, we show that buyers reduced their usage of mortgage financing for offices and for older or lower quality properties during the pandemic. The most closely related paper to our own is that of Loewenstein et al. (2021), who show that mortgaged properties are less likely to be redeployed to a new use. We add to this work in two ways. First, we demonstrate that the presence of mortgage debt not only inhibits redeployment across property types, but also affects smaller renovations and property improvements. Second, weanalyzehowfrictionstorenovationaffectinvestors’ex-antefinancingdecisions. In addition, we make contributions to three strands of the literature. First, we provide a broad summary of patterns regarding the characteristics of properties that are and are not mortgage financed. While there is much work analyzing “all cash” purchases in the residential real estate market (see, for example, Han and Hong (2020) and Reher and Valkanov (forthcoming)), there is significantly less work on this topic with regard to commercial properties. Conklin et al. (2018) alsousetransaction-leveldatatostudybuyers’decisiontotakeoutamortgage;however,theirsample is composed entirely of real estate investment trusts (REITs), which we show differ markedly from other buyers in terms of their usage of mortgage financing.2 Consequently, we provide a morecomprehensiveoverviewofpatternswithrespecttomortgageusageacrossdifferenttypesof CRE-owningentities. 2REITs are about half as likely as other borrowers to purchase properties with mortgage debt. This difference could reflect a greater availability of other funding sources or the need for greater financial flexibility in light of REITs’limitedabilitytoretainnetincome. 4

Second,wecontributetoabroadliteratureonthebenefitsofcollateral. Theexistingworkdemonstrates that pledging collateral (or higher-quality collateral) can reduce borrowing costs (Benmelech et al., 2022; Luck and Santos, 2023), alleviate credit rationing (Stiglitz and Weiss, 1981), mitigate information asymmetries (Boot et al., 1991), and increase borrowing capacity (Benmelechetal.,2005;Cerqueiroetal.,2016). Nonetheless,theusageofsecureddebthasbeendecliningovertime(Benmelechetal.,2024),arguably,inpart,becauseofborrowers’desiretomaintain flexibility in the usage of their assets. In the CRE literature, unencumbered CRE assets have been showntoprovidepropertyinvestorsasourceofliquidityviapotentialassetsalesorfuturesecured borrowing(Conklinetal.,2018;Campelloetal.,2022;Demircietal.,2023). However,unsecured lending generally comes with covenants that may limit overall debt capacity (Giambona et al., 2018; Riddiough and Steiner, 2020). We contribute to this literature by analyzing how secured financing affects operational flexibility for individual properties. We find that unsecured financing helpsfirmsavoidrestrictionsfromrepositioningproperties.3 Third, we contribute to the literature on CRE redevelopment. Munneke and Womack (2020) and Buchler et al. (2023) use information on the likelihood of redevelopment to estimate the value of redevelopment options. In a similar spirit, we use information on the likelihood of financing a purchasewithamortgageforpropertieswithdifferentredevelopmentoptionstoinfertheextentto which secured financing hinders the value of the redevelopment option. Understanding these frictionstoredevelopmentareespeciallysalientnow,giventhatshiftsinrealestatemarketsprompted bythepandemichavelikelydramaticallychangedthebestuseofspace(Guptaetal.,2023). The remainder of the paper proceeds as follows: in Section 2, we describe the data and provide descriptivestatisticsregardingwhichtransactionsaremortgagefinanced. InSection3,wepresent asimplemodelofhowredevelopmentoptionsaffectfinancingdecisions. InSection4,wedescribe ourempiricalapproachandprimaryfindings. InSection5,weconclude. 3ThisresultisalsoconsistentwithMann(1997), whopresentsanecdotalevidencethatconcernsoverthelossof operationalflexibilitycanmotivateunsecuredborrowing,andthemodelofRampiniandViswanathan(2020),which postulates a reduced-from cost of secured financing that counterbalances the greater debt capacity that comes from securedfinancing. 5

2. DATAANDDESCRIPTIVEANALYSIS 2.1. Data Ourprimarydatasourcecomesfrom MSCIRealCapitalAnalytics(RCA).Thedatabaseprovides information on property and loan characteristics for CRE transactions since 2001 for properties above $2.5 million in value. RCA sources information on mortgages from public records data, publicfilings,andindustrycontacts. A few features make these data particularly well suited to the current study. First, RCA identifies the “true buyer” in the transaction, thus allowing us to know the actual entity acquiring a property ratherthan thesubsidiary. Thisfeature allowsusto betteranalyzewhether theacquiringcompany hadexperienceengaginginrenovationorredevelopmentprojects. Second,thedataincludeaquality score (Q-Score), reflecting the price per square foot of a property relative to peer properties. A low Q-Score indicates a lower value relative to what could likely be achieved after renovation and thus is indicative that more of the value of the property comes from the redevelopment option.4 Third,thedatalinkpropertiesovertime. Consequently,wecanobservethecharacteristicsofpropertiesandloansthatareassociatedwithfuturerenovationandredevelopmentdecisions. Thisinformation allows us to understand the property-level factors that influence the likelihood of redevelopmentandstudyhowtheexistenceofproperty-leveldebtcomplicatesthatredevelopment. We identify transactions that are not mortgage financed (colloquially referred to as “cash purchases”) as those without any loan or lender information. This approach would misclassify some mortgaged purchases as cash transactions if RCA was not able to obtain any information on the mortgage loan or lender or if they were unable to provide that information in their data. However, we believe that this source of misidentification is small for two reasons. First, mortgages are 4SeeCvijanovicetal.(2022)foramoredetaileddescriptionofRCA’sQ-Scoremeasureaswellasavalidationof RCA’scoverageandidentificationoftruebuyersbasedonREITdisclosures. 6

public records, so while information about some loan terms or property characteristics might be unavailable, whether there is a mortgage associated with a property should be reliably available. It is relevant to note that our analysis only requires information on whether a mortgage exists, not any specific loan terms. The public records should, in theory, be a comprehensive and complete record of all liens on real property. While a lender could make a mortgage loan without recording it in a public registry, doing so would significantly impair their ability to recoup any losses upon onforeclosurebecauselackofapublicfilingwouldmeanthatotherpartiesorcreditorswouldnot havetorespectthepriorityoftheirlien.5 Second, we verify that the share of cash transactions is consistent with two other data sources. AppendixFigureA1showsthattheratioofCREdebttothecurrentmarketvalueofCREassetsin theU.S.averagesabout17percent. Thiscurrentleverageratioisaboutalignedwithwhatwouldbe expectedgiventhecashsharesestimatedinthispaper,combinedwithnormalunderwritingterms.6 Additionally, Appendix Figure A2 shows that cash shares for institutional investors are similar in both RCA and data from the National Council of Real Estate Investment Fiduciaries (NCREIF). As NCREIF provides more uniform reporting of property-level debt than RCA, this fact gives us confidenceinRCA’scoverageofloanandlenderinformation.7 Our main sample is limited to non-portfolio purchase transactions from 2005 through 2022. We start the sample in 2005 because RCA expanded coverage that year. Estimated cash shares were 5A related concern may be that not all public records are digitized and accessible, but given that we limit our sample to 2005 onward and that RCA transactions are at least $2.5 million in value and therefore largely located in metropolitanareaswithdigitizedrecords,wedonotthinkthisisamajorconcern. 6Typical at-origination LTV ratios for CRE loans are around 60 percent (see, for example, Glancy et al. 2022). After accounting for amortization and property appreciation, the average current LTV for outstanding loans—i.e., what is being measured in the Financial Accounts—would be around 50.6 percent (this calculation is based on 2 percent annual price appreciation, an average of a 10-year loan term, and 30-year average amortization schedules, anduniformlydistributedoriginationdates,whichwouldbebroadlyinlinewiththeaveragesofthesecharacteristics acrossloansasrelayedinGlancyetal.(2022)). Giventhatinvestmentpropertiesandowner-occupiedpropertieshave cashsharesof43percentand70percent,respectively(Figure1),andabouttwo-thirdsofCREpropertiesareowneroccupied(Ghentetal.,2019),wewouldexpectabout61percentofthemarkettobecashfinanced.Thiswouldimplya currentLTVof50.6percent×.39≈20percent. Ifweoverestimatedtheportionofthemarketthatwascash-financed, wewouldexpectthisestimatetobebelow,ratherthanslightedabove,theestimatebasedonaggregateU.S.data. 7Additionally,thefactthatcashpurchasesaremostcommonforprivatebuyersandleastcommonforpublicones is indicative that coverage is reliable. If misclassifications were common, we would expect to see higher estimated cashsharesforprivatebuyerssincetheirfundingismoreopaque. 7

higher before this expansion, raising the concern that loan information was less complete in those earlyyears. Weexcludeportfoliotransactions,asitislessfeasibleforthebuyertomakefinancing basedontheredevelopmentpotentialofindividualproperties. 2.2. DescriptiveStatistics Figure 1 shows the share of purchase transactions (by number) without property-level debt (i.e., the cash share of purchases), split by buyer objective, buyer type, and property type. Regarding buyer objectives, cash purchases are most common for redevelopment projects, at 75 percent. Cash purchases are also on the higher end, at 59 percent, for purchases by intended occupiers, consistent with highly firm-specific assets being more likely to be owned than rented (Smith Jr. and Wakeman, 1985) and less suited for usage as collateral (Benmelech et al., 2005). Properties purchased for investment have cash shares around 46 percent, while cash shares for renovations arelower,at31percent.8 Regarding buyer type, cash purchases are highest for public buyers (e.g., REITs), at 79 percent, and lowest for private buyers, at 44 percent. Regarding property type, cash shares are highest for development sites, at 80 percent; lowest for apartment buildings, at 32 percent; and between 39 and 56 percent for nonresidential property types. These differences in cash purchase shares are reasonablystableovertime,asisshowninFigureA3. These differences provide some hints at motivations for deciding against using mortgage financing to fund purchases. First, differences in credit availability appear to affect capital structure decisions; public buyers, which likely have greater access to unsecured financing, are much less likely to use mortgage financing than private borrowers. Additionally, mortgage usage is highest for apartment buildings, perhaps reflecting greater credit availability, given the involvement of the government-sponsored enterprises in the secondary market. We will account for differ- 8These patterns are broadly similar when shares are weighted by property value (see Figure A4); on a weighted basis, cash purchases are around 70 percent of purchases for occupancy or redevelopment, compared with about 43 percentofpurchasesforinvestment. FigureA5alsoincludesthedistributionofobservationsacrossthecategories. 8

encesincreditavailabilityalongthesedimensionsintheempiricalresultsbyemployingbuyerand property-typefixedeffects. Second, the results are consistent with the hypothesis that buyers use cash financing to maintain operationalflexibilitytoengageinredevelopmentprojects. Namely,cashusageisparticularlyhigh for redevelopment projects or development sites. In the next two sections, we will further develop and more formally test this hypothesis by analyzing differences in financing behavior based on properties’redevelopmentoptionsandbuyers’redevelopmentexperience. Table 1 provides some summary statistics for the full sample of property sales and for samples broken out by whether there is a mortgage associated with the transaction. Since we are interested in how financing decisions affect redevelopment options rather than how renovation and redevelopment projects are funded, this sample includes only purchase transactions for the sake of investment (as opposed to the other objectives listed at the top of Figure 1). The last column presentsthedifferenceinmeansforcash-andmortgage-financedpurchases. Unconditionally,propertiesthatarecashfinancedhavemodestlyhigherQ-Scores,onaverage,but are 1 percentage point more likely to have a Q-Score in the bottom quartile (“Low Q-Score”=1). Cash-financedpropertiesarealsomorelikelytobeyounger,andhaveloweraveragevaluationsbut higherpricespersquarefoot. Additionally,transactionswithshorteraverageholdperiodsaremore likelytobecashfinanced;thisresultisconsistentwithDemircietal.(2023),whodemonstratethat REITsarelesslikelytosellencumberedproperties. Regardingbuyercharacteristics,buyerswithdevelopmentexperience,definedasbuyersforwhich atleast25percentoftransactionsareflaggedasinvolvingrenovation,redevelopment,orconstruction,aremorelikelytopurchasepropertiesallcash. Specifically,11.2percentofcashtransactions areaccountedforbydevelopers,comparedwithonly10.7percentofmortgagedtransactions. The findings are similar when development experience is measured continuously; the average cash buyer has 16.5 percent of their transactions involving some form of development, compared with 15.5 percent for mortgaged transactions. Cash-financed properties are also more likely to be ma- 9

terially improved (i.e., have an at least 20-percentage-point increase in their Q-score in the next transaction), consistent with a greater likelihood of renovation. Of course, these summary statisticsaresubjecttocompositioneffects,sowewillrequiremoreformalanalysistounderstandthese patternsbetter. 3. MODELOFREDEVELOPMENTOPTIONSANDFINANCINGDECISIONS In this section, we present a simple model of how redevelopment options affect financing decisions. In the first subsection, we present a model where CRE investors optimally choose when to redevelop properties. The model establishes the framework we use for estimating cross-sectional differences in the value of redevelopment options. In the second subsection, we extend the model to include leverage and derive how frictions to redeveloping mortgaged properties affect option valuesandfinancingdecisions. 3.1. Model Supposethata newly renovatedpropertyyieldsanetcash flowthatwenormalizeto1. Overtime, thiscashflowdepreciatesatrateδ. Ifpropertyinvestorsdiscountthefutureatrater,thenthevalue ofapropertyaftert yearswillsatisfythepricingequation: rV(t)=e−δt+V(cid:48)(t). (1) Supposethatownersareabletorenovateatcostctoreturnthepropertytothecashflowofanewly builtone. InAppendixB,weshowthatequation(1)canthusbesolvedas   V(t)= e−δt  1+ δ e−(r+δ)(t∗(c)−t) , (2) r+δ  r  (cid:124)(cid:123)(cid:122)(cid:125) (cid:124) (cid:123)(cid:122) (cid:125) Valuewithout ≡ρ(t,c) RenovationOption 10

wheret∗(c)istheoptimaltimeofrenovation,whichweshowtobemonotonicallyincreasinginc.9 This expression says that the increase in the value of the property due to the renovation option— defined in (2) as ρ(t,c)—is decreasing in the time until renovation (i.e,t∗(c)−t). Higher costs of renovationcauseownerstowaitlongertorenovateandreducethevalueoftheoption. Wecanthus derivethefirsthypothesiswetestinthedata. Hypothesis 1. Older and less productive (higher t) properties are more likely to be immediately redeveloped. Thishypothesisfollowsdirectlyfromthefactthatρ(t,c)isdecreasinginthetimeuntilrenovation. A purchaser i would acquire a property j for immediate redevelopment if t∗ −t < 0. If we i,j j assume t is observable and t∗ is distributed according to the cumulative distribution function F, j i,j thentheprobabilitythatapurchaseoccursforimmediateredevelopmentisF(t ). Thisprobability j is increasing in time since renovation (t ) and decreasing in property productivity (since income j relativetonewlyrenovatedproperties,e−δt j,isadecreasingfunctionoftime). In practice, t is typically not directly observed, so when we estimate the value of redevelopment j options,wewillinsteadestimateaprobitbasedonaflexiblefunctionofabuilding’sage(thetime it has had to depreciate) and Q-Score (a direct measure of the property’s relative productivity) to capture the renovation potential of a property. Specifically, we parameterizet −t∗ , reflecting the j i,j value of the renovation option, as t −t∗ =X(cid:48)β +σε , where X is a set of variables measuring j i,j j i,j j the property’s age and quality, and ε follows a standard normal distribution. We then estimate i,j X(cid:48)β Pr(Renovation)=Φ( j ),whichprovidesameasureofthevalueoftherenovationoption.10 σ 9t∗(c)isdefinedimplicitlybythevalue-matchingconditionthatV(t∗)=V(0)−c. 10Moreformally,thevalueoftherenovationoptionwouldbeE(ρ |X ),whichisamonotonicallyincreasingfuncj tionofthefittedrenovationprobability. Weworkwiththefittedprobabilitythatapropertywaspurchasedforrenovationsinceitiseasiertointerpretanddoesnotrequireestimatesofscaleparameters(σ,r,δ). 11

3.2. ModelwithLeverage We now introduce leverage following a trade-off theory approach, though we make some simplifying assumptions on the functional forms of the costs and benefits of debt for ease of exposition. Assume the presence of a mortgage raises the cost of renovation such that the optimal renovation time increases fromt∗ tot∗+∆. Borrowers face a trade off between this cost and a benefit to debt that is proportional to the renovation-option-free value of the property. Denoting this benefit by b, purchasersthenusecashtofinanceapropertyif e−δt V(t;t∗)>V(t;t∗+∆)+b . (3) r+δ Wecanthenderiveoursecondhypothesis. Hypothesis2. Investorsusecashtopurchasepropertieswithgreaterredevelopmentoptions. We can derive this hypothesis by combining equations (2) and (3) to show that buyers use cash if (cid:16) (cid:17) b<ρ(t,c) 1−e−(r+δ)∆ . (4) This expression says that borrowers use cash if the benefit of secured financing, b, is smaller than thedeclineinthevalueoftherenovationoption,theexpressionontheright. Themarginaleffectof increasing the optimal renovation time,t∗, is greater when the renovation option is more valuable, i.e.,whenρ ishigher. Wecanthereforederivetheconditionsunderwhichbuyersimmediatelyrenovate,investwithcash 12

financing,orinvestwithmortgagefinancing:      ImmediatelyRenovate ift i ∗ ,j −t j <0    InvestmentStrategy= InvestwithCashFinancing if0<t∗ −t <max{ζ,0} (5) i,j j       InvestwithMortgageFinancing ift i ∗ ,j −t j >max{ζ,0}, (cid:16) (cid:17) whereζ = 1 ln δ(1−e−(r+δ)∆) isthethresholdtimetorenovationbelowwhichbuyerschooseto r+δ br usecashratherthanmortgagefinancingbasedonequation(4).11 Thedecisionwhethertoimmediatelyrenovate,investwithcashfinancing,orinvestwithmortgage financing could be estimated by ordered probit since those outcomes depend on the same latent variable, t∗−t, but with different thresholds (0 and ζ). However, such an estimation strategy wouldimpose,ratherthantestfor,thefactthatcashpurchasesareusedforpropertieswithagreater renovation option. Consequently, when we test this proposition in the data in the next section, we instead use a probit model predicting whether a property is purchased for immediate development to estimate the likely value of the redevelopment option. We then test whether properties with a greaterredevelopmentoptionaremorelikelytobecashfinanced. 4. METHODOLOGYANDEMPIRICALFINDINGS In this section, we test the two hypotheses from the model and provide some additional analysis regardingtherelationshipbetweenmortgagefinancingandredevelopmentoptions. Inthefirstsubsection, we estimate the likelihood that a property is purchased for the purpose of redevelopment basedonpropertyageandquality. GuidedbytheframeworkinSection3.1,weusetheseestimates to construct our measure of redevelopment potential. In the second subsection, we use this measuretodemonstratethatinvestorsdisproportionatelyusecashpurchasesforpropertieswithgreater 11Ifγ <0,thecostofhavingsecureddebtissmallenoughthatV(t;t∗)<V(t;t∗+∆)+be−δt ∀t∗>t,meaningthat r+δ allpurchasesaremortgagefinanced. 13

redevelopment potential. In the third subsection, we show directly that cash-financed properties are more likely to be subsequently redeveloped or improved. In the fourth subsection, we study theincreaseinredevelopmentoptionvaluesduringtheCOVID-19pandemic. 4.1. Olderorlessproductivepropertiesaremorelikelytoberedeveloped Oursimpletheoreticalframeworkindicatesthatolderorlessproductivepropertiesaremorelikely to be redeveloped. At first blush, this hypothesis appears to be true in our data. In Figure 2, we present binned scatterplot (binscatter) regressions of an indicator of whether a property was purchased for redevelopment on property quality (Q-Score) in the left panel and building age in the right panel. We define redevelopment broadly to include both renovation and redevelopment. The binscatter regressions also control for the natural log of the acreage of the land parcel and includeyear,property-type,andbuyerfixedeffects. TheplotbyQ-Scorealsocontrolsforbuilding ageandtheplotbybuildingagealsocontrolsforQ-Score. Therateatwhichpropertiesarepurchasedforredevelopmentfallssharplyinqualityforproperties in the lowest quintile and then levels off at higher Q-Scores (before jumping again for properties in the highest decile). Effects of age are more linear; the probability of redevelopment rises from about2percentfora10yearoldpropertytoabout8percentfora50-year-oldproperty,andtoover 10percentforan80-year-oldproperty. To more formally test how Q-Score and building age are related to redevelopment, we run the followingregression: Pr(RedevelopmentorRenovation )= f(BuildingAge )+g(Q-Score ) i,j,t j j (6) +ζ +η +ε , p(j,t) t i,j,t where the dependent variable is an indicator for whether the buyer i’s objective in purchasing a property is either renovation or redevelopment (as opposed to investment), f(BuildingAge ) is j 14

a function of building j’s age in years, and g(Q-Score ) is a function of building j’s Q-Score. j We also include property-type fixed effects (ζ ) and quarter fixed effects (η ). We cluster the p(j,t) t standarderrorsbybuyer. We predict the borrower’s intent to alter properties (rather than actual alterations) for two reasons. First, since we are interested in how investors choose to finance property purchases, we want our measureofredevelopmentpotentialtoreflecttheperceivedpotentialatthetimeofpurchaserather than whether the alteration actually occurs. Predictions of intended alteration better capture this concept. Second, the buyer objective is directly reported in the data, while actual alterations need tobeimputedbasedonsubsequenttransactions.12 We use two separate specifications. First, we simply include building age and the Q-Score as independentvariables. Second,weestimatelinearsplinesfortheindependentvariablesofinterest in order to capture the nonlinearities demonstrated in Figure 2. For building age, the knots of the spline are at 5, 25, 50, and 75 years old. For the Q-Score, we place knots at the 25th, 50th, and 75thpercentiles. We estimate equation (6) using two models—first, with OLS and, second, with a probit. The results are presented in Table 2. Columns (1) and (2) include the OLS results, with building age and Q-Score entering linearly in column (1) and with the linear splines in column (2). Columns (3)and(4)includeparallelresultsusingaprobitmodel. The signs of the coefficients are as expected. The coefficient on building age in column (1) indicatesthat,onaverage,apropertythatisoneyearolderhasa0.14percentagepointhigherlikelihood ofredevelopmentorrenovation,whileapropertywithaQ-Scoreof1isalmost2percentagepoints less likely to be purchased for redevelopment or renovation than one with a Q-Score of 0. The results for the linear spline in column (2) indicate that these effects vary across the building age and Q-Score distribution. Consistent with the findings from Figure 2, age fairly consistently increases 12InSection4.3,weshowthatcashfinancedpropertiesaremorelikelytobesubsequentlyimproved.Additionally,in unreportedanalysis,weconfirmthatthemeasuresofintendedalterationareindeedpredictiveofactualimprovements andalterations. 15

the likelihood of intended redevelopment, with sizable effects starting at age 5 and continuing up until effects level off around 75. For Q-Score, higher quality reduces the likelihood of intended redevelopmentsharplyinthefirstquartilebuthasmodesteffectsathigherquartiles. Thecoefficientsfortheprobitmodelincolumns(3)and(4)arehardertointerpretintermsofmagnitudebutgenerallyretainsimilarsigns,significancelevels,andrelativemagnitudes. Asdiscussed in Section 3.1, we use the probit model to construct the fitted probability of redevelopment for properties purchased for investment. Specifically, we use the fitted probabilities from the specification in column(4) to produce a continuous measureof redevelopment potential that isa flexible functionofabuilding’sageandQ-Score. Thismetricwillbeourmainmeasureofthevalueofthe redevelopmentoptionintheremaininganalysis. 4.2. Propertieswithgreaterredevelopmentoptionsarelesslikelytobemortgagefinanced Thesummarystatisticsprovidesuggestiveevidenceforseveralpotentialreasonsastowhybuyers mightforgomortgage-financing: highavailabilityofunsecuredfunding(e.g.,forREITs),avoiding transactioncostsforprojectswithshorterinvestmenthorizons,andfundingpropertieswithahigher asset specificity (e.g., for owner-occupiers). Here, we focus on the role of investors maintaining theirredevelopmentoption,aspredictedinthetheory. Theprimarythreattoidentificationisthatoneoftheseothermotivationsforcashpurchasescorrelateswithredevelopmentoptionvalues,causingtheanalysistoincorrectlyattributethemotivation forcashfinancingtoborrowerstryingtomaintainredevelopmentoptions. Weaddressthesethreats to identification in two ways. First, in the spirit of Khwaja and Mian (2008), we exploit withinbuyervariationtoexaminehowbuyersfundprojectswithhighredevelopmentoptions. Buyerfixed effects control for factors such as desired leverage or the availability of unsecured financing and increaseconfidencethattheestimatedeffectsaredrivenbythedesirabilityoffundinganindividual propertywithcashasopposedtomortgagecredit. 16

Second, we take a difference-in-differences-style approach and test how buyers with development experiencerespondtoredevelopmentoptionscomparedtobuyerswithoutit. Ifredevelopmentoptions correlate with mortgage financing for reasons besides redevelopment options (for example, lenders being reluctant to finance obsolete properties), then this should affect both buyers with and without development experience. The difference in the effect of redevelopment potential on cash financing for developers relative to non-developers therefore plausibly reflects the additional motivationofborrowerstofundpropertieswithcash(orunsecuredfinancing)topreserveredevelopmentoptions.13 Additionally, we supplement these strategies by controlling for other factors that could affect a buyer’s decision to forgo mortgage-financing. First, we add an indicator for whether the property was built in the last two years to control for differences in financing decisions during the lease-up stage of the development process. Second, we control for the size of the land to capture liquidity difficultiesthatcouldarisefromfundinglargerpurchaseswithcash. Third,weincludeanindicator for whether the property was resold within five years since buyers might not take out a mortgage iftheirintendedholdperiodisshorterthanthelengthofatypicalloan. Namely,weestimatethefollowingspecification: Cashpurchase =β Developer ×RedevelopmentProbability i,j,t 1 i j,t (7) +η (cid:48)X +γ +ζ +η +ε , i,j,t i p(j,t) t i,j,t where Cashpurchase is an indicator for whether the purchase of property j by buyer i at time i,j,t t was made without associated property-level debt. Developer is an indicator for whether more i than one-fourth of the buyer’s transactions involve some type of development purpose (renovation, redevelopment, or construction). Redevelopment Probability is the fitted probability that j,t the property would be redeveloped as estimated in Section 4.1. The variable X includes the i,j,t 13Wealsoconsiderspecificationsthatincludebuyer-typefixedeffects(insteadofbuyerfixedeffects),whichcontrol forbroaddifferencesintheavailabilityofcredittodifferentbuyertypeswithoutthesamelossesofobservationsand degreesoffreedomthatresultwhenusingbuyerfixedeffects. 17

aforementionedcontrolsaswellastheuninteractedpropertyredevelopmentprobability. γ,ζ , i p(j,t) and η are buyer, property-type, and quarter-of-transaction fixed effects, respectively. To account t for our use of a generated regressor, the standard errors are estimated via bootstrap, clustering by buyer,with1000replications.14 Note that the sample differs from the analysis in Section 4.1. Here, we only include properties purchased for investment, rather than also having renovation and redevelopment projects in the sample. We do this because we are interested in how redevelopment options affect financing decisions, rather that how renovation and redevelopment projects are financed. If a buyer acquires a property for immediate renovation or redevelopment, they would take out a loan that explicitly allowed for such alterations. The focus here is on the degree to which buyers use cash financing for properties that are more likely to benefit from alterations in the future. This approach is consisting with theoretical framework, which only specifies whether a purchase is mortgage financed for properties not purchased for immediate renovation. (In equation (5), financing options are specifiedonlywhent∗ >t ). i,j j TheestimatesfortheprimaryspecificationarepresentedinTable3.15 Columns(1)and(2)present estimates excluding the buyer or buyer-type fixed effects, with the interaction with the buyer’s development experience added in the second column; columns (3) and (4) present the same specifications but include buyer type fixed effects; and columns (5) and (6) again present the same specificationsbutincludebuyerfixedeffects. The estimates in column (1), which excludes the interaction terms, imply that a property with a 10 percentage point higher redevelopment probability is about 2.1 percentage points more likely to be cash financed. The sign on the indicator for buildings that have been recently built is also as expected: new buildings are over 11 percentage points more likely to be cash financed. We also findthatlargerparcelsarelesslikelytobecashfinanced. 14Buyersaresampledwithreplacement,andredevelopmentprobabilitiesarereestimatedforeachsample. 15In this section, we use our estimated redevelopment probability created in Section 4.1. In Table A1, we run a similar specification using the two main components of redevelopment potential directly: the Q-Score and building age. 18

In column (2), we include the interaction of the redevelopment probability with the indicator for whetherthebuyerisadeveloper. Thecoefficientontheinteractiontermispositiveandstatistically significant,asexpected. Itindicatesthatwhendevelopersbuyaproperty,theirfinancingdecisions are over twice as sensitive to redevelopment options as those of non-developers; a 10 percentage point increase in redevelopment probability raises the use of cash purchases by 3.9 percentage pointsfordevelopers,comparedwith1.6percentagepointsfornon-developers. Columns (3) and (4) repeat the same specifications but include buyer-type fixed effects to account for differences in access to alternative financing options across buyer types. The inclusion of thesebuyer-typefixedeffectsstrengthenstherelationshipbetweenredevelopmentoptionsandcash usageoverallbutdoesnotmateriallyaffectthecoefficientontheinteractionterm. REITshavehigh cash purchase shares despite tending to buy higher-quality properties, so not controlling for buyer typetendstoweakentheestimates.16 We include buyer fixed effects in columns (5) and (6), which control for any buyer-specific access to or preference over various funding sources. The results are again broadly similar, with the coefficient on redevelopment probability increasing yet again but the interaction term remaining comparable to the other specifications with less granular fixed effects. Across the specifications, a 10 percentage point increase in redevelopment probability is found to raise the likelihood of cash financing by roughly 2 percent more for buyers with development experience compared with buyerswithoutit. Figure 3 presents similar estimates from binscatter regressions, thus allowing the relationship between cash purchases and redevelopment potential to be nonlinear. The regression is separately estimated for developers and non-developers, including the same fixed effects as in equation (7). The results confirm that developers are relatively more likely to use cash financing when purchasing properties with high redevelopment potential. The usage of cash financing is fairly similar across these types of buyers for properties with a redevelopment probability under 5 percent, but 16Inunreportedresults,wealsorunthisspecificationexcludingREITs. Theresultsarequantitativelysimilar. 19

thedifferenceincreases(aboutlinearly)forpropertieswithgreaterredevelopmentpotential. 4.3. Cashfinancingandredevelopmentoutcomes How well do financing decisions by developers relate to actual redevelopment activity? If developers use cash financing to ease frictions on subsequent renovations or redevelopment, we would expect cash purchases to be predictive of whether properties are actually altered after purchase. Answering this question is complicated by the fact that the RCA data report the purpose of the acquisition in terms of whether the buyer intends to renovate or redevelop a property but generally does not report whether the buyer eventually goes on to undertake such activities after buying. To try to gain insight into such activities, we generate two proxies for whether properties are improvedbasedonreportinginsubsequenttransactions(ifavailable). First,weimputethataproperty is renovated if any of the following occur: the next transaction has a purpose listed as renovation, redevelopment, or construction; the next purchase updates the year built or year renovated field to indicate that rebuilding or renovation occurred since the previous transaction; or the property type changes to indicate the building was repurposed. Second, we impute improvements based on the change to the Q-Score, since property improvements would increase the value of the property for the next transaction. We flag a property as improved if the Q-Score rises by 0.2 between transactions. We then run regressions identical to those presented in Table 3 columns (2), (4), and (6) (i.e., the specifications with the interaction) but with indicators of renovation or improvement as thedependentvariablesandwithacashpurchaseindicatorreplacingtheredevelopmentprobability variable. TheestimatespredictingtheseimprovementvariablesaredisplayedinTable4. Overall, the results indicate that cash purchases by developers do predict future renovations and improvements. Columns(1)through(3)indicatethatpurchasesbydevelopersarealmost6percent more likely to be renovated in the future and that cash purchases by developers are around an additional 2 percentage points more likely to be renovated. The coefficient on the interaction 20

between the cash purchase and developer indicators stays fairly stable across specifications with buyer-typeandbuyerfixedeffects. Columns (4) through (6) indicate that cash purchases are, on average, between 3.0 and 4.2 percentage points more likely to be improved in the future. In the specifications without buyer fixed effects, cash purchases by developers are another 4 percentage points more likely to be improved inthefuture,buttheeffectgoesawaywhenbuyerfixedeffectsareadded. Oneexplanationforthis latterresultisthatthedeveloperindicatorisconstructedbasedonameasureofthefrequencywith which the buyer is flagged as buying with the intention to renovate or redevelop; thus, the measure may struggle to capture the tendency to make improvements of the type that are not directly reportedintheRCAdata. While this analysis provides suggestive evidence in favor of the hypothesis that mortgage financing impedes future alterations, there are a few important caveats required. First, the proxies for whetheralterationoccurareimperfect. Mostnotably,significantenoughredevelopmentcancause the property identifier in RCA to change, restricting our ability to identify future redevelopment. We are thus less likely to observe redevelopment if the investor undertakes it themselves (i.e., the situationweareprincipallystudying)thaniftheyselltoanotherpartywiththepurposeofredevelopment. Second, given the previous evidence that investors use cash to purchase properties with redevelopmentpotential,wecannotinterpretthecoefficienton“Cashpurchase”asentirelyreflecting the effects of mortgage-related frictions. Instead, the estimates likely reflect a combination of bothdirecteffectsofcashpurchases,andthepreviouslystudiedselectioneffects.17 17Theempiricalstrategyreliesonageandqualityaffectingmortgagefinancingthroughtheireffectonredevelopmentoptionvalues,sowedonotwanttoexplicitlycontrolforageandqualityintheseregressions.However,whenwe addthecontrolsforQ-scoreandagetothisspecification,thecoefficientsonthecashindicatorarelargelyunchanged andremainsignificant.Thisresultindicatesthattheeffectsofcashfinancingdonotentirelyreflecttheselectioneffects documentedinthecoreofthepaper. However,weareunclearonhowtointerpretthisfindinggiventhemechanical relationshipbetweenQ-Scoreandimprovement. 21

4.4. RedevelopmentoptionvaluesincreasedduringtheCOVID-19pandemic The COVID-19 pandemic provides another source of variation in redevelopment options to study. Thepandemiclikelyincreasedoptionvaluesforacoupleofreasons. First,itincreaseduncertainty, particularly for the CRE market, thus it likely increased option values. Indeed, in an extension to the model with stochastic cash flows (see Appendix B.2), we demonstrate that an increase in uncertainty(thevolatilityofthecashflowprocess)increasesrenovationoptions.18 Second, it prompted a shift in how space was used, increasing the need for some space to be redeployed or, at least, updated. These effects are particularly prominent for office properties, which—as of the time of this paper’s distribution—are contending with rising vacancies, substantial uncertainty regarding the long term demand for space, and the potential need for widespread redeployment to alternative property types. Given these factors, we would expect the pandemic to raise redevelopment option values and prompt an increase in the share of purchases made with cash. Of course, identifying causal effects of the COVID-19 pandemic on redevelopment option values and property financing decisions is complicated by the fact that lending standards also changed during the pandemic. Changes in lending standards could have (1) affected borrowers’ access to mortgagefinancingand(2)increasedtheuseofcashpurchasesforreasonsthathavenothingtodo withredevelopmentoptionvalues. To plausibly identify the channel we are interested in, we again use a difference-in-differences specification where we compare properties with different redevelopment probabilities before and after the pandemic. If the pandemic did affect redevelopment option values, we would expect an increaseintheuseofcash-financingforpropertieswithgreaterredevelopmentpotential. 18Thatuncertaintyincreasesoptionvaluesisawellknownresult(see,e.g.,DixitandPindyck1994). 22

Werunthefollowingregression: Cashpurchase =β COVID-19 ×RedevelopmentProbability i,j,t 1 t i,t (8) +η (cid:48)X +γ +ζ +η +ε , i,j,t i p(i,t) t i,j,t where COVID-19 is equal to 1 starting in 2020 and continuing through the remainder of our t sample. The redevelopment probability is the measure constructed in Section 4.1 and used to measure redevelopment options in the other results. We include buyer (γ), property-type (ζ ), i p(j,t) andyear-quarter(η )fixedeffects. Additionally,asintheprevioussubsections,weincludeavector t ofcontrolsthatincludeCBSAfixedeffects,anindicatorfornewlybuiltproperties,thenaturallog of the size of the land parcel, and an indicator for whether the property is sold within five years. Standarderrorsarebootstrappedasinthepreviousspecificationsandclusteredbybuyer. Giventhedramaticchangeinwork-from-homepoliciesduringthepandemic,uncertaintyincreased for office properties in particular. Following the same logic as the COVID-19 regressions, we run an additional regression specification where we replace the redevelopment probability with an indicator for office properties. If the redevelopment option value of office properties increased more during the pandemic relative to the redevelopment option of other properties, we would expectcashpurchasesofthesepropertiestohavealsoincreased. The results are presented in Table 5. Columns (1) through (3) include the specifications using the redevelopment probability, with each column adding different fixed effects. Columns (4) through (6) report results from parallel regressions but replace the redevelopment probability with an office indicator. The results in columns (1) through (3) indicate that the relationship between cash financing and redevelopment probability rose during the pandemic. Across specifications, a 10percentage-point increase in redevelopment probability is found to raise the likelihood of cash financing by roughly 2 percentage points more during COVID relative to before it. This effect is comparable in magnitude with the increase in cash financing for developers relative to nondevelopersfoundinSection4.2. 23

Officepropertieswerealsomorelikelythanotherpropertytypestobepurchasedwithcashduring the pandemic. In column (4), the results indicate that there is a roughly 4 percent greater increase in cash purchases for office properties during the pandemic relative to other property types. The estimateissimilarwhenincludingbuyer-typefixedeffectsincolumn(5)butfallstounder2percent whenincludingbuyerfixedeffects. 5. CONCLUSION OurresultsindicatethatCREinvestorsconsideraproperty’sredevelopmentpotentialwhendecidinghowtofinanceapurchase. MortgagesonCREpropertiesoftenrequiretheownertorelinquish some control over property management to the lender and can therefore create additional frictions toredevelopment. Weprovideevidencethatbuyersstrategicallydecidewhethertotakeoutmortgageswiththesefrictionsinmind. Usingwithin-borrowervariationtoaccountfordifferencesinfinancingavailability, we show that properties with greater redevelopment potential are more likely to be cash financed, particularlywhenthebuyerhasexperienceinundertakingrenovationandredevelopmentprojects. These effects grew in magnitude during the pandemic, consistent with COVID-19 increasing the importance of renovation and redevelopment options. Office properties, in particular, had a strong rise in the usage of cash financing during the pandemic. These findings can help explain the significantnumberofCREpropertiesthatarepurchasedwithoutmortgagefinancing. 24

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Figure1: CashPurchaseShares Renovation 0.31 Investment 0.46 Buyer Objective Occupancy 0.59 Redevelopment 0.75 Private 0.44 Institutional 0.55 Buyer Type User/Other 0.68 Equity Fund 0.75 Public 0.79 Apartment 0.32 Hotel 0.39 Office 0.51 Property Type Retail 0.53 Industrial 0.56 Dev Site 0.80 0 .2 .4 .6 .8 1 Cash Purchase Share (unweighted) Note: ThisistheshareofCREpurchasesthatarecashfinanced(i.e.,financedwithoutmortgages)bybuyerobjective (top),buyertype(middle),andpropertytype(bottom). Condoconversionsareexcludedastheyarespecifictomultifamilyproperties. Sharesareunweighted;equivalentvalue-weightedstatisticsareshowninFigureA4. Source: Authors’calculationsusingMSCIRCAdata. 29

Figure2: RedevelopmentbyQ-ScoreandAge )tnecrep( erahS tnempolevedeR 51 01 5 0 .2 .4 .6 .8 1 Q-Score (a)ByPropertyQuality )tnecrep( erahS tnempolevedeR 21 01 8 6 4 2 0 20 40 60 80 100 Property Age (years) (b)ByAge Note: TheplotsareproducedusingtheStatacommand“binsreg”(Cattaneoetal.,2019). Eachbinscatterregression includesyear-quarterandproperty-typefixedeffects. Additionally,theproperty-qualityplotcontrolsforage,andthe ageplotcontrolsforpropertyquality. AhigherQ-Scoreindicatesahigher-qualitypropertyrelativetoapeergroup. Thedependentvariableisanindicatorforwhetherthepropertywaspurchasedforrenovationorredevelopment. The dotsreflectestimatedredevelopmentsharesbydecileoftheindependentvariableofinterest,whilethelinesplotsemilinearregressionestimateswithacubicB-spline. Source: Authors’calculationsusingMSCIRCAdata. 30

Figure3: CashPurchasesbyRedevelopmentPotential )tnecrep( erahS hsaC 55 05 54 04 53 Developer Non-developer 1 3 5 7 9 11 13 15 17 19 Redevelopment Probability (percent) Note: TheplotsareproducedusingtheStatacommand“binsreg”(Cattaneoetal.,2019). Eachbinscatterregression includesyear-quarter,property-type,andbuyerfixedeffects. Thedotsreflectestimatedcashpurchasesharesbydecile of renovation probability, while the lines plot semi-linear regression estimates with a cubic B-spline. Estimates for developersareinred,andthosefornon-developersareinblue. Source: Authors’calculationsusingMSCIRCAdata. 31

Table1: SummaryStatistics Full Cash Mortgage Difference Sample Purchases Purchases (1) (2) (3) (4) Q-Score 0.51 0.52 0.50 0.02** (0.30) (0.31) (0.29) (0.00) LowQ-Score 0.26 0.26 0.26 0.01** (0.44) (0.44) (0.44) (0.00) Age 34.94 33.47 36.12 -2.65** (27.07) (26.98) (27.08) (0.10) SoldWithin5Years 0.17 0.17 0.18 -0.01** (0.38) (0.37) (0.38) (0.00) HoldingPeriod 4.98 4.75 5.15 -0.40** (3.54) (3.66) (3.44) (0.02) Value(millions) 14.59 13.48 15.54 -2.07** (47.50) (43.70) (50.51) (0.16) PriceperSq. Ft. 231.40 235.75 227.58 8.16** (235.89) (251.68) (221.00) (0.85) RedevelopmentProbability(%) 9.01 9.17 8.89 0.28** (6.02) (6.34) (5.77) (0.02) BuyerDevelopmentShare(%) 15.95 16.50 15.48 1.01** (14.06) (14.27) (13.86) (0.05) Developer(%) 10.92 11.23 10.67 0.56** (31.20) (31.57) (30.87) (0.11) ImminentImprovement(%) 15.18 18.39 13.17 5.21** (35.88) (38.74) (33.82) (0.28) Note:Columns(1),(2),and(3)presentthemeanandstandarddeviation(inparentheses)ofvariouspropertyortransactioncharacteristicsforthefullsampleofpropertyinvestments,cashpurchases,andmortgagepurchases,respectively. Column(4)presentsthedifferenceinmeans,andstandarderrorofthedifference,forcashpurchasesascomparedwith mortgagepurchases. Thefullsampleislimitedtonon-portfoliopurchasetransactionsin2005orlaterwherethebuyer has indicated that their objective is investment. “Low Q-Score” is an indicator for a Q-Score in the bottom quartile of the distribution. “Developer” is defined as a buyer with a development share above 25 percent. “Redevelopment Probability”isthefittedvaluepredictingtheprobabilitythatapropertyispurchasedforrenovationorredevelopment (seeSection4.1). ImminentImprovementisanindicatorforwhethertheQ-scoreincreasesbyatleast20percentage pointsatthetimeofthenexttransaction(seeSection4.3). +,∗,and∗∗ indicatesignificanceat10percent,5percent, and1percentlevels,respectively. Source: Authors’calculationsusingMSCIRCAdata. 32

Table2: PredictorsofRedevelopmentorRenovation PurchasedforRedevelopmentorRenovation (inpercentagepoints) OLS Probit (1) (2) (3) (4) BuildingAge(years) 0.14** 0.01** (0.01) (0.00) Q-Score -1.87** -0.25** (0.45) (0.02) Age0–5 0.05 -0.04** (0.05) (0.01) Age5–25 0.35** 0.04** (0.01) (0.00) Age25–50 0.17** 0.01** (0.02) (0.00) Age50–75 0.12** 0.01** (0.03) (0.00) Age75–100 0.00 -0.00 (0.03) (0.00) Q-Score: Quartile1 -30.99** -2.37** (2.00) (0.10) Q-Score: Quartile2 4.40** 0.36** (1.04) (0.08) Q-Score: Quartile3 3.85** 0.19* (1.00) (0.08) Q-Score: Quartile4 13.63** 0.88** (1.55) (0.10) R2 0.040 0.045 a Observations 249,145 239,857 249,145 239,853 Y¯ 8.49 8.22 8.49 8.23 sd(Y) 27.87 27.47 27.87 27.47 PropertyTypeFE (cid:88) (cid:88) (cid:88) (cid:88) Year-QuarterFE (cid:88) (cid:88) (cid:88) (cid:88) Note:Thesampleislimitedtorefinanceandsaletransactionswherethebuyerobjectiveisinvestment,redevelopment, orrenovation. Thedependentvariableisanindicatorofwhetherthebuyer’sobjectiveisredevelopmentorrenovation, multiplied by 100. Columns (2) and (4) fit a linear spline in age and Q-Score, and the coefficient estimates reflect slopeswithinaparticularageorQ-Scorebin. Y¯ andsd(Y)reportthemeanandstandarddeviationofthedependent variableineachregressionsample,respectively,ofthedependentvariableineachregressionsample.Standardserrors, inparentheses,areclusteredbybuyer. +,∗,and∗∗ indicatesignificanceat10percent,5percent,and1percentlevels, respectively. Source: Authors’calculationsusingMSCIRCAdata. 33

Table3: CashPurchasesandRedevelopmentOptions CashIndicator(inpercentagepoints) (1) (2) (3) (4) (5) (6) RedevelopmentProbability 21.30** 15.68** 36.97** 31.66** 48.73** 44.52** (5.45) (5.42) (4.59) (5.15) (4.33) (4.23) RedevelopmentProbability×Developer 22.33** 20.41** 19.07* (8.27) (7.21) (7.61) Developer -1.44 -1.05 (1.30) (1.05) Age<2 10.88** 10.83** 8.53** 8.48** 5.20** 5.18** (0.97) (0.98) (0.99) (0.99) (0.71) (0.71) ln(LandAreainAcres) -1.18** -1.19** -1.76** -1.76** -1.86** -1.86** (0.17) (0.17) (0.13) (0.13) (0.11) (0.12) SoldWithin5Years -2.02** -2.01** -1.28* -1.28* 0.95+ 0.95* (0.63) (0.63) (0.55) (0.56) (0.48) (0.47) R2 0.102 0.102 0.143 0.144 0.329 0.330 a Observations 127,307 127,307 125,103 125,103 116,977 116,977 Y¯ 42.14 42.14 41.72 41.72 42.1 42.1 sd(Y) 49.38 49.38 49.31 49.31 49.37 49.37 PropertyTypeFE (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) Year-QuarterFE (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) CBSAFE (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) BuyerTypeFE - - (cid:88) (cid:88) - - BuyerFE - - - - (cid:88) (cid:88) Note: The sample is limited to purchase transactions in 2005 or later where the buyer has indicated their intention is investment. The dependent variable is an indicator for whether the property is cash financed, scaled by 100 so estimatescanbeinterpretedinpercentagepoints. TheredevelopmentprobabilityiscalculatedasdescribedinSection 4.1. Y¯ and sd(Y) report the mean and standard deviation, respectively, of the dependent variable in each regression sample. Standard errors, in parentheses, are bootstrapped using 1000 replications, clustering by buyer. +, ∗, and ∗∗ indicatesignificanceat10percent,5percent,and1percentlevels,respectively. Source: Authors’calculationsusingtheMSCIRCAdata. 34

Table4: CashPurchasesasaPredictorofImprovementorRenovation RenovationIndicator ImprovementIndicator (inpercentagepoints) (1) (2) (3) (4) (5) (6) CashPurchase -1.01** -1.12** -0.85* 3.04** 3.80** 4.17** (0.32) (0.33) (0.38) (0.49) (0.51) (0.55) CashPurchase×Developer 1.91* 2.17** 2.03* 4.08** 3.80** -0.47 (0.78) (0.78) (0.94) (1.12) (1.13) (1.39) Developer 5.61** 5.56** 4.41** 4.42** (0.54) (0.54) (0.70) (0.70) ln(LandAreainAcres) 1.48** 1.41** 0.86** -0.62** -0.43** -0.36* (0.10) (0.10) (0.11) (0.13) (0.13) (0.15) Age<2 -6.29** -6.33** -5.13** -6.73** -6.37** -2.66** (0.51) (0.52) (0.63) (0.68) (0.69) (0.79) SoldWithin5Years 2.20** 1.92** 1.24** 0.37 0.48 0.76 (0.31) (0.30) (0.35) (0.46) (0.46) (0.49) R2 0.036 0.037 0.090 0.037 0.040 0.150 a Observations 86,119 85,322 76,156 43,274 42,963 36,153 Y¯ 14.79 14.81 14.93 14.99 15.02 14.54 sd(Y) 35.5 35.52 35.64 35.7 35.72 35.25 PropertyTypeFE (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) Year-QuarterFE (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) CBSAFE (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) BuyerTypeFE - (cid:88) - - (cid:88) - BuyerFE - - (cid:88) - - (cid:88) Note: The redevelopment probability is calculated as described in Section 4.1. Y¯ and sd(Y) report the mean and standarddeviation,respectively,ofthedependentvariableineachregressionsample. Standarderrors,inparentheses, areclusteredbybuyer. +,∗,and∗∗indicatesignificanceat10percent,5percent,and1percentlevels,respectively. Source: Authors’calculationsusingMSCIRCAdata. 35

Table5: CashPurchasesduringtheCOVID-19Pandemic CashIndicator(inpercentagepoints) (1) (2) (3) (4) (5) (6) RedevelopmentProbability 18.30** 33.82** 46.38** (5.26) (2.98) (4.41) RedevelopmentProbability×COVID-19 24.99* 26.92** 19.26* (10.39) (6.76) (9.12) Office×COVID-19 4.37** 4.01** 2.19 (1.21) (1.18) (1.45) Age<2 11.01** 8.66** 5.29** 9.49** 6.42** 3.25** (1.00) (0.63) (0.72) (1.00) (1.03) (0.69) ln(LandAreainAcres) -1.19** -1.76** -1.86** -1.05** -1.64** -1.86** (0.17) (0.09) (0.11) (0.16) (0.12) (0.11) SoldWithin5Years -2.02** -1.29** 0.94+ -0.68 -0.19 2.06** (0.65) (0.34) (0.48) (0.54) (0.50) (0.42) R2 0.102 0.144 0.330 0.090 0.131 0.309 a Observations 127,307 125,103 116,977 154,637 151,521 143,406 Y¯ 42.14 41.72 42.1 43.09 42.5 43.07 sd(Y) 49.38 49.31 49.37 49.52 49.43 49.52 PropertyTypeFE (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) Year-QuarterFE (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) CBSAFE (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) BuyerTypeFE - (cid:88) - - (cid:88) - BuyerFE - - (cid:88) - - (cid:88) Notes: TheCOVID-19indicatorissetequalto1fortransactionsin2020:Q1orlater. Theredevelopmentprobability iscalculatedasdescribedinSection4.1.Y¯ andsd(Y)reportthemeanandstandarddeviation,respectively,ofthedependentvariableineachregressionsample. Standarderrors,inparentheses,arebootstrappedusing1000replications, clusteringbybuyer. +,∗,and∗∗indicatesignificanceat10percent,5percent,and1percentlevels,respectively. Source: Authors’calculationsusingMSCIRCAdata. 36

A. DATAAPPENDIX A.1. FurtherDetailsonAppendixExhibitsReferencedinMainText Figure A1 shows aggregate leverage in the CRE and RRE markets. The leverage ratios reflect the average loan-to-value (LTV) ratios for properties that are mortgage financed, as well as the share of properties that have a mortgage. Given that real estate is marked to market in the Financial Accountswhiledebtiskeptatbookvalue,priceappreciationovertimedecreasesleveragerelative toat-originationLTVratios,alsocontributingtolowaggregateleverage. A.2. AlternativeMeasuresofRedevelopmentPotential In Table A1, we run regressions similar to those outlined in equation (7) but using different measures of redevelopment potential. Specifically, we replace the redevelopment probability with an indicatorforwhethertheQ-Scoreisinthebottomquartileandanindicatorforwhethertheproperty isover25yearsofage. Columns(1)through(3)includeestimatesexcludingthebuyerorbuyer-typefixedeffects,layering in the interaction terms related to redevelopment potential one at a time; columns (4) through (6) present the same specifications but include buyer-type fixed effects; and the last three columns againpresentthesamespecificationsbutincludebuyerfixedeffects. The findings are qualitatively similar to those shown in Table 3, in which information on age and qualitywerecombinedintoasinglemeasureofrenovationpotential. Lower-qualitypropertiesare more likely to be cash financed. Properties with low Q-Scores are predicted as having a roughly 4 percentage point higher cash share in specifications without buyer controls (column 1), rising to abouta6percentagepointeffectinspecificationswithbuyertypeorbuyerfixedeffects(columns4 and7). Incontrasttothemainresults,olderpropertiesarepredictedashavinglowercashpurchase sharesaftercontrollingforpropertyquality;however,theeffectgoesawaywhenbuyerfixedeffects 37

areadded,indicatingthattheresultsaredrivenbybuyer-specificomittedvariables. Theresultslookingatdifferencesacrossbuyerswithandwithoutdevelopmentexperiencearemore uniformly consistent with the primary results. Developers are more likely to use cash financing thanotherbuyers,butonlywhenthepropertyhasatleastoneofthecharacteristicstoindicatethat ithasredevelopmentpotential(advancedageorlowQ-Scores). Focusingontheresultsincolumn (9)—thespecificationwherebothpropertycharacteristicsareinteractedwiththedeveloperindicator and buyer fixed effects are included—we find that having a low Q-Score raises the likelihood of cash financing by about 5.8 percentage points for non-developers and 8.5 percentage points for developers. As a bit under half of investment properties are cash financed, these results imply that low Q-Score properties are over 10 percent more likely to be purchased with cash overall, and over 15 percent more likely for buyers with development experience. Advanced age increases the likelihood of using cash financing by about 2 percentage points for developers while having little effect on other buyers. Differences between developers and non-developers tended to be slightly strongerintheotherspecificationswithoutbuyerfixedeffects(columns3and6). Similar results are shown in Figure A6, which present binscatter regression estimates of the relationshipbetweencashfinancingandQ-Scoreorage,bythebuyer’sdevelopmentexperience. 38

FigureA1: DebttoAssetsintheFinancialAccounts: CommercialandResidentialRealEstate )tnecrep( stessA ot tbeD 05 04 03 02 01 0 Residential 1-4 Family CRE - Including Multifamily CRE - Excluding Multifamily 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 5 6 6 7 7 8 8 9 9 0 0 1 1 2 2 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 Note:Thefigureplotstimeseriesofcommercialrealestate(CRE)andresidentialrealestate(RRE)debttoassets.CRE debt is measured as “all sectors; commercial mortgages; asset” on Table L.220 (series FL893065505.Q). RRE debt ismeasuredas“allsectors;one-to-four-familyresidentialmortgages;asset”onTableL.214(seriesFL893065105.Q). We follow Ghent et al. (2019) in their definition of CRE and RRE assets. CRE assets are measured as the sum of “nonfinancialnoncorporatebusiness;nonresidentialrealestateatmarketvalue”and“nonfinancialcorporatebusiness; real estate at market value” on Tables B.103 and B.104, respectively (series FL115035035.Q and FL105035005.Q, respectively). RRE assets are measured as “households and nonprofit organizations; real estate at market value” on TableB.101(seriesFL155035005.Q).WhenweincludeallmultifamilymortgagesintoourCREdebtmeasure(series FL893065405.Q), we also include in the denominator “nonfinancial noncorporate business; residential real estate at marketvalue”(seriesFL115035023.Q). Source: Authors’ calculations using the Federal Reserve Board, Statistical Release Z.1, “Financial Accounts of the UnitedStates.” 39

FigureA2: ComparisonofCashPurchaseSharesbetweenRCAandNCREIF )tnecrep ni( erahS hsaC 08 06 04 02 0 NCREIF RCA Apartment Hotel Industrial Office Retail Note: TheRCAsampleislimitedtosaletransactionsbyinstitutionalbuyersbetween2005and2020. TheNCREIF sampleislimitedtosaletransactionsbetween2005and2020. Source: Authors’calculationsusingtransaction-leveldatafromNCREIFandMSCIRCA. 40

FigureA3: TimeTrendsbyBuyerObjective,BuyerType,andPropertyType tnecreP 001 09 08 07 06 05 04 03 02 01 0 Investment Occupancy Redevelopment Renovation 2005 2008 2011 2014 2017 2020 2023 tnecreP 001 09 08 07 06 05 04 03 02 01 0 Institutional Private Public User/Other 2005 2008 2011 2014 2017 2020 2023 tnecreP 001 09 08 07 06 05 04 03 02 01 0 Apartment Dev Site Hotel Industrial Office Retail 2005 2008 2011 2014 2017 2020 2023 Note: The figure plots the share of CRE purchases over time that are cash financed by buyer objective (top), buyer type(bottomleft),andpropertytype(bottomright). Sharesareweightedbythepropertyvalue. Thesampleislimited tonon-portfoliosaletransactions. Source: Authors’calculationsusingMSCIRCAdata. 41

FigureA4: CashPurchaseShares(weighted) Renovation 0.26 Investment 0.43 Buyer Objective Redevelopment 0.68 Occupancy 0.70 Private 0.38 Institutional 0.42 Buyer Type Public 0.66 Equity Fund 0.67 User/Other 0.75 Apartment 0.30 Hotel 0.43 Office 0.44 Property Type Retail 0.49 Industrial 0.63 Dev Site 0.76 0 .2 .4 .6 .8 1 Cash Purchase Share (weighted) Note: ThefigureplotstheshareofCREpurchasesthatarecashfinanced(i.e.,notfinancedbyamortgage)bybuyer objective(top),buyertype(middle),andpropertytype(bottom). Sharesareweightedbythepropertyvalue. Condo conversionsareexcludedastheyarespecifictomultifamilyproperties. Source: Authors’calculationsusingMSCIRCAdata. 42

FigureA5: CategoryShares(unweighted) Renovation 3.88 Occupancy 4.28 Buyer Objective Redevelopment 11.52 Investment 80.33 Equity Fund 0.03 Public 3.77 Buyer Type User/Other 7.95 Institutional 9.65 Private 78.61 Hotel 5.97 Dev Site 8.48 Office 17.62 Property Type Industrial 20.92 Retail 21.99 Apartment 25.02 0 10 20 30 40 50 60 70 80 90 100 Percent of Observations (unweighted) Note: Thefigureplotstheshareofobservationsacrosscategoriesofbuyerobjective(top), buyertype(middle), and propertytype(bottom). Condoconversionsareexcludedastheyarespecifictomultifamilyproperties. Source: Authors’calculationsusingMSCIRCAdata. 43

FigureA6: CashPurchaseSharesbyDevelopmentExperience erahS hsaC 56 06 55 05 54 04 Developer Non-developer 0 .2 .4 .6 .8 1 Q-Score (a)ByPropertyQuality erahS hsaC 05 84 64 44 24 04 Developer Non-developer 0 20 40 60 80 100 Property Age (b)ByAge Note: ThefiguresareproducedusingtheStatacommand“binsreg”(Cattaneoetal.,2019). Eachbinscatterregression includes year, property-type, and buyer fixed effects. The dots reflect estimated cash purchase shares by decile of Q-Score(left)orage(right),whilethelinesplotsemi-linearregressionestimateswithacubicB-spline. Theestimates fordevelopersareinred,andthosefornon-developersareinblue. Source: Authors’calculationsusingMSCIRCAdata. 44

TableA1: CashpurchasesandRedevelopmentOptions CashIndicator(inpercentagepoints) (1) (2) (3) (4) (5) (6) (7) (8) (9) LowQ-Score 3.84** 2.82** 2.95** 5.39** 4.40** 4.54** 6.29** 5.71** 5.77** (0.46) (0.53) (0.52) (0.43) (0.51) (0.50) (0.57) (0.65) (0.64) Age>25 -3.57** -3.56** -4.09** -2.15** -2.15** -2.71** 0.25 0.26 -0.14 (0.49) (0.48) (0.56) (0.44) (0.44) (0.52) (0.46) (0.46) (0.52) LowQ-Score×Developer 4.97** 4.50** 4.75** 4.27** 2.95** 2.69** (1.09) (1.07) (0.95) (0.95) (1.03) (1.03) Age>25×Developer 2.63* 2.71** 1.98* (1.05) (0.94) (0.89) Developer -0.35 -1.79 -0.03 -1.50 (1.07) (1.34) (0.77) (1.01) Age<2 8.88** 8.84** 8.80** 6.85** 6.82** 6.78** 4.27** 4.25** 4.24** (0.96) (0.96) (0.96) (1.01) (1.01) (1.01) (0.73) (0.73) (0.72) ln(LandAreainAcres) -1.50** -1.51** -1.51** -2.12** -2.13** -2.13** -2.13** -2.14** -2.14** (0.16) (0.16) (0.16) (0.13) (0.13) (0.13) (0.12) (0.12) (0.12) SoldWithin5Years -2.19** -2.20** -2.19** -1.56** -1.58** -1.56** 0.69 0.69 0.70 (0.61) (0.61) (0.61) (0.54) (0.54) (0.54) (0.46) (0.46) (0.46) R2 0.101 0.102 0.102 0.142 0.142 0.143 0.327 0.327 0.327 a Observations 132,077 132,077 132,077 129,753 129,753 129,753 121,762 121,762 121,762 Y¯ 41.97 41.97 41.97 41.55 41.55 41.55 41.9 41.9 41.9 sd(Y) 49.35 49.35 49.35 49.28 49.28 49.28 49.34 49.34 49.34 PropertyTypeFE (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) Year-QuarterFE (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) CBSAFE (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) BuyerTypeFE - - - (cid:88) (cid:88) (cid:88) - - - BuyerFE - - - - - - (cid:88) (cid:88) (cid:88) Note: Thesampleislimitedtopurchasetransactionsin2005orlaterwherethebuyerhasindicatedtheirintentionisinvestment. Y¯ andsd(Y)reportthemeanand standarddeviation,respectively,ofthedependentvariableineachregressionsample. Standarderrors,inparentheses,areclusteredbybuyer. +,∗,and∗∗ indicate significanceat10percent,5percent,and1percentlevels,respectively. Source: Authors’calculationsusingMSCIRCAdata. 45

B. THEORYAPPENDIX Inthissectionoftheappendix,weprovidefurtherdetailsonthesolutiontothemodeldescribedin Section 3. First, we derive the value function shown in Equation (2) and characterize the solution for the optimal renovation time. Second, we present an extension that adds stochastic fluctuations inpropertyincomes. B.1. Derivations Equation(1)hasthesolution: e−δt V(t)= +Aert, (9) r+δ whereAisaconstantdeterminedbytheboundaryconditionandoptimalitycondition: V(t∗)=V(0)−c, V(cid:48)(t∗)=0. Thefirstconditionisthevalue-matchingconditionthatthevalueofthepropertyatthetimeofrenovationisthevalueofanewlyrenovatedpropertynetofconstructioncosts. Thesecondcondition isthesmooth-pastingconditionrequiredfort∗ tobeoptimal. Wecanusethesmooth-pastingconditiontosolveforAasafunctionoft∗. Differentiating(9)with respecttot,evaluatingatt∗,andsettingtheequationto0,wecanobtainthefollowing: δ A(r+δ)= e−(r+δ)t∗ . r 46

SubstitutingAinto(9)givesustheexpressioninequation(2):   V(t)= e−δt  1+ δ e−(r+δ)(t∗(c)−t) . (10) r+δ  r  (cid:124) (cid:123)(cid:122) (cid:125) ≡ρ The optimal renovation threshold, t∗, is defined implicitly by the value-matching condition that V(t∗)=V(0)−c. Evaluating(2)att∗ and0,wecansimplifythisexpressionto 1 1 δ e−δt∗ − − e−(r+δ)t∗ +c = 0. r r+δ r(r+δ) Applyingtheimplicitfunctiontheoremthusimplies ∂t∗ (cid:18) δ (cid:19)−1 = e−δt∗ (1−e−rt∗ ) >0. ∂c r This expression demonstrates that t∗ increases monotonically in the cost of renovation. To summarizehowrenovationcostsaffectpropertyvalues,whenciszero,t∗ =0,andpropertyvaluesare 1. Higher renovation costs then cause renovations to occur later (highert∗) and property values to r decline, reflecting a smaller value of the renovation option (since ∂ρ <0). In the limit,t∗ goes to ∂t∗ ∞ascgoesto∞,andthevalueoftherenovationoptiongoesto0. B.2. ExtensionwithStochasticCashFlows Inthebaselinemodel,theonlychangesinincomecomefromdepreciation. Underthisassumption, income (and hence property values) are a deterministic function of time since renovation. This setup is useful for motivating the primary analysis, as redevelopment option values are a simple functionoftime. Consequently,themodeliscloselyrelatedtotheempiricalworkwhichmeasures redevelopment option values in part by age. However, having a deterministic income flow means that we miss an important component of the option value: the ability to adjust actions following 47

theresolutionofuncertainty. In this section, we present an extension of the model with stochastic income flows. We show that the primary insight from the baseline model holds: redevelopment options values rise as incomes decline towards the redevelopment threshold (which is now defined by an income cutoff rather than time). The extension also allows us to generate an additional prediction: greater income uncertainty increases redevelopment option values and induces some investors to switch to cash financing. Supposethatpropertyincome,denotedX,followsageometricBrownianmotionprocess: dX t =−δdt+σdZ . t X t Denoting the renegotiation threshold X∗, property values in the continuation region X ∈ (X∗,∞) satisfy: 1 rV(X)=X−δV(cid:48)(X)X+ σ2X2V(cid:48)(cid:48)(X), (11) 2 whichhasthesolution: X V(X)= +AX−γ, r+δ (cid:16) (cid:112) (cid:17) whereγ =− δ +.5σ2− (.5σ2+δ)2+2σ2r /σ2 >0.19 The rest of the derivation proceeds as before but noting that V(·) is a function of income rather thantime. X∗ andAsatisfythevalue-matchingandsmoothpastingconditions: V(X∗)=V(1)−c, V(cid:48)(X∗)=0. Using the smooth pasting condition to solve for A(X∗) and substituting back intoV(X) gives the 19−γ isthenegativerootofthequadratic.5σ2Z2−(.5σ2+δ)Z−r=0. Thegeneralsolutiontoequation(11)also hasatermrelatedtothepositiveroot,butwecanomititastheconstantofintegrationis0. 48

valuefunctionattheoptimalX∗:   X  1 (cid:18) X∗(cid:19)γ+1 V(X)= 1+ , (12) r+δ  γ X    (cid:124) (cid:123)(cid:122) (cid:125) ≡ρ where X∗ is defined implicitly by the value matching condition. To characterize X∗, we can simplifyto: (X∗)γ+1−(1+γ)X∗+γ(1−c(r+δ))=0. (13) Wethenapplytheimplicitfunctiontheoremtoshowthat: ∂X∗ γ(r+δ) =− <0 ∂c (1+γ)(1−(X∗)γ) ∂X∗ ln(X∗)(X∗)γ+1−X∗+1−c(r+δ) =− (14) ∂γ (1+γ)((X∗)γ−1) X∗ (cid:18) 1 ln(X∗) (cid:19) = − <0. 1+γ γ 1−(X∗)−γ The third line comes from substituting (13) back into the second line to remove the term c(r+ δ).20 These equations show that owners wait longer to renovate when (1) renovation costs are higher, and (2) when cash flows are more variable. The logic behind (1) is the same as in the baseline model: when costs are higher, a greater increase in cash flows is needed to justify renovation. The effectin(2)reflectsagreaterreturntorenovationbeingneededtooffsetthelossoftheoptionvalue ofdelayinganirreversibleinvestment(DixitandPindyck,1994). We can also use these expressions to characterize the value of the renovation option, ρ. First, it isimmediatelyobviousfrom(12)thatrenovationoptions(i.e.,ρ)aremorevaluableforproperties withlowercashflows. 20Theinequalityinthethirdlineusesthecharacteristicofnaturallogarithmsthatln(x)=lim Xα−1 andthefact α→0 α thattherightexpressionisincreasinginα. 49

Second, we can see that renovation options are more valuable when uncertainty is higher. Differentiatingequation(12)withrespecttoσ showsthat: ∂ρ (cid:18) −1 (cid:18) X∗(cid:19) X∗(cid:19) γ =ργ +ln +(1+γ) σ ∂σ γ X X   (15)  (cid:18) X∗(cid:19) ln(X∗)  = ργ ln + >0, σ  X (X∗)−γ−1  (cid:124)(cid:123)(cid:122)(cid:125)  (−) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (−) (−) where (cid:16) (cid:112) (cid:17) 2 .5σ2+δ − (.5σ2+δ)2+2rσ2 ∂γ γ ≡ = <0. σ ∂σ σ3 NotethatthelastlinecomesfromsubstitutingintheexpressionforX from(14). γ 50