Monetary Policy and Homeownership: Empirical Evidence, Theory, and Policy Implications

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1344 May 2022 Monetary Policy and Homeownership: Empirical Evidence, Theory, and Policy Implications Daniel A. Dias and Joao B. Duarte Please cite this paper as: Dias, Daniel A. and Joao B. Duarte (2022). “Monetary Policy and Homeownership: Empirical Evidence, Theory, and Policy Implications,” International Finance Discussion Papers 1344. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2022.1344. NOTE: International Finance Discussion Papers (IFDPs) 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 International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Monetary Policy and Homeownership: Empirical Evidence, Theory, and Policy Implications ∗ Daniel A. Dias Joa˜o B. Duarte † ‡ May 18, 2022 Abstract Weshowthatmonetarypolicyaffectshomeownershipdecisionsandarguethatthis effect is an important and overlooked channel of monetary policy transmission. We first document that monetary policy shocks are a substantial driver of fluctuations in the U.S. homeownership rate and that monetary policy affects households’ housing tenurechoices. Wethendevelopandcalibrateatwo-agentNewKeynesianmodelthat canreplicatetheestimatedtransmissionofmonetarypolicyshockstohomeownership rates and housing rents. We find that the calibrated model provides an explanation to the “price puzzle” and delivers two important results with policy implications. First, the homeownership decision channel amplifies the redistributive effects of monetary policy, with contractionary shocks benefiting more outright homeowners and disadvantaging more renters and homeowners with a mortgage. Second, a monetary authority that reacts to a price index that includes housing rents generates excess house price,rents,andoutputvolatilityandlargerrealeffects. JELclassificationcodes: E31,E43,R21. Keywords: Monetary policy; Homeownership; Housing rents and housing prices; Inflationdynamics;Housingtenurechoice;“Pricepuzzle”. ∗ThispaperisamajorrevisionofJo˜aoB.Duarte’sjobmarketpaper,DuarteandDias(2015),titled“HousingandMonetaryPolicyintheBusinessCycle: WhatdoHousingRentshavetoSay?”. Theauthorsthank, withoutimplicating, ChrisSims, KurtMitman, GiancarloCorsetti, RandallWright, AdrienAuclert, Harald Uhlig, Stephen Parente, Dan Bernhardt, Minchul Shin, Geoffrey Hewings, Mark Wright, Alejandro Justiniano, Leonardo Melosi, Lawrence Christiano, Marco Bonomo and various participants at various seminar series for helpful suggestions and discussions. This research was supported by the Paul Boltz Fellowship and the UIUC campus research board with an Arnold O. Beckman Research Award. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the BoardofGovernorsoftheFederalReserveSystemorofanyotherpersonassociatedwiththeFederalReserve System. Allerrorsareourown. †BoardofGovernorsoftheFederalReserveSystemandCEMAPRE.Email: daniel.dias@frb.gov. ‡NovaSchoolofBusinessandEconomics. Email: joao.duarte@novasbe.pt. 1

1 Introduction “Likeothers,Ithinktherecentinflationdataaremoderatelyencouraging. Icontinuetoseerisks. Ifyou’re notsatiatedwithrisks,I’lladdonemore,whichisthatifthehousingmarketreallyweakensandpeoplego backtorenting,wecouldgetthesamephenomenonthatwesawlastyear,bywhichrentsaredrivenupand wegetaneffectworkingthroughsheltercosts. SoIagreewiththosewhostillviewtherisktoinflationas beingtiltedtotheupside.” —BenBernanke,MeetingoftheFederalOpenMarketCommitteeonAugust7,2007 Doesmonetarypolicyplayaroleinhomeownershipdecisions? Ifso,doesitmatterfor thetransmissionofmonetarypolicy? Inthispaperweaddressthesetwoquestionsbyempiricallyshowingthatmonetarypolicyaffectshomeownershipdecisionsandbyproviding model-basedevidencethatthisisanimportantchanneloftransmissionofmonetarypolicy. Wefirstshowthatmonetarypolicyshocksareanimportantdriveroffluctuationsinthe homeownership rate and that monetary policy affects households’ homeownership decisions. Next, we develop a two-agent New Keynesian model with a segmented housing market in which households choose to rent or buy that matches the empirical evidence. Using a calibrated version of this model, we additionally show that the homeownership decisionchannelsubstantiallyaffectsthetransmissionofmonetaryshockstohouseprices, rents, and output and that the transmission of monetary policy through this channel amplifiestheredistributiveeffectsofmonetarypolicy.1 Tomeasuretherelativeimportanceofmonetarypolicyshocksforhomeownershipfluctuations,weuseaggregateU.S.dataandestimateaproxystructuralvectorautoregression (SVAR) and a structural vector moving average (SVMA) identifying the monetary policy shocks with the high-frequency external instruments proposed by Jarocin´ski and Karadi (2020)andMiranda-AgrippinoandRicco(2021).2 WiththeSVARweanalyzethedynamics effectsofmonetarypolicyshocksonthevariablesincludedinthemodelandalsoestimate the importance of such shocks for variation of the variable. As in previous work, Dias and Duarte (2019), we find that in response to a contractionary monetary policy shock the homeownershipratefallsandhousingrentsincreasewhilehousepricesdecrease.3 Inaddi- 1Throughoutthepaperweusetheterms“homeownershipdecisionchannel”,“homeownershipchannel”, and “housing tenure choice channel” interchangeably, and in all cases we are referring to the additional effectsofmonetarypolicythatoccurfromhouseholdschoicebetweenrentingorowningthehometheylive inresponsetounexpectedchangesinmonetarypolicy. 2Bothinstrumentsseparatetheeffectoninterestratesthatisduetopuremonetarypolicysurprisesfrom theeffectoninterestratesthatisduetonewinformationabouttheFedsviewoftheeconomy. 3Inpreviousresearch,DiasandDuarte(2019),weshowedthatthehomeownershipratefallsandhousing rents increase after a contractionary monetary policy shock, in this paper we expanded on our previous resultsbyshowingthattheyarerobusttousingamorerefinedmonetarypolicyinstrumentandbyproviding an estimate of the importance of monetary policy shocks for fluctuations in the aggregate homeownership 2

tiontotheSVARmodel,wealsoestimateanSVMAmodelbecauseitallowsustoestimate an upper and a lower bound for the relative importance of the monetary policy shock for homeownership rate dynamics without assuming invertibility of the model, as shown by Plagborg-Møller and Wolf (2021a). Using this methodology, we find that monetary policy shocks are an important driver of fluctuations in the aggregate rate of homeownership in theUnitedStates,accountingforasmuchas34%ofthelong-runvariationofthisvariable. We then resort to the American Housing Survey (AHS) microdata to provide empirical evidencethatmonetarypolicyaffectshomeownershipdecisionsatthehouseholdleveland thatitaffectshousingsupplyforrentalandownership. Atthehouseholdandhousingunit levels, we estimate simple logit models in which the dependent variable measures transition from renting to owning or from owning to renting. We find that in response to a 25 basispointscontractionarypolicyshock,therateoftransitionfromrentingtohomeownershipfallsbyabout15%andtherateoftransitionfromhomeownershiptorentingincreases by 2.1%. At the same time, in response to the same contractionary monetary policy shock, the rate of transition of housing units from rental to ownership declines by 1% and rate of transition of housing units from ownership to rental increases by 3.4%. When looking at the two sides of the housing market, the relative demand for and the relative supply of rental units, we find that the response of the relative supply of rental units to a monetary policyshockisinsufficienttomeetthechangeintherelativedemandforrentalunitstothe samemonetarypolicyshock. To account for our empirical findings, we propose a standard two-agent New Keynesian model extended with a homeownership decision margin and adjustment costs on the relativesupplyofhousingforrentingvis-a-visowning. Thesetwoadditionalfeaturesofthe proposedmodelgeneratethekeymechanismbehindthechannelofmonetarypolicytransmissionthatoperatesthroughhomeownershipdecisions. Thismechanismisasfollows. A positive interest rate surprise increases the cost of borrowing to finance a house purchase. Ahigher cost forpurchasinga houseincentivizesthemarginalborrower torentinsteadof owning. From a housing demand perspective, as more borrowers switch to renting, the aggregate demand for renting rises driven through this extensive margin adjustment. At the same time, from a housing supply perspective, landlords observing higher rents respond by investing in housing stock for renting. However, because of adjustment costs, the supply of rental housing responds less than proportionally to the increase in demand for renting. As a consequence, housing rents may increase in equilibrium. One feature of this model is that it can generate a temporary increase in measures of inflation like the consumer price index (CPI) or personal consumption expenditures (PCE) price index folrate. 3

lowing a contractionary monetary policy shock, a result that is known in the literature as the “price puzzle” (Sims (1992)). This temporary increase of the CPI or PCE occurs when the increase in rents due to a contractionary monetary shock is large enough to offset the declineinthepriceoftheothergoodsandservicesincludedinthesemeasuresofinflation. We calibrate the model to match a set of data moments related to long-run dynamics. Wethenevaluatethemodelbycomparingitsimpulseresponsefunctionstotheuntargeted empirical counterpart obtained from the proxy SVAR and find that the calibrated model matches well the empirical results concerning the monetary transmission to the selected variables. Weadditionallyshowthatforthemodeltomatchtheempiricalfindingsitmust both have a housing tenure choice margin and a segmented housing market. Without one ofthesetwofeatures,theresponseofhousingrentswouldbetheoppositeofwhatwefind inthedata. The calibrated model is then used to show that the new homeownership channel of monetary policy transmission we uncover in this paper has important implications for monetary policy. We find that monetary policy shocks generate redistribution between homeowners with a mortgage and renters by affecting the price-to-rent ratio. We also find that borrowers (homeowners with a mortgage and renters) are worse-off when facing contractionary monetary policy shocks relative to savers (outright homeowners and landlords). The reason is that borrowers face increased costs to finance a house purchase andhigherrents,andsavers,byowningthehousingstockforrenting,benefitfromhigher house rents revenue. The existence of redistributive effects between savers and borrowers frommonetarypolicyiswellknown,butweshowinthepaperthattheseeffectsareamplifiedbythehomeownershipchannelofmonetarypolicy. Assuch,amonetaryauthoritythat wishestobalanceitsgoalsofpricestabilityandmaximumemploymentwithsocialwelfare shouldtaketheresultsinthispaperinconsiderationwhensettingmonetarypolicy. Moreover, we find that the homeownership channel of transmission of monetary policyhasimplicationsforhowcentralbanksrespondtomeasuredinflation. Namely,wefind thatamonetaryauthoritythatreactstopriceindexesthatincludehousingrents,suchasthe consumerpriceindex(CPI)orthepersonalconsumptionexpendituresindex(PCE),generates more house price, rents, and output volatility and larger real effects than a monetary authoritythattargetsameasureofinflationwithouthousingcosts. Becausetheresponseof housingrentstomonetarypolicyshocksgoesintheoppositedirectionofallothernominal final goods prices, the CPI (or the PCE) falls less than actual inflation. By using the CPI (orthePCE)asameasureofinflation,theinterestrateadjustmenttowardsthesteadystate is slower than otherwise would need to be if the monetary authority were responding to measures of inflation that exclude rents/shelter. This happens because the monetary au- 4

thorityneedstobemoreaggressivetopushdowntheapparentlymorepersistentinflation whenmeasuredbytheCPI.Hence,targetingtheCPIleadstohighervolatilityintheeconomyandlargeroutputlossesthanwhenthemonetaryauthoritytargetsinflationmeasures thatexcludehousingcosts. The rest of the paper is organized as follows: in section 2 we discuss our results in light of existing literature and how we contribute to it; in section 3 we provide empirical evidence on the effect of monetary policy on the level of aggregate homeownership and on the effect of monetary policy on the decision to own or rent; in section 4 we present a model that can account for the main empirical patterns shown in section 3; in section 5 we describe the calibration of the model and compare the results obtained with the model with the empirical results obtained in 3; in section 6 we present the results on interest rate transmission, on the redistributive implications, and the consequences for monetary policy;insection7weprovidesomeconcludingremarks. 2 Related Literature and Contribution The paper contributes to three large strands of the literature: the literature on monetarypolicytransmission,theliteratureonhousingandmacroeconomics,andtheliterature on the determinants of housing tenure choices. We contribute to the literature on monetary policy transmission by introducing and studying a new channel of monetary policy - the homeownership decision channel of monetary policy.4 The literature on channels of transmission of monetary policy is extensive and very dynamic, with new channels being frequently identified. As summarized in Mishkin (1996), the more traditional channels of monetary policy include the interest rate channel, the exchange rate channel, the equity price channel, and the credit channel. More recently, however, new channels have been identified. Examples of these more novel channels of monetary policy are the risk-taking channel (examples of papers discussing this channel include Jime´nez et al. (2014), Bruno andShin(2015),andMoraisetal.(2019)),thedepositschannel(Drechsleretal.(2017)),and thefloatingratechannel(examplesofpapersdiscussingthischannelincludeGarrigaetal. (2017),Ippolitoetal.(2018)). There has also been recent work linking monetary policy transmission to features of the housing market, and our paper is mainly related to this area of the literature. For instance, using the Euro Area area as a lab, Corsetti et al. (2021) shows that the strength of monetarytransmissionstronglycorrelateswiththecountry’shomeownershiprateandthe 4AsinBernankeandGertler(1995),wethinkofatransmissionchannelofmonetarypolicyasbeingaset offactorsandinstitutionalfeaturesoftheeconomythatamplifyandpropagateconventionalinterestrateeffects. 5

fraction of adjustable rate mortgage contracts. Using U.S. data, Beraja et al. (2019) and Eichenbaum et al. (2022) note that the effect of monetary policy in the economy through the refinancing of mortgages, which usually results in mortgage payment savings for borrowers, depends on the distribution of savings in the economy and how much people can save in total by refinancing. The results in these two papers imply that monetary policy ispath-dependent,meaningthattheeffectoftoday’smonetarypolicyshocksmaydepend on the history of these shocks. Another implication of these two papers is that the effect of monetary policy through the mortgage refinancing channel is heterogeneous and timevarying, with the potential gains from refinancing varying across agents and over time. Hedlund et al. (2017) model the joint distribution of housing and mortgage debt in the context of a heterogeneous New Keynesian model to study how monetary policy shocks transmit through the housing market. Their main results are that housing prices are relevantforaggregateconsumptiondynamics. Monetarypolicyhasasymmetriceffectsoneconomic activity, with responses to contractionary shocks being stronger than expansionary monetarypolicyshocks,andthatmonetarypolicyismoreeffectiveinahigh-loan-to-value environment. Inamoreempiricalcontribution,Cloyneetal.(2019)showsthatmonetarypolicytransmission at the household level depends on the housing tenure status of the household, with the critical difference coming from the effects on consumption of outright homeowners (those without any mortgage) and of homeowners with a mortgage or renters. We contribute to this literature by showing that monetary policy affects households’ tenure choice decisions and that frictions in housing supply for ownership and renting affect the relative price of houses and rents. We show that when monetary policy loosens (tightens), more (less) households move from renting to owning and that fewer (more) households movefromowningtorenting. Thisresultisconsistentwiththeaggregatehomeownership rateincreasing(decreasing)afteranexpansionary(contractionary)monetarypolicyshock, as shown in previous work (Dias and Duarte (2019)) and confirmed again in the current paper. One consequence of these effects on house prices and rents is that shelter-related expenses, either mortgage payments or rents, change for some households, affecting the income available for consumption of non-shelter goods or services. One noteworthy difference in our work relative to that of Cloyne et al. (2019) is that we that find housing rents increase in response to a contractionary monetary policy shock, while they find that housing rents fall. A possible explanation for this different finding most probably stems from the different datasets used. While they use microdata at the household level, we use aggregate data. This paper focuses on aggregate housing rents because they constitute a significantcomponentofCPI,thusaffectinginflationdynamics. 6

We also contribute to the literature on housing and macroeconomics by proposing a modelthatallowsstudyingtheimplicationsofchangesintheaggregatelevelofhomeownership for business cycle dynamics. The literature on housing and macroeconomics is also extensive,coveringmanyaspectsofhowhousinginteractswiththeoverallmacroeconomy. AnexcellentsummaryofthisliteratureisthatofPiazzesiandSchneider(2016). Withinthis literature, our paper is closest to Iacoviello (2005) and Iacoviello and Neri (2010), but with akeydifferenceinhowthesupplyofhousingforrentingandforownershipismodeled. In termsofthemodelingchoiceswemake,ourapproachissimilartocontemporaryandseparate work by Greenwald (2018).5 While Greenwald (2018) focuses on how the structure ofthemortgagemarketinfluencesthepropagationofmacroeconomicshocks,whereaswe are primarily interested in how monetary policy propagates through its effects on housing tenure decisions. Unlike most of the literature on housing and macroeconomics, in our paper we consider a segmented housing market where transaction costs and nominal rigidities prevent the supply of housing for rental and ownership from quickly adjusting tochangesindemand.6 Withasegmentedhousingmarket,thepriceofhousesintheshort run can be different from the discounted value of rents, which means that there may be fluctuationsinthehouseprice-to-rentratio. Inadditiontothemodelingcontribution,wealsocontributetotheliteratureonhousing and macroeconomics by providing estimates of the importance of monetary policy shocks for fluctuations in the homeownership rate. Using the methodology of Plagborg-Møller and Wolf (2021a), we estimate that monetary policy shocks can account for as much as 34%ofthelong-runvariationinthehomeownershiprate. Toputthisvalueinperspective, Plagborg-Møller and Wolf (2021a) estimate that monetary policy shocks account for close to 0% of the variation in consumer price growth. Our application estimates that monetary policy shocks can account for at most 30% of the variation of consumer price growth, but thisresultdependsonthemonetarypolicyinstrumentused. UsingtheMiranda-Agrippino and Ricco (2021) instrument, we find much lower importance of monetary policy shocks for consumer price growth variation, which is more in line with the results in Plagborg- Møller and Wolf (2021a). As such, our results show that monetary policy is likely to be at 5Togenerateadistributionofhomeownersandrenters,wealsoembedthehouseholdheterogeneityina singlefamilyusingtheassumptionofmarketcompletenesswithinthefamily. Thissimplifyingassumption wasfirstsuggestedbyRagot(2018). 6One paper that also allows for a segmented housing is Sommer et al. (2013). In this paper, the authors carefully model the U.S. housing market to study the effects of fundamentals on house prices and rents. Sommer et al. (2013)’ model is richer than ours, but this higher richness comes at the cost of not being as tractable as ours and therefore either impossible or very difficult to use for the analysis of business cycle dynamics. Another paper that shows how segmented housing markets affect housing price dynamics is GreenwaldandGuren(2021). 7

leastasimportantforfluctuationsintheaggregatehomeownershiprateasitisfortherate ofinflation. Wealsocontributetotheliteratureonthedeterminantsofhousingtenurearrangements byprovidingevidencethatmonetarypolicyisonedriverofthechoicebetweenowningor rentingahome. Thisliteraturefocusestypicallyonstructuralfactorssuchastaxregimesor life-cyclemotivesasforcesdrivingthechoicebetweenowningorrenting-seeforexample Henderson and Ioannides (1983) or Weiss (1978). We contribute to this literature by providing a factor that can explain fluctuations in the timing of housing tenure decisions (for example, why specific cohorts of the population transitioned from renting to ownership earlier/later than other cohorts) but also provides a source of fluctuations in rents, which, as shown in Sinai and Souleles (2005), can be an essential factor for households choosing toowninsteadofrenting. Finally, the model we propose provides an explanation for the “price puzzle” (Sims (1992))throughtheeffectofmonetarypolicyonhousingrents. Namely,withrentsmoving in the same direction of interest rates, and because the shelter component of the consumer price index (or personal consumption expenditures index) is almost entirely based on the price of rents (directly through the cost of rental housing or indirectly through the way rents from the rental market are used to calculate the owner’s equivalent rent), it is possible to see in the short run a rise (decline) in consumer prices when interest rates rise (decline). As such, for some parameterizations of the model, the rise in housing rents followingacontractionarymonetarypolicyshockcanbesufficientlyhightooffsetthedecline inthepricesofothergoodsorservices. Insuchacase,theaggregateconsumerpriceindex (not inflation as defined in the model) may rise in response to a contractionary monetary policyshock(i.e.,the“pricepuzzle”). 3 Empirical Evidence of the Effect of Monetary Policy on the Aggregate Homeownership Rate and on Housing Tenure Decisions Inthissection,weuseU.S.aggregate-,household-,andhousing-unit-leveldatatostudy theeffectsofmonetarypolicyonthehomeownershiprateandonhouseholds’andhousing unitowners’housingtenurechoicedecisions. 8

3.1 Monetary Policy and the Homeownership Rate - Evidence from Aggregate U.S. data WeuseU.S.aggregatedatatoanalyzehowmonetarypolicyaffectstheaggregatehomeownership rate in the U.S. economy and how important it is for this variable and also to study the dynamic effects of monetary policy shocks on several macroeconomic variables. This analysis takes the results in Dias and Duarte (2019) as the starting point and expands on them. We first introduce the relevant methodologies and then present and discuss the results. 3.1.1 Methodology To identify the effects of monetary policy on the variables of interest, we use a proxy SVARmodelandanSVMAmodelwithinstrumentalvariables. Thispartfirstdiscussesthe monetarypolicyinstrumentweuseandthenpresentsthetwoeconometricmethodologies used. Instruments. To identify the effect of monetary policy on key variables of interest, we use two high-frequency monetary policy instruments. The first one is the instrument developed by Jarocin´ski and Karadi (2020) and the second one is the instrument constructed byMiranda-AgrippinoandRicco(2021). Unlike previous high-frequency monetary policy instruments, both of these instruments separate the effect on interest rates due to pure monetary policy surprises from the effectoninterestratesthatisduetonewinformationabouttheFed’sviewoftheeconomy. To separate the monetary news from economic outlook news embedded in the Fed’s communications, Jarocin´ski and Karadi (2020) simultaneously look at high-frequency movements in interest rates and equity prices during a narrow window of time (10 minutes before and 20 minutes after the communication) around the Fed’s policy announcement. These authors’ idea is that news about monetary policy and news about the state of the economy have distinct effects on interest rates and equity prices. While a pure monetary shockhasanegativecorrelationwithequityprices–whenmonetarypolicyloosens,ceteris paribus, equity prices rise, and vice-versa –, information about the economy shock makes interest rates and equity prices move in the same direction – when interest rates fall because the Fed perceives a negative economic outlook, equity prices are also expected to decline because equity prices are supposed to reflect future profits which correlate positivelywiththeperformanceoftheeconomy,andviceversa. Withasimilarobjectivetothat of Jarocin´ski and Karadi (2020), but using a different approach, the instrument proposed 9

byMiranda-AgrippinoandRicco(2021)insteadisolatesthepuremonetarysurprisesfrom theinformationchannelbyprojectingmarket-basedmonetarysurprisesaroundpolicyannouncementsontheirlagsandonthecentralbanks’informationsetformedbytheGreenbookforecasts. These two monetary policy instruments are widely used in the macroeconomics literature, and, therefore, we do not expand much on the details of the two instruments’ construction. ThereaderinterestedinthedetailsunderlyingtheconstructionandjustificationforthevalidityoftheseinstrumentscanfindthisinformationinJarocin´skiandKaradi (2020) and in Miranda-Agrippino and Ricco (2021). However, it is helpful to formally definetheexternalinstruments,asthedefinitionwillbeusefulfordiscussingtheeconometric methodologiesused. For a variable Z to be a valid instrument, it must simultaneously meet the relevance t andexogeneityconditions: 1. Relevance: E[(cid:15) Z ] = 0 i,t t (cid:54) 2. Exogeneity: E[(cid:15) Z ] = 0 i = j j,t t ∀ (cid:54) Additionally, it is also useful to express the instrument as a (linear) function of the structuralshockandmeasurementerror,asdoneinPlagborg-MøllerandWolf(2021a): Z = α(cid:15) +σ ν (1) t i,t v t Withα = 0,σ 0,andν awhitenoiserandomvariable. Theexpressioninequation1will v t (cid:54) ≥ be particular relevant for the discussion of the forecast variance decomposition methodology. Proxy SVAR Model. We use a proxy SVAR model to study the dynamic effects of a monetary policy shock on the variables of interest. An SVAR model for Y , an n 1 vector t × ofobservabletimeseriesvariables,withplagscanbewrittenas: Y = A +A Y +A Y +...+A Y +Hε . (2) t 0 1 t−1 2 t−2 p t−p t This expression can be re-written in a more succinct way by using the lag-operator notation: A(L)Y = Hε , (3) t t In equation 3, A(L) = I (cid:80)p A (Ll) and each matrix A (Ll), for l 1, is an n n n − l=0 l l ≥ × matrixofcoefficientsassociatedwithlagl,H isann nmatrixofimpactcoefficients,and × 10

ε is a vector of n structural shocks. This equation characterizes all the dynamics of the t variables in the model. As usual, the structural shocks are assumed to have a linear effect onthevariablesincludedinthemodelandtobeuncorrelatedatallleadsandlags. Our goal is to separate the effects of monetary policy shocks on the variables Y in the t model while controlling for any possible policy/feedback rule and other co-movements in the data. The elements in matrix H are the contemporaneous effect of a change in the structural shock associated with that matrix element. For example, column j of matrix H correspondstothecontemporaneouseffectofstructuralshockj oneachvariableincluded in the vector Y . For ease of notation, as in Stock and Watson (2012), we assume that the t monetarypolicyshockcorrespondstothefirstcolumnofH,andwedenoteitasH . 1 Given the definitions above, we can re-write the model in its structural vector moving averageformulation: Y = A(L)−1Hε (4) t t Following equation 4, the impulse response function (IRF) of Y to a monetary policy t shockisgivenby Y = A(L)−1H (5) t 1 All the parameters in A(L) can be obtained by estimating equation 2 by ordinary least squares (OLS). Note that matrix H is not directly estimable by OLS, and with OLS, we can only estimate the reduced form innovations η = Hε . To identify the monetary policy t t shocks that are included in η , we use the external instrument based on high-frequency t identification of shocks approach as in Gertler and Karadi (2015) (with the obvious difference that we use the more refined monetary policy instruments of Jarocin´ski and Karadi (2020)andMiranda-AgrippinoandRicco(2021)),whichcombinestheexternalinstrument approach to identification of structural shocks as in Stock and Watson (2012) and Mertens and Ravn (2013) with high frequency event studies around monetary policy announcements as in Kuttner (2001), Gurkaynak et al. (2005), Hamilton (2008), and Campbell et al. (2012). This approach will provide us with an estimate of the parameters in H , which we 1 thenusetoidentifythemonetarypolicyshocksandthecorrespondingIRFsofallthevariables in Y to a monetary policy shock. All the details on the exact procedure can be found t inGertlerandKaradi(2015). Dynamic Variance Decomposition Using SVMA Models with Instrumental Variables. To understand the relative importance of different structural shocks for the dynamics of a variable of interest, we could have just used the same proxy SVAR model that we just 11

discussed to compute the forecast error variance decomposition. However, as argued in Plagborg-Møller and Wolf (2021a), the results based on this approach would be highly dependent on certain assumptions, such as invertibility of the model. The forecast variance decomposition methodology proposed by Plagborg-Møller and Wolf (2021a) allows ustoestimateboundsfortheimportanceofmonetarypolicyshocksonvariablesofinterest withouthavingtomakemanyassumptionsontheunderlyingeconomicmodel. Plagborg-Møller and Wolf (2021a)’s approach to measure the relative importance of a structural shock for the dynamics of a particular macroeconomic variable is intuitively simple but difficult to present in a concise manner. Therefore, we only present the main ideas behind the method and refer the reader to the original paper for a more detailed expositionofthemethodologyanditsimplementation. As a starting point, and for simplicity of exposition, following the exposure of the methodology in Plagborg-Møller and Wolf (2021a), we follow Plagborg-Møller and Wolf (2021a) and assume that SVMA representation of equation 4 has no dynamics and expand itbyseparatingthestructuralshock(cid:15) fromtheotherstructuralshocks. 1,t (cid:88) n(cid:15) Y = Θ ε + Θ ε (6) t ·,1,0 1,t ·,j,0 j,t j=2 Basedontheexpressionin6,theforecastvarianceratiocanbewrittenas: Var[Y (cid:15) ] Θ2 i,t 1,t i,1,0 FVR = 1 | = (7) i,0 − Var[Y ] Var[Y ] i,t i,t TheexpressionforFVR canbere-writtenasafunctionoftheinstrumentZ (defined i,0, t inequation1): 1 Cov[Y ,Z ]2 i,t t FVR = (8) i,0 α2 Var[Y ] i,t While equation 8 provides an exact expression for the forecast variance ratio based on the observed instrument, because the estimation of α is infeasible, it is impossible to provideapointestimateoftheforecastvarianceratio. Plagborg-MøllerandWolf(2021a)’skey contribution is to show that, under the assumption that a valid instrument for the shock of interest exists and that it is possible to express the variables Y as in 6, it is possible to t constructinformativeboundsonthetrueforecastvarianceratio. To arrive at the lower bound for the true forecast error variance ratio, Plagborg-Møller andWolf(2021a)notethatα2 Var(Z ) = α2+σ2. Thisinequalityimpliesthatthequality ≤ t v of the instrument, measured by the signal-to-noise ratio α2 , will determine how tight or σ2 v wide the lower bound for the true forecast variance ratio is. It is easy to see that α−2 ≥ 12

(Var(Z ) = α2 +σ2)−1, and if σ = 0 (case of a perfect instrument) , then this lower bound t v v exactlyestimatesα,whereasifσ isverylarge,thesignal-to-noiseratiobecomesverysmall v pushingthelowerboundofforecastvarianceratiotowardszero. To derive the upper bound for the true forecast error variance ratio, Plagborg-Møller andWolf(2021a)makethepointthat,themostthatthevariablesincludedinY canexplain t ofZ (inthesenseofalinearprojection)isboundedabovebywhatthestructuralshock(cid:15) t 1,t can explain of the instrument Z (this is a theoretical upper bound as the structural shock t is not observed). That is, the explained sum of squares of a linear projection of (cid:15) on Z 1,t t is exactly α2, and, any linear projection of Y on (cid:15) will be at most as high as α2. More t 1,t formally, this means that Var E[Z Y ] α2, and, consequently, α−2 Var E[Z Y ] −1. t t t t { | } ≤ ≤ { | } Whenthemodelisinvertible,thatis,whenthevariablesinY perfectlyspanthestructural t shocks,thentheinequalitybindsandα−2 = Var E[Z Y ] −1. t t { | } Plagborg-Møller and Wolf (2021a) expand on these insights to derive upper and lower bounds for a more general case, which allows for rich dynamics of the variables. In the empirical application, we use the more general formulation of the interval estimation for theforecastvarianceratios(andthecorrespondingconfidenceintervals). 3.1.2 ResultsandDiscussion Havingpresentedthemostrelevantaspectsofthemethodologiesweuse,wenowturn to the results. In Figure 1, we show the estimated impulse response functions of the variables included in the VAR model – the federal funds rate, house rents, excess bond premium, the homeownership rate, house prices, consumer prices measured by the CPI, and GDP – to a 25 bps contractionary monetary policy shock. The federal funds rate, the excess bond premium, and the homeownership rate are expressed in levels, while the CPI, GDP, house prices, and house rents are expressed in log differences. For the variables expressedinlevels,theresultsinFigure1arethenon-cumulativeimpulseresponsefunctions, whereas for the variables expressed in log-differences, the results in the same Figure correspond to the cumulative impulse response functions. The results in this Figure are not new as we had obtained very similar results in previous work (Dias and Duarte (2019)). However, it is reassuring to see that the results are robust to using new monetary policy instruments – those proposed by Jarocin´ski and Karadi (2020) and by Miranda-Agrippino and Ricco (2021) – that account for the information about the economy contained in monetary policy announcements relative to results based the instrument of Gertler and Karadi (2015) (which does not separate the pure monetary policy channel from the information channel of monetary policy). It is also reassuring to see that, as shown in Figure 1 the two 13

monetary policy instruments yield qualitatively and quantitatively similar results.7 Because the focus of the paper is on the effects of monetary policy on homeownership and housingtenurechoices,andtheresultsfortheothervariablesarestandardintheliterature, we focus the discussion of the results that pertain to the effect of monetary policy on the homeownership rate, house rents, and house prices. As we had found in previous work, when the Fed unexpectedly tightens monetary policy, the homeownership rate declines and stays persistently lower for several years. At the same time, housing rents initially increasebeforeadjustingdownaftersomeyears. Asforhouseprices,asshownpreviously, these decline after the monetary authority tightens its monetary policy. Altogether, we interpret these three results as evidence that monetary policy affects housing tenure choice decisions by affecting the relative cost of ownership relative to renting – in the following subsection, we use household- and housing unit-level data to test this hypothesis more formally. For the other variables included in the model – the federal funds rate, the excess bond premium, GDP growth, and the growth rate of the consumer price index – our results are in line with those in the literature. In the case of the growth rate of the consumer priceindex,albeitwithalowermagnitudeinthecaseoftheMiranda-AgrippinoandRicco (2021) instrument, the estimated impulse response functions show an initial increase in prices in response to a monetary policy shock (i.e., “price puzzle”). However, we are not too concerned with this result because, as discussed in Ramey (2016), small differences in the sample and identification can give rise to differences in the initial response of the consumerpriceindextomonetarypolicyshocks. While Figure 1 shows that the homeownership rate, house prices, and housing rents respond strongly to monetary policy shocks, it is also important to know how much monetary policy shocks contribute to the variation in these variables. To answer this question, we use the dynamic variance decomposition methodology of Plagborg-Møller and Wolf (2021a)thatwesummarizedearlier. TheresultsofthisdecompositionareshowninFigure 2.8 We estimate that monetary policy shocks are an important driver of fluctuations in housepricesandrents. Intheshort-run(inthefirst1.5yearsaftertheshock),monetarypol- 7InAppendixCweshowresultsbasedonlocalprojectionsusingaproxyVARmodeltoidentifythestructural shocks. As expected, given the results of Plagborg-Møller and Wolf (2021b), showing the asymptotic equivalence between LP regressions and VAR models, the two methodologies yield very similar quantitativeandqualitativeresults. Also,asobservedwiththeVARmethodology,theresultsdonotdependonthe instrumentused. 8InAppendixCweshowtheforecasterrorvariancedecompositionresultsbasedontheproxyVARmodel that we used to obtain the impulse response functions shown in Figure 1. Overall, the two methodologies yieldsimilarresults. 14

Figure1: ImpulseResponseFunctionsofSelectMacroeconomicVariablestoa25bpsMonetary PolicyShock 0.6 0.4 0.2 0.0 0.2 − 0 4 8 12 16 20 noitaived% FederalFundsRate Houserent 0.50 0.35 0.20 0.05 0.10 − 0 4 8 12 16 20 0.10 0.05 0.00 0.05 − 0.10 − 0 4 8 12 16 20 noitaived% ExcessBondPremium Homeownershiprate 0.10 0.05 0.00 0.05 − 0.10 − 0 4 8 12 16 20 0.300 0.425 − 1.150 − 1.875 − 2.600 − 0 4 8 12 16 20 noitaived% Houseprice CPI 0.400 0.275 0.150 0.025 0.100 − 0 4 8 12 16 20 Horizon(quarter) 0.200 0.075 − 0.350 − 0.625 − 0.900 − 0 4 8 12 16 20 Horizon(quarter) noitaived% GDP MR JK Note: The Figure shows the estimated impulse responses of the different variables included in the analysis to a 25 bps contractionary monetary policy shock. The results in the Figure are based on the proxy- SVAR methodology described in section 3, using the two alternative monetary policy instruments, that of Miranda-AgrippinoandRicco(2021)(inred)andthatofJarocin´skiandKaradi(2020)(inblue),whichwere alsodescribedinthesamesection. Bothinstrumentsisolatethepuremonetarysurprisesfromtheinformation content present in the Fed’s communications. The solid lines are the impulse-response function point estimates,whiletheshadedareasarethe68%confidenceintervals. Theconfidenceintervalswerecomputed from1,000drawsusingaparametricbootstrapasproposedinStockandWatson(2018). icy shocks can explain up to 40 percent of variations in rents, whereas in the medium-run (after 1.5 years), monetary policy shocks can explain as much as 43 percent of fluctuations in house prices. As for the homeownership rate, we estimate that monetary policy shocks can account for as much as 34 percent. This result is significant because the homeown- 15

Figure 2: Contribution of U.S. Monetary Policy Shocks to the Dynamic Variance of Select MacroeconomicVariables FVRofFederalFundsRate FVRofHouseRentGrowth 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 0 4 8 12 16 20 0 4 8 12 16 20 FVRofExcessBondPremium FVRofHomeownershipRateChanges 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 0 4 8 12 16 20 0 4 8 12 16 20 FVRofHousePriceGrowth FVRofCPIGrowth 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 0 4 8 12 16 20 0 4 8 12 16 20 Horizon(quarter) FVRofGDPGrowth 1.0 0.8 MR JK 0.6 0.4 0.2 0.0 0 4 8 12 16 20 Horizon(quarter) Note: the Figure shows the forecast variance ratio of the different variables included in the analysis to a U.S.monetarypolicyshockbasedonthedynamicvariancedecompositionmethodologyofPlagborg-Møller and Wolf (2021a). The results are based in two alternative monetary policy instruments, that of Miranda- Agrippino and Ricco (2021) (in red) and that of Jarocin´ski and Karadi (2020) (in blue). Both instruments isolatethepuremonetarysurprisesfromtheinformationcontentpresentintheFed’scommunications. The solid lines report the point estimates and the dashed lines the 90% confidence intervals for the identified sets of forecast variance across different variables and forecast horizons. The confidence intervals were computedfrom1,000drawsusingabootstrapprocedureasproposedinKilianandLu¨tkepohl(2017). 16

ership rate tends to be a relatively slow-moving variable which is, as our results suggest, highlyinfluencedbymonetarypolicyshocks. The results for the excess bond premium are the same as those found by Plagborg- MøllerandWolf(2021a). ForGDP,weestimatethatmonetarypolicyshockscanberesponsible for as much as 39 percent of the fluctuations in the rate of GDP growth - Plagborg- Møller and Wolf (2021a) obtained a similar result for industrial production. Unlike what Plagborg-Møller and Wolf (2021a) found for the rate of growth of the CPI when using the Jarocin´ski and Karadi (2020) monetary policy shocks instrument, we estimate that monetarypolicyshockscanaccountforashighas34percentoffluctuationintherateofgrowth of the CPI. However, when using the Miranda-Agrippino and Ricco (2021) monetary policyshockinstrument,weestimatethatmonetarypolicyaccountsforlessthan15percentof fluctuations in the rate of growth of the CPI, a result that is much more similar to the findingsofPlagborg-MøllerandWolf(2021a). Thefedfundsrateisanothervariableforwhich we found substantial differences in results depending on the monetary policy instrument used. In particular, while based on the Jarocin´ski and Karadi (2020) instrument, monetary policyshockscanexplaincloseto80percentofthefedfundsratevariationintheshortrun, basedontheMiranda-AgrippinoandRicco(2021)instrument,monetarypolicyshocksare at most responsible for 40 percent of the variation in the fed funds rate in the short run. While understanding what may be driving these differences in the results is important, it is beyond the scope of our paper, and therefore we leave it for future research. At the same time, the most important results for this paper, namely those concerning the homeownership rate, housing rents, and house prices, the two instruments yield very similar results. 3.2 Monetary Policy and Housing Tenure Choice Decisions - Evidence from Household- and Housing Unit-Level Data 3.2.1 Data We use the national American Housing Survey (AHS) data to test whether monetary policyaffectshousingtenuredecisions. ThissurveyisconductedbytheU.S.Censusevery two years (in odd-numbered years) between May and September. The survey follows a sampleofhousingunitsandcollectsinformationoncharacteristicsofthehousingunitand thepeople(orhousehold)livinginthathousingunit(inthecasethatthehousingunitisnot vacant). Onekeycharacteristicofthehousingunitisitstenurestatus. Thatis,whetherthat houseisownedbythepersonlivinginitorwhetheritisarental. Wealsoknowwhethera specifichouseholdisrentingorisahomeownerwiththisinformation. 17

At the household level, we have information about the current tenure status through the information regarding tenure status of the housing unit. And, because the survey asks the household about its housing tenure status 12 months prior, we are also able to know whether a household switched tenure status in the last year. Unlike for housing units, the surveydoesnotfollowhouseholdsovertime. The AHS data are available at a biennial frequency from 1973 to 2019. However, in our empirical exercises we only use 1991 to 2015. We restrict the sample to start in 1991 and endin2015becausethemonetarypolicyinstrumentweuse,thehigh-frequencymonetary instrument constructed by Jarocin´ski and Karadi (2020), is only available for the period 1991to2016. InAppendixAweprovidedetailedinformationonthedataweuseandhow weconstructedthedifferentvariables. An alternative source for studying housing tenure transitions is the Panel Study of IncomeDynamicsdatabase. BachmannandCooper(2014)usethisdatabasetostudyhousing tenure transitions in the U.S. market and compare their results to those obtained with the AHSdatabase,andtheyreportthattheempiricalpatternsobservedwiththetwodatabases are broadly similar. We chose to use the AHS database because it simultaneously allows us to study housing tenure decisions at the household level and changes in housing unit type-fromrentaltoownershipandviceversa. Onekeydifferencebetweenourstudyand that of Bachmann and Cooper (2014) is that these authors mostly look at transitions during the business cycle, whereas we look explicitly at household and housing unit tenure transitionsrelatedtochangesinmonetarypolicy. To match the frequency of the AHS data, which are biennial, we construct a biennial monetary policy shock by summing the quarterly Jarocin´ski and Karadi (2020) monetary policyshockspertainingtotheyearofthesurveyandtheyearbefore. Tobeabletousean additionalyearoftheAHSdata,wedecidedtouseonly4quartersofdatafortheyear1991, astheJarocin´skiandKaradi(2020)monetarypolicyshocksareavailablefortheperiod1991 to2016. q=0 (cid:88) MPJK = MPJK,quarterly (9) t t,q q=−7 Forexample,themonetarypolicyshockmeasurefor2005isthesumofallthequarterly monetarypolicyshocksbetween2004:Q1and2005:Q4(8quartersintotal). 18

3.2.2 Methodology Tostudytheeffectofmonetarypolicyonhousehold’stenuredecisionsandonhousing unit owners, we estimate simple logit models in which the dependent variable measures transition from renting to owning or from owning to renting - both for households and housing units. For households rent-to-own transitions, the dependent variable is an indicator variable equal to 1 if the household is currently a homeowner but was a renter 12 months before, and 0 if the household is currently a renter and was also a renter before. For housing units rent-to-own transitions, the dependent variable is an indicator variable that takes the value 1 if the housing unit is now for ownership but two years prior was a rental unit, while it takes the value 0 if the housing unit is a rental unit currently and two yearsbefore. In the case of the own-to-rent transitions of households, the dependent variable is an indicatorvariableequalto1ifthehouseholdiscurrentlyarenterbutwasahomeowner12 monthsbefore,and0ifthehouseholdiscurrentlyahomeownerandwasalsoahomeowner before. Forown-to-renttransitionsofhousingunits,thedependentvariableisanindicator variableequalto1ifthehousingunitiscurrentlyarentalunitbutwasanowner-occupied unit two years before, and 0 if the housing unit is currently a rental and was also a rental before. Weestimatethefollowingrent-to-ownandown-to-rentequations: Prob(HH = renter HH = owner) = Logit(λ+γMPJK +δDHH) i,t | i,t−1 t i,t (10) Prob(HU = rental HH = ownership) = Logit(λ+γMPJK +δDHU) i,t | i,t−2 t i,t Prob(HH = owner HH = renter) = Logit(α+βMPJK +θDHH) i,t | i,t−1 t i,t (11) Prob(HU = ownership HH = rental) = Logit(α+βMPJK +θDHU) i,t | i,t−2 t i,t (cid:88) Prob(HH = renter HH = owner) = Logit(λ+ γ MPJK dHH +δDHH) i,t | i,t−1 j t ∗ i,t i,t (12) (cid:88) Prob(HU = rental HH = ownership) = Logit(λ+ γ MPJK dHU +δDHU) i,t | i,t−2 j t ∗ i,t i,t (cid:88) Prob(HH = owner HH = renter) = Logit(α+ β MPJK dHH +θDHH) i,t | i,t−1 j t ∗ i,t i,t (13) (cid:88) Prob(HU = ownership HH = rental) = Logit(α+ β MPJK dHU +θDHU) i,t | i,t−2 j t ∗ i,t i,t 19

In equations 10, 11, 12, and 13, the function Logit(.) is the standardized logit function exp(.) , DHH = dregion,dageter,dincquar and DHU = dregion are indicator variables 1+exp(.) i,t { i,t i,t i,t } i,t { i,t } for the U.S. region where the housing unit is located (dregion ), the age tercile (dageter ), or i,t i,t the income quartile (dincquar ) the household belongs to - the superscripts “HH” and “HU” i,t denote variables that are specific to the household and to the housing units transition regressions, respectively.9 In the equations pertaining to household transitions, in addition to regional controls and interactions, we also include some household characteristics to better account for life-cycle motives for being a renter or a homeowner. Namely, we includeinformationaboutthehousehold’s(orheadofhousehold’s)ageasolderhouseholds are more likely to be homeowners. Similarly, we also control for household’s income, as higher income households are more likely to be homeowners. Besides including controls fortheregion(householdsandhousingunits),age,andincome(onlyhouseholds),wealso allow the effects of monetary policy to depend on the region where the house is located (thisinteractioncanbedoneinbothhousingunitandhouseholdtransitionequations)and on the age and income of the household (this interaction can only be done in household transitionequations). In addition to the more granular regressions at the household and housing unit levels, we also use the individual AHS data to construct aggregate measures of the share of renters and the share of housing units that are rentals.10 These regressions will allow us to provide additional evidence for the effect of monetary policy on housing tenure decisions in addition to that from the results of the own-to-rent and rent-to-own transition based on equations10,11,12,and13. Weestimatethefollowinglinearmodels: ∆Srenter = γ +λMPJK +κ +(cid:15) (14) j,t t j j,t ∆Srental = γ +λMPJK +κ +(cid:15) (15) j,t t j j,t ∆Srenter = γ +λMPJK +(cid:15) (16) t t t ∆Srental = γ +λMPJK +(cid:15) (17) t t t 9Theheadofhouseholdagetercilesandhouseholdincomequartilesarebasedonthesampledistribution ofagesandincomeswithineachcohortoftheAHSsurvey. 10In section A of the Online Appendix, we detail how we use the individual AHS data to construct the aggregatemeasuresoftheshareofhouseholdsthatarerentersandtheshareofhousingunitsthatarerentals. 20

In equations 14 and 15, the dependent variables are the change in the share of householdsthatrentandtheshareofhousingunitsthatarerentalunitsintheregionandperiod, respectively. In these equations, κ are region fixed effects. In equations 16 and 17, the j dependent variables are the change in the share of households that rent and the share of housingunitsthatarerentalunitsintheperiod,respectively. 3.2.3 ResultsandDiscussion WenowturntothediscussionoftheempiricalresultsusingtheAHSdata,startingwith thoseinTables1and2. Table 1 shows the effect of monetary policy shocks on the transitions from renting to owningforbothhouseholdsandhousingunits,whileTable2showstheeffectofmonetary policy shocks on the transitions from renting to owning for both households and housing units. The two tables show that monetary policy shocks affect the decision of individual households and owners of housing units to transitions from renting to owning or from renting to owning. For both household and housing units, as shown in Table 1, the results shows that the probability of a household transitioning from renting to owning declines and also that the the probability of a housing unit switching from being rental to being owner occupied also declines. Similarly, as shown in Table 2, when monetary policy tightens,theprobabilityofahouseholdtransitioningfromowningtorentingincreasesandalso thattheprobabilityofahousingunitswitchingfrombeingbeingowneroccupiedtobeing a rental also increases.11 The results in Tables 1 2 are consistent with those based in aggregatedata,whichshowthattheaggregatehomeownershipratefallswhenmonetarypolicy tightens. Theresultsinthesetablesalsoshowthatit’snotjusttherelativedemandforrentingvis-a-visowningthatchangesasaresultofamonetarypolicyshock,therelativesupply ofhousesforrentalvis-a-visforowner-occupiedalsochangeinresponsetothesameshock. To help with the interpretation of the results in Tables 1 and 2, we used the results from columns (1) and (4) from the two tables to calculate the marginal effect of a 25 basis pointscontractionarymonetarypolicyshockonthetransitionprobabilitiesfromrentingto owningandfromowningtorenting. TheresultsfromthisexerciseareshowninTable3. The results in this table suggest that changes in monetary policy conditions are particularly important for transitions of households from renting to owning, as the average rateoftransitionfromrentingtoowningfallsbycloseto15%whenmonetarypolicytight- 11Notethatthetransitionprobabilitiesforhouseholdsandhousingunitsarenotdirectlycomparablebecauseofdifferencesintimehorizons. ForhouseholdtransitionstheAHSdatasetonlyprovidesinformation relativetooneyearpriortothesurvey,whileforhousingunitstransitionstheinformationprovidedbythe survey only allows to study transitions in two-year periods, corresponding to the frequency of the survey usedintheconstructionoftheAHSdataset. 21

Table1: Effectofmonetarypolicyshocksontheprobabilityofahouseholdbecomingahomeownerandontheprobabilityofahousingunitbecomingowneroccupied. Variables Probabilityofbecomingowner Probabilityofbecomingowner-occupied (1) (2) (3) (4) (5) MPShock -0.706 -0.706 -0.614 -0.043 -0.046 (0.257)*** (0.260)*** (0.252)** (0.227) (0.227) Midwest 0.486 0.668 0.202 (0.038)*** (0.053)*** (0.056)*** South 0.518 0.649 0.402 (0.052)*** (0.067)*** (0.039)*** West 0.265 0.158 0.193 (0.050)*** (0.071)** (0.050)*** 2nd agetercile -0.102 (0.042)** 3rd agetercile -0.285 (0.138)** 2nd incomequartile 0.987 (0.028)*** 3rd incomequartile 1.830 (0.036)*** 4th incomequartile 2.648 (0.027)*** Constant -2.057 -2.404 -3.686 -2.699 -2.923 (0.131)*** (0.135)*** (0.133)*** (0.069)*** (0.089)*** N 222,386 222,386 222,386 120,284 120,284 Note: The Table shows results of logit regressions in which the dependent variable in columns (1)-(3) is a dummyvariablethattakesthevalue1ifthehouseholdswitchedfromrentingtoowningahouseinthe12 monthspriortothesurveyinterviewand0ifitthehouseholdcontinuestorent;and,thedependentvariable in columns (4)-(6) is a dummy variable that takes the value 1 if the housing unit switched from being a rental to being an owner-occupied house during the the two year period between surveys; the monetary policyshockwasconstructedwiththehigh-frequencymonetaryshockinstrumentofJarocin´skiandKaradi (2020). Dataforhouseholdtransitionsarebiennialfrom1991to2015andfrom1991to2013forhousingunit transitions. Standarderrorsclusteredbyperiodinparentheses. *,**,and***denotestatisticalsignificanceat 10%,5%,and1%. ens by 25 basis points. However, the effects for other housing market transitions are not negligible. Overall, the results in this table also suggest that households are more responsivetomonetary policyshocksthantheowners ofhousingunits. Namely,thedemandfor rental/ownership reacts faster to a monetary policy shock than the supply of housing for rental/ownership. In the next three tables, we extend the results of Tables 1 and 2 by considering interactions of the monetary policy shock with region, age, and income indicator variables – weconsider allinteractions inthe caseofhousehold transitions,but inthe caseof housing 22

Table 2: Effect of monetary policy shocks on the probability of a household becoming a renter andontheprobabilityofahousingunitbecomingarental. Variables Probabilityofbecomingrenter Probabilityofbecomingrental (1) (2) (3) (4) (5) MPShock 0.090 0.072 0.107 0.137 0.128 (0.192) (0.190) (0.214) (0.070)* (0.070)* Midwest 0.187 -0.030 -0.241 (0.037)*** (0.042) (0.027)*** South 0.318 0.063 0.093 (0.062)*** (0.063) (0.041)** West 0.505 0.465 0.354 (0.051)*** (0.057)*** (0.064)*** 2nd agetercile -1.475 (0.028)*** 3rd agetercile -2.671 (0.081)*** 2nd incomequartile -0.723 (0.037)*** 3rd incomequartile -1.531 (0.028)*** 4th incomequartile -2.322 (0.034)*** Constant -2.631 -2.911 -0.444 -3.485 -3.544 (0.127)*** (0.098)*** (0.103)*** (0.034)*** (0.046)*** N 442,899 442,899 442,899 284,112 284,112 Note: The Table shows results of logit regressions in which the dependent variable in columns (1)-(3) is a dummy variable that takes the value 1 if the household switched from owning to renting a house in the 12 months prior to the survey interview and 0 if it the household continues to own; and, the dependent variable in columns (4)-(6) is a dummy variable that takes the value 1 if the housing unit switched from beingowner-occupiedhousetobeingarentalduringthethetwoyearperiodbetweensurveys;themonetary policyshockwasconstructedwiththehigh-frequencymonetaryshockinstrumentofJarocin´skiandKaradi (2020). Dataforhouseholdtransitionsarebiennialfrom1991to2015andfrom1991to2013forhousingunit transitions. Standarderrorsclusteredbyperiodinparentheses. *,**,and***denotestatisticalsignificanceat 10%,5%,and1%. units we can only consider region interactions, as age and income are household-specific characteristics. Table4showstheeffectofmonetarypolicyshocksontransitionprobabilitiesfromrenting to owning and from owning to renting for households and housing units interacted with indicator variables for the regions the house is located. For households, columns (1) and (3), there is little regional heterogeneity, as the effects are relatively similar for all re- 23

Table3: Marginaleffectofamonetarypolicyshockontherent-to-ownandown-to-renttransitionprobabilities Rent-to-Own Own-to-Rent No 25bps Marginal % No 25bps Marginal % MPshock MPshock effect difference MPshock MPshock effect difference (1) (2) (3) (4) (5) (6) (7) (8) Households 11.3% 9.7% -1.7% -14.6% 6.7% 6.9% 0.1% 2.1% Housingunits 6.3% 6.2% -0.1% -1.0% 3.0% 3.1% 0.1% 3.4% Note: The Table shows the effect of a 25 basis points monetary policy shock on the transition probabilities from renting/rental to owning/ownership and from owning/ownership to renting/rental for households andhousingunits. Thevaluesincolumns(1)and(2)areobtainedusingtheresultsshowninTable1,while the results in columns (5) and (6) are obtained using the results shown in Table 2. Columns (3) and (7) are obtained by subtracting columns (2) and (1) and (6) and (5), respectively; columns (4) and (8) are obtained bydividingcolumns(3)and(1)and(7)and(5),respectively. gions. Incontrast,forhousingunits,columns(2)and(4),thereismoreheterogeneity,with housing units located in the Midwest being more reactive to monetary policy shocks than housing units located the other regions. What drives thesedifferences is beyond the scope ofthispaper,butitissomethingworthwhileexploringfurtherastherecouldbeimportant differences across U.S. regions in the transmission of monetary policy through the homeownershipchannel.12 Asalreadynoted,weincludeinformationaboutheadofhouseholdageandhousehold income in some of the model specifications to control for life-cycle motives in the decision of becoming an owner/renter. In addition to controlling for these household characteristics, we also consider the possibility that monetary policy affects households housing decisions based on their age and income. Tables 5 and 6 show the results of the effect of monetary policy shocks on housing tenure decisions interacted with age and income information,respectively. Column (1) in Table 5 shows that the effect of monetary policy on households decision to move from renting to owning increases with the household’s age. This result suggests thatsomehouseholdspursuehomeownershiplateintolife,but,thatthedecisiontobecome ahomeownerismoresensitivetomonetarypolicyconditionsforolderhouseholds. In the case of transitions from owning to renting, the results in column (2) show that younger households (those in the first and second terciles of the age distribution) are unlikely to move from being homeowners to being renters when monetary policy conditions change. This insensitivity may be due to most mortgages in the United States being fixed, which makes the cost of homeownership to be less responsive to changes in interest rates. However,resultsincolumn(2)showthathouseholdsinthethirdtercilearequiteresponsiveto 12Corsettietal.(2021)showthatcross-countrydifferencesinhousingmarketcharacteristicsareanimportantdriverofheterogeneouspass-throughofmonetarypolicytoeuro-areacountries. 24

Table 4: Effect of monetary policy shocks on the probability of a household or housing unit changinghousingtenure-interactionwithU.S.region Variables Prob. ofbecoming: Owner Owner-occupied Renter Rental (1) (2) (3) (4) MPShock*U.S.East -0.658 -0.016 -0.100 0.056 (0.274)** (0.362) (0.213) (0.164) MPShock*U.S.Midwest -0.675 -0.158 0.140 0.151 (0.298)** (0.150) (0.177) (0.052)*** MPShock*U.S.South -0.743 -0.063 0.079 0.064 (0.284)*** (0.261) (0.213) (0.101) MPShock*U.S.West -0.719 0.053 0.103 0.257 (0.212)*** (0.179) (0.192) (0.176) Midwest 0.483 0.175 0.221 -0.225 (0.054)*** (0.050)*** (0.033)*** (0.027)*** South 0.503 0.394 0.344 0.095 (0.064)*** (0.046)*** (0.067)*** (0.036)*** West 0.255 0.204 0.534 0.386 (0.066)*** (0.063)*** (0.048)*** (0.068)*** Constant -2.395 -2.918 -2.936 -3.556 (0.137)*** (0.098)*** (0.093)*** (0.043)*** N 222,386 120,284 442,899 284,112 Note:TheTableshowsresultsoflogitregressionsinwhichthedependentvariableincolumn(1)isadummy variable that takes the value 1 if the household switched from renting to owning a house in the 12 months priortothesurveyinterviewand0ifitthehouseholdcontinuestorent; thedependentvariableincolumn (2) is a dummy variable that takes the value 1 if the housing unit switched from being a rental to being an owneroccupiedhouseduringthethetwoyearperiodbetweensurveys; thedependentvariableincolumn (3)isadummyvariablethattakesthevalue1ifthehouseholdswitchedfromowningtorentingahousein the12monthspriortothesurveyinterviewand0ifitthehouseholdcontinuestoown;and,thedependent variable in column (4) is a dummy variable that takes the value 1 if the housing unit switched from being a owner-occupied house to being a rental during the the two year period between surveys; the monetary policyshockwasconstructedwiththehigh-frequencymonetaryshockinstrumentofJarocin´skiandKaradi (2020). Dataforhouseholdtransitionsarebiennialfrom1991to2015andfrom1991to2013forhousingunit transitions. Standarderrorsclusteredbyperiodinparentheses. *,**,and***denotestatisticalsignificanceat 10%,5%,and1%. changes in monetary policy, and that, when monetary policy tightens some of these older households decide to sell and become renters. We see this result for older households as suggestive that some older households try to maximize sale value of their homes, and, oncetheyseeinterestratesgoinguptheydecidetosellbecausetheyunderstandthathouse pricesarelikelytogrowslower. Turningnowtotheresultspertainingtotheinteractionofmonetarypolicywithhouseholdincome,showninTable6. Column(1)inthistableshowstheresultsforthetransition 25

Table 5: Effect of monetary policy shocks on the probability of a household changing housing tenure-interactionwiththeheadofhouseholdage Variables Prob. ofbecomingowner Prob. ofbecomingrenter (1) (2) MPShock*1stagetercile -0.405 -0.074 (0.232)* (0.247) MPShock*2ndagetercile -0.716 0.086 (0.273)*** (0.199) MPShock*3rdagetercile -1.358 0.783 (0.507)*** (0.217)*** Midwest 0.670 -0.030 (0.053)*** (0.042) South 0.649 0.064 (0.067)*** (0.063) West 0.159 0.465 (0.071)** (0.057)*** 2ndagetercile -0.153 -1.453 (0.041)*** (0.031)*** 3rdagetercile -0.455 -2.564 (0.125)*** (0.074)*** 2ndincomequartile 0.986 -0.725 (0.028)*** (0.038)*** 3rdincomequartile 1.830 -1.534 (0.036)*** (0.029)*** 4thincomequartile 2.646 -2.323 (0.026)*** (0.034)*** Constant -3.653 -0.467 (0.126)*** (0.103)*** N 222,386 442,899 Note:TheTableshowsresultsoflogitregressionsinwhichthedependentvariableincolumn(1)isadummy variablethattakesthevalue1ifthehouseholdswitchedfromrentingtoowningahousebetweeninthe12 monthspriortothesurveyinterviewand0ifitthehouseholdcontinuestorent;and,thedependentvariable incolumn(2)isadummyvariablethattakesthevalue1ifthehouseholdswitchedfromowningtorenting a house in the 12 months prior to the survey interview and 0 if the household continues to own the house itlivesin; themonetarypolicyshockwasconstructedwiththehigh-frequencymonetaryshockinstrument ofJarocin´skiandKaradi(2020). Dataarebiennialfrom1991to2015. Standarderrorsclusteredbyperiodin parentheses. *,**,and***denotestatisticalsignificanceat10%,5%,and1%. from renting to owning, and, despite some variation, there is no clear pattern with respect to the effect of monetary policy on households tenure choice decisions depending on income level. In contrast, the results in column (2), which are for the transition from owning to renting, show that only the households in the lowest income quartile are more likely to movefromowningtorentingonceinterestratesincrease. 26

Table 6: Effect of monetary policy shocks on the probability of a household changing housing tenure-interactionwithhouseholdincome Variables Prob. ofbecomingowner Prob. ofbecomingrenter (1) (2) MPShock*1stincomequartile -0.864 0.294 (0.302)*** (0.164)* MPShock*2ndincomequartile -0.661 0.013 (0.254)*** (0.235) MPShock*3rdincomequartile -0.421 0.035 (0.232)* (0.246) MPShock*4thincomequartile -0.688 0.020 (0.263)*** (0.293) Midwest 0.668 -0.030 (0.053)*** (0.042) South 0.649 0.064 (0.067)*** (0.063) West 0.159 0.466 (0.071)** (0.057)*** 2ndagetercile -0.101 -1.476 (0.042)** (0.028)*** 3rdagetercile -0.285 -2.670 (0.138)** (0.081)*** 2ndincomequartile 1.021 -0.761 (0.040)*** (0.040)*** 3rdincomequartile 1.904 -1.566 (0.043)*** (0.034)*** 4thincomequartile 2.677 -2.358 (0.036)*** (0.035)*** Constant -3.729 -0.418 (0.145)*** (0.105)*** N 222,386 442,899 Note:TheTableshowsresultsoflogitregressionsinwhichthedependentvariableincolumn(1)isadummy variablethattakesthevalue1ifthehouseholdswitchedfromrentingtoowningahousebetweeninthe12 monthspriortothesurveyinterviewand0ifitthehouseholdcontinuestorent;and,thedependentvariable incolumns(2)isadummyvariablethattakesthevalue1ifthehouseholdswitchedfromowningtorenting a house in the 12 months prior to the survey interview and 0 if the household continues to own the house itlivesin; themonetarypolicyshockwasconstructedwiththehigh-frequencymonetaryshockinstrument ofJarocin´skiandKaradi(2020). Dataarebiennialfrom1991to2015. Standarderrorsclusteredbyperiodin parentheses. *,**,and***denotestatisticalsignificanceat10%,5%,and1%. TheresultsfromTables5and6indicatethatthetransmissionofmonetarypolicythrough thehomeownershipchanneldependsonhouseholdcharacteristics. Inparticular,wefound younger households to be less sensitive to changes in monetary policy conditions than older households, while lower income households are more responsive to changes in in- 27

terestratesthanhigherincomehouseholds. The last set of results in this section pertains to the estimation results of equations 14, 15,16,and17,whichareshowninTable7. Table7: Effectofmonetarypolicyshocksontheaggregateshareofrentersandontheaggregate shareofrentalunits Variables ∆Rentershare(percent) ∆Rentalshare(percent) (1) (2) (3) (4) (5) (6) MPShock 2.41 2.41 2.49 2.82 2.82 2.82 (1.25)* (1.29)* (1.03)** (1.83) (1.89) (1.05)** R2 0.08 0.08 0.08 0.11 0.11 0.14 N 52 52 13 52 52 13 RegionFE N Y N N Y N Data U.S.Regional U.S.Regional U.S.Aggregate U.S.Regional U.S.Regional U.S.Aggregate Note: TheTableshowsresultsofOLSregressionsinwhich: thedependentvariableincolumns(1)and(2)is thechangeintheshareofhouseholdsinagivenU.S.Censusregion(Northeast,South,Midwest,andWest) thatrenttheplacetheylivein;thedependentvariableincolumn(3)isthechangeintheshareofhouseholds intheUniteStatesthatrenttheplacetheylivein;thedependentvariableincolumns(4)and(5)isthechange intheshareofhousingunitsinagivenU.S.Censusregionthatarerentals;thedependentvariableincolumn (6)isthechangeintheshareofhousingunitsintheUniteStatesthatarerentals;themonetarypolicyshock wasconstructedwiththehigh-frequencymonetaryshockinstrumentofJarocin´skiandKaradi(2020). Data are biennial from 1991 to 2015. Standard errors, in parentheses, are robust to heteroskedasticity and serial correlation. *,**,and***denotestatisticalsignificanceat10%,5%,and1%. The first three columns in Table 7 show results on the effect on monetary policy on the the change in the aggregate share of households that rent, while the last three columns show results on the effect on monetary policy on the the change in the aggregate share of housing units that are rentals. In line with the results concerning the effect of monetary policyonhouseholdsandhousingunitstransitionprobabilityfromowningtorentingand from renting to owning, the results in this table show that the renter share increases when monetarypolicytightensandalsothattheshareofhousingunitsforrentingalsoincrease. It is important to note once again that the household and housing unit results are not directly comparable because of differences in the time horizon considered for the transitions from rent to own and own to rent. Without taking this difference into consideration, the results in Table 7 could suggest that housing units adjust faster than households do in response to a monetary policy shock, because the coefficients in the last three columns are slightlylargerthanthecoefficientsinthefirstthreecolumns. However,becausetheresults for households only include transitions in the previous 12 months, while the results for housingunitsarebasedona2-yearhorizon,resultsinthistablesuggestthat,similartothe results in Tables 1 and 2, households are more responsive to monetary policy shocks than housing units (i.e., the relative demand for rental housing is more responsive to monetary policyshocksthantherelativesupplyofrentalhousing). Thisdifferenceislikelythemain 28

reason for why housing rents increase (decrease) and the homeownership rate decreases (increases)wheninterestratesincrease(decrease). The results in this section, both based on aggregate and household and housing unit level data, provide strong evidence that monetary policy simultaneously affects house prices, house rents, and the aggregate homeownership rate by affecting the decision of individual households to rent or to own and also by affecting the decision of housing unit owners to rent or sell their properties. A question that remains to be answered is why do thesefindingsmatter. Weaddressthisquestionintheremainderofthepaper. 4 Theory To account for the empirical results presented in the previous section, we propose a two-agent New Keynesian model with a segmented housing market in which agents can choose between owning or renting. The proposed model builds on existing models that include a housing sector, such as those of Iacoviello (2005) and Iacoviello and Neri (2010), and extends them by incorporating a segmented housing market and the possibility of somehouseholdschoosingbetweenowningorrentingthehousetheylivein. 4.1 The Environment The economy is set in discrete-time and features two types of families — borrowers andsavers—eachpopulatedbyacontinuumofinfinitely-livedhouseholdswithmeasure one. The savers have full access to credit markets and behave as Ricardian agents. The borrowers face a collateral constraint along the lines of work by Campbell and Hercowitz (2005), Iacoviello (2005), Iacoviello and Neri (2010), and Calza et al. (2013). Hence, the borrowers borrowing limit is a function of the value of their house. In our theoretical environment, the borrowers’ borrowing constraint is always binding. Consequently, they are assumed to behave in a “hand-to-mouth” fashion. Also, the households belonging to the borrowers family differ in their preferences concerning owning a house: they receive extra utility from these services for the same quantity of housing services if they own a houseinsteadofrentingone. Forsimplicity,weassumethatonlythehouseholdsbelonging totheborrowersfamilyneedtochoosebetweenowningorrenting.13 13Thisassumptiondoesnotaffectthequalitativenatureofhowthetenurechoicechannelaffectsthemonetarypolicytransmissiondynamics. Itonlyhasquantitativeimplications. 29

We assume that the housing stock in the economy is fixed, but that the share of housing for ownership/rental can be adjusted in response to changes in demand for the two typesofhousing(forownershipandforrental). Realestatebrokersprovidehousingrental services buying them from landlords and selling them with a markup. The brokers are the source of rigidity in housing rents. The landlords buy/sell housing stock for owning and rent it to the brokers, subject to adjustment costs. The latter can be motivated by higher maintenance costs for renting, less favorable tax treatment relative to owning, and the necessity of rehabilitation work. These housing stock adjustment costs are the source ofhousingmarketsegmentationinourmodel. Finally, in terms of the supply of final goods, we assume that wholesale firms produce themwithaconstantreturntoscaletechnologythatusesthelaborofbothagents(borrowers and savers) as its only inputs. Consumers buy the final good from retailers, who sell thewholesalegoodswithamarkupbutcanonlyadjustthepricesoftheirgoodsatrandom times(asinCalvo(1983)). Therefore,retailersareasourceofnominalrigidityinthiseconomy. We assume that savers own all types of firms in the economy. The savers’ problem is standard. The savers’, the wholesalers’, and the retailers’ problems are the same as in Iacoviello (2005). The only difference is that the savers in our model also own the brokers andthelandlords. 4.2 Households The households’ utility function is standard and is the same for both borrowers and savers. Households get utility from consuming the final good and housing services, but theygetdisutilityfromworking.14 Theinstantaneousutilityfunctionisgivenby h1−φ Lη u(c,h,L) = lnc+ . 1 φ − η − Borrowers Households in the borrowers family can choose to own or rent a house every period. These households are heterogeneous regarding the utility they get from owning a house but they all get the same utility when renting. We assume that, for a given house size, these households get higher utility owning than when renting it. This difference in utility isgivenbyρ . Weassumethat,everyperiod,eachhouseholdreceivesani.i.d. drawρ from i i CDF F(ρ). Also, inspired by the work of Ragot (2018), we assume that each household 14We assume utility is separable in money balances, which results in the quantity of money having no implicationsfortherestofthemodeland,therefore,areignored. 30

in the borrowers family trade a complete set of contracts for consumption and housing services within their own family, providing perfect insurance against idiosyncratic risk. The borrowers’ social planner problem is one of maximizing the following lifetime utility function: (cid:88) ∞ (cid:26)(cid:90) 1 (cid:18) (hi)1−φr(cid:19) (cid:18) (hi)1−φo (cid:19) (Li)η (cid:27) E (β(cid:48))t lnci +(1 Ii) jr t +Ii jo t +ρi t di , 0 t − t 1 φr t 1 φo t − η t=0 0 − − subjectto: (cid:90) 1 R (cid:90) 1 ci +Iiq ∆hi +(1 Ii)hil +bi t−1 di = bi +w(cid:48)Lidi t t t t − t t t t−1 π t t t 0 t 0 (cid:20) (cid:21) π bi IiE mq hi t+1 , t ≤ t t t+1 t R t whereE istheexpectationoperatorconditionalontimezeroinformation;β (0,1)isthe 0 ∈ discountfactor;ci isconsumptionofborroweriattimet;Ii 0,1 isanindicatorfunction t t ∈ { } that takes the value of 1 if borrower i decides to own and zero if she decides to rent; hi t denotes housing services; ρ is the utility that household i receives when she chooses to i own; Li are hours of work; q denotes the real housing price; l is the real housing rent; R t t t t is the gross nominal interest rate; π is the gross inflation rate; w(cid:48) is the real wage; m is the t t loan-to-valueratio;andbi isborrowinginrealterms. t Proposition1. Ifρ arei.i.d. drawsfromacontinuouscdfF(ρ),then:15 i (i) foreachhousehold,thedecisiontoownortorentisdeterminedbyasinglecutoffrule. Households with ρi > ρ¯ choose to own, while households with ρi < ρ¯ choose to rent, with ρ¯ being t t t t t the individual draw of the household that, for given prices, is indifferent between renting or owningahouse. Assuch,ineachperiodtheshareofhomeownersisgiven1 F(ρ¯) = α ; t t − (ii) theconsumptionandhoursofworkallocationsarethesameacrossallborrowers; (iii) housing services and bond holdings (bi) allocations, although different between homeowners t andrenters,willbethesameacrossrentersandhomeowners. AccordingtoProposition1,theproblemoftheborrowers’socialplannercanberewrittenas: 15TheproofofProposition1canbefoundinsectionBoftheOnlineAppendix. 31

(cid:88) ∞ (cid:26) (cid:18) (ho)1−φo(cid:19) (cid:18) (hr)1−φr(cid:19) (L(cid:48))η(cid:27) max E (β(cid:48))t lnc(cid:48) +α jo t + (1 α ) jr t t , c(cid:48),ho,hr,bo,br,L(cid:48) 0 t t 1 φo − t 1 φr − η t t t t t t t=0 − − subjectto R c(cid:48) +α q ho α q ho +(1 α )l hr +α bo t−1 = α bo +w(cid:48)L(cid:48) (18) t t t t − t−1 t t−1 − t t t t−1 t−1 π t t t t t (cid:20) (cid:21) π bo E mq ho t+1 (19) t ≤ t t+1 t R t br = 0, (20) t wheretheshareofhomeownersisgivenby: α = 1 F(ρ¯) (21) t t − with ρ¯ = u((c(cid:48))∗,(hr)∗,(L(cid:48))∗) u((c(cid:48))∗,(ho)∗,(L(cid:48))∗) (22) t t t t − t t t The star superscript in equation 22 denotes that these are optimal allocations given pricesanddistributionsofhomeownersandrenters. Theseoptimalallocationsareusedby eachhouseholdtodecidewhethertheyshouldrentorownahouse. ThefirstorderconditionwithrespecttoL(cid:48) isgivenby t w(cid:48) (L(cid:48))η−1 = t (23) t c(cid:48) t Whilethefirstorderconditionswithrespecttoho,hr andbo whencombinedwiththose t t t relatedtoconsumptionare: α q (cid:20) α q β(cid:48) (cid:21) α jo(ho)−φo = t t E t t+1 λ mq π (24) t t co − t co − t t+1 t+1 t t+1 l jr(hr)−φr = t (25) t cr t (cid:20) (cid:21) α R t = E β(cid:48)α t +λ R (26) co t t co π t t t t+1 t+1 Theaggregatedemandofborrowersthatarehomeownersisgivenby: h(cid:48) = α ho (27) t t t 32

Savers In our setting, the savers’ problem is standard. These agents do not need to choose between owning or renting; we assume they own a house and simply have to maximize theirlifetimeutilitygiventheresourcesthatareavailabletothem: (cid:88) ∞ (cid:18) (L )η(cid:19) E βt lnc +jlnh t (28) 0 t t − η t=0 R t−1 s.t. : c +q (h h )+b = b +w L +F t t t t−1 t t t t t − π t Inequation 28,F arelump-sum profitsreceivedfrom brokers,landlords, andretailers. t Thefirstorderconditionsaregivenby: (cid:20) (cid:21) 1 R t = βE (29) t c c π t t+1 t+1 (cid:20) (cid:21) q j q t t+1 = +βE (30) t c h c t t t+1 w Lη−1 = t (31) t c t 4.3 Housing Supply The supply of housing for ownership and for renting plays a crucial role in the model. To start, we assume that the total stock of housing is fixed and is equal to H ¯ .16 The total stock of housing is then split into a part that is for ownership, Ho, and another part that is t for rent, Hr, with H ¯ = Ho + Hr. While the total housing stock is fixed, the split between t t t housing for ownership and housing for renting can change over time in response to the relative price of each type of housing. In the model, it’s the landlords who can make these adjustments. To adjust the housing stock mix, landlords either buy housing stock that is availableforowningandrentitorsellhousingstockthatwasavailableforrent. Finally,we assumethathousingrentsaresticky.17 Asthedurationofrentalcontractsistypicallylonger 16Wecouldhaveincludedahousingproductionsectorinthemodel,but,besidescomplicatingtheanalytics ofthemodelatouchmore,itwouldn’tmaketoomuchdifferenceforourconclusions. Forourmodel,what mattersistherelativesupplyofhousingforrentingandforhomeownershipandhowfastthesetwostocks canadjustinresponsetochangesindemand. Addingahousingconstructionssectorwouldhavebeenmore realistic, but, because housing construction takes time, it wouldn’t have made the adjustment of relative supplyofhousingsufficientlyfastforourresultstogoaway. 17Theassumptionofstickyrentsisinlinewithempiricalobservation, asshowninGallinandVerbrugge (2019). However,incontrasttoGallinandVerbrugge(2019),whosemainobjectivewastoexplainwhyrents are sticky, we consider a simple model of rent stickiness that assumes that only a fraction of housing rents canbeadjustedeveryperiodasinastandardCalvopricesettingassumption. Thissimplificationshouldnot 33

thanasingleperiod,weassumethatonlyafractionofthesecontractschangespricesevery period. Tomodelthisrentstickiness,weassumethattherearerealestatebrokerswhobuy housingservicesfromthelandlordsandsellthematamarkuptohouseholds. Themarkup canbemotivatedbymanagementcostsandrealestatebrokers’fees. Landlords There is a unit mass of landlords that own the housing stock for renting. They competitively rent each unit of their housing stock for lL to real estate brokers that resell the t housing services at l = XrlL, where Xr is the brokers’ markup. They invest/disinvest by t t t t buying/selling housing stock and converting it into renting stock. However, when they invest/disinvest, they face adjustment costs. In particular, we assume that the adjustment costs depend on the size of the investment relative to the current stock of renting housing andthattheyareconvex. Theadjustmentcostsaregivenby (cid:18) Ir (cid:19)2 Hr ζ = ψ t q t−1 (32) t Hr t 2 t−1 Inourmodel,theadjustmentcostsaremotivatedbytransactionandconstructioncosts faced by landlords. One example of transaction costs that a landlord faces when buying a houseisthetaxeslevied. Moreover,landlordsneedtopayformaintenanceandrehabilitationexpenseswhenplacingahouseforrenting. Consider the problem of a landlord that owns the capital stock for renting HR at time t−1 t. Therepresentativelandlord’sproblemis: (cid:32) (cid:33) (cid:88) ∞ l (cid:18) Ir (cid:19)2 Hr maxE Λ t Hr q Ir ψ t q t−1 Ir,Hr 0 t Xr t − t t − Hr t 2 t t t=0 t t−1 s.t. : Hr = Ir +Hr (33) t t t−1 where Λ = (cid:81)t πτ is the saver’s relevant discount factor. Given that the total houst τ=0 Rτ−1 ingstockisfixed,thehousingstockforowningisgivenby Ho = H ¯ Hr. (34) t t − t Thefirst-orderconditionsofthelandlordsforIr andHr aregivenby t t havematerialimplicationsforourresults. 34

Ir µ = q +ψq t (35) t t t Hr t−1 (cid:34) (cid:35) l π ψ (cid:18) Ir (cid:19)2 π µ = t +E t+1 q t+1 + t+1 µ (36) t Xr t R 2 t+1 Hr R t+1 t t t t Inequations35and36,µ istheLagrangianmultiplierassociatedwiththelawofmotion t ofthehousingforrentingstock. Thisquantityistheshadowvalueoftheconstraint,which correspondstohowmuchthelandlordwouldvaluehavingtheconstraintrelaxed. Note that, the landlords act as arbitrageurs in the housing market, with their actions guaranteeingthat,inthesteadystate,thepriceofhousingisequaltothesumofthepresent value of all future rents: q = l . In the short run, however, there may be deviations Xr (1−β) ss from this no arbitrage condition due to housing mix adjustment costs and rent stickiness. Ontheonehand,sincehousingpricesarenotsticky,butrentsare,thesluggishadjustment ofrentswillimplythattherewillbedeviationsfromtheno-arbitrageconditionintheshort run. On the other hand, adjustment costs will also prevent the housing for renting stock from adjusting fast enough when faced with different demand conditions, contributing to deviations from the no-arbitrage condition between ownership and renting in the short run. RealEstateBrokers We assume that the housing rental sector is monopolistic competitive and that there is nominal rigidity in this sector, with prices following Calvo-style contracts. Real estate brokers play the role of intermediaries in the housing rental market. They rent the landlord’s housing stock, differentiate it at no cost, and rent it to households at a markup over the marginal cost. The CES aggregates of these housing services are converted back into homogeneous housing services by households. Each period, a fraction 1 θr of real estate − brokers set prices optimally, while a fraction θr cannot do so. These assumptions deliver thefollowinghousing-rentalPhillipscurve: l πl = π t (37) t t l t−1 Xr lnπl = βE lnπl κrln t (38) t t t+1 − Xr ss whereπl isthegrossnominalhousingrentinflationandκr = (1 θr)(1 βθr)/θr. t − − 35

4.4 Final Goods Sector Thefinalgoodssectorhastwotypesoffirms,competitivewholesalefirmsthatproduce wholesalegoodsandmonopolisticcompetitiveretailerswhosellthegoodstoconsumers. Wholesalers Wholesalefirmshirelabortoproducewholesalegoods. Theysolve: Y max t w L w(cid:48)L(cid:48) (39) X − t t − t t t where X above is the markup of final goods over wholesale goods. The production t technologyis: Y = A Lν(L(cid:48))1−ν. (40) t t t t Thefirst-orderconditionsofthewholesalersare Y t w = ν (41) t L X t t Y w(cid:48) = (1 ν) t . (42) t − L(cid:48)X t t Retailers Retailers face monopolistic competition and implicit costs of adjusting nominal prices following Calvo-style contracts (this is a similar assumption to how real estate brokers can adjust housing rents). Retailers buy wholesale goods Y from wholesale firms at price t Pw in a competitive market, differentiate the goods at no cost, and sell them at a markup t X = P /Pw over the marginal cost. The CES aggregates of these goods are converted t t t into homogeneous consumption goods by households. A fraction of retailers θ can set prices optimally each period, while a fraction 1 θ cannot choose prices optimally. These − assumptionsdeliverthefollowingconsumption-sectorPhillipscurve: X t lnπ = βE lnπ κln (43) t t t+1 − X ss whereκ = (1 θ)(1 βθ)/θ. − − 36

4.5 Consumer Price Index Inourmodeltherearetwogoodsthatareconsumed: finalgoodsandhousingservices. Theinflationrateofaconsumerpriceindexthatfollowsthepricechangesofbothgoodsis givenby: l lnπCPI = (1 ω)lnπl +ωlnπ = (1 ω)ln t +lnπ , (44) t − t t − l t t−1 where ω is the steady-state consumption share of total expenditure. Equation 44 shows how a measure of inflation, such as the CPI, that both includes the prices of consumption and shelter, both reflects changes in inflation (π ) and relative prices of goods ( lt ). This t lt−1 relative price effect would be present in any model with multiple goods, but this effect becomes particularly important if relative prices change in response to monetary policy. If thehousingservicesexpenditureshare(1 ω)respondedquicklytochangesintherelative − price of renting, then the CPI would provide a more precise measure of inflation. When realrentsincrease,theexpenditureshareonhousingservicesfallsashouseholdsubstitute housing services with consumption of final goods. This assumes that all agents substitute housing services consumption when housing rents increase, but that is not necessarily the case as we will shown. Importantly, there are two practical reasons as to why the expenditure share used in CPI does not get adjusted quickly following a monetary policy shock. First, the expenditure shares that are used as weights in the construction of the CPI are only updated every two years. Second, even if these expenditure shares were updated more frequently, they would not just be reflecting the effects of monetary policy shocks, but of all shocks hitting the economy. As such, the expenditure shares would be adjusting to offset the effect of monetary policy on rents. For these two reasons, we chose to use fixed expenditure shares in CPI inflation following a monetary policy shock, as is done in practice. 4.6 Interest Rate Rule As is standard in this literature, the monetary authority sets the gross nominal interest rateaccordingtoaTaylorrule: (cid:18) Y (cid:19)(1−rR)rY R = RrR (πCPI)(1−rR)rπ t−1 R1−rR(cid:15)R (45) t t−1 t−1 Y ss t ss where R and Y are the steady-state real interest rate and output, respectively. The rule ss ss allowsforinterestrateinertiaviatheparameterr > 0. Also,theinterestratereactstopast R 37

(CPI) inflation and output. The strength of the reaction of interest rates to deviations of inflation and output from steady state is determined by the parameters r and r , respec- π Y tively. Finally,(cid:15)R isawhitenoiseshockthatcapturesinterestratesurprises. t 4.7 Equilibrium Theequilibriuminthiseconomyisasequenceofallocations c(cid:48),h(cid:48),L(cid:48),hr,ho,α ,ρ ,c ,h , { t t t t t t t t t b ,bo,br,L ,Ho,Hr,Ir,Y ,ζ ∞ andasequenceofvalues w(cid:48),w ,q ,l ,π ,πCPI,R ,πl,X ,Xr, t t t t t t t t r }t=0 { t t t t t t t t t t µ ,λ ∞ satisfyingequations(18)-(45)andthefollowingmarketclearingconditions:18 t t }t=0 Goodsmarket: c +c(cid:48) = Y ζ (46) t t t − t Housingrentalmarket: Hr = (1 α )hr (47) t − t t Housinghomeownershipmarket: Ho = h +h(cid:48), (48) t t t given h ,h(cid:48) ,α ,P ,R and the sequence of monetary shocks eR ∞ , together { −1 −1 −1 −1 −1 } { t }t=0 withtherelevanttransversalityconditions. 4.8 Model Solution We chose to use a second-order perturbation method around the steady state to solve the model because, for households to choose between owning or renting, they need to compare the utility they get from owning a house with that of renting19. Using a secondorder approximation is crucial, because it is well known in the literature (see Kim and Kim(2003))thatfirst-orderapproximationsgiveinaccuratesolutionstowelfareanalysisas thesedon’tconsidersecondmoments. 5 Calibration and Model Evaluation In this section we calibrate the model described in the previous section by choosing parameters that allow the model to match a set of data moments pertaining to the U.S. economy. We then evaluate the model calibration by comparing outcomes of the model withempiricalresultsthatwerenottargetedinthecalibrationandshowtheimportanceof the inclusion in the model of a housing tenure choice and a segmented housing market to matchtheempiricalresultspresentedinsection3. 18ThebondsmarketissuppressedbecauseofWalras’slaw. 19Thesecond-orderperturbationdoesnotyieldhigherprecisionthanafirst-orderperturbationforinflation measuresthough,becausetheyarealreadywrittenusingalinearapproximation 38

5.1 Calibration The calibrated parameter values are presented in Table 8. For the heterogeneous extra utility received when owning a house distribution F(ρ), we chose the uniform functional form, so that ρi U(0,b). As a consequence, the share of borrowers that are homeowners t ∼ isgivenby: ρ¯ t α = 1 . (49) t − b In terms of preferences, we set the discount factor of savers β = 0.99 as is standard to match a quarterly interest rate of around 1%. As for the discount factor of the borrowers, we follow Iacoviello and Neri (2010) and set β(cid:48) = 0.97. This value is also very close to the value used in Greenwald (2018). We set the savers’ housing preference j = 0.04 to match thehousingstocktoGDPratioof1.35. Therenters’andhomeowners’housingpreferences essentiallyregulatethe steady-state housingshareoftotal expenditure, sowesetjr = 0.08 and jo = 0.24 to match the average housing weight in total expenditures in the CPI in 2019. The other housing preferences parameters φo and φ are the inverse price elasticity r of intensive-margin demand for homeowners and renters housing, respectively. For the homeowners we set this elasticity φo = 1 as in Iacoviello (2005), Iacoviello and Neri (2010) andGreenwald(2018),whileforrenterswesetφr = 2basedonAlbouyetal.(2016),which estimates this inverse price elasticity to be somewhere between 1.5 and 2.24. We calibrate η = 2 so that the inverse Frisch elasticity is set to 1, as is standard in the literature. Given thatweonlymodelthehomeownershipdecisionfortheborrowers,wejointlycalibratethe lower and upper bound, a = 0.4 and b = 0.1, of the uniform distribution to match the − U.S.averagehomeownershiprateofhand-to-mouthagentsreportedinKaplanetal.(2014) ofapproximately50%. We follow Kaplan et al. (2014)’s results and make the share of hand-to-mouth agents to approximately 32%, which implies that the share of hand-to-mouth agents that rent is 16% of the whole population. The average homeownership rate in the U.S. between 1983 and 2019 is approximately 65%, which means 35% of the households rent a house. Hence, 19%ofthehouseholdsrentahouse butdonotfaceliquidityconstraints. Inourmodel,we abstract from these agents because we assume that they have preferences towards owning that are always sufficiently far from the indifferent agent, thus yielding the impact of monetary surprises on housing tenure decisions of these agents to be negligible. Thus, in the model, we focus on explaining changes in the aggregate homeownership rate in response to monetary policy shocks rate solely coming from changes in the hand-to-mouth households’housingtenurechoices. 39

Table8: ParameterValues: BaselineCalibration Parameter Name Value Internal Target/Source Preferences β Saverdiscountfactor 0.99 Y Standard β(cid:48) Borr.discountfactor 0.97 N IacovielloandNeri(2010) j Saverhousingpreference 0.04 Y Housing stock to GDP ratio of 1.35, IacovielloandNeri(2010) jr Borr. that rents housing prefer- 0.08 N Rentershousingshareoftotalexpenditure ence inCPI jo Borr. thatownshousingprefer- 0.24 N Homeown.withoutstd.mortgagehousing ence shareoftotalexpenditureinCPI η Labordisutility 2 N Standard φr Inv. priceelasticityofintensive- 2 N Albouy et al. (2016), Howard and Liebermargindemandforrentalhous- sohn(2021)estimatesrange=[1.5,2.24] ing φo Inv. priceelasticityofintensive- 1 N Iacoviello (2005), Iacoviello and Neri margindemandforhomeowner (2010),Greenwald(2018) housing a Lowerlimitofowningextraser- -0.4 Y U.S.averagehomeownershiprateofhandvices to-mouth households in Kaplan et al. (2014):50%,α =0.5 ss b Upperlimitofowningextraser- 0.1 Y U.S.averagehomeownershiprateofhandvices to-mouth households in Kaplan et al. (2014):50%,α =0.5 ss Housingsector ψ Rental housing stock adjust- 1.6 Y Increaseinrentalunitssharetwoyearsafmentcost tera25bpsmonetarypolicyshock(Table7, column6) Xr Rentalbrokersmarkup 2.2 Y Zillow, U.S. average price-to-rent ratio, ss q /(l 4)=11.4 ss ss ∗ θr Rentsstickiness 0.83 N GallinandVerbrugge(2019) m Loan-to-valueratio 0.85 N Iacoviello and Neri (2010), Greenwald (2018) H¯ Totalhousingstock 1 N Normalization Finalgoodssector θ Pricestickiness 0.84 N IacovielloandNeri(2010) ν Saverslaborincomeshare 0.79 N Iacoviello and Neri (2010), Kaplan et al. (2014) X Retailersmarkup 1.15 N IacovielloandNeri(2010) ss A TFP 1.057 Y Y =1 ss Monetarypolicy π Steadystateinflation 1 N IacovielloandNeri(2010) ss r Taylorrulesmoothing 0.7 N IacovielloandNeri(2010) R r Taylorrule(GDP) 0.13 N IacovielloandNeri(2010) Y r Taylorrule(CPI) 1.5 N Standard π Next, we turn to the calibration of parameters related to the housing sector. We set the parameter regulating the adjustment costs of the housing stock mix ψ = 1.6 to match the 40

housing supply response to a 25 basis points average surprise over two years estimated from the AHS microdata. As reported in column 6 of Table 7, we find that the rental share increasesbyapproximately2.82percentagepointsinresponsetoapositive100basispoints monetary policy shock. Consequently, a positive shock of 25 basis points corresponds to anincreaseof0.7percentagepointsintherentalshare. Withψ = 1.6,apermanentshockof 25 basis points in the interest rate over two years gives a response in the rental share that matches our empirical findings. We set the share of real estate brokers that cannot adjust rentsθr = 0.83tomatchtheshareofrentsthatdonotchangein6monthsreportedinTable 1 of Gallin and Verbrugge (2019). The landlords first-order conditions in the steady-state imply that q = l /(Xr (1 β)). We use this condition to calibrate Xr = 2.2 such that t t ss − ss we match the U.S. average price-to-rent ratio of 11.4. The loan-to-value ratio m = 0.85 is takenfromIacovielloandNeri(2010)andGreenwald(2018),andthetotalhousingstockis normalizedto1. For the final goods sector, we set the share of retailers that cannot adjust their prices on a given period to be θ = 0.84, which is the same parameter value choice in Iacoviello and Neri (2010). We follow Iacoviello and Neri (2010) and Kaplan et al. (2014) and set the savers labor income share ν = 0.79. The retailers markup is calibrated to X = 1.15 as in ss Iacoviello and Neri (2010), and the TFP parameter A is set such that output at the steady stateisnormalizedto1. Finally,fortheTaylorrule,wefollowIacovielloandNeri(2010)andsetthesteady-state inflation πCPI = π = 1, the interest rate smoothing parameter r = 0.7, the response to ss ss R outputgapparameterr = 0.13,andtheresponsetoinflationparameterr = 1.5. Y π 5.2 Model Evaluation Havingdiscussedtheparametervalueschoices,wenowevaluatetheoverallcalibration of the model by comparing the responses of selected variables to a monetary policy shock inthemodeltothoseobtainedwithaproxySVARandthatwerepresentedinsection3.1.2. This comparison provides a credible test to our proposed theory because the calibration of the model does not target any of the empirical impulse response functions estimated with the proxy SVAR. Moreover, except for the housing supply dynamic response, the calibrationofthemodelonlytargetslong-rundatamoments. In Figure 3, we show how the transmission of monetary policy shocks to the federal funds rate, house rents, homeownership rate, house price, CPI inflation and GDP implied by the model compares with that of the proxy SVAR.20 The model matches the empiri- 20Since we are only modeling the borrowers’ homeownership rate change, a 1 p.p. change in the share 41

Figure3: Modelvs. ProxySVARimpulseresponsefunctions 0.4 0.2 0.0 0 4 8 12 16 20 noitaiveD FederalFundsRate 0.2 0.1 0.0 0.1 − 0 4 8 12 16 20 noitaived% HouseRent 0.0 0.1 − 0.2 − 0 4 8 12 16 20 noitaiveD Homeownershiprate 0.2 0.0 0.2 − BenchmarkModel 0.4 ProxyVAR − 0 4 8 12 16 20 noitaived% HousePrice 0.1 0.0 0 4 8 12 16 20 Horizon(quarter) noitaived% CPIInflation 0.00 0.25 − 0.50 − 0.75 − 1.00 − 0 4 8 12 16 20 Horizon(quarter) noitaived% GDP Note: theFigurecomparesthemodelresponsestoa25basispointmonetarypolicyshocktotheuntargeted empiricalresponsesestimatedwiththeproxySVARusingtheJarocin´skiandKaradi(2020)instrumenttoa shock of the same size. The dashed lines report the 68% confidence intervals for the proxy SVAR impulse responsefunctions. cal monetary transmission to the selected variables well, especially from a qualitatively point of view. Broadly consistent with our empirical findings, the model predicts that the homeownershiprateandhousepricesfallwhilehouserentsrisefollowingacontractionary monetarypolicysurprise. Inthebenchmarkcalibrationofthemodel,theriseinrentsisnot enough make the CPI increase at impact, but it increases in the following period. This result is consistent with the well-known “price puzzle” (Sims (1992)), in which consumer pricesriseafteracontractionarymonetarypolicyshock. Therefore,ourmodelprovidesan of α corresponds to a 0.32 p.p. change in the aggregate homeownership rate. For further details, see the t discussioninsection5.1. 42

explanation for the “price puzzle” based on the effect of monetary policy shocks on house rents,and,consequently,onthesheltercomponentoftheCPI(orPCE). While the model matches very well the empirical impulse response functions from a qualitatitve point of view, the model could be improved to better match the empirical response functions from a quantitative point of view. For example, a common way that is used in the literature to improve the quantitative fit of models like ours is the introduction of habit formation into households formation as in Iacoviello and Neri (2010). In our benchmarkmodelwechosetonotincludehabitformationorotherfeaturesthatcouldhelp with improving the model fit because: (i) the focus of the paper is on understanding the mechanisms involved in the homeownership decision channel of monetary transmission; and (ii) we want to keep the estimated empirical impulse responses untargeted in the calibration of the model so that we can use them in the evaluation of the calibration. It is our viewthatamorestripped-downmodelmakestheillustrationofthemechanismsharper. 5.3 The Role of the Housing Demand and Supply in Matching the Empirical Results To show the importance of the homeownership decision margin and of a segmented housing market, we compare the transmission of monetary policy when these elements arepresentinthemodeltowhentheyarenot. Homeownership Decision Starting with the homeownership decision margin, to compare the transmission of a 25-bps contractionary monetary policy shock when borrowers areabletoswitchbetweenownershipandrentaltowhentheyarenot,wemaketheshareof homeownersandrenterstobeconstant. InFigure4,weshowtheresultsofthisexperiment relativetotheresultsobtainedwiththebaselinespecificationofthemodel. The results in Figure 4 show that, without a housing tenure choice margin, housing rents decline, and CPI inflation, which is a weighted average of housing and non-housing prices, declines much more than in the baseline model. For both variables, the model responses are at odds with the the empirical responses. Due to (CPI) inflation being less persistent in the model without a housing tenure choice margin, the federal funds rate declines faster when the hosing tenure choice margin is not present and goes below baseline much earlier than in the baseline. For the other variables, the differences are relatively minor and they are mostly the reflection of differences in the path of interest rates in the two models. House prices fall in both model specifications, but are somewhat more volatile when the housing tenure margin is present (fall by more at the beginning and increase by 43

Figure4: Importanceofthehousingtenurechoicemarginformatchingtheempiricalresults 0.2 0.1 0.0 0 4 8 12 16 20 noitaiveD FederalFundsRate baseline 0.2 nochangeinhomeownershiprate 0.0 0.2 − 0.4 − 0 4 8 12 16 20 noitaived% HouseRent 0.0 0.1 − 0.2 − 0 4 8 12 16 20 noitaiveD Homeownershiprate 0.2 0.0 0.2 − 0.4 − 0 4 8 12 16 20 noitaived% HousePrice 0.0 0.1 − 0.2 − 0 4 8 12 16 20 Horizon(quarter) noitaived% CPIInflation 0.00 0.25 − 0.50 − 0.75 − 1.00 − 0 4 8 12 16 20 Horizon(quarter) noitaived% GDP Note: thisFigureshowsthedynamicsresponsesofmacroeconomicaggregatestoa25basispointspositive shock in the nominal interest rate in the baseline calibration and in an alternative calibration in which the homeownershiprateisconstantandtheadjustmentcostsarezeroψ =0. r more later on). Similarly, the effects on GDP are relatively similar for both model specifications, but GDP is somewhat more volatile when the hosing tenure choice margin is present. Segmented Housing Market. Turning now to the importance of a segmented housing market for matching the empirical results. Similarly to what we did for the case of the homeownership decision margin, to show the importance of the housing market being segmentedformatchingtheempiricalresults,wesimulatethemodelwithoutanyhousing supply adjustment costs (this corresponds to setting the parameter φ = 0) and compare r theresultswiththosebasedonthebaselinemodelspecification. Theresultsofthisexercise 44

areshowninFigure5. Figure5: Importanceofasegmentedhousingmarketformmatchingtheempiricalresults 0.2 0.1 0.0 0 4 8 12 16 20 noitaiveD FederalFundsRate ψr =1.6:baseline 0.2 ψr =0 0.0 0.2 − 0 4 8 12 16 20 noitaived% HouseRent 0.0 0.1 − 0.2 − 0 4 8 12 16 20 noitaiveD Homeownershiprate 0.2 0.0 0.2 − 0.4 − 0 4 8 12 16 20 noitaived% HousePrice 0.00 0.05 − 0.10 − 0.15 − 0 4 8 12 16 20 Horizon(quarter) noitaived% CPIInflation 0.00 0.25 − 0.50 − 0.75 − 1.00 − 0 4 8 12 16 20 Horizon(quarter) noitaived% GDP Note: this Figure shows the responses of macroeconomic aggregates to a 25 basis points positive shock in the nominal interest rate for the baseline and for two alternative scenarios in which the adjustment cost parameterissettoψ =0andψ =100. r r Figure 5 shows that, without housing market segmentation (ψ = 0), the model is not r abletomatchtheempiricalfindingthathousingrentsincreaseintheshortrunfollowinga contractionarymonetarypolicyshock. Whenmarketsarenotsegmented,landlordsfacing higher demand for renting, immediately convert housing units available to homeownership for renting at no cost. As a consequence, supply of housing for renting increases and bringsdownhousingrentsinequilibrium. Similar to the case without a housing tenure choice margin, when the housing market is not segmented (that is, the supply of housing for ownership and for rental can adjust as 45

fastasneededinresponsetochangesindemand),houserentsdeclineafteracontractionary monetarypolicyshockandsodoesCPIinflation. Alsosimilartothecasewithoutahousing tenure choice margin, the fed funds rate declines faster than in the baseline case and goes below steady sate two quarters after the initial shock. Because the housing tenure choice margin is available, the homeownership rate declines, likely reflecting some temporary fluctuations in the house price-to-rent ratio. In the model without a segmented housing market,housepricesdeclinelessthaninthebaselinemodelspecificationandsodoesGDP. After having shown in this section how the model proposed in section 4 can match the empirical regularities shown in section 3, in the next section we discuss why these results matterandwhatimplicationstheremaybeformonetarypolicy. 6 The Homeownership Decision Channel of Monetary Policy Transmission Inthissectionwediscussthemechanismunderlyingthehomeownershipdecisionchannelofmonetarypolicyanditsimplicationsformonetarypolicy. 6.1 The Mechanism Underlying the Homeownership Decision Channel of Monetary Policy To better understand how the homeowneship decision channel of monetary policy operates, we look at the responses of borrowers’ and savers’ housing demand, consumption and labor supply allocation to a monetary policy shock, and also at the response of housingsupplytothesameshock. Figure6showsthemodelresponsesofhousingdemandfor borrowers and savers (panel a), housing supply (panel b), consumption and labor supply ofborrowersandsavers(panelc)toa25-bpscontractionarymonetarypolicyshock. Whileinthemodeleverythingismovingsimultaneously,itisusefultothinkaboutthe dynamic effects of the monetary policy shock sequentially. When interest rates rise unexpectedly,thecostofhomeownershipforborrowersalsorises. Thehighercostofhomeownershipfromhigherinterestratesmakessomeborrowersthatwerehomeownerstobecome renters, which pushes up the demand for rental housing. Due to the increased demand for rental housing, rents increase, which also increases the income that savers get from the rental houses they own. The decline in borrowers’ demand for housing for ownership pushes house prices down, while savers’ higher income pushes their demand for housing up,whichactsasabackstopforhousepricestherebypreventingthemfromfallingfurther. 46

Figure6: ModelImpulseResponseFunctionsofHousingDemand,HousingSupply,Consumption,andLaborSupplytoa25-bpsContractionaryMonetaryPolicyShock (a)Housingdemand 4.5 3.5 2.5 1.5 0.5 0.5 −1.5 −2.5 −3.5 −4.5 − 0 4 8 12 16 20 Horizon(quarter) noitaived% Homeowners’aggregatehousingdemand 0.5 h:savers 0.0 h0:borrowers − 0.5 1.0 − 1.5 − 2.0 − 2.5 − 3.0 − 0 4 8 12 16 20 Horizon(quarter) noitaived% Borrowers’individualhousingdemand ho:homeowner hr:renter (b)Housingsupply 0.03 0.02 0.01 0.00 0 4 8 12 16 20 Horizon(quarter) noitaiveD Rentalhousinginvestment: Ir Rentalhousingstock: Hr 0.05 0.00 0 4 8 12 16 20 Horizon(quarter) (c)Consumptionandlaborallocations 0.5 0.0 0.5 − 1.0 − 1.5 − 2.0 − 2.5 − 3.0 − 0 4 8 12 16 20 Horizon(quarter) noitaived% Consumption 0.5 0.0 0.5 − 1.0 c:savers − c0:borrowers − 1.5 2.0 − 0 4 8 12 16 20 Horizon(quarter) noitaived% Hoursofwork L:savers L0:borrowers Note:thisFigureshowsinpanelsa),b),andc)themodelresponsestoa25-bpsincreaseinthenominalinterest rateinthebenchmarkcalibrationofthemodelofhousingdemandforborrowersandsavers,housingsupply, andconsumptionandlaborsupplyofborrowersandsavers,respectively. Assuch,andasshowninpanela)ofFigure6,theamountofhousingownedbyborrowers declinesafteracontractionarymonetarypolicyshock,whiletheamountofhousingowned bysaversincreases. 47

Due to higher interest rates, the cost of homeownership, which is a function of house prices and interest rates, increases and as a result borrowers that are homeowners reduce theamountofhousingservicestheyconsume. Higherrentsalsopushdowntheconsumption of housing services of renters, but by less than that that of homeowners because rents riselessthanthehomeownershipcost. Weknowthatrentsriselessthanthecostofownership because otherwise there wouldn’t be homeowners becoming renters as the results in Figure3show. Following the increase in demand for rental housing and the decline of house prices, as shown in panel b) of Figure 6, landlords choose to increase their rental housing stock. This increase in the supply of housing for rental is insufficient to meet in the increase in demand,whichexplainsthehigherrents. Withrespecttoconsumptionandlaborsupplydecisionsofsaversandborrowers(there isnodifferenceintheseallocationbetweenborrowersthatarehomeownersandthosethat are renters), panel c) of Figure 6 shows that initially both savers and borrowers cut consumption and reduce labor supply. However, in the periods after the monetary shock, savers increase consumption above steady state values while borrowers’ consumption remains below its steady state amount for more than 8 periods. For both savers and borrowers labor supply falls immediately in response to the contractionary monetary policy shock, but borrowers’ labor supply quickly rises above steady state levels while savers’ laborsupplyisbelowsteadylevelsforalongperiod. The differences between housing demand, consumption, and labor supply choices of borrowers and savers clearly suggest that a contractionary monetary policy shock in this modelwillbewelfareimprovingforsaversbutwelfarereducingforborrowers. InFigure7 wesummarizethesechangesinallocationsintermsofconsumptionequivalentvariation. Asexpectedfromtheresultsinpanelsa)andc)ofFigure6,butalsobecauseitisawellestablished result in the literature, savers’ welfare increases while borrowers’ decreases (panel a) in Figure 7) following a contractionary monetary policy shock. Among borrowers, as could be expected from the results shown in panel a) of Figure 6, both renters and homeownersarenegativelyaffectedbyacontractionarymonetarypolicyshockbuthomeownersmorethanrenters(panelb)ofFigure7). 6.2 Implications for Monetary Policy After having explained how monetary policy transmits when the homeownership decisionchannelofmonetarypolicyisatplay,wenowdiscusstheimplicationsformonetary policy. 48

Figure7: Impactofa25-bpscontractionarymonetarypolicyshockonwelfareacrossagents (a)Savervs. borrower 1.0 0.5 0.0 0.5 − 1.0 − 1.5 − 2.0 − 2.5 − 0 4 8 12 16 20 Horizon(quarter) )%(noitairavEC (b)Borrower-homeownervs. borrower-renter Welfare 0.0 Savers Borrowers 0.5 − 1.0 − 1.5 − 2.0 − 2.5 − 0 4 8 12 16 20 Horizon(quarter) )%(noitairavEC Welfare Borr.homeowner Borr.renter Note: panel (a) shows the welfare change, measured in consumption equivalent variation, for borrowers andsavers,followingacontractionarymonetarypolicyshockof25basispoints;panel(b)showsthewelfare changeforborrowers-homeownersandborrowers-saversfollowingthesameshockasinpanel(a). Redistributive Effects We have thus far shown that, in response to a contractionary shock, savers are better off while borrowers are worse off. This redistributive effect of monetarypolicyiswellknown,andthereforenotspecifictoourmodel. Whatisimportant to know in the context of our model, is whether the homeownership channel of monetary policy amplifies or tapers such redistributive effect. To answer this question, we compare the welfare effects of a 25 basis points contractionary monetary policy shock under the baseline model and a model without the homeownership channel of monetary policy. In the model without the homeownership channel of monetary policy borrowers can’t move betweenowningandrentingandhousingsupplycanbeadjustedatnocost-thesearethe features that we showed in Section 5 to be necessary to match the empirical results, and thereby generate a homeownership decision channel of monetary policy. The results of thisanalysisareshowninpanela)ofFigure8 Ascanbeseeninpanela)ofthisFigure,whenthehomeownershipchannelofmonetary policyisatplay,theredistributiveeffectsofmonetarypolicybetweensaversandborrowers get amplified. The dashed lines in panel a) of Figure 8 lie between the solid lines in the same panel, meaning that savers gain less and borrowers lose less in a model without the housing tenure choice of monetary policy than in a model with this channel. One implicationformonetarypolicyisthatithasstrongerredistributiveeffectsthanpreviously thought, which could render different monetary policy choices once these differences are accountedfor. Withregardstothedifferencesofwelfareamongborrowers,panelb)ofFigure8shows 49

Figure 8: Impact of a 25-bps contractionary monetary policy shock on welfare across agents withandwithoutthehousingtenurechoicechannelofmonetarypolicy (a)Savervs. borrower 1.0 0.5 0.0 0.5 − 1.0 − 1.5 − 2.0 − 2.5 − 0 4 8 12 16 20 Horizon(quarter) )%(noitairavEC (b)Borrower-homeownervs. borrower-renter Welfare 0.0 0.5 − 1.0 − 1.5 − Savers:benchmark 2.0 − Savers:nohomeownershipchannel Borrowers:benchmark − 2.5 Borrowers:nohomeownershipchannel 3.0 − 0 4 8 12 16 20 Horizon(quarter) )%(noitairavEC Welfare Borr.homeowner:benchmark Borr.homeowner:nohomeownershipchannel Borr.renter:benchmark Borr.renter:nohomeownershipchannel Note:panel(a)showsthewelfarechange,measuredinconsumptionequivalentvariation,forborrowersand savers, following a contractionary monetary policy shock of 25 basis points with and without the housing tenure choice channel of monetary policy; panel (b) shows the welfare change for borrowers-homeowners andborrowers-saverswithandwithoutthehousingtenurechoicechannelofmonetarypolicyfollowingthe sameshockasinpanel(a). that renters lose more when the housing channel of monetary policy is at play. In cumulative terms, they lose 1.3 pp. in consumption equivalent variation because of the homeownership channel. This result comes from the fact that rents go up, which reduces their available income for consumption of other goods. For homeowners, the results are less clear cut. At impact, homeowners’ welfare loss is lower because some homeowners decide to switch to renting when interest rates increase, which helps house prices decrease more when the housing tenure choice channel of monetary policy is in effect. As house prices start to rise again, and because house prices increase more in the baseline model, the welfare losses become larger when the housing tenure choice of monetary policy is present than when is not. In net terms the borrowers-homeowners lose 0.3 pp. more of consumptionequivalentwhenthehomeownershipchannelispresent. A Taylor Rule with a Measure of Inflation Without Housing Costs As shown in equation 45, when inflation is measured by CPI, movements in CPI reflect both changes in underlying inflation (π ) and changes in rents (or the price of rents relative to that of cont sumption of other goods). Because rents move in the opposite direction to inflation in responsetoamonetarypolicyshock,monetarypolicythatrespondstoCPIwillattimesbe responding to changes in relative price movements that were induced by monetary policy itself. Tounderstandtheimplicationfromthisfeedbackloopformonetarypolicy,wecom- 50

pare the effects of a 25 basis points monetary policy shock when the central bank follows a Taylor rule with inflation measured by CPI (πCPI) and when the central bank follows t follows a Taylor rule with a measure of inflation without housing costs (π ).21 The results t ofthisexerciseareshowninFigure9. Figure 9: Impulse responses when the central bank reacts to a measure of inflation without housingcosts 0.2 0.0 0 4 8 12 16 20 noitaiveD FederalFundsRate baseline:TaylorrulereactingtoCPI 0.2 Taylorrulereactingtoπ 0.0 0 4 8 12 16 20 noitaived% HouseRent 0.0 0.1 − 0.2 − 0 4 8 12 16 20 noitaiveD Homeownershiprate 0.0 0.5 − 0 4 8 12 16 20 noitaived% HousePrice 0.00 0.05 − 0 4 8 12 16 20 noitaived% CPIInflation 0.0 0.5 − 1.0 − 0 4 8 12 16 20 Horizon(quarter) noitaived% GDP π 0.0 0.1 − 0 4 8 12 16 20 Note:theFigureshowstheresponseofmacroeconomicaggregatestoamonetarypolicyshockinthebaseline calibrationandmodifiedversionofthebaselineinwhichtheTaylorrulereactstoπ, ameasureofinflation thatexcludeshousingcosts,insteadofπCPI,ameasureofinflationthatincludeshousingcosts. Figure9showsthat,relativetothebaselinecase(correspondingtoaTaylorrulereacting to CPI), when the central bank responds to a measure of inflation without housing costs, 21In the context of our model, a measure of inflation without housing costs corresponds exactly to the underlyinglevelofinflationintheeconomy,but,inpractice,thisdoesnotneedtobethecase. Whatismost importantisthatthecentralbankfollowsaTaylorrulewithameasureofinflationthatdoesn’tincludeany componentthatmovesinthesamedirectionasinterestrates. 51

realeffectsofmonetarypolicyaresmallerasGDPfallslessandthereislessGDPvolatility (20% less) as GDP monotonically recovers towards steady following a monetary policy shock. At the same time, house prices and rents are both less volatile (24% and 28% less, respectively) when the central bank responds to a measure of inflation without housing costs than when the central bank responds to CPI. When the central bank follows a Taylor rule with a measure of inflation that excludes housing costs, interest rates are kept high for a shorter period of time and they return to steady faster than when the central bank follows a Taylor rule that targets CPI. With regards to the underlying inflation, measured byπ ,volatilityisaboutthesamewhenthemonetaryauthoritytargetsCPIorameasureof t inflationwithouthousingcosts. In addition to the different effects on GDP, house prices, rents, and the path of interest rates, when the central bank targets a measure of inflation without housing costs, in response to a monetary policy shock, the homeownership rate responds less, and CPI inflationrespondsmorethanwhenthecentralbanktargetsCPI. Taken all together, the results in Figure 9 suggest that a central bank may be better able to achieve its goals by targeting a measure of inflation without housing costs than a measureofinflationthatincludeshousingcosts(suchastheCPI). ToquantifythewelfarebenefitsfromthecentralbankfollowingaTaylorrulewithmeasureofinflationwithouthousingcosts,wecalculatetheconsumerequivalentvariationafter a monetary policy shock under the baseline case and the case of a Taylor rule with a measureofinflationwithouthousingcosts. TheresultsofthisexerciseareshowninFigure 10. This Figure shows that, when the central bank targets a measure of inflation without housing costs, the redistributive effects of monetary policy are smaller – borrowers lose less and savers gain less after a contractionary monetary policy shock. And, among borrowers,bothrentersandhomeownersarelessnegativelyaffectedbyacontractionarymonetary policy shock. In Figure 10, some of the welfare gains from the central bank targeting a measure of inflation without housing costs disappear after about 6 to 8 quarters after the monetary policy shock, but, even after accounting for this, the redistributive effects of monetarypolicyarestillsmallerandbothrentersandhomeownersarebetteroff. It is important to note that the discussion of which inflation measure to target is only relevant only when the homeownership decision channel of monetary policy is at play. If monetary policy did not make households choose between owning or renting and the housing market was able to quickly adjust to changes in demand, housing rents would respond to monetary policy in the same way as other goods (Figures 4 and 5) there would not be a feedback loop from inflation to monetary policy that makes monetary policy less 52

Figure 10: Welfare effects of a 25-bps contractionary monetary policy shock when the central bankreactstoameasureofinflationwithouthousingcosts (a)Savervs. borrower 1.0 0.5 0.0 0.5 − 1.0 − 1.5 − 2.0 − 2.5 − 0 4 8 12 16 20 Horizon(quarter) )%(noitairavEC (b)Borrower-homeownervs. borrower-renter Welfare 0.0 0.5 − 1.0 − 1.5 − Savers:benchmark 2.0 Savers:Taylorrulereactingtoπ − Borrowers:benchmark 2.5 Borrowers:Taylorrulereactingtoπ − 0 4 8 12 16 20 Horizon(quarter) )%(noitairavEC Welfare Borr.homeowner:benchmark Borr.homeowner:Taylorrulereactingtoπ Borr.renter:benchmark Borr.renter:Taylorrulereactingtoπ Note: panel (a) shows the welfare change, measured in consumption equivalent variation, for borrowers andsavers,followingacontractionarymonetarypolicyshockof25basispointswhentheTaylorruletargets πCPI, ameasureofinflationthatincludeshousingcosts, andwhentheTaylorrulestargetsπ, ameasureof inflation that excludes housing costs; panel (b) shows the welfare change for borrowers-homeowners and borrowers-saverswhentheTaylorruletargetsπCPI andwhentheTaylorrulestargetsπfollowingthesame shockasinpanel(a). effectiveandmorecostlyfromanoutputlosspointofview. 7 Concluding Remarks This paper shows that monetary policy transmits to the economy through its effects on households’ homeownership decisions, and that this channel has implications for monetarypolicy. To arrive at this conclusion, the paper first empirically shows that monetary policy shocks are an important driver of the aggregate homeownership rate and that this effect is due to monetary policy shocks affecting households decisions to transition from renting to owning and vice-versa. To account for these empirical facts, the paper proposes a two-agentNewKeynesianmodelextendedwithahousingtenuredecisionandadjustment costs on housing supply. Using a version of the model calibrated to the U.S. economy, the paper shows that monetary policy effects on housing tenure decisions amplify the redistributive effects of monetary policy and that when the central bank targets a price index that includes housing costs (which are directly and indirectly measured by housing rents) itcangenerateexcessivevolatilityofhouseprices,rents,andeconomicactivityandmonetarypolicyhaslargerrealeffectswhichproduceslargerlossesinoutput. 53

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Online Appendix for “Monetary Policy and Homeownership: Empirical Evidence, Theory, and Policy Implications” A Data Description A.1 Aggregate U.S. Data In the aggregate data analysis portion of this paper, we use several publicly available macroeconomicvariables. Thetablebelowlistsanddefinesallthesevariablesandprovides thecorrespondingsources. TableA1: Aggregatemacroeconomicdata Series Source SeriesDescription Sample U.S.GDP FRED Quarterlydata,SeasonallyAdjusted 1981:Q1-2017:Q4 One-YearRate Owncalculation Quarterlyaverageoftheone-yearrate 1981:Q1-2017:Q4 monthlydata,SeasonallyAdjusted Housing Prices FRED All-TransactionsHousePriceIndexfor 1981:Q1-2017:Q4 (USSTHPI) the United States, Index 1980:Q1=100, NotSeasonallyAdjusted HousingRents Owncalculation Quarterlyaverageofthehousingrents 1981:Q1-2017:Q4 monthlydata,SeasonallyAdjusted Homeownership Rate FRED Homeownership Rate for the United 1981:Q1-2017:Q4 (RSAHORUSQ156SN) States,Percent,SeasonallyAdjusted ExcessBondPremium GilchristandZakrajsˇek(2012) 1990:Q1-2012:Q4 JKmonetarypolicyshock Jarocin´ski and Highfrequencymonetarypolicyshock 1991:Q1-2016:Q4 Karadi(2020) instruments that separates monetary policy developments from economic outlook information from the Fed’s communications MR monetary policy Miranda- SameasJKmonetarypolicyshock 1990:Q1-2009:Q4 shock Agrippino and Ricco(2021) A.2 Annual Housing Survey Data With the exception of the monetary policy shock, all the data underlying the analysis ofhouseholdtenurestatusandhousingunittypetransitionscomefromthepubliclyavailable Annual Housing Survey database that is compiled by the U.S. Census Bureau. This database has two main surveys, the national and the metro area surveys, and it covers a very large of aspects relating to U.S. household living arrangements and characteristics A-1

FigureA1: MacroeconomicVariablesandInstrumentsTimeSeries 10 8 6 4 2 0 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020 Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan % FFR 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00 0.25 − 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020 Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan 001 gol∆ ∗ Houserent 2.5 2.0 1.5 1.0 0.5 0.0 0.5 − 1.0 − 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020 Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan % ebp 69 68 67 66 65 64 63 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020 Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan % Homeownershiprate 4 3 2 1 0 1 − 2 − 3 − 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020 Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan 001 gol∆ ∗ Houseprice 1.5 1.0 0.5 0.0 0.5 − 1.0 − 1.5 − 2.0 − 2.5 − 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020 Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan 001 gol∆ ∗ CPI 2 1 0 1 − 2 − 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020 Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan 001 gol ∗ GDP JK(2020)instrument MR(2021)instrument 0.2 0.2 0.1 0.1 0.0 0.0 0.1 − 0.1 − 0.2 − 0.2 − 0.3 − 0.3 − 0.4 − 0.4 − 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020 Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Note:thisFigureshowsthetimeseriesdataforallthevariablesandexternalinstruments(Jarocin´skiand Karadi(2020)andMiranda-AgrippinoandRicco(2021))usedintheestimationoftheProxySVAR. of the U.S. housing stock. For the analysis in this paper, we only used a small subset of variableswhichwelistanddescribehowtheywereusedinTableA2. A-2

TableA2: DatafromAHSdatabaseusedintheanalysis Variableusedinanalysis Definition Usedvariable(s)fromAHSdatabase Housingunittype Indicatorvariableforthehousingunitetenurestatus. This “tenure” for years 1991, 1993, 1995, 1997, 1999, variabletakesthevalue1ifthehousingunitisdeemedfor 2001,2003,2005,2007,2009,2011,2013,and2015 rentaland0ifdeemedforownership.Othertypesofhousing unittenurestatus(e.g.”Occupiedwithoutpaymentofrent”) wereexcludedfromthesample. Housing unit rent-to-own Indicatorvariabletakingthevalue1ifthehousingunitwas “tenure” for years 1991, 1993, 1995, 1997, 1999, transition arentalunit2yearsbeforeandisanowner-occupiedunit 2001,2003,2005,2007,2009,2011,2013 currently,andthevalue0ifthehousingunitwasarentalunit 2yearspriorandstillisarentalunitcurrently. Housing unit own-to-rent Indicatorvariabletakingthevalue1ifthehousingunitwasa “tenure” for years 1991, 1993, 1995, 1997, 1999, transition owner-occupiedunit2yearsbeforeandisnowarentalunit, 2001,2003,2005,2007,2009,2011,2013 andthevalue0ifthehousingunitwasowner-occupied2 yearspriorandstillisowner-occupied. Households rent-to-own Indicatorvariabletakingthevalue1ifthehouseholdliving “xaten”foryear1991,1993,and1995; “xten”for transition inthehousingunitwasrenting1yearbeforeandownsnow, years1997,1999,2001,2003,2005,2007,2009,2011, andthevalue0ifthehouseholdwasowning1yearbefore 2013;“mgv1type”foryear2015. Combinedwith andisowningnow variable“tenure”,whichprovidesinformationon currenthousingunittype Households own-to-rent Indicatorvariabletakingthevalue1ifthehouseholdliving “xaten”foryear1991,1993,and1995; “xten”for transition inthehousingunitownedthehouseitlivedin1yearbefore years1997,1999,2001,2003,2005,2007,2009,2011, andrentsnow,andthevalue0ifthehouseholdwasrenting 2013;“mgv1type”foryear2015. Combinedwith 1yearbeforeandisrentingnow. variable“tenure”,whichprovidesinformationon currenthousingunittype Change in the aggregate Difference between the number of all households that “xaten”foryear1991,1993,and1995; “xten”for householdrentalshare switched from owning to renting and the number of years1997,1999,2001,2003,2005,2007,2009,2011, all households that switched from renting to owning di- 2013;“mgv1type”foryear2015. Combinedwith vided by the total number of households in the year. variable“tenure”,whichprovidesinformationon (cid:80)N i=1Own−to−renti−(cid:80)N i=1Rent−to−owni currenthousingunittype N Change in the aggregate Differencebetweentheshareofhousingunitsineveryyear “tenure” for years 1991, 1993, 1995, 1997, 1999, shareofrentalunits thatisarental. (cid:80)N i= t 1Rentali (cid:80)N i= t 1 −2Rentali 2001,2003,2005,2007,2009,2011,2013 Nt − Nt−2 Agetercile Indicatorvariablestakingthevalue1iftheheadofhouse- “age”foryears1991,1993,1995,1997,and1999; hold’sagefallsinagivenagetercileforthesampleofheads “hhage” for years 2001, 2003, 2005, 2007, 2009, ofhouseholdinagivenyear,and0otherwise. 2011,2013,and2015 Incomequartile Indicatorvariablestakingthevalue1ifthehousedhold’sin- “zinc2”foryears1995,1997,1999,2001,2003,2005, comefallsinagivenincomequartileforthesampleofheads 2007,2009,2011,and2013;“hincp”foryear2015 ofhouseholdinagivenyear,and0otherwise. Region Indicatorvariablestakingthevalue1ifhousingunitislo- “region” for years 1991, 1993, 1995, 1997, 1999, catedinoneofU.S.fouradministrativeregionsasdefinedby 2001,2003,2005,2007,2009,2011,and2013;“ditheU.S.CensusBureau:East,Midwest,South,andWest. vision”foryear2015 Note:theAHSdatabaseisavailableonlinehereandthedefinitionofeachofthevariablesinthedatabasecanbefound here. Note: the AHS database is available online here and the definition of each of the variables inthedatabasecanbefoundhere. B Proof of Proposition 1 Startwiththeborrowers’socialplannerproblemofmaximizing: (cid:88) ∞ (cid:26)(cid:90) 1 (cid:18) (hi)1−φr(cid:19) (cid:18) (hi)1−φo (cid:19) (Li)η (cid:27) E (β(cid:48))t lnci +(1 Ii) jr t +Ii jo t +ρi t di , 0 t − t 1 φr t 1 φo t − η t=0 0 − − where E is the expectation operator conditional on time zero information, β (0,1) is 0 ∈ the discount factor, ci is consumption of borrower i at time t, Ii 0,1 is an indicator t t ∈ { } A-3

function that takes the value of 1 if borrower i decides to own and zero if she decides to rent, hi denotes housing services, ρ is the extra utility i.i.d. draw from F(ρ) that agent i t i receiveswhenowningahouseandLi arehoursofwork,subjectto t (cid:90) 1 R (cid:90) 1 ci +Iiq ∆hi +(1 Ii)hil +bi t−1 di = bi +w(cid:48)Lidi t t t t − t t t t−1 π t t t 0 t 0 (cid:20) (cid:21) π bi IiE mq hi t+1 , t ≤ t t t+1 t R t where q , l , R , π , w(cid:48), m and bi denote the real housing price, real housing rent, gross t t t t t t nominal interest rate, gross inflation rate, real wage, loan-to-value ratio and borrowing in realterms,respectively. Thefirstorderconditionwithrespecttoci is t 1 = γ , (B1) ci t t where γ is the Lagrange multiplier associated with the budget constraint. This condition t implies that the optimal consumption is the same for all households. Let us denote this consumptionbyc(cid:48). Next,thefirstorderforLi isthefollowing: t t w (Li)η−1 = t . (B2) t c(cid:48) t Thisconditionimpliesthatoptimalhoursworkedwillalsobethesameforallhouseholds. Hence,conditionsB1andB2proveresult(ii)ofProposition1. Finallythefirstorderconditionforhi isgivenby: t  (cid:16) (cid:17) jo(hi)−φo = qt E β(cid:48)qt+1 +λ m q π ifI = 1 t c(cid:48) t − t c(cid:48) t+1 t t t+1 t+1 t (B3) jr(hi)−φr = lt ifI = 0 t c(cid:48) t t whereλ istheLagrangemultiplieroftheborrowingconstraint. Thislastconditionimplies t that the optimal housing services allocation ho will be the same across all homeowners t I = 1, and that the optimal housing services allocation hr will be the same across all t t of those who rent I = 0. However, depending on house prices and rents, the housing t allocations can be different between homeowners and renters. With this, we prove result (iii) of Proposition 1. We now turn to prove result (i). In each period, the borrowers’ social planner will have each household i owning a house instead of renting if and only if she A-4

receiveshigherinstantaneousutilityfromitthanotherwise:  1 ifandonlyif jo(hi t )1−φo +ρi > jr(hi t )1−φr I = 1−φo t 1−φr (B4) t 0 otherwise. Becauseρi isdrawnfromacontinuouscdfF(ρ)withanon-negativesupporttherewill t beauniqueρ¯ thatmakesahouseholdindifferentbetweenowningandrenting. Therefore, t households with ρi > ρ¯ choose to own a house, while those with ρi < ρ¯ decide to rent a t t t t house. Hence,theshareofhomeownerswillbegivenbyα = 1 F(ρ¯). t t − A-5

C Robustness Checks C.1 Local Projections Jorda` (2005)introducedthelocalprojections(LP)methodasanalternativetoVARmodels for the purpose of studying the dynamic effects of shocks on variables of interest. As shown in Plagborg-Mller and Wolf (2021), LP and VAR estimators are simply two dimension reduction techniques with common estimand but different finite-sample properties. In addition, Miranda-Agrippino and Ricco (2021) show that the different finite-samples are mostly related to a bias-variance trade-off, particularly at longer horizons: LP provide lower bias but higher variance when compared with VAR estimators. For the sake of robustness, we show how the dynamic responses of monetary shocks look like when estimatedbyLPandstructuralshocksareidentifiedinthesamewayaswiththeSVAR.In Figure C1 we show the results based on LP. As expected, the results are qualitatively the same as those obtained with the SVAR model and that were presented in subsection 3.1.2 ofthemaintext. Theresultsarebasedonthetwoestimationmethodsarealsoverysimilar quantitatively. C.2 FEVD based on proxy SVAR Instead of using the SVMA methodology of Plagborg-Møller and Wolf (2021a) to estimate the importance of a shock for forecast variance of the variables in the response in response to the monetary policy shock, we could have used the Proxy SVAR model to compute the forecast error variance decomposition (FEVD) of the variables in the model in response to the same monetary policy shock. While we prefer the result based on the SVMA methodology, we also computed the FEVD based on the proxy SVAR model. Figure C2 shows the forecast error variance decomposition (FEVD) estimates from the Proxy SVAR,whichrequiretheassumptionofthemodelbeinginvertible. NotwithstandingthefactthattheSMVAapproachyieldsintervalsfortheforecastvariance ratio whereas the proxy SVAR yields point estimates for the FEVD, we find that the results are broadly similar. Moreover, we also find that the results in Figure C2 are very similarforbothinstruments. A-6

Figure C1: Impulse Response Functions of Select Macroeconomic Variables to a 25 bps MonetaryPolicyShockUsingLocalProjections 0.6 0.3 0.0 0.3 − 0.6 − 0 4 8 12 16 20 noitaived% FederalFundsRate Houserent 0.10 0.05 0.00 0.05 − 0.10 − 0 4 8 12 16 20 0.2 0.1 0.0 0.1 − 0.2 − 0 4 8 12 16 20 noitaived% ExcessBondPremium Homeownershiprate 0.100 0.025 − 0.150 − 0.275 − 0.400 − 0 4 8 12 16 20 0.200 0.025 0.150 − 0.325 − 0.500 − 0 4 8 12 16 20 noitaived% Houseprice CPI 0.40 0.25 0.10 0.05 − 0.20 − 0 4 8 12 16 20 Horizon(quarter) 0.2 0.1 0.0 0.1 − 0.2 − 0 4 8 12 16 20 Horizon(quarter) noitaived% GDP MR JK Note: resultsinthefigurearebasedonthelocalprojectionsmethod(Jorda` (2005))combinedwiththeproxy VAR approach to identify the impact effects of the monetary shock on the variables of interest (Miranda- AgrippinoandRicco(2021)); themonetarypolicyshockinstrumentusedfortheresultsdisplayedinredis that of Miranda-Agrippino and Ricco (2021) and the instrument used for those reported in blue is that of Jarocin´skiandKaradi(2020)comingfromtheirthepoorman’ssignrestrictionapproach. Bothinstruments isolatethepuremonetarysurprisesfromtheinformationcontentpresentintheFed’scommunications. The solid lines report the impulse response functions point estimates, while the shaded areas report the 68% confidenceintervals.Theconfidenceintervalswerecomputedfrom1,000drawsusingaparametricbootstrap asproposedinStockandWatson(2018). A-7

Figure C2: Contribution of Monetary Policy Shocks to the Forecast Error Variance of Select MacroeconomicVariables FederalFundsRate Houserent 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 0 4 8 12 16 20 0 4 8 12 16 20 ExcessBondPremium Homeownershiprate 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 0 4 8 12 16 20 0 4 8 12 16 20 Houseprice CPI 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 0 4 8 12 16 20 0 4 8 12 16 20 Horizon(quarter) GDP 1.0 0.8 MR 0.6 0.4 JK 0.2 0.0 0 4 8 12 16 20 Horizon(quarter) Note: theforecasterrorvariancedecompositionofthemonetarypolicyshockresultsinthefigurearebased ontheproxySVARdescribedinthemethodologysectionofthepaper;themonetarypolicyshockinstrument usedfortheresultsdisplayedinredisthatofMiranda-AgrippinoandRicco(2021)andtheinstrumentused for those reported in blue is that of Jarocin´ski and Karadi (2020) coming from their the poor man’s sign restriction approach. Both instruments isolate the pure monetary surprises from the information content presentintheFed’scommunications.Thesolidlinesreportthepointestimates,whiletheshadedareasreport the90%confidenceintervals. Theconfidenceintervalswerecomputedfrom1,000drawsusingaparametric bootstrapasproposedinStockandWatson(2018). A-8