Loan Modifications and the Commercial Real Estate Market

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Loan Modifications and the Commercial Real Estate Market David Glancy, Robert J. Kurtzman, and Lara Loewenstein 2022-050 Please cite this paper as: Glancy, David, Robert J. Kurtzman, and Lara Loewenstein (2022). “Loan Modifications and the Commercial Real Estate Market,” Finance and Economics Discussion Series 2022-050. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2022.050. 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.

Loan Modifications and the Commercial Real Estate Market∗ David Glancy†1, Robert Kurtzman‡1, and Lara Loewenstein§2 1Federal Reserve Board 2Federal Reserve Bank of Cleveland July 26, 2022 Abstract Banks modify more CRE loans than CMBS, contributing to better loan performance when property incomes decline. However, banks have higher delinquencyratesforless-stressedloans,consistentwithmodificationpolicies encouraging strategic default. Motivated by these facts, we develop a tradeoff theory model in which lenders vary in their modification technologies. Modification frictions discourage strategic renegotiation, enabling CMBS to offer higher LTV loans and attract borrowers seeking higher leverage. The modelproducescross-lenderdifferencesinLTVsandspreadsconsistentwith the data. Reducing modification frictions at CMBS decreases welfare by restrictingdebtcapacityfortheborrowersthatvalueitmost. Keywords: commercialrealestate,modifications,LTV JELClassification: G21,G22,G23,R33 ∗Thanks to Andra Ghent, Tim Riddiough, Alexei Tchistyi and the audiences at the 2022 AREUEANationalConference,theFederalReserveBoardFinanceForum,andtheClevelandFed for helpful comments and suggestions. The views expressed in this paper are solely those of the authorsanddonotreflecttheopinionsoftheFederalReserveBoard,theFederalReserveBankof Cleveland,ortheFederalReserveSystem. †FederalReserveBoardofGovernors,DivisionofMonetaryAffairs,20thandConstitutionNW, Washington,D.C.20551;email: david.p.glancy@frb.gov ‡FederalReserveBoardofGovernors,DivisionofResearchandStatistics,20thandConstitution NW,Washington,D.C.20551;email: robert.j.kurtzman@frb.gov §Federal Reserve Bank of Cleveland, 1455 E 6th St, Cleveland, OH 44114; email: lara.loewenstein@clev.frb.org

1. INTRODUCTION Whenborrowersareunderstress,onewaylenderspreventcostlydefaultsandforeclosures is by modifying loan terms. Modifications were particularly important duringtheCOVID-19pandemic,whenwidespreadforbearancehelpedloanperformance remain resilient despite an unprecedented economic shock. Of course, such policies are not without their tradeoffs; easy modification policies can induce the classical moral hazard problem whereby healthy borrowers seek unneeded accommodation from lenders. If borrowers cannot commit to refraining from strategic renegotiations, lenders may require stringent underwriting terms to mitigate this risk. Theseconsiderationsareespeciallyrelevantinthecommercialrealestate(CRE) loan market, where lenders differ notably in their ability to modify loans, foreclosure costs are high, and borrowers are known to act strategically.1 While banks modify CRE loans frequently, institutional factors restrict commercial mortgagebacked securities (CMBS) servicers, contributing to lower modification rates and higherdelinquencyratesforCMBSloans(Figure1). Incontrast,therelativeeaseof modification at banks encourages strategic renegotiation, resulting in tighter leveragelimitsonbankloanstocompensate. Consequently,modificationsentailatradeoff between flexibility and moral hazard (and the stringent terms that result from it). This paper analyzes this trade-off, and assesses the implications for loan performance and underwriting, the matching of borrowers to different lenders, and borrowerwelfarewhenlendersdifferintheirpropensitytomodifyloans. Ourfirstcontributionistouseloan-leveldatatodocumenthowCREloanmodifications differ across lenders. We demonstrate that banks modify CRE loans more often and more preemptively (that is, for less-stressed properties) compared to CMBS. These liberal modifications appear to bolster loan performance, as bank CRE loans are less likely to become delinquent when stressed (measured by either the COVID-19 shock or weak property cash flows). However, banks have higher rates of both delinquency and modification for loans against less-stressed proper- 1SeeBrownetal.(2006)forevidenceofhighforeclosurecosts, andFlynnJr. etal.(2021)for evidence of strategic renegotiation. See Appendix A for a discussion of how institutional factors impedeloanmodificationsforCMBSrelativetobalancesheetlenders. 2

ties, suggesting that their willingness to modify such loans encourages strategic default. Our second contribution is to develop a model of CRE loan underwriting and renegotiation that is consistent with the empirical findings. We use the calibrated model to address several questions about the broader implications of these differences. How do modification frictions affect the origination terms offered by different lenders? How do these differences in terms affect the sorting of borrowers into lenders? Andwhatarethewelfareimplicationsofreducingmodificationfrictions? In the model, lenders are able to modify required loan payments, helping to reduce the risk of inefficient liquidations. However, the prospect of a favorable modification causes some borrowers to renegotiate loans unnecessarily, increasing modification rates for loans against some modestly stressed properties. In turn, lenders with lower modification frictions have lower delinquency rates for stressed properties but higher strategicdefaults for some less-stressed properties, consistent withtheempiricalfindings. In equilibrium, high-modification lenders offer contracts with stricter loan-tovalue (LTV) limits to mitigate their higher renegotiation risk. The key trade-off from a borrower’s perspective is then between the higher debt capacity at lowmodification lenders and the increased downside protection at high-modification lenders. This trade-off induces borrowers with higher demand for leverage to sort intolow-modificationlenders. We calibrate the model to match moments related to underwriting terms and modificationratesobservedinthedata. Thecalibratedmodelproduces(untargeted) cross-lender differences in average LTVs and spreads that are consistent with the data. CMBS loans have higher spreads and LTVs, on average, reflecting the willingness of CMBS to make high-LTV loans. Though banks require higher spreads foranygivencontract—compensationforexpectedmodificationcosts—theymake fewer loans to borrowers that will pay a premium for leverage, as such borrowers are better served by CMBS. This sorting effect causes CMBS loans to have higher LTVsandspreadsthanbankloans. The endogenous sorting of borrowers into lenders in the model is also critical for evaluating welfare. Motivated by a temporary easing of modification restric- 3

tions during the COVID-19 pandemic, we examine the effect of reducing modification frictions at CMBS.2 Under our calibration, though most borrowers overall benefit from lower frictions, this is not the case for most CMBS borrowers. Easing modificationrestrictionsreducestheavailabilityofhigh-LTVCMBSloansandthus lowersaveragewelfarebyrestrictingleverageforthosewhomostbenefitfromit. Our work contributes to the literature examining differences in the loan portfolios of various types of CRE lenders. Glancy et al. (Forthcoming) show that such differences in bank, CMBS, and life insurer portfolios can be explained by supply-side factors affecting their competitiveness for different market segments. Our model effectively endogenizes such segmentation by LTV, showing that modification frictions can explain the cross-lender LTV differences in the data. Also related,GhentandValkanov(2016)showthatCMBSdisproportionatelyholdloans against larger properties than banks. Lenders differ along other margins that we do notconsiderinthispaper. Asexamples,Blacketal.(2017,2020)provideevidence that banks make comparatively riskier loans, and Downs and Xu (2015) show that timetoresolutionofdistressedloansiscomparativelylongerforCMBS.3 Our work also contributes to a large theoretical literature on loan renegotiation and resolution in corporate finance and CRE. Our modeling of modifications follows Hackbarth et al. (2007) in that borrowers make a take-it-or-leave-it offer to reduce flow debt service costs.4 More specific to the CRE market, Riddiough and Wyatt (1994a,b) examine equilibrium workout/default outcomes in games where foreclosure costs incentivize lenders to restructure loans and borrowers to strategically default. Our model differs in that we allow modifications to break down and resultinaforeclosure,enablingustoanalyzetheeffectsofmodificationfrictions. Last, we contribute to the empirical literature on renegotiation vs. default in 2TheIRStookstepstotemporarilyallowmoremodificationsunderREMIClawsintheCOVID- 19crisis. SeethediscussioninAppendixAforfurtherdetails. 3Though we focus on differences in the demand for leverage, our model could be extended to accountforothersuchheterogeneity. Variationintimetoresolutioncouldbemodeledasdifferent foreclosure costs by lender type, and variation in borrower risk could be modeled as different net operatingincomevolatilities. 4WepresentanextensionofthemodelwherelendershavebargainingpowerinAppendixD.We showthatlenderbargainingpowerisasubstituteformodificationfrictionsintermsofdiscouraging strategicdefault. 4

both residential real estate (RRE) and CRE loan markets. The work on CRE has historicallyreliedonlifeinsurerdata(Snyderman,1991;Brownetal.,2006). More recent work analyzes renegotiations for bank and CMBS loans. Flynn Jr. et al. (2021) examine the impact of a 2009 change in real estate mortgage investment conduit (REMIC) laws on CMBS modification rates. Glancy et al. (2021) show that recourse mitigates renegotiation risk for bank loans and expands the range of contracts available to borrowers. Motivated by this latter finding, we allow lenders in the model to differ in their use of recourse and show that accounting for the effectsofrecourseonbankunderwritingresultsinabettermatchtothedata. Our empirical analysis illustrates some key differences between CRE and RRE loan modifications. During the housing bust in the 2000s, RRE modification rates weregenerallylow,withonlymodestdifferencesbetweensecuritizedandportfolio loans (Adelino et al., 2013; Agarwal et al., 2011). We find much higher modification rates for bank CRE loans (17 percent per quarter overall for bank CRE loans duringtheCOVID-19pandemic,comparedtounder10percentfordistressed RRE loans during the housing bust) and much larger differences across lender types. A possible explanation for this difference is greater asymmetric information for RRE loans. Nonpecuniary factors can play a large role in households’ default decisions (Guiso et al., 2013), which can discourage loan modification since lenders cannot identifywhichloansarelikelytocurewithoutsupport(Adelinoetal.,2013). InformationasymmetriesarelikelylesspronouncedforCREloans,thusenablinghigher modification rates and creating a larger role for institutional factors in determining modificationoutcomes. The outline for the rest of the paper is as follows. In Section 2, we present empirical evidence on differences in CRE loan modification rates across lender types. InSection3,wewritedownthemodel. InSection4,wepresentthemodelcalibration,quantitativeresults,andwelfarecounterfactuals. InSection5,weconclude. 5

2. CRELOANMODIFICATIONSINTHEDATA In this section, we use loan-level data from banks and CMBS to better understand differences in their modification and delinquency rates. We show that bank CRE loan modifications are both more preemptive, supporting the less-troubled loans that CMBS rarely modify, and more responsive to stress, expanding notably when strainsemerge. Bankshavelowerdelinquencyratesonmore-distressedloans,suggestingthatmodificationsbolsterloanperformance,buthigherdelinquencyrateson less-distressed loans, consistent with borrowers strategically defaulting to secure a modification. 2.1. DataSources We rely on two data sources: monthly data on CMBS loans from Trepp and quarterly data on CRE loans held by large US banks from Federal Reserve Y-14Q filings.5 Each data source provides information on loan terms, property characteristics,andloanperformanceovertime. We include in the analysis first-lien commercial loans secured by stabilized, non-owner-occupied, nonresidential properties in the United States.6 We exclude construction and land development loans and owner-occupied CRE loans—loan types predominantly provided by banks—to maintain a similar sample of loans for banksandCMBS.7 We exclude loans secured by multifamily properties, as government-sponsored enterprises account for a large share of such lending and terms differ notably from thoseforotherpropertytypes. Wealsoexcludesomeminorpropertytypes(forexample, healthcare) for which there is no consistent categorization across banks and CMBS.Thesefilterslimitoursampletoloansbackedbyindustrial,lodging,office, 5TheY-14reportingpanelconsistsofbankswithconsolidatedassetsof$50billion($100billion startingin2019). Banksreportloanswithacommittedbalanceof$1millionormore. Thedataare atthefacilitylevel,but,asmostfacilitieshaveonlyoneloan,wetreatthedataasbeingattheloan level. 6Additionally,forCMBSloans,welimitoursampletoconduit,singleasset-singleborrower,or largeloandeals. 7Wedropanyloanforwhichthereportedpropertyvalueisanestimateforthepropertyonceit iscompletedorstabilized(asopposedtothevaluebeingreported“asis”). 6

and retail properties. Finally, we exclude loans that are cross-collateralized or are missing information on the location of the collateral. Table 1 provides information onoriginationcharacteristicsforthissampleofloansbypropertyandlendertype. Theidentificationofloanmodificationsdiffersforthetwotypesoflenders. For CMBS, modification dates and some details on the type of modification are either directly reported by the servicers or derived by our data vendor (Trepp). This information includes whether the modification involved a maturity date extension, a principal reduction, a rate reduction, the capitalization of interest or principal payments, forbearance, or a combination of various modification types. For banks, we impute modifications by identifying changes in loan terms over time, similar to the methodology of Adelino et al. (2013). Specifically, a loan is considered modified ifitswitchedfrombeingamortizingtointerestonly,ifthecommittedbalancerises (indicatinginterestpaymentsareaddedtotheloanbalanceaspartofaforbearance plan),ifthecommittedbalancefallsintandemwithapositivecumulativecharge-off (indicatingawrite-off),ifthematuritydateisextended(outsideofapre-negotiated renewal),oriftheloanenterstroubleddebtrestructuring.8 Foralllendertypes,wesubdividemodificationsintotwobroadtypes: thosethat resultinareductioninpaymentsandthosethatdonot. Thelattercategoryislargely made up of loan extensions.9 This category can also include other changes, such as adding or removing recourse or cross-collateralization from a loan, though in our data these modifications are rare. Modifications that result in payment changes include interest rate reductions, changes in the amortization schedule (including a switch to interest only), forbearance, and more substantial loan restructurings, suchasanA/BsplitforaCMBSloan.10 Whileweprovidedescriptiveinformation for overall modification rates, we focus most of our attention on payment modifications. Nonpayment modifications—most notably, extensions—might occur for reasons besides preventing default. For example, banks might be willing to extend 8Additionally,weconsiderchangesinoriginationdates,whichoccurwhenthereisasubstantial changeinaloan’sterms. 9Loanextensionsallowaborrowertoavoidneedingtorefinancetomakeaballoonpaymentat maturity. 10FigureE.2intheappendixprovidesdetailsontheshareofoutstandingloanbalancesthathave receivedmodificationsbylendertype. 7

aloanattheendofitstermbecauseithasgoodriskcharacteristics. The two performance measures of interest are whether a loan is modified or 90 days delinquent in a quarter. Delinquency and modification rates are not always directlycomparableacrosslenders: asinglebankmodificationcanappearmultiple times (for example, if a forbearance period spans quarter-end), and delinquency ratesareaffectedbythedurationwithwhichdelinquentloansarereported. Forthis reason, our primary analysis predicts whether loans that had not been previously modified or 90 days delinquent become so in a given quarter. This measure of first modificationordelinquencyisnotsensitivetoreportingdifferencesandthusbetter reflectstherateatwhichsucheventsoccur. Weanalyzehowloanperformanceacrosslendersdiffersbythedegreeofstress the loan is experiencing. In the time-series analysis, this amounts to studying changes in modifications and delinquency during the pandemic (covering 2020:Q1 to 2021:Q2). In our cross-sectional analysis we look at loan performance across two different dynamic measures of loan risk: LTV and the debt-service coverage ratio (DSCR). LTV, defined as the ratio of the loan balance to the most recent appraised property value, reflects the ability of the borrower to pay back the loan by sellingorrefinancingtheproperty. DSCR,definedastheratioofthecollateral’snet operating income (NOI) to annual debt obligations, measures how well the propertycansupportthedebtservicecostsassociatedwiththeloan. WecalculateDSCR ourselves using estimated annual debt service obligations and the reported current NOI. To account for the fact that NOI is necessarily a backward-looking measure, wecalculateDSCRusingtheyear-aheadNOI. 2.2. ModificationandDelinquencyRatesOverTime From Figure 1, we see that CRE loans held in banks’ portfolios are modified much more frequently than loans in CMBS pools. In the quarters leading up to the pandemic, banks modified loans at a rate of about 1.5 percent per quarter, while modificationsofCMBSloanswerealmostnonexistent. Bycontrast,ratesatwhichloans become90daysdelinquentweremodestlyhigherforCMBS. During the pandemic, these differences widened in absolute terms. Transitions 8

intodelinquencyspikedforCMBS,reachingapeakofaround5percentperquarter in 2020:Q3, while remaining under 1 percent for bank loans.11 Bank loans instead saw a spike in modification rates. Bank loans received modifications at a rate of nearly 10 percent per quarter in 2020:Q1, rising to a rate of 17 percent by the end of 2020. Meanwhile, the CMBS modification rate remained under 5 percent for all quarters. In Table 2, we disaggregate the information in Figure 1 by property type and modification type. Banks are much more likely to modify loans across property types, with modification rates in 2018 and 2019 that range from 1.3 to 3.2 percent across property types, compared to under 0.1 percent for CMBS. Banks also experienced a larger increase in their modification rates during the pandemic, driven predominantly by payment modifications (mainly forbearances). The modification rate for bank lodging loans rose to 16 percent per quarter during the first year and a half of the pandemic. For other property types, modification rates still rose to near10percentperquarter. Meanwhile,forCMBS,modificationratesonlyroseto around4percentforlodgingloanswhileremainingunder1percentforotherproperty types. In the last column of Table 2 we show the share of loans that received either a payment modification or became 90 days delinquent, thus measuring the share of loans not making promised payments either due to delinquency or modification.12 Modifications for bank loans are high enough that these overall distress rates are much higher than those for loans in CMBS pools, both before and during thepandemic,despitethehigherdelinquencyratesforCMBS. Togetamoreaccurateestimateofthedifferenceintheprobabilityofreceiving a modification for bank portfolio loans versus those in CMBS, we pool data across lenders and estimate linear probability models predicting modification and delinquency with lender type, while controlling for an array of risk characteristics. Our 11We define a loan as delinquent when it is 90+ days past due. Therefore, the loans entering delinquencyinthethirdquartergenerallystartedtomisspaymentsinthesecondquarter. 12Sinceloanscanbothbemodifiedandbecome90daysdelinquentwithinaquarter,thisratemay notbetheexactsumoftherateofpaymentmodificationsanddelinquencies. 9

regressionstakethefollowingform: Mod ×100= β CMBS +β CMBS ×COVID i,t 1 i 2 i t +α X +α X ×COVID +γ +ν +δ +ζ +ε , (1) 1 i,t 2 i,t t t i i i i,t where CMBS and COVID are indicators of whether loan i is funded by CMBS i t and whether quarter t is 2020:Q1 or later, respectively. X contains the following i,t loan-level controls: log origination amount, term in years, an indicator for whether the loan is interest only, current LTV and DSCR, and LTV and DSCR at origination. Wealsoincludetimefixedeffects(γ ),originationyearfixedeffects(ν),state t i fixed effects (δ), and property-type fixed effects (ζ). The dependent variable is i i multiplied by 100, so that the coefficients provide predicted effects in percentage points. Our left-hand-side variables are indicators for whether loan i was modified or became 90 days delinquent in quartert. To account for differences in the reporting of modifications or delinquency, in each regression we remove observations after thefirstinstanceoftheoutcomeofinterest. Thatis,delinquencyregressionspredict whether previously performing loans first become seriously delinquent in time t, and modification regressions similarly predict the occurrence of a modification for previously unmodified loans.13 As a result, our sample size varies slightly in each column. We present results from these regressions in columns (1)-(3) of Table 3. The results confirm the general patterns shown in Figure 1. Column (1) shows that aftercontrollingforloan-levelcharacteristics,banksandCMBShavesimilardelinquency rates pre-COVID, with CMBS loans having delinquency rates that are 0.06 percentage points lower. However, CMBS see a much larger spike during the pandemic,withthedelinquencyraterising0.29percentagepointsmorethanforbanks. Column(2)showsthatCMBShavemodificationratesthatare1.5percentagepoints below banks in normal times, with the difference rising by an additional 4.4 percentage points during the pandemic. These results are similar for payment modifi- 13AllowingformultiplemodificationsresultsinlargerdifferencesbetweenbankandCMBSmodificationrates. 10

cations,shownincolumn(3). 2.3. ModificationandDelinquencyRatesbyPropertyPerformance The time-series evidence suggests that banks modify loans more than CMBS, increase modifications more in times of stress, and provide more preemptive modifications—modifying loans even for less troubled property types. Here, we examine the extent to which such patterns hold in the cross-section by looking at the propensity of lenders to modify loans when the property securing them experiencesstress. Figure 2 displays delinquency, modification, and overall distress rates (defined as either a delinquency or a modification) by current DSCR or LTV. Each panel shows a binned scatterplot, where each bin reflects the average within a quantile of observations based on DSCR or LTV. Reported values are residualized on quarter, propertytype,originationyear,andstate×CBSAfixedeffects. Thetwoleft-handpanelsofFigure2showdelinquencyratesbyDSCRandLTV for banks and CMBS. Each panel tells a similar story: when property performance metricslookfavorable(DSCRsareabove1.5orLTVsarebelow60),bankloansare more likely to become delinquent. However, when conditions deteriorate, CMBS are more likely to become delinquent. For both lenders, high LTVs or low DSCRs increasethelikelihoodofdelinquency,buttheeffectsaremuchstrongerforCMBS. The middle two panels show modification rates for the two lender types. These illustratethreecharacteristicsofbanks’modificationbehaviorthatparallelthetimeseriesresults. First,banksprovidemodificationstoloansacrosstheentirespectrum of DSCR and LTV. Second, banks are more preemptive in their modifications. For example, the modification rate for bank loans starts to increase sharply as LTVs rise above 75 percent, whereas modifications are fairly flat for CMBS until LTVs reach around 100 percent. Third, modification rates for bank loans that are in clear distress(thosewithlowDSCRsorhighLTVs)aremuchhigherthanratesforCMBS loans in the same range. As such loans are likely to benefit from a modification, thelackofmodificationsforCMBSislikelyindicativeofconstraintsonthepartof CMBSservicersinmodifyingsuchloans. 11

Last, the two right panels compare loan distress rates across the two lender types. We define a distressed loan as one that becomes delinquent or receives a payment modification in a given quarter. Either way, this reflects the rate at which borrowers cease to maintain promised loan payments due to a delinquency or a lender-providedmodification. For loans that are clearly vulnerable (DSCRs below 1 and LTVs above 100), distress rates on CMBS and bank loans are broadly similar. The key difference between banks and CMBS for such loans is the composition of why borrowers are not maintaining payments: distressed CMBS loans are mostly delinquent, while distressed bank loans are mostly modified. This result suggests that bank loans in this range are only avoiding default because of active modifications provided by banks. In contrast, the higher distress rate for bank loans that are not observably troubled is suggestive of strategic behavior on the part of borrowers to obtain a modificationwhenitisnotnecessarilyneeded. These findings can also be demonstrated through regressions similar to those from equation (1) but with the CMBS dummy interacted with the loan’s LTV and DSCR rather than the COVID dummy. Columns (4)-(6) of Table 3 present the results of this analysis.14 The main findings from Figure 2 broadly hold. Low DSCRsincreasethelikelihoodofmodificationordelinquency,withbanksseeinga largerincreaseinmodificationsandCMBSseeingalargerincreaseindelinquency. Higher LTVs raise the likelihood of delinquency but raise the likelihood of modificationonlyforbanks.15 14Tofocusoncross-sectionaldifferences,werestrictthesampletothepre-COVIDperiod. LTV andDSCRaredemeanedsothatthecoefficientonCMBS reflectsthepredictedeffectforaloanat i theaverageLTVandDSCR. 15ThereislittledifferenceintheeffectsofhigherLTVsondelinquencyacrosslenders. Thismay bebecausepropertyvaluesareonlyupdatedwhenthereisanewappraisal,hinderingtheabilityof theLTVmeasuretoaccuratelymeasurestressesinpropertyvaluations. 12

2.4. Discussion Tosummarize,relativetoCMBS,wehaveshownthat: 1. banksmodifymoreloansoverall; 2. banksmodifyloanspreemptively; 3. bankshavehighermodificationanddelinquencyratesforless-stressedloans, consistentwithmodificationsencouragingstrategicdefault; 4. bank borrowers cease making promised loan payments at similar rates for more-stressed loans, but these occurrences mostly consist of modifications forbanksanddelinquenciesforCMBS. WhywouldCRElendersdiffersosubstantiallyinthepropensitytomodifytheir loans? Whileitispossiblethattherearefundamentaldifferencesbetweenbankand CMBS borrowers that affect the returns to modification, the fact that modification rates differ so substantially, even for clearly distressed borrowers, indicates that lendersdifferintheirabilitytomodifyloans. A review of institutional factors affecting the lenders supports this hypothesis. CMBS are restricted in their ability to modify loans by both their pooling and servicing agreements (which define the rights and responsibilities of the mortgage servicer) and by IRS policies (which define when a modified mortgage would constitute a new loan, thereby threatening the securitization vehicle’s REMIC status and subjecting it to federal taxation).16 In contrast, the other major CRE lenders are typically the sole debt holder, face minimal restrictions on loan modifications, andwereencouragedbyregulatorstomodifyloansduringthepandemic. InMarch 2020, banks’ regulators issued a joint statement actively encouraging banks to take “proactive actions that can manage or mitigate adverse impacts [of COVID-19] on borrowers.” Life insurers, which we emphasize less due to data limitations, were similarly encouraged “to work with borrowers who are unable, or may becomeunable,tomeettheircontractualpaymentobligationsbecauseoftheeffectsof 16We provide more details on the regulatory environment affecting modifications for banks and CMBS in Appendix A, including a more thorough discussion of how tax considerations restrict CMBSmodificationoptions. 13

COVID-19.”17 Inshort,institutionaldifferencesbetweenCMBSandbalance-sheet lendersplausiblyresultintheselendersdifferinginloanmodificationtechnologies. Intheremainderofthispaper,weexplorehowthesedifferencesinmodification abilityaffectthebroaderCREmarket. Whiletheabilitytomodifyloansmaybenefit borrowers in times of stress, the specter of strategic renegotiation may restrict the range of contracts that banks are willing to offer. That is, if bank borrowers cannot commit to not strategically negotiating lower loan payments, banks may require largerdownpaymentstomitigatethismodificationrisk. Indeed,Table1showsthat CMBS loans have higher average LTVs than bank loans across property types, and Appendix Table E.1 demonstrates that these differences hold controlling for other observablecharacteristics.18 3. MODEL Intheprevioussection,wepresentedempiricalevidencethatthereisheterogeneity in the propensity to modify troubled loans across lender types. Motivated by this finding, we now present a trade-off theory model adapted to aspects of the CRE market in which lenders differ in their ability to modify loans that can match the factspresentedinSection2.4. We start by deriving expressions for the values of equity and debt in this environment. We then solve for the equilibrium modification strategies, the set of contracts (LTVs and spreads) offered by a competitive loan market, and the loan contracts optimally chosen by borrowers. We then derive how borrowers optimally 17We do not emphasize life insurers in Section 2 because the limited detail on loan terms and low reporting frequency for life insurer data prevent us from accurately identifying modifications. The statement from the National Association of Insurance Commissioners is available athttps://content.naic.org/sites/default/files/inline-files/INT%2020-03%20%20-%20TDR%20for% 20COVID-19%3B%20Consolidated%20Appropriations%20Act%20Update.pdf. 18The regressions predict the effect of the loan being in a CMBS pool on LTV, controlling for other observable characteristics. Two controls stand out as affecting the results: spreads and recourse. First, higher CMBS LTVs partially reflect higher spreads. This result is consistent with CMBS borrowers having a higher demand for leverage, a pattern that endogenously comes out of themodelstudiedinSection3. Second, predictedLTVdifferencesacrosslendersarelargerwhen we account for recourse, which enables some bank borrowers to have higher LTVs (Glancy et al., 2021). Toaccountforthismechanism,weallowlendersinthemodeltovaryinrecourseuseaswell asmodificationability. 14

sort into lenders, which differ in modification ability. Finally, we aggregate across heterogeneousborrowerstosolveforlenders’equilibriumloanportfolios,accountingforbothdifferencesinloanoffersacrosslendersandtheendogenoussortingof borrowersintolenders. 3.1. EnvironmentandValueFunctions We start by considering the problem of a particular property investor negotiating a loan contract from a particular lender. At time t =0, the investor buys a property partially using perpetual, defaultable debt with a flow coupon payment ofC (to be endogenized later). Let the after-tax NOI from this property at time t (denoted X ) t followageometric-Brownianmotionprocess: dX t =µdt+σdZ . t X t Lenders and property investors are risk neutral and discount cash flows at the risk-freerater. Therefore,thepresentvalueofpromisedcouponpaymentsis C and r thepresentvalueoffutureNOIis Xt . InvestorsearnaflowreturnofX −(1−τ)C, r−µ t where τ is the effective tax rate that determines the tax advantage of debt and thus thedemandforleverage.19 In the event of default at time t, the lender can foreclose on the property and recover the unleveraged property value, less a proportional foreclosure cost αF ∈ [0,1). In addition, motivated by the finding that loans with recourse are less likely to be modified (Glancy et al., 2021), we allow for the availability of recourse to affect loan recoveries. Specifically, lenders can claim a fraction θ ∈ [0,1−τ) of the present value of promised debt payments from a deficiency judgment, paying a proportionalcostofαD ∈[0,1].20 19Theeffectivetaxrate, τ, isastandardparameterintrade-offtheorymodels. τ determinesthe sizeofthetaxshieldand,hence,thedemandforleverage. Itcanstandinmoregenerallyforother factors that affect the demand for leverage, such as liquidity needs or wedges in required returns betweenborrowersandlenders. 20θ =0 for non-recourse loans, such as most CMBS or life insurer loans. For recourse loans (themajorityofbankloans),θ reflectshowmuchborrowersactuallyexpecttopayinadeficiency judgment. Evenafullrecourseloanwouldhavealowθ iftheborrowerhasfewoutsideassets. θ is boundedaboveby1−τ toensurethatthereexistsavalueofX >0suchthatborrowerschooseto t 15

Therecoveryintheeventofforeclosure,R(X),istherefore X C R(X)=(1−α F) +(1−α D)θ . r−µ r The deadweight costs of foreclosure leave room for mutually beneficial loan modifications with the purpose of forestalling loan defaults. Following Hackbarth et al. (2007), borrowers can make a take-it-or-leave-it offer to the lender to lower their debt service at time t to some amount S(X). In Appendix D, we extend the model to allow lenders to have some bargaining power. We show that borrowers musthavesignificantbargainingpowerforthemodeltomatchtheobserveddifferencesinLTVsacrosslendersinthedata.21 We make one key departure from Hackbarth et al. (2007) in how renegotiationswork: whiletheloanisoperatingundermodifiedtermsandpayingS(X)<C, negotiations break down at an exogenous rate λ, resulting in foreclosure.22 Therefore, by varying λ, one can study how differences in modification frictions affect outcomesinthemarket. In equilibrium, the borrower optimally chooses when to renegotiate their loan and what debt service amount to offer. Since borrowers can make a take-it-orleave-it offer, when they seek a modification, they choose a strategic debt service offer S(X) so as to make the lender indifferent between foreclosing and accepting themodification. InAppendixB,wederivethisequilibriumofferas S(X)=(1−α F)X+(1−α D)θC. Regarding when renegotiation occurs, after NOI falls below an endogenous threshold X , lenders become willing to accept a sufficiently low debt service payn renegotiatetheirloan. 21Intuitively, if lenders have more bargaining power, strategic renegotiation becomes less of a concernsinceborrowersgainlessfromtheprocess. Weshowthatwhenlendershavemorebargainingpower,modificationfrictionsareassociatedwithlowerLTVloans,afindingthatisinconsistent with the observed LTV differences between banks and CMBS. Furthermore, borrowers uniformly choose low-friction lenders when lenders have bargaining power, as modification frictions are no longerneededtoenablehigh-LTVlending. 22OurmodelalsodiffersfromHackbarthetal.(2007)inthatallloansarefirstlien;thatis,weare notstudyingdifferencesindebtprioritystructure. 16

ment for borrowers to choose to renegotiate their loan. As a result, there are two regions in the model: a low region (denoted L) where X ≤X and lenders receive n loanpaymentsS(X)<C,andahighregion(denotedH)whereX >X andlenders n receive loan paymentsC. In Appendix B, we derive the following equations definingthevaluesofdebtandequity,D(X)andE(X)respectively,intheseregions: (cid:20) (cid:21) C X C X D (X;C,X )= −( )−γ (1−(1−α D)θ) −(1−α F) n H n r X r r−µ n X C D (X;C,X )=(1−α F) +(1−α D)θ L n r−µ r (cid:20) (cid:21) (2) X (1−τ)C X X C E (X;C,X )= − −( )−γ η n −η H n x c r−µ r X r−µ r n 1−(1−αF)(1−τ) λθC (1−τ)(1−αD)θC E (X;C,X )= X− − , L n r+λ −µ r(r+λ) r+λ where λ(1−τ−θ)+r(1−τ)(1−(1−αD)θ) η ≡ c r+λ λ +(1−αF)(1−τ)(r−µ) η ≡ x r+λ −µ (cid:18) (cid:113) (cid:19) γ = µ−.5σ2+ (.5σ2−µ)2+2σ2r /σ2 are positive constants determined by parameter values. η and η reflect the sensic x tivitiesofE(X)topropertyvaluesandcouponpaymentsattherenegotiationthreshold, respectively, and γ reflects the inverse of the risk of downward movements in NOI. Wecanthendeterminetherenegotiationthreshold,X ,fromthesmooth-pasting n conditionthat ∂E H (Xn) = ∂E L (Xn) : ∂X ∂X X γ η C n c = . (3) r−µ 1+γ η r x (cid:124) (cid:123)(cid:122) (cid:125) ≡ρ(λ) Equation3impliesthatborrowerschoosetorenegotiatealoanwhenthevalueof 17

theunleveredpropertyfallsbelowafractionρ(λ)ofthepresentvalueofpromised debt service payments. In Appendix C.1, we analytically characterize ρ. We show thatthemodificationboundaryisdecreasinginλ,meaningthatborrowersaremore willing to continue making promised debt payments when modifications are less certain. ∂ρ That is negative is consistent with the patterns for modification and delin- ∂λ quency rates shown in Figure 2. ρ(λ) determines Xn—the threshold DSCR below C which borrowers modify loans. Since ρ decreases with λ, there is an intermediaterangeofDSCRssuchthatborrowersfrombanks(lowλ lenders)wouldmodify, andsometimesgodelinquent,whileborrowersfromCMBSwouldcontinuemaking promised payments. Figure 3 demonstrates this fact. The figure plots debt service payments (S(X) or C) as a function of X for two loans that are identical except t for λ. The cross-hatched region shows the range of X such that only bank loans t undergo renegotiation and possible default (consistent with banks’ higher rates of delinquencyandmodificationforless-stressedproperties). ForX belowthisrange, t all borrowers renegotiate, but more negotiations fail for CMBS (consistent with CMBS’ higher delinquency rates and lower modification rates for stressed properties). 3.2. LenderPricingofLTV Having solved for borrowers’ optimal renegotiation strategy (the modification threshold and strategic debt service amount), we can determine the contracts offered by a competitive loan market. Substituting (3) into (2), we can solve for the values of debt and equity for a given NOI and coupon payment. Since lenders will not originate a loan that borrowers would immediately renegotiate, available loan termsaredeterminedbythevaluationofloansintheH region,whichisgivenby   (cid:32) X (cid:33)−γ C  D (X;C)= 1− r−µ χ, (4) H r  ρC   r  (cid:124) (cid:123)(cid:122) (cid:125) ≡s 18

where ρ is as in (3), s is the loan rate spread, and χ reflects the lender’s loss from modifyingtheloan: C −D(X ) χ ≡ r n C (5) r =1−(1−α D)θ −(1−α F)ρ. Giventheexpressionforχ in(5),weseethatshastheintuitiveinterpretationofbeingtheproductofthelikelihoodofmodificationandthelossgivenmodification.23 Sinceloansinitiallypriceatpar,theinitialloanbalancewillbeD (X ;C),mak- H 0 ingthecouponpaymentC=rmD (X ;C),whererm isthemortgagerate. Evaluat- H 0 ing at X and substituting in forC, equation (4) can be rearranged to express LTV 0 asafunctionofloanratespreads: 1 sγ(1−s) LTV(s)= , (6) 1 χγρ where LTV ≡ D H (X 0 ;C) is the ratio of loan size to the unlevered property value. X 0 /(r−µ) Also,notethatwiththissubstitution,s= rm−r.24 rm The above expression is effectively the credit supply curve: it determines the scheduleofloantermsthatlendersarewillingtoofferpropertyinvestors. Itisclear thatlendersarewillingtoofferhigherLTVsforagivenspreadwhenborrowersare more willing to maintain promised debt payments instead of seeking a modification (ρ is low) or when their losses from a modification are lower (χ is low). In Appendix C.2, we present the comparative statics of this supply curve with respect to λ. We show that lenders are willing to offer higher LTVs for loans with higher modificationfrictionsbecauseofhowmodificationfrictionsaffectthemodification boundary. In short, while the ability to modify loans provides borrowers some insurance 23Moreformally,thefirsttermgivesthefairpriceofasecuritythatpays1atthetimeofmodification. 24Thisconceptofspreadsisconvenientforpresentingtheexpressionsthatfollow. Whenwetake themodeltothedata,weusethemoreconventionalspreadsmeasurerm−r= s r. 1−s 19

againstdownwardmovementsinNOI,thisgaincomesatacost. Lendersanticipate losses from strategic modification requests and provide less favorable loan terms at origination. Lenders are unwilling to offer high-LTV, easily modified loans, as borrowerswouldimmediatelybeabletonegotiatemorefavorableterms. Borrowers thus need to provide some protection from strategic renegotiation, either through a highdownpaymentorfrictionalmodifications.25 To understand how borrowers evaluate these trade-offs and ultimately choose whichtypeoflendertoborrowfrom,weneedtosolveforwhichavailablecontracts borrowers choose and evaluate welfare at the optimal contract. We do this in the nextsubsection. 3.3. EquilibriumPricing,LTV,andWelfare Firms choose the debt contract that maximizes firm value v(X;C) = E (X;C)+ H D (X;C). Substituting in equations (2) and (3) and simplifying, v(x;C) can be H writtenas (cid:32) X (cid:33)−γ X τC C r−µ v(X;C)= + − Λ , (7) r−µ r ρC r r where λ λ Λ≡τχ+ θ(α D+τ(1−α D))+ ρ(α F+τ(1−α F)) r+λ r+λ −µ is the deadweight cost from entering the modification region (as a share of C). τχ r is the lost tax shield due to the lower coupon rate at modification, and the rest of the expression reflects the expected loss due to modifications breaking down (deadweightrecoverycostsandthelossoftheremainingtaxshield).26 25Appendix C.2 also shows that recourse provides protection against strategic renegotiation, so borrowerscanalsopledgeotherassetsasanalternativetomakingahighdownpayment. 26Itisusefultonotethatwhenµ =0,Λcanbewrittenas     Λ| µ=0 = τ C− C S(X n ) + r+ λ λ    θ (cid:124) αD (cid:123) + (cid:122) ραF (cid:125) + τ S( C X n )    . (cid:124) (cid:123)(cid:122) (cid:125) (cid:124)(cid:123)(cid:122)(cid:125)  Foreclosurecosts (cid:124) (cid:123)(cid:122) (cid:125)  Lostdebtshield Pricingofbreakdownrisk Lostdebtshield frommod frommodbreakdown 20

Taking the first-order condition of (7) with respect toC, we can show that borrowerschoosethecontractwithaspread: τχ s∗ = , (8) (1+γ)Λ whereΛisdefinedin(7). Having now found the optimal spread chosen by the borrower, we can close themodelandpresentclosed-formexpressionsfortheLTVchosenbytheborrower andforborrowerwelfare. TofindtheequilibriumLTV,evaluatethesupplyfunction fromequation(6)atthechosenspreadfromequation(8)andobtain (cid:18) (cid:19)1 (cid:18) (cid:19) 1 τ γ Λ−τχ LTV = ρ −1 γ+ . (9) 1+γ (1+γ)Λ Λ Recovering C∗ from the expression for s in (4) using (8) and then substituting C∗ into (7), we obtain the value of the property investment for the optimal loan contract:   (cid:18) (cid:19)1 v(X 0 )= X 0  1+τ γ τ γ ρ −1 . (10) r−µ  1+γ (1+γ)Λ  (cid:124) (cid:123)(cid:122) (cid:125) ≡ν 3.4. ChoiceofLenders The results thus far determine how a particular borrower i, defined by a set of risk characteristicsandleveragepreferences,choosesloantermsfromaparticularlender j, defined by λ . In this subsection, we model the selection of borrowers into difj ferent lenders, effectively endogenizing λ as the optimal choice from a menu of contractsofferedbydifferenttypesoflenders. First, consider a borrower i with a particular set of characteristics b ≡ (τ, σ, i i i µ, αF). This borrower needs to choose a particular lender j ∈ J to borrow from, i i Thatis,whenmodificationsdonotbreakdown,thedeadweightlosscomesfromthelosttaxshield duetolowerdebtpayments. Deadweightlossesriseasλ risesbecause,inadditiontothelowertax shield, thereisariskofmodificationsbreakingdown, resultinginforeclosurecostsbeingrealized andtheremainingdebtshieldalsobeingremoved. 21

with each j defined by a particular (λ ,θ ).27 The borrower does this so as to maxj j imize the value of a property investment with a mortgage from j. From equation (cid:16) (cid:17)1 (10), this amounts to maximizing ν ≡ τ γi τ γi ρ−1, where i and i, j i,j i1+γi (1+γi )Λi,j i,j subscripts refer to functions evaluated for borrower and borrower-lender characteristics,respectively. In reality, one would not expect all sorting in the CRE market to be driven by differences in modification frictions or the use of recourse. CRE lenders may also differ in risk tolerance, desired investment horizons, or various other dimensions (Glancy et al., Forthcoming). To reflect these unmodeled factors affecting sorting, we add unobserved heterogeneity in preferences for CRE lenders so that borrowers match to lenders probabilistically based on their value from borrowing from a particularlender(insteadofmatchingperfectlytothelenderwiththehighestν ). i,j In particular, we assume that i chooses j if ν z ≥ ν z ∀k ∈ J, where z i,j i,j i,k i,k i,k is an i.i.d., Fre´chet distributed random variable reflecting unobserved preferences with CDF P(Z <z)=exp(−z−ε). With this setup, the probability that borrower i chooseslender j is28 νε i,j P (b)= . (11) j i ∑ νε i,k k∈J Inshort,ν determinestheaveragebenefitthatigetsfromobtainingamortgage i,j from j. This amount reflects how well a particular lender’s available terms match a borrower’s preferences. Borrowers seeking high-LTV loans (those with a high τ) may like the higher debt capacity that can be found from lenders with a higher λ, while other borrowers may prefer the downside protection offered by lenders with alowerλ. 27GivenbanksarethemainrecourselenderintheCREmarket,wemakeθ alendercharacteristic. 28Note thatas ε →∞, theprobability ofchoosing the lenderwith the highest ν →1. That is, i,j in the limit, this setup encapsulates the situation where lenders maximize welfare as measured in equation(10). 22

3.5. Aggregation Having now determined how borrowers sort into particular lenders, we can solve for the portfolio characteristics of different lenders. Let f(b) denote the probability density function of borrower characteristics.29 Given the sorting implied by equation (11), the distribution of borrower characteristics for the loans made by a particularlender j willbe f (b)= P j (b)f(b) . j (cid:82)P j (b)f(b)db We obtain the average characteristics for the loans of a given lender by integrating over this distribution. For example, the average unlevered LTV for lender (cid:82) j would be LTV (b)f (b)db, where LTV (b) comes from equation (9) evaluated j j j ataparticularsetofborrowerandlendercharacteristics. Thisexpressionshowsthatlenders’portfolioswilldifferfortworeasons. First, lenders offer different terms, reflecting differences in λ and the effect λ has on loan outcomes. That is, lenders differ in the loans that would be made to an identical borrower. Second, lenders differ in which borrowers they serve. Borrowers disproportionately sort into the lenders that better match their preferences, creating differences in, for example, borrowers’ willingness to accept higher spreads to achievehigherleverage. 4. QUANTITATIVERESULTS Wenow examinethequantitativeimplications ofthemodel. Lendersdifferin their ability to modify loans, resulting in a varied willingness to make high-LTV loans. Borrowersareheterogeneousintheirdemandfordebt,causinghigherdemandborrowers to sort into lenders offering higher debt capacity. The first section presents results from a two-lender calibration, where lenders differ only in their ability to modifyloans. Thesecondsectionaddsarecourselendertothecalibration,improving the model’s ability to hit untargeted moments. The final subsection examines thewelfareimplicationsofreducingmodificationfrictionsinCMBS. 29InSection4,wewillquantitativelyexploreheterogeneityinτ toanalyzetheeffectsofsorting basedonleveragedemand. However,hereweconsiderthemoregeneralcasewithheterogeneityin otherborrowercharacteristics. 23

4.1. Two-LenderCalibrationoftheModel Westartbycalibratingparametersforatwo-lendercalibrationofthemodel,where borrowerschoosebetweenbanksandCMBS,whichdifferonlyintherateatwhich modifications break down. We then investigate how modification frictions affect LTVs and spreads for loans from these lenders. This calibration is less realistic quantitativelythanthecalibrationconsideredinthenextsubsection,butitprovides ausefulfirststepinunderstandingthemechanicsofthemodel. 4.1.1. Calibration To provide a broad overview of the calibration, we directly set µ, λ , and some j parameters of f(b) based on values from the data or the related literature. We then jointlycalibratetheremainingparameterstomatchrelevantmomentsinthedata. Regarding lender parameters, we set λ for each lender to equate λj to the j r delinquency-to-modification rates reported in Table 4 (0.64 for banks, 7.76 for CMBS). In this version of the calibration, both lenders are considered to be nonrecourse (θ =0), so any difference between the lenders reflects the effects of modij ficationfrictions. Regarding the borrower parameters, we will start by discussing parameters related to the distribution of borrower characteristics, as other moments involve integrating over this distribution. We allow τ to be heterogeneous so as to study how borrowers sort into lenders based on their demand for debt. We assume that τ ∼β(a,b,τ,τ)andcalibratetheseparameterstomatchthedistributionofLTVsin i CMBSpools,omittingthehighestandlowestpercentilestoreducetheeffectsofreportingerrorsandoutliers.30 τ andτ aresettomatchthelowestandhighestCMBS LTVs in the data (30 percent and 75 percent, respectively). The shape parameters, a and b, come from the joint calibration, with the mean and residual standard deviation of CMBS LTV as the corresponding target moments.31 We assume that the 30WefocusonCMBS,sincethelackofrecourseorrelationshiplendingmeansthedata-generating processforCMBSlikelyalignsbestwiththefactorsincorporatedintothemodel,withloanunderwritingandperformancedrivenbythecashflowsoftheunderlyingproperty. 31Some variation in CMBS LTVs reflects factors that are not accounted for in the model, for example,differencesinLTVlimitsbypropertytypes. SinceallofthevariationinCMBSLTVsin 24

value from leverage is capitalized into appraisals and transaction prices, so that the true LTV for a property is LTV j (s∗) , where LTV(s∗) is the optimal unlevered LTV 1+νi,j from equation (9), and ν is the markup on the property value due to the benefits i,j ofleveragefromequation(10). Turningtotheremainingparameters,wesetµ =.01sothataverageNOIgrowth matches the 1 percent average rent growth in An et al. (2016).32 r is targeted to match the 5.5 percent national cap rates in CBRE Econometric Advisors data.33 αF is targeted to produce the 30 percent average foreclosure cost in Brown et al. (2006).34 σ targets the 2.51 percent average spread on CMBS loans. Finally, we calibrate ε, which reflects the sensitivity of market shares to changes in ν , to i,j match the elasticity of CMBS market shares with respect to loan rates in Glancy etal.(Forthcoming).35 We present the results from our calibration in Table 5. The top panel reports parameters that are either directly set or exactly determined by other parameters, whilethebottompanelreportsparametersdeterminedinthejointcalibration. τ isestimatedtorangefrom0.04to0.45,withadistributionthatisright-skewed. Given the estimated required return of 7 percent, the modification breakdown rates arecalibratedas0.05and0.55forbanksandCMBS,respectively. NOIisestimated as having a volatility of 27 percent, and the calibrated αF implies that recoveries themodelreflectsborrowerpreferences, wetargettheresidualstandarddeviationaftercontrolling forsize,amortization,duration,paripassustatus,andyearandpropertytypefixedeffects. 32An et al. (2016) use panel data on property-level rents from 2001:Q2 to 2010:Q2 to estimate theirmodel. SeeTable3fortheGLSestimateoflong-termaveragerentgrowthweuse. 33Themeannationalcaprate(NOIasafractionofpropertyvalue)intheCBREdatais5.5percent, averagingoverpropertytypesandquartersfrom2012to2019. Thecaprateinthemodelis r−µ . 1+νi,j Sincethenumeratorisheterogeneous,thetargetistheaverageoverborrowersandlenders. 34Basedonasampleofdistressedlife-insurer-ownedcommercialproperties,Brownetal.(2006) find that sales prices were about 30 percent lower than transfer values after accounting for capital expenditures. Note that 1−αF is the recovery as a share of the unlevered property value, so the foreclosurecostrelativetotheactualpropertyvalueis1−1−αF . 1+νi,j 35InTable6,theauthorsestimatethata25basispointincreaseinCMBSloanrates—equivalent to a 1 percentage point origination fee per a common heuristic—causes about a quarter of CMBS borrowerstoswitchtobanks. Wecalibrateε sothatsuchadeclineinthevalueofborrowingfrom CMBSreducestheCMBSmarketsharebyaboutaquarter. Thatis,a25basispointshockreduces values by 1 percent of the loan size (or the LTV ratio as a percent of the property value). For example, the shock would be the equivalent of a 0.65 percentage point decline in ν for a 65 i,CMBS percentLTVloan. 25

average78percentoftheunleveredpropertyvalue.36 The right-most columns indicate that the model is successful at fitting the targeted moments. The targeted moments in the joint calibration—cap rates, foreclosure costs, CMBS spreads, the mean and dispersion of CMBS LTVs, and the sensitivity of CMBS market shares to rate shocks—are all hit within at least two decimalplaces. 4.1.2. EffectsofModificationFrictionsonLTVsandSpreads Withthecalibratedmodel,wecannowinvestigatehowmodificationfrictionsaffect CREloanmarketoutcomes. Figure4plotshowmarketsharesofbanksandCMBS (depictedbytheblueandredareas,respectively)varybyτ. Thefigureadditionally plots LTVs (left panel) and spreads (right panel) as functions of τ for both lenders (shown by the equivalent color lines). This figure therefore displays both how underwriting terms vary for a particular borrower (different terms given τ) and how borrowerssortintolenders(differentmarketsharesbyτ). LTVs for CMBS loans are more responsive to differences in τ than for bank loans. The bank LTV function is increasing but flattens out quickly, reflecting the tight limits banks need to impose to prevent strategic renegotiation. The CMBS LTV function is steeper, meaning that CMBS increase LTV more for borrowers seekingleverage. ThispatternresultsinCMBShavinghigherLTVsthanbanksfor loanstohighτ borrowers. Incontrast,CMBSloanshavelowerLTVsforlowτ borrowers,asdifficultymodifyingloansincreasestherisksassociatedwithleverage. Though CMBS do not uniformly have higher LTVs for all borrowers, variation in market shares causes CMBS to have more high-LTV loans in their portfolio. Highτ borrowers,unabletoreceivehigh-LTVloansfrombanks,disproportionately borrowfromCMBS,asshownbyCMBSmarketsharesincreasinginτ. Simplyput, the higher debt capacity at CMBS is valued by high-demand borrowers, causing CMBStomakeproportionallymoreloanstosuchborrowers. Differences in spreads across lenders are more consistent across borrowers; banks require a premium in order to offset expected future declines in cash flows 36Note that this is the volatility of NOI of a single property, so it will naturally be higher than estimatesusingindexdata. 26

from modifications. As a result, banks charge higher spreads for all τs. However, while banks require higher spreads for all borrowers, there are offsetting compositional effects. Spreads increase monotonically in τ since high τ borrowers choose high-spread, high-LTV loans. Since CMBS make more loans to the types of borrowersthatchoosehigh-spreadloans,theycanstillhavehigherspreads,onaverage, ifthesortingeffectisstrongenough. Table 6 shows the average LTV and spread by lender type for the two-lender calibration. Differences in these averages reflect both variation in loan outcomes at a particular τ and the sorting effects from lenders serving different customers. CMBS have LTVs of 64 percent and spreads of 2.43, as in the data. Of greater interest are the bank results, as those moments are not targeted in the calibration. The calibrated model is also successful at reproducing bank LTVs: bank LTVs are 58 percent in the data and 59 percent in the model. However, the model misses with spreads: spreads on bank CRE loans are 16 basis points below CMBS in the databutare12basispointsaboveCMBSinthemodel. Thatis,thepremiumbanks charge to modify loans is more than enough to offset the sorting effects, resulting inbankshavinghigherspreadsthanCMBS,contrarytothedata. Overall, this calibration is useful for understanding the effects of modification frictions. Sincethelendersdifferonlyinλ,allofthedifferencesbetweenbanksand CMBS documented here reflect the effects that modifications have on loan underwritingandlenderselection. Thisanalysisclearlyshowsthatmodificationfrictions enablehigherLTVlendinganddisproportionatelyattractborrowersseekinghigher leverage. However,quantitativelythemodelmissesinsomedimensions: bankspreadsare toohigh(bynearly30basispoints)andtheirLTVlimitsaretoolow(nobankloans have LTVs above 65 percent). These results suggest that bank loans have other characteristics that mitigate the effects strategic renegotiation has on loan pricing andLTVlimits. Tobettermatchthedata,wenextaddinarecourselender. Section 3showsthatrecourseactsasasubstituteformodificationfrictionsbydiscouraging strategic renegotiations, increasing debt capacity, and lowering the cost of bank CRE loans. As most bank loans have recourse (Glancy et al., 2021), failing to account for these effects may contribute to the overly high bank spreads in the 27

model. 4.2. Three-LenderCalibrationoftheModel In this section, we add a recourse lender to the calibration and show that the model comesveryclosetoreproducingtheaverageLTVsandspreadsinthedata. 4.2.1. Calibration Relative to the calibration in Section 4.1.1, we make two major changes. First, weexpandthesetoflenders(J)thatborrowerscanchoosefrom. Weconsiderthree lendertypes,differinginbothmodificationfrictionsandrecourse,thatbroadlyspan the various kinds of credit available from the major CRE lenders: (λ ,θ) repre- Bank sents modifiable, recourse loans such as typical bank loans; (λ ,0) represents CMBS low-modification, non-recourse loans such as CMBS loans; and (λ ,0) repre- Bank sents modifiable, non-recourse loans such as those provided by life insurers and somebanks.37 Forbrevity,werefertothesethreelendersasbanks,CMBS,andlife insurers,respectively,thoughbanksprovidebothrecourseandnon-recoursecredit. Thesecondmajorchangeisthattwomorevariablesnowneedtobeaddedtothe joint calibration: θ and αD. The recourse parameter, θ, generally determines the effects of recourse on supply, and the cost of deficiency judgments, αD, generally determines the extent to which borrowers respond to recourse by choosing lower spreads or higher LTVs.38 We thus estimate θ and αD to match the 20 basis point effect of recourse on spreads and 2.8 percentage point effect of recourse on LTVs found in Glancy et al. (2021).39 We additionally alter the target change in market 37WedonotemphasizelifeinsurersinSection2becauseofdatalimitations.Wetreatlifeinsurers asidenticaltobanksintermsofmodifications,astheirregulatorsalsoencouragedthemtoprovide accommodationtostressedborrowers,andtheyalsosawlittleincreaseinloandelinquencyduring thepandemic. Despitetheinferiordata,accountingforlifeinsurersisrelevantastheyareoneofthe three major CRE lenders, with a 15 percent market share, roughly comparable to CMBS (Glancy etal.,Forthcoming). 38We are loose with our notation by now denoting θ as the amount of recourse when there is recourse,ratherthantheamountofrecourseforaparticularlender. 39Theauthorsuseloan-leveldatafrombankCREportfoliostoidentifytheseeffects, exploiting cross-loan variation in recourse controlling for other loan and property characteristics. Since the studyisofbankloans,themodelmomentisthedifferenceinLTVsandspreadsforloanswithand withoutrecoursefortheborrowersthatsortintobanks. 28

share from a 25 basis point CMBS shock to reflect the fact that there is another lenderthatborrowerscanswitchto. Insteadoftargetingtheroughlyone-quarterof borrowersthatswitchtobanks,wenowtargetthe37.5percentofCMBSborrowers thatswitchtoeitherbanksorlifeinsurersinGlancyetal.(Forthcoming). We present results from the three-lender calibration in Appendix Table E.2. MostoftheparametersareinlinewiththosefromTable5. Theright-mostcolumns indicate that the model is still successful at fitting the targeted moments beyond those that are set directly. Regarding the new parameters, the value for θ indicates that banks expect to lose about 7.5 percent of the present value of promised debt payments from a deficiency judgment upon foreclosure, while the value for αD indicatesthatbanksexpecttoloseover40percentofthisduetothecostsofcollecting adeficiencyjudgment. 4.2.2. AverageLTVsandSpreads Figure5plotshowmarketshares,LTVs,andspreadsvarybyτ forthethreelenders. ThefiguretellsastorysimilartotheoneportrayedinFigure4. Asbefore,LTVsat CMBS are more responsive to borrower demand, resulting in higher CMBS LTVs for high τ borrowers relative to other lenders. CMBS also continue to achieve higher market shares at higher τs and to provide lower spreads throughout the distribution. While the differences between high and low λ lenders are similar, there is now variation within the low λ lenders. Recourse lenders provide higher LTVs and lowerspreadsthannon-recourselendersthroughoutthedistribution. LTVlimitsfor the recourse lender are less tight, resulting in that lender making loans with LTVs above the maximum LTV provided by the non-recourse lender. In turn, this availability of higher-LTV loans allows the recourse lender to achieve a greater market share at intermediate levels of demand (though the highest-demand borrowers still predominantlygotoCMBS). What do these patterns mean for the average portfolio characteristics of the lenders? Table 7 shows the average LTVs and spreads by lender type for the threelender calibration. The results align well with the averages for the primary lenders 29

in the market. Average LTV differences in the model are as expected given the sorting effects and differences in LTVs displayed in Figure 5: CMBS have the highest LTVs at 64 percent, followed by the recourse lender at 60 percent, and then the non-recourse balance-sheet lender at 56 percent. These match up well with the data as banks have an average LTV of 58 percent (in between that of the recourse and non-recourse lender), and life insurers have an average LTV of 56 percent(equalingthatofthenon-recoursebalance-sheetlender).40 Spreads are also reasonably close to those in the data. Average spreads for balance-sheet lenders in the model and data all fall within a 9 basis point range, running from 2.18 percent for life insurers and 2.27 percent for banks, with the LTVs for the balance-sheet lenders in the model falling in between. In the model, the direct effect of recourse on loan rate spreads roughly offsets the sorting effect from the recourse lender serving more high τ borrowers, resulting in loan rate spreadsthataresimilar.41 Overall, the three-lender calibration is successful at capturing patterns in the data. Accounting for the effects of recourse reduces the overly high spreads for modifiable loans in the two-lender calibration. Adding the recourse lender lowers spreadsforbalance-sheetlendersbecausemostsuchloansnoweitherhaverecourse (providing protection from renegotiation) or go to borrowers seeking low LTVs. Finally, recourse increases debt capacity and thus addresses the very tight LTV limitsforbankloansimpliedbythetwo-lendercalibration. 40AppendixFigureE.3plotsthedistributionofat-originationLTVforloansfrombanks,CMBS, andlifeinsurers. AsdiscussedinGlancyetal.(Forthcoming),CMBSloanstendtoreceivehigher LTVs,withmodalLTVsaround70percent,comparedtoaround65percentforbanks. Thesehigher LTVsforbankloansarenotduetodifferencesinotherobservablecharacteristics,asCMBSloansare predictedtohavehigherLTVsevencontrollingforlocation,propertytype,loansize,amortization, andoriginationyear,asshowninTableE.1. 41Life insurers have risk-sensitive capital requirements that cause them to concentrate in safer loans(Glancyetal.,Forthcoming).Asthemodelonlyaccountsfordifferencesintheuseofrecourse andloanmodificationsacrosslenders,thismechanismdoesnotexplaintheslightlylowerspreadsat lifeinsurers. 30

4.3. Welfare With a quantitatively reasonable calibrated model in hand, we can now investigate the welfare implications of changing modification frictions. We focus on the effectsofreducingfrictionsatCMBS,asthosefrictionstosomedegreereflectpolicy choicesthatcanbealtered. Indeed,theIRSissuedguidancetoenablemoremodifications during the pandemic, likely contributing to the decline in the delinquencyto-modification ratio shown in Table 4 and the spike in CMBS forbearances shown in Appendix Figure E.2.42 Were such an easing of modification restrictions to be made permanent, how would this affect the welfare of those subsequently seeking acommercialmortgage? In the model, welfare is reflected in ν —that is, the increase in property value i,j (relative to the unlevered value) achieved with a loan from j. Higher spreads, lower allowable leverage, or a greater risk of losing the property in a foreclosure reducethisvalue. Consequently,thewelfareimplicationsofchangingmodification frictions depend on the counteracting effects frictions have in easing underwriting termsbutreducingprotectionagainstpricedeclines. Figure 6 plots ν and ν , normalized to ν , for different values of i,Bank i,CMBS i,Life τ. The line for banks, in blue, thus shows how borrowers view recourse (since banks and life insurers differ only in θ ), while the line for CMBS, in red, shows j how borrowers value modification frictions (since CMBS and life insurers differ only in λ ). Both lines are increasing in τ, reflecting the fact that recourse and j modification frictions both facilitate higher LTV lending by discouraging strategic default. Consistent with the market shares shown in Figure 5, life insurers are preferredatthelowestτs,CMBSatthehighestτs,andbanksinbetween. The dashed red line shows the relative value for CMBS after reducing λ by a factor of 5. Reducing modification frictions rotates the CMBS value function toward that of life insurers. While some borrowers benefit from the reduction in modificationfrictions—thatis,theoneswithlowerdemandforleverage—theoverall effect on welfare is negative. Since CMBS make few loans to borrowers with 42TheIRStookstepstoallowmoremodificationsunderREMIClawsduringthepandemic. See IRSguidanceavailableathttps://www.irs.gov/pub/irs-drop/rp-20-26.pdf. 31

low τs—their value functions are well below those of banks and life insurers for suchborrowers—thebenefitsrealizedbylowτ borrowersaresmallonaverage. As aresult,reducingmodificationfrictionsisassociatedwithlowerwelfareonaverage. This effect is seen more clearly in Figure 7, which plots how expected welfare is affected by reducing the modification breakdown rate at CMBS by a factor of 5. RecallfromSection3.4thatborrowersmaximizez ν ,wherez isaFre´chetdisi,j i,j i,j tributed random variable. The figure plots ν(τ)=E(max {ν z }) when CMBS i j i,j i,j modification frictions are reduced by a factor of 5, relative to the expected value in thecalibratedmodel.43 This average value reflects how much the value of borrowing from CMBS changes for a given τ and how likely CMBS are to lend to different borrowers. The figure shows that while there is a welfare gain for low τ borrowers, the gain is small (under 1 percent) since most of these borrowers will not choose CMBS loans. Welfarechangesmorenotablyforhighτ borrowers,whoaremorerelianton CMBS. Welfare declines by over 4 percent for the borrowers with the highest demand for leverage. In aggregate, averaging across borrowers, this change amounts toalittlemorethanahalfpercentagepointdeclineinaggregatewelfare.44 Altogether, the welfare exercise demonstrates the importance of variety in loan underwriting. While most borrowers benefit from the ability to modify loans, CMBS serve an important niche in the market. Difficulties in modifying loans enable borrowers to achieve higher leverage than is available from lenders for which strategic renegotiation is more of a concern. Reducing CMBS’ advantage in this regardisthuscostly,bothonaverageandespeciallyforhigh-leverageborrowers. 43Integrating over the idiosyncratic lender preferences, we get that the expected welfare for a borrowerwithagivenτ is: ν(τ i )=E(max j {ν i,j z i,j })=Γ( ε− ε 1 )(∑ν i ε ,j )ε 1 , j∈J whichisincreasingineachν ,withagreaterinfluencefromthelenderswithahigherν . i,j i,j 44The results are qualitatively similar in the two-lender calibration of the model, as the same mechanisms are at play: small gains at low τs are offset by declines for the higher τ borrowers thataremorelikelytouseCMBScredit. Quantitatively, thewelfarecostsofeasingmodifications are higher in the two-lender calibration (nearly a 1 percent decline in welfare), as non-recourse balance-sheetlendersareaworsesubstituteforhigh-LTVCMBSloans. 32

5. CONCLUSION We investigate how differences in the ability to modify loans affect CRE loan outcomes. Empirically, we demonstrate that banks are more likely to modify loans than CMBS and are more willing to offer preemptive modifications. To better understand the equilibrium implications of these modification patterns, we build a tractable trade-off theory model adapted to the CRE market where modification frictions differ between lender types. We show that modification frictions discourage strategic renegotiation and facilitate higher LTV lending. In turn, borrowers demanding higher leverage disproportionately match to lenders with higher modification frictions. The model can thus explain why CMBS loans have higher average LTVs than bank loans. The model also allows us to evaluate the effects of changing modification frictions. Reducing modification frictions at CMBS constricts the range of contracts offered by CMBS and lowers welfare for borrowers seekinghigherLTVloans. References Adelino, Manuel, Kristopher Geradi, and Paul Willen (2013). “Why don’t lenders renegotiate more home mortgages? Redefaults, self-cures and securitization.” Journal of Monetary Economics, 60(7), pp. 835–853. doi:10.1016/j.jmoneco. 2013.08.002. Agarwal, Sumit, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet, and Douglas D. Evanoff (2011). “The role of securitization in mortgage renegotiation.” Journal of Financial Economics, 102(3), pp. 559–578. doi: 10.1016/j.jfineco.2011.07.005. An, Xudong, Yongheng Deng, Jeffrey D. Fisher, and Maggie Rong Hu (2016). “Commercial real estate rental index: A dynamic panel data model estimation.” RealEstateEconomics,44(2),pp.378–410. doi:10.1111/1540-6229.12101. Black, Lamont, John Krainer, and Joseph Nichols (2017). “From origination to renegotiation: A comparison of portfolio and securitized commercial real estate 33

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FEDS Working Paper 79, Board of Governors of the Federal Reserve System. doi:10.17016/FEDS.2021.079. Guiso, Luigi, Paola Sapienza, and Luigi Zingales (2013). “The determinants of attitudes toward strategic default on mortgages.” The Journal of Finance, 68(4), pp.1473–1515. doi:10.1111/jofi.12044. Hackbarth, Dirk, Christopher A. Hennessy, and Hayne E. Leland (2007). “Can the trade-offtheoryexplaindebtstructure?” TheReviewofFinancialStudies,20(5), pp.1389–1428. doi:10.1093/revfin/hhl047. Leland, Hayne E. (1994). “Corporate debt value, bond covenants, and optimal capital structure.” The Journal ofFinance, 49(4), pp. 1213–1252. doi:10.1111/j. 1540-6261.1994.tb02452.x. Riddiough, Timothy J. and Steve B. Wyatt (1994a). “Strategic default, workout, and commercial mortgage valuation.” The Journal of Real Estate Finance and Economics,9(1),pp.5–22. doi:10.1007/BF01153586. Riddiough,TimothyJandSteveBWyatt(1994b). “Wimportoughguy: Sequential default risk and signaling with mortgages.” The Journal of Real Estate Finance andEconomics,9(3),pp.299–321. doi:10.1007/BF01099281. Snyderman, Mark P. (1991). “Commercial mortgages: Default occurrence and estimated yield impact.” Journal of Portfolio Management, 18(1), pp. 82–87. doi: 10.3905/jpm.1991.409383. Trepp,LLC.(2012-2021). “CommercialRealEstateLoan-LevelData.” 35

Delinquency Rate Modification Rate etaR ycneuqnileD 5 4 3 2 1 0 Banks CMBS 1 1 1 1 Q Q Q Q 8: 9: 0: 1: 1 1 2 2 0 0 0 0 2 2 2 2 etaR noitacifidoM 02 51 01 5 0 Banks CMBS 1 1 1 1 Q Q Q Q 8: 9: 0: 1: 1 1 2 2 0 0 0 0 2 2 2 2 Figure 1: BANK AND CMBS DELINQUENCY AND MODIFICATION RATES. Note: Modifications include both payment and nonpayment modifications. Rates are calculated as the share of all outstanding loans in a given quarter that become 90 days delinquent or receive a modification (in percentage terms), where all loans more than 120 days delinquent have beenremovedfromthesample. Source: Authors’calculationsusingTreppCMBSdataandY-14H.2Schedule. 36

Rate Loans Orig.Amt Orig. Orig. IO Floating Recourse Spread Term (#) (Mil.$) LTV DSCR (percent) Rate(percent) (percent) (percent) Banks Industrial 4,809 9 59 2.6 2.28 7 17 53 76 Lodging 1,975 22 58 3.5 2.63 7 27 61 61 Office 8,591 19 60 2.7 2.24 7 27 56 68 Retail 10,690 8 58 2.5 2.27 7 17 51 74 CMBS Industrial 1,104 14 63 1.9 2.54 9 52 3 1.9 Lodging 3,233 25 62 2.2 2.81 9 26 5 1.2 Office 4,238 36 62 2.0 2.48 9 66 7 2.4 Retail 6,554 18 64 1.8 2.47 10 55 2 0.6 Table 1: LOAN ORIGINATION CHARACTERISTICS FOR BANK AND CMBS LOANS. Note: Limited to loans originated between 2012 and 2019. Bank loans are limited to those originated after a lender begins reporting. All values are unweighted means. IO is interest-only. Source: Authors’ calculations using Trepp CMBSdataandY-14H.2Schedule. 37

2018:Q1–2019:Q4 2020:Q1–2021:Q2 Mod. Rate Delinq. Mod. Rate Delinq. Delinq. orPay Delinq. orPay All Pay Other All Pay Other Rate Mod. Rate Mod. Banks Industrial 1.36 1.25 1.29 0.09 1.32 9.05 8.92 1.27 0.07 8.98 Lodging 3.18 2.93 1.98 0.24 3.15 16.48 15.82 2.69 0.99 16.50 Office 1.87 1.60 1.69 0.10 1.69 10.51 10.17 1.73 0.13 10.26 Retail 1.42 1.25 1.45 0.11 1.35 9.82 9.23 2.10 0.23 9.43 CMBS Industrial 0.06 0.04 0.02 0.24 0.27 0.05 0.02 0.03 0.30 0.31 Lodging 0.05 0.02 0.03 0.30 0.31 4.18 2.71 1.48 4.55 7.16 Office 0.08 0.02 0.06 0.21 0.23 0.23 0.08 0.16 0.39 0.46 Retail 0.05 0.01 0.04 0.26 0.27 0.65 0.42 0.24 1.25 1.64 Table 2: MODIFICATION AND DELINQUENCY RATES. Note: Average quarterly modification and 90-day delinquency ratesforbankandCMBSportfolios. Modificationratesarecalculatedastheshareofloans(inpercentageterms)thatare lessthan120daysdelinquentthatreceiveamodificationinagivenquarter. Delinquencyratesarecalculatedastheshare ofloans(inpercentageterms)thatarelessthan120daysdelinquentandbecome90daysdelinquentinthegivenquarter. Source: Authors’calculationsusingTreppCMBSdataandY-14H.2Schedule. 38

Delinquency AllMods PaymentMods Delinquency AllMods PaymentMods (1) (2) (3) (4) (5) (6) CMBS -0.0579∗∗ -1.467∗∗∗ -1.292∗∗∗ -0.0499∗∗∗ -1.798∗∗∗ -1.626∗∗∗ (0.0243) (0.0442) (0.0397) (0.0178) (0.0338) (0.0299) CMBS×Covid 0.291∗∗∗ -4.374∗∗∗ -4.163∗∗∗ (0.0588) (0.108) (0.0972) CMBS×LTV 0.00154 -0.0111∗∗∗ -0.0123∗∗∗ (0.00102) (0.00193) (0.00171) CMBS×DSCR -0.149∗∗∗ 0.315∗∗∗ 0.193∗∗∗ (0.0295) (0.0560) (0.0496) LTV 0.0126∗∗∗ 0.00228 0.000627 0.0117∗∗∗ 0.0106∗∗∗ 0.00954∗∗∗ (0.00129) (0.00234) (0.00211) (0.00105) (0.00200) (0.00177) DSCR -0.231∗∗∗ -0.184∗∗∗ -0.122∗∗∗ -0.164∗∗∗ -0.301∗∗∗ -0.180∗∗∗ (0.0202) (0.0369) (0.0332) (0.0205) (0.0389) (0.0344) N 516,507 515,173 515,392 426,960 426,337 426,480 R2 0.02 0.04 0.03 0.00 0.02 0.01 MeanofDep.Var.forBanks(%) .11 2.02 1.69 1.39 1.09 1.0 QuarterFEs Y Y Y Y Y Y Orig.YearFEs Y Y Y Y Y Y StateFEs Y Y Y Y Y Y PropertyTypeFEs Y Y Y Y Y Y ControlsandFEs×Covid Y Y Y - - - Sample 2012:Q1–2021:Q2 2012:Q1–2021:Q2 2012:Q1–2021:Q2 2012:Q1–2019:Q4 2012:Q1–2019:Q4 2012:Q1–2019:Q4 Table 3: LINEAR PROBABILITY REGRESSIONS. Note: All regressions are of the form described in equation (1). The sample includes loans that are less than 120 days delinquent with at-origination DSCRs greater than one. Modification regressionspredictfirstmodification,soloan-quarterobservationsafteraloanmodificationareremovedfromthesample. This causes observation numbers to vary across specifications. The dependent variables of interest are whether a loan goes 90 days delinquent (Columns 1 & 4), receives a modification (Columns 2 & 5), or receives a payment modification (Columns 3 & 6) in a quarter. Columns (1)-(3) include the interaction of the COVID and CMBS indicators. Columns (4)-(6) restrict the sample to the pre-COVID period and instead include the CMBS indicator interacted with the current LTVandDSCR.Dependentvariablesaremultipliedby100,socoefficientsreflectpredictedeffectsinpercentagepoints. Source: Authors’calculationsusingTreppCMBSdataandY-14H.2Schedule. 39

Delinquency by DSCR Modifications by DSCR Distress by DSCR etaR ycneuqnileD 4 5.3 3 5.2 2 5.1 1 5. 0 Banks CMBS 0 .25 .5 .75 1 1.25 1.5 1.75 2 2.25 2.5 DSCR etaR noitacifidoM 4 5.3 3 5.2 2 5.1 1 5. 0 Banks CMBS 0 .25 .5 .75 1 1.25 1.5 1.75 2 2.25 2.5 DSCR etaR ssertsiD 4 5.3 3 5.2 2 5.1 1 5. 0 Banks CMBS 0 .25 .5 .75 1 1.25 1.5 1.75 2 2.25 2.5 DSCR Delinquency by LTV Modifications by LTV Distress by LTV etaR ycneuqnileD 4 5.3 3 5.2 2 5.1 1 5. 0 Banks CMBS 0 20 40 60 80 100 120 LTV etaR noitacifidoM 4 5.3 3 5.2 2 5.1 1 5. 0 Banks CMBS 0 20 40 60 80 100 120 LTV etaR ssertsiD 4 5.3 3 5.2 2 5.1 1 5. 0 Banks CMBS 0 20 40 60 80 100 120 LTV Figure2: DELINQUENCYANDMODIFICATIONRATESBYCURRENTDSCRANDLTV.Note: Dataincludeloan-quarter observations in 2012q1–2019q4. Rates are in percentage points. All values are residualized on origination year, quarter, property type, and state by CBSA fixed effects. Plots are binned scatterplots where observations are binned according to the residualized value of the x-axis. When looking across LTV, observations are binned into the following quantiles: {5,10,15,20,30,40,50,60,70,80,85,90,92.5,95,97.5,99}. When looking across DSCR, observations are binned into the following quantiles: {1,2.5,5,7.5,10,15,20,30,40,50,60,70,80,85,90,95}. All loans 120 days or more delinquent are excluded. We remove loans that have a DSCR at origination of less than one. Source: Authors’ calculations using TreppCMBSdataandY-14H.2Schedule. 40

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Current Income (X t) ecivreS tbeD Lender Banks CMBS Region only bank loans modify Figure 3: DEBT SERVICE COSTS BY CURRENT NOI. Note: This figure plots debt service costs as a function of current NOI (X ) for two lenders with identical t promisedcouponsbutdifferentλs. Paymentsforlenderwithalowλ (“banks”)are shown in blue, and payments for the high λ lender (“CMBS”) are shown in red. Thecross-hatchedregionshowstherangeofincomeswhereonlythelowλ loanis modified. 41

2012:Q1-2019:Q4 2020:Q1-2021:Q2 Banks 0.64 0.48 CMBS 7.76 1.06 Table 4: DELINQUENCY-TO-MODIFICATION RATIOS. Note: Values are the ratio of delinquency rates to modification rates by lender type and time period. We use these values to calibrate λj, reflecting the breakdown risk in the model. Source: r Authors’calculationsusingTreppCMBSdataandY-14H.2Schedule. 42

EstimatedParameters ModelFit Parameter Estimate Moment Target Model DirectlySet µ 0.010 RentGrowth,Anetal. (2016) 1% 1% τ 0.044 MinCMBSLTV 30% 30% τ 0.448 MaxCMBSLTV 75% 75% λ 0.046 λBank =BankDelinquency-to-ModRate .64 .64 Bank r λ 0.552 λCMBS =CMBSDelinquency-to-ModRate 7.76 7.76 CMBS r JointlyEstimated r 0.071 AverageCapRate,CBRE 5.50% 5.50% αF 0.222 30%ForeclosureCost,Brownetal. (2006) 30% 30% σ 0.270 AverageLoanSpread 2.43% 2.43% ε 7.009 Effectof25bpshockonCMBSshare -24.4% -24.4% a 1.297 AverageCMBSLTV 0.64 0.64 b 1.727 DispersioninCMBSLTV 0.08 0.08 Table 5: CALIBRATION RESULTS. Note: From left to right, this table presents (1) the variable to be calibrated, (2) the calibrated value, (3) a description of the corresponding target, (4) the targeted moment in the data, and (5) the value of that momentinthecalibratedmodel. 43

LTVs Spreads 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Leverage Demand ( ) redneL yb VTL Lender Bank 0.035 CMBS 0.030 0.025 0.020 0.015 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Leverage Demand ( ) redneL yb daerpS Lender Bank CMBS Figure 4: LTVS AND SPREADS BY τ, TWO-LENDER CALIBRATION. Note: Lines show either the LTV (left) or loan ratespread(right)chosenbyaborrowerfromagivenlenderatagivenτ. Theshadedregionsshowthemarketsharefora givenlender. Bluelinesandregionsshowbankunderwritingtermsandmarketsharesbyτ,andredlinesandareasshow thesequantitiesforCMBS. 44

Lender Data Model LTVs Bank 58 59 CMBS 64 64 Spreads Bank 2.27 2.55 CMBS 2.43 2.43 Table 6: AVERAGE LTVS AND SPREADS, TWO-LENDER CALIBRATION. Note: This table presents average LTV and spreads by lender in the data and the model. Source: Authors’calculationsusingTreppCMBSdataandY-14H.2Schedule. 45

LTVs Spreads 0.7 0.6 0.5 0.4 0.3 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Leverage Demand ( ) redneL yb VTL Lender Bank 0.035 CMBS Life 0.030 0.025 0.020 0.015 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Leverage Demand ( ) redneL yb daerpS Lender Bank CMBS Life Figure 5: LTV AND SPREAD BY τ, THREE-LENDER CALIBRATION. Note: Lines show either the LTV (left) or loan rate spread (right) chosen by a borrower from a given lender at a given τ. The shaded regions show the market share by lender. Resultsforbanks,CMBS,andlifeinsurersareshowninblue,red,andgreen,respectively. 46

Lender Data Model LTVs Banks 58 60 CMBS 64 64 Life 56 56 Spreads Bank 2.27 2.21 CMBS 2.43 2.43 Life 2.18 2.25 Table7: AVERAGE LTVS AND SPREADS, THREE-LENDER CALIBRATION. Note: This table presents average LTV and spreads by lender in the data and the model. Source: Authors’calculationsusingTreppCMBSdata,NAIC,andY-14H.2Schedule. 47

1.1 1.0 0.9 0.8 0.1 0.2 0.3 0.4 Leverage Demand ( ) efiL ot evitaleR eulaV Lender CMBS CMBS: 1/5th Breakdown Rate Bank Figure 6: VALUES BY τ AND LENDER TYPE. Note: Solid lines show ν i,Bank and ν ,respectively,normalizedtoν ,fordifferentvaluesofτ. Thedashedred i,CMBS i,Life lineshowsν normalizedtoν ,fordifferentvaluesofτ whenλ isreduced i,CMBS i,Life byafactorof5. 48

1.00 0.99 0.98 0.97 0.96 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Leverage Demand ( ) enilesaB ot evitaleR eulaV Figure 7: CHANGE IN WELFARE FROM REDUCING λ CMBS BY FOUR-FIFTHS. Note: This figure plots ν(τ) over τ, normalized by its respective value for the i baselinethree-lenderparameterizationwhenλ isreducedbyafactorof5. 49

A. INSTITUTIONALOVERVIEW:CMBSVS.BANKS In this appendix, we briefly review institutional factors that affect the willingness ofdifferentlenderstoofferCREloanmodifications. A.1. CMBSModificationRestrictions CMBShavealwaysbeenlimitedinhoweasilytheycanmodifyloansandthetypes of modifications they can provide. The two most important reasons for this are thatCMBSareREMICsandtheyhavepoolingandservicingagreements(PSAs)— legallybindingcontractsthatlimittheactionsofthepartiesinvolvedinrunningthe CMBS.45 AREMICisanentitysatisfyingcertaincriteria,includinghavingeffectivelyall of its investments in qualified mortgages and real estate property (including property in foreclosure). REMICs are exempt from federal income taxes. This exemption allows them to avoid double taxation when they issue pass-through securities to investors. Qualified mortgages must meet certain criteria, including being transferredtotheREMIConitsstart-upday. To maintain REMIC status, the REMIC cannot add new loans or property in years subsequent to its start-up day. This can make loan modifications difficult to pursue as a substantially modified loan may be considered a new loan. This new loan will not have been transferred to the REMIC on its start-up day and, therefore, will jeopardize the entity’s REMIC status. There are exceptions to this rule, including modifications that are “occasioned by default or a reasonably forseeable default,” but even if the modification falls into an exception, there is a danger that themodifiedloanwillviolateanotherREMICrequirement. REMIC rules have changed over time. During the global financial crisis, the IRS updated the rules to allow more flexibility for modifications with the REMIC structure. The rule issued in 2009 relaxed the forseeable default requirement to allow modifications if the servicer determines that “there is a significant risk of defaultofthepre-modificationloanuponmaturityoftheloanoratanearlierdate.” 45OtheraspectsofCMBSalsomakemodificationsmoreprohibitive.Forexample,CMBSreceive creditratings,andcertainmodificationswillrequireanewrating. 50

Despite this more lenient rule, there were still concerns about making significant modifications to loans (see Flynn Jr. et al. 2021 for further details on this rule change and its effects). Another major rule change occurred in the pandemic when the IRS issued a statement temporarily allowing forbearances within the REMIC structure. This rule change led to a number of forbearances that were historically extremelyuncommoninCMBS.46 InadditiontomaintainingREMICstatus,eachCMBSpoolhasaPSAthatoutlines potential additional restrictions that the special servicer must abide by when modifying loans. For example, a 2016 PSA provides specific guidance on the specialservicer’sabilitytodeferinterest: The Special Servicer shall use its reasonable efforts to the extent possible to cause each Specially Serviced Loan to fully amortize prior to theRatedFinalDistributionDateandshallnotagreetoamodification, waiver, or amendment of any term of any Specially Serviced Loan if such modification, waiver or amendment would ...provide for the deferral of interest unless interest accrues on the related Mortgage Loan ortherelatedServicedWholeLoanattherelatedMortgageRate. PSAsalsooutlineotherpartiesthathavetherighttoconsenttomodifications. These consent requirements can also complicate, or at least delay, the approval of modifications. This can be particularly problematic when the relevant parties are inundatedwithrequests,aswasthecaseearlyoninthepandemic. A.2. BankModificationEncouragement In contrast to CMBS, where modifications can be curtailed by REMIC rules and PSA restrictions, banks have fewer impediments to modification. Since banks are typicallythesoleholderoftheloan,theywillrarelyhaveconflictsofinterestacross differentinvestorstocomplicateloannegotiations. Instead,modificationdecisionsaremoresensitivetobanks’assessmentsofhow a modification would affect the likely recovery from a potentially distressed loan 46SeeIRSRev. Proc2020-26athttps://www.irs.gov/pub/irs-drop/rp-20-26.pdf. 51

and by the views of supervisors as to the risks associated with such modifications. On this second point, banks’ regulatory agencies actively encouraged lenders to workwiththecustomerswhowereadverselyaffectedbythepandemic. A joint press release from US bank regulatory organizations in March 2020 read:47 The agencies view prudent loan modification programs offered to financial institution customers affected by COVID-19 as positive and proactive actions that can manage or mitigate adverse impacts on borrowers,andleadtoimprovedloanperformanceandreducedcreditrisk. ... RegardlessofwhethermodificationsareconsideredTDRsorareadverselyclassified,agencyexaminerswillnotcriticizeprudenteffortsto modifytermsonexistingloansforaffectedcustomers. A follow-up press release in April reaffirmed and further clarified this regulatory stance. B. VALUEFUNCTIONSSOLUTIONS In this section we derive the equilibrium strategic debt service offer from renegotiations, S(X), and the functions defining the values of debt and equity as a function ofcurrentNOI. Sincelendersandborrowersareriskneutral,thevaluefunctionsfordebtandequityintheH andLregionsmustsatisfytheordinarydifferentialequations(ODEs): 47The text from the March 2020 press release is available at https://www.federalreserve.gov/ newsevents/pressreleases/bcreg20200322a.htm, and a revision to that interagency statement pertainingtotheCARESActisavailableathttps://www.federalreserve.gov/newsevents/pressreleases/ bcreg20200407a.htm. 52

1 rD (X)=C+µXD(cid:48) (X)+ σ2X2D(cid:48)(cid:48)(X) H H H 2 1 rD (X)=S(X)+µXD(cid:48) (X)+ σ2X2D(cid:48)(cid:48)(X) L L L 2 1 rE (X)=X−(1−τ)C+µXE(cid:48) (X)+ σ2X2E(cid:48)(cid:48)(X) (12) H H H 2 1 rE (X)=X−(1−τ)S(X)+µXE(cid:48)(X)+ σ2X2E(cid:48)(cid:48)(X) L L L 2 C +λ(−θ −E (X)), L r where λ(−θC −E (X)) reflects the expected loss to equity holders from renegotir L ationbreakingdown.48 First, we determine S(X) based on the equilibrium condition that lenders are indifferent between modification and foreclosure. We then solve this set of ODEs tofindtheresultantvaluefunctions. Sinceborrowersmakeatake-it-or-leave-itoffer to their lender, the value of debt must equal the recovery value from foreclosure: D (X)=(1−αF) X +(1−αD)θC. We can then substitute D (X), D(cid:48) (X), and L r−µ r L L D(cid:48)(cid:48)(X)intothesecondlineofequation(12)andsolveforS(X)as L S(X)=(1−α F)X+(1−α D)θC. (13) OncewesubstitutethisexpressionforS(X)intothefourthlineofequation(12), wecanseethattheremainingthreeODEstaketheform 1 cV(X)=a+bX+V(cid:48)(X)µX+ σ2X2V(cid:48)(cid:48)(X), 2 whichhassolution a b V(y)= + y+A y−γ+A yζ, c c−µ γ ζ whereγ >0andζ >1arefunctionsofc, µ,andσ,andA andA areconstantsto γ ζ 48ThistermdoesnotenterintoD (X)becauseS(X)issetsothatthelenderisindifferentbetween L continuationandforeclosure. 53

bepinneddownbyboundaryconditions.49 We can solve this set of ODEs as a function of the renegotiation boundary, X , n using a set of value-matching and asymptotic conditions. Using the asymptotic conditions,wecanshowthat C D (X)= +ADX−γ H r γ X C D (X)=(1−α F) +(1−α D)θ L r−µ r (14) X (1−τ)C E (X)= − +AEX−γ H r−µ r γ 1−(1−αF)(1−τ) λθC (1−τ)(1−αD)θC E (X)= X− − . L r+λ −µ r(r+λ) r+λ The other nonlinear term in D (X) is eliminated by the condition that H lim D (X)= C. D (X) is determined by the equilibrium condition that banks X→∞ H r L are indifferent between foreclosure and renegotiation. The other nonlinear term in E (X) is eliminated by the condition that the value of the default option goes to H 0 as X →∞. The non-linear terms in E (X) are eliminated by the conditions that L lim E (X)= −λθC − (1−τ)(1−αD)θC andlim E (X)= −θC.50 X→0 L r(r+λ) r+λ λ→∞ L r Theremainingconstants(AE andAD)areidentifiedbythevaluematchingcon- γ γ ditions that D (X )=D (X ) and E (X )=E (X ). For these equations to hold, H n L n H n L n 49 Notethatc=rinallequationsexceptforthefunctionE (X),forwhichc=r+λ. Wedonot L definetheexponentsγ andζ forthatequation,becauseitsconstantsare0. Thatis,E (X)islinear. L γ andζ thereforearedefinedastheexponentsthatcorrespondwiththeothervaluefunctions: (cid:18) (cid:113) (cid:19) γ = µ−.5σ2+ (.5σ2−µ)2+2σ2r /σ2>0 (cid:18) (cid:113) (cid:19) ζ =− µ−.5σ2− (.5σ2−µ)2+2σ2r /σ2>1. Notethatlim γ =∞andlim γ =0,soahigherγ meanslowervolatility. σ→0 σ→∞ 50 λθC isthepresentdiscountedvalueofadeficiencyjudgmentpayoutof θC withanexponenr(r+λ) r tially distributed arrival time, and (1−τ)(1−αD)θC is the present discounted value of debt payments r+λ (excludingtaxshields)madebeforenegotiationbreaksdown.Combined,theygivethevalueofpaymentsbythepropertyinvestor—theonlycashflowwhenthepropertyisyieldingnoincome. The second condition says that if negotiation breaks down immediately, the value in the renegotiation stateis −θC,reflectinganimmediatedeficiencyjudgment. r 54

thevaluefunctionsinthenon-renegotiationregionmustbe C X C D (X)= −( )−γ[ −D (X )] H L n r X r n (cid:20) (cid:21) C X C X = −( )−γ (1−(1−α D)θ) −(1−α F) n r X r r−µ n (15) X (1−τ)C X X (1−τ)C E (X)= − −( )−γ[ n − −E (X )] H L n r−µ r X r−µ r n (cid:20) (cid:21) X (1−τ)C X X C = − −( )−γ η n −η , x c r−µ r X r−µ r n where η and η are as in (2). With (14) and (15), we obtain the value functions c x shownin(2). C. COMPARATIVESTATICSANDANALYTICRESULTS Inthissection,weanalyzethecomparativestaticsforkeyfunctionsinthemodel. C.1. CharacterizationoftheModificationBoundary C.1.1. Comparativestaticsforrecourse(∂ρ) ∂θ Substitutingequation(2)intoequation(3),wecanexpressρ explicitlyas: γ r+λ −µ λ(1−τ−θ)+r(1−τ)(1−(1−αD)θ) ρ(λ,θ)= . (16) 1+γ r+λ λ +(1−αF)(1−τ)(r−µ) Bydifferentiatingequation(16)withrespecttoθ,itisclearthathigherrecourse discouragesborrowersfromseekingamodification: ∂ρ γ r+λ −µ λ +r(1−τ)(1−αD) =− <0. (17) ∂θ 1+γ r+λ λ +(1−αF)(1−τ)(r−µ) The two mechanisms by which recourse affects ρ are most clearly shown in the numerator of the last expression. The first term (λ) reflects the fact that firms are less willing to renegotiate because they are concerned that negotiations might break down, causing them to lose a deficiency judgment. This does not depend 55

on αD because it reflects the borrower’s losses instead of the lender’s recoveries. That is, even if lenders cannot recover anything from a deficiency judgment, they can still impose a cost on borrowers, making borrowers more hesitant to force a modification. Thiseffectishigherwhennegotiationsaremorelikelytobreakdown (λ ishigh). The second term (r(1−τ)(1−αD)) reflects the effect of recourse on debt service payments on modified loans. Recourse loans give lenders more bargaining power in a renegotiation due to their higher recovery in foreclosure (note this term is proportional to the recovery rate (1−αD)). This means that recourse borrowers need to make higher modified loan payments than non-recourse borrowers and thus are less quick to force a modification. This mechanism is more relevant when λ is low, as firms expect to maintain the modified payment terms longer before negotiationpotentiallybreaksdown. C.1.2. Comparativestaticsformodificationfrictions(∂ρ) ∂λ Sinceρ = γ ηc,thesensitivityofthedefaultboundarytomodificationfrictionsis 1+γ ηx ρ ∂ηc ∂ηx λ = ∂λ − ∂λ . ρ η η c x To evaluate this, it is helpful to simplify the expressions for η and η and x c differentiatethemwithrespecttoλ: λ η =1−(1−α D)θ − (τ+α D θ) c r+λ ∂η −r =⇒ c = (τ+α D θ) ∂λ (r+λ)2 η =(1−α F)(1−τ)+ λ (cid:0) 1−(1−α F)(1−τ) (cid:1) x r+λ −µ =⇒ ∂η x = r−µ (cid:0) 1−(1−α F)(1−τ) (cid:1) . ∂λ (r+λ −µ)2 ρ Substitutingintheseexpressions,wecansolvefor λ as ρ 56

ρ r τ+αDθ λ =− × ρ r+λ λ(1−τ−θ)+r(1−(1−αD)θ) r−µ 1−(1−αF)(1−τ) − × <0. r+λ −µ λ +(r−µ)(1−αF)(1−τ) Asbothtermsarenegative,thisderivativeshowsthatthemodificationboundary is decreasing in λ.51 That is, higher modification frictions cause borrowers to be willingtomaintainpromiseddebtpaymentsforlowerlevelsofNOI. C.1.3. Characteristicsofρ inthelimit The economic mechanisms affecting modification boundaries are most easily understood in the limiting cases. Taking the limits of equation (16) as λ goes to 0 or ∞,wecanfindthemodificationboundarywhenmodificationsneverbreakdown,or whentheyimmediatelybreakdown: γ 1−(1−αD)θ lim ρ = λ→0 1+γ 1−αF (18) γ lim ρ = (1−τ−θ). λ→∞ 1+γ Atthelowerlimitforλ,therenegotiationboundaryisthesameasinHackbarth et al. (2007) except for the term (1−αD)θ, reflecting how much recourse affects thenegotiationboundarywhenmodificationsneverbreakdown. Sincenegotiations neverbreakdownatthelowerlimit,recourseonlyaffectsmodificationstotheextent that it affects the lender’s bargaining power. Therefore, the boundary only shifts to the extent that lenders can recover losses from a deficiency judgment. Higher foreclosure costs raise the renegotiation threshold because lenders are willing to accept a lower debt service payment to avoid a foreclosure, motivating borrowers torenegotiate. At the other limit, as λ → ∞, negotiations break down immediately. In this 51Weassumethatθ <1−τinordertoensurethatdefaultispossible.Otherwise,thecombination ofthetaxshieldandrecoursewouldbesuchthat,forasufficientlyhighλ,borrowerswouldnotseek amodificationevenifincomeswere0. 57

case, the decision to renegotiate is a decision to accept foreclosure. This limit corresponds to the default threshold in Leland (1994)—shifted to reflect recourse— where firms are choosing an optimal default threshold instead of a renegotiation threshold. At this limit, the recourse share matters on its own, instead of the recourse share times the recovery rate. Without modifications, recourse affects the default boundary because it imposes losses on the borrower and discourages them from defaulting. This expression says that borrowers will be willing to maintain debtpaymentsevenwhenthepresentvalueofNOIfallsbelowthepresentvalueof promised debt payments to preserve the option value of the loan (γ is decreasing in σ), to preserve their debt shield (the τ term), and to avoid a deficiency judgment (the θ term). Foreclosure costs no longer matter, as they affect the lender’s recovery,nottheborrower’sloss. Atintermediatevaluesofλ,bothsetsofmechanismsmatter: lenders’potential recoveries affect borrowers’ incentives to modify, as this determines payments required on modified loans, while borrowers’ losses in foreclosure affect incentives to modify, as borrowers know that negotiations may break down before exiting the renegotiationregion. Theextenttowhicheachfactormattersdependsonhowclose λ istoeitherextreme. C.2. ComparativeStaticsforSupplyCurves Hereweanalyzehowrecourseandmodificationfrictionsaffectsupplycurves—that is, the LTVs that lenders are willing to offer for a given loan rate spread. Comparative statics with respect to θ and λ are similar, as both variables affect supply by changingthemodificationboundary. Forthisreason,weanalyzetheeffectsofthese variablestogether. Substituting χ from (5) into the supply curve defined in (6) and differentiating with respect to θ and λ, we can see that recourse or higher modification frictions 58

inducebankstoofferhigherLTVsforagivenspread:   ∂LTV(s;θ,λ) (1−αF)ρ−γχ ρ  =LTV(s) λ >0   ∂λ γχ ρ   (cid:124) (cid:123)(cid:122) (cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (−forλ>0) (−) (19)   ∂LTV(s;θ,λ) (1−αF)ρ−γχ ρ 1−αD =LTV(s) θ + >0,   ∂θ γχ ρ γχ   (cid:124) (cid:123)(cid:122) (cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (−forλ>0) (−) (+) where ρ and ρ are the partial derivatives of ρ with respect to θ and λ, respec- θ λ tively,whichwereshowntobenegativeinAppendixC.1. As 1−αD and γχ are positive, it is clear that the sign of the comparative statics depends critically on the sign of (1−αF)ρ −γχ. This expression measures the sensitivity of loan supply to changes in the modification boundary, accounting for both the direct effects of changing ρ in equation (6), and the effects operating through χ.52 This sensitivity can be shown to be 0 for λ =0 and positive for λ > 0. To see why, substitute in χ from equation (5) and ρ(0,θ) from equation (18). This shows that the expression is 0 for λ =0. Note also that (1−αF)ρ−γχ is increasing monotonically in ρ (since ρ enters negatively in χ). As ρ is monotonically decreasing in λ, the expression is monotonically decreasing in λ. Since (1−αF)ρ−γχ =0forλ =0andisdecreasinginλ,itisnegativeforallλ >0. Having derived the direction of the effects of recourse and modification frictions on supply, we now discuss the economics involved. Focusing first on the top line of (19), which shows how modification frictions affect LTV, we can see that λ affects the supply curve entirely by shifting the modification boundary. When λ is higher, the renegotiation threshold (ρ) is lower, since the risk of negotiations breakingdowndiscouragesrenegotiationatthemargin. Lenderscanthereforeoffer a higher original LTV and achieve the same risk of modification, and thus allow 52These effects work in opposite directions. A lower modification boundary directly increases allowableLTVs;however,asmodificationsoccuratlowerpropertyvalues,loanlosseswhenmodificationsdooccurarehigher. Weshowherethatthefirsteffectwinsoutwhenλ >0. 59

higher LTVs for a given spread. Overall, this term shows that increased modification frictions (λ ↑) lower the modification boundary (ρ ↓), which allows borrowers to take out a higher LTV for a given spread (LTV(s) ↑). That is, credit supply is increasinginλ. The second line in (19) shows how the availability of recourse affects LTVs. The first term is similar to the previous expression. Increasing recourse shifts the supplycurveoutbyloweringthemodificationboundary. However,thereisoneadditional term, 1−αD , which reflects the extent to which recourse reduces loss given γχ default. Thus, recourse affects supply in two ways: first, it discourages borrowers from seeking modifications (as with increasing λ), and, second, it directly affects recoveries when lenders foreclose. Both of these forces contribute to a positive relationshipbetweenLTVandrecourse. D. BARGAININGPOWEREXTENSION D.1. AddingBargainingPowertotheModel Inthissection,weextendthemodeltoallowlenderstohavesomebargainingpower in loan modification negotiations. As before, borrowers choose the threshold at which to pursue a modification. However, instead of the modified payment being determinedbyatake-it-or-leave-itofferfromtheborrower,nowS(X)isdetermined by a more general bargaining process. Let β denote the bargaining power of the lender in modification renegotiations. When β = 0, the borrower has all of the power,andmodificationoutcomesareasbefore: S(X;β =0)isasinequation(13). Whenβ =1,thelenderhasallofthebargainingpowerandmakesatake-it-or-leaveit offer to the borrower to modify the debt service amount, denoted S(X;β = 1). Finally,whenβ ∈(0,1),themodifieddebtserviceamountisaweightedaverageof these two outcomes, with a weight of β on the outcome where the lender sets the offer: S(X;β)=βS(X;β =1)+(1−β)S(X;β =0). To determine the modified debt service amount for a given bargaining power, we thus need to solve for S(X;β = 1). By a similar logic to what was laid out in 60

Appendix B, given all the bargaining power, lenders would set S(X) to make the borrower indifferent to foreclosure: E (X)=−θC. From equation (12), this value L r functionwouldbesatisfiedforS(X;β =1)= X+θC. 1−τ Combined with equation (13), we get that the modified debt service amount whenlendershavebargainingpowerβ is (cid:18) (cid:19) (cid:18) (cid:19) β β S(X;β)= (1−β)(1−α F)+ X+ (1−β)(1−α d)+ θC, 1−τ 1−τ whichisincreasinginβ,particularlywhenforeclosurecostsarehigher. The differential equations defining debt and equity values in the modification regionare: 1 rD (X;β)=S(X;β)+µXD(cid:48) (X)+ σ2X2D(cid:48)(cid:48)(X) L L L 2 +λ(R(X)−D (X)), L 1 rE (X;β)=X−(1−τ)S(X;β)+µXE(cid:48)(X)+ σ2X2E(cid:48)(cid:48)(X) L L L 2 C +λ(−θ −E (X)), L r whichareasbefore,besidesthechangetoS(X)andthefactthattheR(X)−D (X) L doesnotdropoutoftheequationforD (X)(sincelendersarenolongerindifferent L toforeclosure). ThesolutionstotheseequationsforthenewS(X)functionare (cid:32) (cid:33) β τ X D (X;β)= (1−α F)+ ( +α F) L 1+ λ 1−τ r−µ r−µ (cid:32) (cid:33) β τ C + (1−α D)+ ( +α D) θ 1+λ 1−τ r r (cid:32) (cid:33) 1−β X 1−β C E (X;β)= (α F+τ(1−α F)) + (α D+τ(1−α D))−1 θ . L 1+ λ r−µ 1+λ r r−µ r The expressions for the high region are the same as in equation (14), besides a 61

changeintheconstantspinneddownbyboundaryconditions. Thesenewconstants are found using the value matching conditions D (X ) = D (X ) and E (X ) = H n L n H n E (X ). For these equations to hold, the value functions in the non-renegotiation L n regionmustbe C X C D (X)= −( )−γ[ −D (X )] H L n r X r n (cid:20) (cid:21) C X C X = −( )−γ η −η n D,C D,X r X r r−µ n X (1−τ)C X X (1−τ)C E (X)= − −( )−γ[ n − −E (X )] H L n r−µ r X r−µ r n (cid:20) (cid:21) X (1−τ)C X X C = − −( )−γ η n −η , E,X E,C r−µ r X r−µ r n forconstants (cid:32) (cid:33) β τ η =1− (1−α D)+ ( +α D) θ D,C 1+λ 1−τ r β τ η =(1−α F)+ ( +α F) D,X 1+ λ 1−τ r−µ 1−β η =1−τ−θ + (α D+τ(1−α D))θ E,C 1+λ r 1−β η =1− (α F+τ(1−α F)). E,X 1+ λ r−µ Therestoftheresultsfollowanalogously,butwithnewdefinitionsforρ,χ,and Λ,reflectinghowbargainingpoweraffectsthemodificationboundary,lenders’loss frommodification,andthedeadweightcostofmodification,respectively: γ η E,C ρ(λ,θ,β)≡ 1+γ η E,X χ(λ,θ,β)≡η −ρ(λ,θ,β)η D,C D,X Λ(λ,θ,β)≡η −η −ρ(λ,θ,β)(η −η ). D,C E,C D,X E,X Namely D (X;C), LTV(s), ν(X;C), s∗, LTV, and ν(X ) are still as in Equa- H 0 62

tions (4), (6), (7), (8), (9) and (10), respectively, but with the revised definitions above. D.2. EffectsofBargainingPower Now we analyze how adjusting the extent of lenders’ bargaining power affects outcomes in the model. First, it is clear that η and η , are decreasing in β, D,C E,C while η and η are increasing in β. It follows immediately that higher lender D,X E,X bargaining power discourages borrowers from renegotiating—ρ is decreasing in β—and that lenders’ losses from modifications are lower (given a particular ρ). Namely,byshiftingcashflowstolendersintheeventofamodification,lenderbargaining power prevents borrowers from renegotiating loans until they face a larger decline in cash flows. In turn, lenders are more willing to affordably offer higher LTVloans,becauseitislesscostlyforthemwhenborrowersareunderwater. It is also readily apparent that lender bargaining power interacts with modification frictions. β and λ always appear together in these expressions, with β divided by 1+ λ or 1+λ. Therefore, as modification frictions get higher, the effects of r−µ r bargaining power get smaller. Note that ρ(λ,θ,1)=lim ρ(λ,θ,β). Namely, λ→∞ if lenders have full bargaining power, the effect of modification breakdowns on the renegotiationboundarygoesaway. Asborrowersrealizenosurplusfrommodifications,renegotiationsoccuratthepointthataborrowerwouldotherwisedefaultina modelwithoutmodifications(thedefaultthresholdinLeland1994). We explore the quantitative implications of lenders having bargaining power in Figure E.4.53 The top-left panel shows the difference between CMBS and bank LTVsbyleveragedemand(τ)andlenderbargainingpower(β). Whenlendershave no bargaining power (β = 0), CMBS make higher LTV loans to borrowers with higher demand. In this case, modification frictions discourage strategic default and enable higher debt capacity. However, the quantitative analysis shows that even modest amounts of bargaining power can offset this effect. Once lender bargainingpowerdiscouragesstrategicdefault,banksconsistentlymakehigherLTVloans acrossborrowers,asthelowermodificationbreakdownratereducestheriskofneg- 53Allparametersotherthanβ comefromthe3lendercalibrationshowninAppendixTableE.2. 63

ativeequityresultinginforeclosure. The top-right panel displays the probability that a borrower with demand τ chooses a CMBS loan for different values of β. When lenders do not have bargaining power, CMBS are able to take on a high share of loans from high demand borrowers,supportedbythehigherdebtcapacitythatmodificationfrictionsenable. However, as β rises, modification frictions do less to discourage renegotiation, and predominantly just increase the risk of costly foreclosures. As CMBS cease to provide a benefit relative to low-friction lenders, their market share falls to be negligibleathigherβs. Finally,thebottompanelsshowtheaggregateimplicationsofchangingbargainingpowerafteraccountingfortheendogenousselectionoflendersandaggregating over borrowers. The bottom-left panel shows that CMBS only make higher LTV loans overall than balance sheet lenders when β is low. When lenders with low modification frictions have bargaining power, they can reap the benefits of more effective loss mitigation with only minimal concern about strategic renegotiation, thusenablinghigherLTVloans. The bottom-right panel shows that CMBS’ market share falls rapidly as lender bargaining power rises. CMBS’ sole advantage in the model is that modification frictions discourage strategic renegotiation. Once there is another factor restricting earlyrenegotiationforbankloans,theprimarydifferencebetweenlendersbecomes that CMBS are less capable of managing losses for stressed loans, leaving little reasontoborrowfromCMBS. Overall, the quantitative results justify the assumption that borrowers hold the bargaining power. Changing this assumption results in CMBS making lower LTV loans than balance sheet lenders, at odds with the fact that CMBS have the highest LTVs in the data. Moreover, CMBS are unable to compete with low-friction lenders, at odds with the fact that CMBS arrangers voluntarily restrict loan modifications in Pooling and Servicing Agreements, yet borrowers nonetheless choose thissourceofcredit. 64

E. APPENDIXTABLESANDFIGURES etaR ycneuqnileD 5 4 3 2 1 0 CMBS All Commercial Banks CCAR Banks 1 2 3 4 1 2 3 4 1 2 3 4 1 q q q q q q q q q q q q q 8 8 8 8 9 9 9 9 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 Figure E.1: SHARE OF BALANCES THAT ARE 90+ DAYS DELINQUENT OR IN NON-ACCRUAL. Note: Shares are in percentage points. Source: Authors’ calculationsusingTreppCMBSdata,CallReports,andY-14H.2Schedule. 65

Outstanding Modified Bank Loans Outstanding Modified CMBS Loans ecnalaB gnidnatstuO fo erahS 6. 5. 4. 3. 2. 1. 0 Forbearance Payment Change Extension 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q 2:2:3:3:4:4:5:5:6:6:7:7:8:8:9:9:0:0:1: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ecnalaB gnidnatstuO fo erahS 80. 60. 40. 20. 0 Forbearance Hope Note Other Payment Change Extension Other Modification 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 J a n J ul J a n J ul J a n J ul J a n J ul J a n J ul J a n J ul J a n J ul J a n J ul J a n J ul J a n J ul FigureE.2: BANK AND CMBS MODIFICATION TYPES. Note: ShareofoutstandingbalancesthathavereceivedamodificationsinceJanuary2012. Outstandingbalancesarelimitedtoloansthatarecurrentorlessthan120daysdelinquent. A “hope note” is a type of CMBS modification where an underwater loan is split into two pari passu pieces, generally also withanequityinjectionfromtheborrower,wheretheApieceispaidoffasnormal,andtheBpiece(orhopenote)isonly repaidifthepropertyvaluerecovers. Source: Authors’calculationsusingTreppCMBSdataandY-14H.2Schedule. 66

LTV(inpercentagepoints) FullSample Non-recourseloans (1) (2) (3) (4) CMBS 2.397∗∗∗ 1.684∗∗∗ 3.665∗∗∗ 2.923∗∗∗ (0.178) (0.182) (0.196) (0.199) InterestOnly -1.853∗∗∗ -1.959∗∗∗ -2.131∗∗∗ -2.071∗∗∗ (0.185) (0.188) (0.206) (0.209) ln(OriginationAmount) 1.775∗∗∗ 1.960∗∗∗ 0.853∗∗∗ 1.195∗∗∗ (0.0731) (0.0752) (0.0888) (0.0926) InterestRateSpread 2.225∗∗∗ 2.780∗∗∗ (0.113) (0.142) N 45,290 43,103 23,296 22,357 R2 0.16 0.16 0.15 0.17 Orig. YearFEs Y Y Y Y PropertyTypeFEs Y Y Y Y CBSA×StateFEs Y Y Y Y Table E.1: LTV REGRESSIONS. Note: Each column presents a regression predicting at-origination LTV with lender type for the combined sample of bank and CMBS loans. Columns (1) and (2) include all first-lien loans on stabilized propertiesinthesample,withcolumn(2)addingacontrolforloanratespreads. Columns (3) and (4) exclude bank loans with recourse from the sample, with column (4) including the spread control. Source: Authors’ calculations using Trepp CMBS data andY-14H.2Schedule. 67

EstimatedParameters ModelFit Parameter Estimate Moment Target Model DirectlySet µ 0.010 RentGrowth,Anetal. (2016) 1% 1% τ 0.046 MinCMBSLTV 30% 30% τ 0.456 MaxCMBSLTV 75% 75% λ 0.045 λBank =BankDelinquency-to-ModRate .64 .64 Bank r λ 0.544 λCMBS =CMBSDelinquency-to-ModRate 7.76 7.76 CMBS r JointlyEstimated r 0.070 AverageCapRate,CBRE 5.50% 5.50% αF 0.235 30%ForeclosureCost,Brownetal. (2006) 30% 30% σ 0.268 AverageLoanSpread 2.43% 2.43% ε 10.722 Effectof25bpshockonCMBSshare -37.5% -37.5% a 1.042 AverageCMBSLTV 0.64 0.64 b 1.952 DispersioninCMBSLTV 0.08 0.08 θ 0.075 EffectofRecourseonLTV 2.80 2.80 αD 0.421 EffectofRecourseonSpreads -20bp -20bp Table E.2: CALIBRATION RESULTS, THREE-LENDER MODEL. Note: From left toright,thistablepresents(1)thevariabletobecalibrated,(2)thecalibratedvalue, (3) a description of the corresponding target, (4) the targeted moment in the data, and(5)thevalueofthatmomentinthecalibratedmodel. 68

ytisnedk 50. 40. 30. 20. 10. 0 CMBS Bank Life 0 20 40 60 80 100 LTV FigureE.3: LTV DISTRIBUTION. Note: DistributionofLTVsforloanssecuritized in CMBS and held on portfolio by commercial banks or life insurance companies. Sampleislimitedtoloansoriginatedbetween2012and2019onindustrial,lodging, office, or retail properties. Bank loans are limited to first lien loans on stabilized properties. Source: Authors’calculationsusingTreppCMBSdata,NAIC,andY-14 H.2Schedule. 69

0.0 0.2 0.4 0.6 0.8 1.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Leverage Demand () )( rewoP gniniagraB redneL CMBS LTV - Bank LTV (pp) 5 -9 -8 -6 -4 -2 0 2 4 6 0.0 0 -11 -12 -10 -9 -7 -5 -4 -2 -1 0.2 5 -14 -15 -15 -13 -12 -11 -10 -9 -8 0.4 10 -16 -19 -19 -18 -17 -16 -15 -15 -14 0.6 15 -19 -22 -23 -23 -22 -22 -21 -21 -20 20 0.8 -21 -26 -27 -28 -27 -27 -27 -26 -26 25 1.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Leverage Demand () )( rewoP gniniagraB redneL CMBS Market Share (pp) 60 2 5 9 14 21 30 40 50 61 50 1 3 4 7 10 13 17 22 28 40 1 1 2 3 4 6 7 8 10 30 0 1 1 2 2 2 3 3 3 20 0 0 1 1 1 1 1 1 1 10 0 0 0 0 0 1 0 0 0 0.85 0.80 0.75 0.70 0.65 0.60 0.0 0.2 0.4 0.6 0.8 1.0 Lender Bargaining Power () redneL yb VTL 16 Lender Bank 14 CMBS Life 12 10 8 6 4 2 0 0.0 0.2 0.4 0.6 0.8 1.0 Lender Bargaining Power () )%( erahS tekraM SBMC Figure E.4: QUANTITATIVE RESULTS WITH LENDER BARGAINING POWER. Notes: The top-left panel shows the differenceinLTVsbetweenCMBSandbanksforaborrowerwithagivenτ (onthex-axis)whenlendershavebargaining power β (on the y-axis). The top-right panel shows the probability that a borrower with a given τ borrows from CMBS (as opposed to banks or life insurers) when lenders have bargaining power β. The bottom-left panel plots average LTV as a function of β for bank, CMBS, and life insurer portfolios, averaging over the borrowers that select into each lender. The bottom-right panel shows CMBS’ overall market share as a function of β. Parameter values (other than β) are as in AppendixTableE.2. 70