Monetary Policy, Housing Rents, and Inflation

K.7 Monetary Policy, Housing Rents, and Inflation Dynamics Dias, Daniel A. and João B. Duarte Please cite paper as: Dias, Daniel A. and João B. Duarte (2019). Monetary Policy, Housing Rents and Inflation Dynamics. International Finance Discussion Papers 1248. https://doi.org/10.17016/IFDP.2019.1248 International Finance Discussion Papers Board of Governors of the Federal Reserve System Number 1248 May 2019

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1248 May 2019 Monetary Policy, Housing Rents, and Inflation Dynamics Daniel A. Dias and João B. Duarte NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. 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, Housing Rents, and Inflation Dynamics ∗ DanielA.Dias† Joa˜oB.Duarte‡ May2019 Abstract In this paper we study the effect of monetary policy shocks on housing rents. Our main findingisthat,incontrasttohouseprices,housingrentsincreaseinresponsetocontractionary monetarypolicyshocks. Wealsofindthat,afteracontractionarymonetarypolicyshock,rental vacanciesandthehomeownershipratedecline. Thiscombinationofresultssuggeststhatmonetarypolicymayaffecthousingtenuredecisions(ownversusrent). Inaddition, weshowthat, withtheexceptionofthesheltercomponent, allothermaincomponentsoftheconsumerprice index (CPI) either decline in response to a contractionary monetary policy shock or are not responsive. Thesefindingsmotivatedustostudythestatisticalpropertiesofalternativemeasures ofinflationthatexcludethesheltercomponent. Wefindthatmeasuresofinflationthatexclude shelter have most of the statistical properties of the widely used measures of inflation, such as theCPIandthepriceindexforpersonalconsumptionexpenditures(PCE),buthavehigherstandarddeviationsandreactmoretomonetarypolicyshocks. Finally, weshowthattheresponse ofhousingrentsaccountsforalargeproportionofthe“pricepuzzle”foundintheliterature. JELclassificationcodes: E31,E43,R21. Keywords: Monetarypolicy;Housingrents;Inflationdynamics;“Pricepuzzle”;Housingtenure. ∗The authors thank, without implicating, the editor Jonathan Wright, two anonymous referees, Alejandro Justiniano, Anne Villamil, Antonella Tutino, Dan Bernhardt, Harald Uhlig, Igor Ezio, Leonardo Melosi, Mark Wright, Rui Zhao,StephenParente,WoongYongPark,ChrisSims,andvariousparticipantsattheChicagoFedseminar,theFederal ReserveBoardseminar,theBankofPortugalresearchseminarseries,theGeorgetownCenterforEconomicResearchBiennialConference,the“InteractionbetweenHousingandtheEconomy”workshop,the2015EconometricSocietyWorld Congress,andthemacroreadinggroupattheUniversityofIllinoisatUrbana-Champaign(UIUC)forhelpfulsuggestions anddiscussions. ThisresearchwassupportedbythePaulBoltzFellowshipandtheUIUCcampusresearchboardwith anArnoldO.BeckmanResearchAward. Jo˜aoB.DuartegratefullyacknowledgesfinancialsupportfromtheADEMU projectandtheFundac¸˜aoparaaCieˆnciaeTecnologia(FCT).Thispapersupersedesthepaper“TheEffectofMonetary PolicyonHousingTenureChoicesasanExplanationforthePricePuzzle”andincorporatessomeoftheempiricalresults presented in an earlier version of the paper “Housing and Monetary Policy in the Business Cycle: What do Housing RentsHavetoSay?”.Theviewsinthispaperaresolelytheresponsibilityoftheauthorsandshouldnotbeinterpretedas reflectingtheviewsoftheBoardofGovernorsoftheFederalReserveSystemorofanyotherpersonassociatedwiththe FederalReserveSystem.Allerrorsareourown. †BoardofGovernorsoftheFederalReserveSystemandCEMAPRE.Email:daniel.dias@frb.gov. ‡NovaSchoolofBusinessandEconomics.Email:joao.duarte@novasbe.pt.

1 Introduction It is now a well-established result that the housing sector plays an important role in the transmissionmechanismofmonetarypolicy(Iacoviello(2005),DelNegroandOtrok(2007),Calzaetal. (2013),andLuciani(2015)areexamplesofstudiesshowingtheeffectsofmonetarypolicyonhousing). Mostoftheliteratureonhousingandmonetarypolicyhasprimarilyfocusedonhouseprices and residential investment, and, to the best of our knowledge, there are no studies on the effect of monetary policy on housing rents. In this paper we fill this gap in the literature and use a smallscale proxy structural vector autoregressive (SVAR) model to study the effect of monetary policy shocksonhousingrents. Ourmainfindingisthat,incontrasttohouseprices,housingrentsincreaseafteracontractionary monetary policy shock. We also find that, after a contractionary monetary policy shock, rental vacanciesandthehomeownershipratedecline. Thiscombinationofresultssuggeststhatmonetary policy may affect housing tenure decisions (own versus rent). In addition, we show that, with the exceptionofshelter,allothermaincomponentsoftheconsumerpriceindex(CPI)orthepriceindex ofpersonalconsumptionexpenditure(PCE)either declineinresponsetocontractionarymonetary policyshocksorarenotresponsive. Thesefindingsmotivatedustostudythestatisticalproperties ofalternativemeasuresofinflationthatexcludethesheltercomponent. Relativetothewidelyused measuresofinflation,suchastheCPIorPCE,thesealternativemeasuresofinflationhaveaslightly lower mean, a slightly higher variance, but similar autocorrelation patterns to those of existing measures of inflation. Importantly, we find that these alternative measures of inflation react more to monetary policy shocks. We also show that the response of housing rents accounts for a large proportionofthe“pricepuzzle”foundintheliterature. Ourfindingscontributetotheliteratureon housingandmacroeconomicsandtotheliteratureoninflationdynamics. Although housing was not completely absent from the macroeconomics literature before the globalfinancialcrisis,itwasseenasaminorcomponentoftheeconomywhichdidnotdeservespecialattention(PiazzesiandSchneider(2016)). However,sincethegreatfinancialcrisis,housinghas gainedmuchmoreattentioninthemacroeconomicsliterature,asitbecameclearthathousingwas much more important than previously recognized. A distinctive characteristic of housing is that it isnotonlyanasset(thelandandthedwelling)butalsoaconsumptiongood(intheformofhousingservices). Asaconsumptiongood,housingserviceshavethelargestweightintheconsumption bundle ofthe typicalhousehold, and, formost households, theirhouse istheir most importantas- 1

set. Assuch,shocksthataffectthecostofhousingconsumptionorthepriceofhousesarelikelyto havefirst-ordereffectsinthewelfareofmosthouseholds. Wecontributetothisliteraturebyshowing that monetary policy affects the housing market by simultaneously affecting house prices and houserents,butwithoppositeeffectsonsuchpricesandrents. Our finding about the effect of monetary policy on housing rents has important implications forinflationdynamicsbecause,directlyandindirectly,rentshaveaweightofabout30%intheCPI and about 15% in the PCE. Therefore, the response of consumer prices to monetary policy shocks combines the responses of housing and non-housing prices. We show that, relative to the CPI and the PCE, a measure of prices that excludes shelter prices has a larger response to monetary policy shocks than do the measures of prices that include all goods. In other words, we find that low responses of overall consumer prices to monetary policy shocks are the result of strong opposing movements in nominal housing rents and the nominal prices of all other goods in the economy. ThisresultsuggeststhatconsumerpricesintheUnitedStatesmaybemoreresponsivetomonetary policyshocksthancurrentlythought(GertlerandKaradi(2015),PivettaandReis(2007)). Ahigher levelofconsumerpriceresponsivenesshasimplicationsforthetrade-offbetweenpricestabilityand economicgrowth. Ontheonehand, themonetarypolicyauthoritycancontrolpriceswithsmaller monetary shocks; on the other hand, if prices are more responsive to monetary policy shocks, the monetary authority will possibly have to accept higher inflation when it tries to close negative outputgaps. (Foradiscussionaboutthetradeoffbetweenpricestabilityandeconomicgrowth,see Woodford(2000),Ercegetal.(2000),orDebortolietal.(2017)). Finally,wefindthat,fortheapproachesforidentifyingmonetarypolicyshocksthatstillproduce a “price puzzle” (Romer and Romer (2004), and Bernanke et al. (2005)), the measures of inflation thatexcludesheltercostsshowamuchreduced“pricepuzzle”. Therefore,theresponseofhousing rentstomonetarypolicyshocksgoesalongwayinexplainingthispuzzle. Therestofthepaperisorganizedasfollows: insection2,wepresenttheempiricalmethodology and describe the data used; in section 3, we present the results relating to the effects of monetary policy on housing rents; in section 4, we discuss the implications of housing prices for inflation dynamics;andinsection5,weconclude. 2

2 Methodology Tostudytheeffectofmonetarypolicyonhousingrents,weuseasmall-scaleproxySVARmodel asinGertlerandKaradi(2015). Wedescribethisapproachinthenextsub-section,andthedatawe use, the way we select the number of lags in the SVAR model, and how we conducted statistical inferenceinthefollowing. 2.1 ProxySVAR LetY beann 1vectorofobservabletimeseriesvariables. AnSVARwithplagsisgivenby: t × Y = A Y +A Y +...+A Y +Hε , (1) t 1 t−1 2 t−2 p t−p t whereI ,A fori = 1,...,pandH aren nmatrices,andε avectorofnstructuralshocks. Equation n i t × 1canberewrittenwithlag-operatornotationinacompactrepresentationas A(L)Y = Hε , (2) t t whereA(L) = I A L ... A Lp. Weassumethatthelagorderpisknownandthatthedet(A(z)) n 1 p − − − has all roots outside the unit circle so that the data generating process is invertible. This equationcharacterizesalldynamicsoftheobservabletime-seriesvariablesinthemodel. Thestructural shocksareassumedtobeuncorrelatedatallleadsandlags. We are interested in disentangling the policy/feedback rule and monetary policy shocks. In other words, we want to study the effect of monetary policy surprises on the dynamics of the observable series Y . The column j of matrix H provides the contemporaneous effect of a change in t structural shock j on each variable in Y . Following Stock and Watson (2012) notation, we assume t thatthemonetarypolicyshockcorrespondstothefirstcolumnofH andwedenoteitasH . 1 Theimpulseresponsefunction(IRF)ofY withrespecttoamonetarypolicyshockisthengiven t by ∂Y t = A(L)−1H (3) 1 ∂ε 1t The parameters A(L)−1 can be identified directly from equation 1 with Hε = η innovations, t t whichwecanestimateviaordinaryleastsquares. However,H remainstobeidentified. Toidentify 1 the monetary policy shocks, H , we use the external instrument based on high-frequency identifi- 1 3

cationofshocksapproachasinGertlerandKaradi(2015),whichcombinestheexternalinstrument approachtoidentificationofstructuralshocksasinStockandWatson(2012)andMertensandRavn (2013) with high frequency event studies around monetary policy announcements as in Kuttner (2001),Gurkaynaketal.(2005),Hamilton(2008),andCampbelletal.(2012). Weneedanexternalinstrument,Z ,thatfulfillsthefollowingassumptions: t 1. Relevance: E(ε Z ) = α = 0 1t t (cid:54) 2. Exogeneity: E(ε Z ) = 0,j = 2,...,n jt t These two assumptions show that a valid set of instruments must be correlated with the structuralmonetarypolicyshock,butnotwithotherstructuralshocks. AsinGertlerandKaradi(2015), we use changes in the three-month-ahead monthly federal funds futures around a monetary policy announcement as a valid instrument. The difference before and after a policy announcement represents the change in the expectations of financial market participants due to an unanticipated monetary policy action. The main concept behind using an external instrument is that, when regressing the VAR innovations η on the instrument Z , the fitted value of the regression identifies t t the structural shock up to its sign and scale. Further details on the derivation of structural shocks usingexternalinstrumentsarepresentedinStockandWatson(2012),MertensandRavn(2013),and GertlerandKaradi(2015).1 2.2 Data,LagSelection,andStatisticalInference Toestimatethemodeldescribedintheprevioussub-sectionweusedeitherfiveorsixvariables. These variables are a combination of a common set of four variables (industrial production, CPI, one-yearTreasuryrate, andexcessbondpremium, correspondingtothefourvariablesusedinthe simpleVARmodelinGertlerandKaradi(2015))withoneortwomorevariables,whicharechosen based on the question we are addressing. In most of our empirical applications we use monthly data, but in one of our analysis we use quarterly data due to data availability. The monthly data runfromJanuary1983toDecember2017,whilethequarterlydatarunfrom1981:Q1to2017:Q4. In Tables2and3intheAppendixwedescribeallthedatathatweuse. 1TheGertlerandKaradi(2015)shockisnotcriticismfree. Ramey(2016)arguesthattheshockmaybeunanticipated butnotexogenoustotheeconomy. Assuch, iftheeconometriciandoesnotaccountfortheFed’sprivateinformation aboutthestateoftheeconomy,thevalidityoftheinferencebasedonthisshockmaybelimited. Inaddition,thisshock alsoincludestheso-calledinformationshock,andthereforeitisnotapuremonetarypolicyshock;JarocinskiandKaradi (2018)tacklethisissue. 4

WhenusingmonthlydatatoestimatetheSVARmodel,wefollowGertlerandKaradi(2015)and selectthenumberoflags,p,intheSVARmodeltobe12.2 Whenusingquarterlydatatoestimatethe SVAR model, we use 4 lags to be consistent with the number of lags that we use in the estimation withmonthlydata. A final, but very important, component of our methodology has to do with the way we make statistical inference. Following Bru¨ggemann et al. (2016) and Jentsch and Lunsford (2016), who show that, in the presence of heteroskedasticity, it is incorrect to use a wild bootstrap method to estimate the distribution of impulse responses in the context of proxy SVARs, we use a moving block bootstrap method to estimate the distribution of impulse responses.3 The algorithm of the residual-based moving block bootstrap we use is the same as in Mertens and Olea (2018), which uses the same procedure as Jentsch and Lunsford (2016) but without the centering of the proxies in step 4 of their procedure. To initialize the algorithm we choose a block of length (cid:96) and compute the number of blocks N = [T/(cid:96)], where [.] rounds up to the nearest integer so that N(cid:96) T.4 Next ≥ we collect the n (cid:96) blocks of the innovations η and the proxy variable. Then, we independently t × drawN integerswithreplacementfromtheset 1,...,T (cid:96)+1 ,placingequalprobabilityoneach { − } elementoftheset,collecttheblocksofresidualsandproxiesusingthedrawnintegersaspositional indexes,andwecentertheresidualstoensurethattheyhaveazero-mean. Newdataaregenerated using the data generating process with the newly constructed residuals. Finally, we re-estimate the reduced VAR model parameters and H , and compute the impulse responses. We repeat this 1 process 5000 times in order to get the distribution of impulse responses. From this distribution of impulseresponses,weshowthemedianimpulseresponseandthe68%confidencebands.5 3 The Effect of Monetary Policy Shocks on Housing Rents Inthissectionwepresentthemainresultofthepaper—theeffectofmonetarypolicyonhousing rents —, provide an explanation for the result based on the effect on monetary policy shocks on 2BoththeAkaikeandSchwarzinformationcriteriaapproachessuggestusing3lagsinstead, buttobeclosertothe literature,wechosetouse12lags. Nevertheless,weconductedarobustnessanalysiswith3lags,andtheresultsremain unchanged. 3Wenotethat,asdiscussedinMertensetal.(2018),thereareotheralternativemethodstoestimatethedistribution of impulse responses in the context of SVARs that are also asymptotically consistent. While all our results are based onamovingblockbootstrapmethod,wealsoimplementedtheDeltamethodandaparametricbootstrapdescribedin Montiel-Oleaetal.(2016),andtheresultsobtainedwiththesemethodsareinlinewiththoseobtainedusingthemoving blockbootstrapmethod. 4Wepickthelengthoftheblockusing(cid:96)=5.03T1/4asinJentschandLunsford(2016). 5See Jentsch and Lunsford (2016) for a more detailed description of the algorithm as well as for theoretical results concerningtheconsistencyofthemovingblockbootstrapprocedure. 5

housingtenuredecisions,andshowthattheresponseofrentsisdifferentfromthatofthepricesof goodsorotherservices. IndustrialProduction HousingRents 0.5 0.6 0 0.4 0.5 0.2 − 1 0 − 1.5 0.2 − 0 6 12 18 24 30 36 42 − 0 6 12 18 24 30 36 42 PriceLevel One-YearRate 0.1 0.4 0 0.2 0.1 − 0 0.2 − 0.3 0.2 − 0 6 12 18 24 30 36 42 − 0 6 12 18 24 30 36 42 ExcessBondPremium 0.4 0.2 0 0.2 − 0 6 12 18 24 30 36 42 Figure 1: Baseline results: percentage responses of the baseline model variables to a 25 bps monetary policy shock identified with high-frequency surprises on federal funds 3-month futures around policy meetings.Theredlinecorrespondstothemedianresponseandtheshadedareascorrespondto68%confidencebands,whichwerecomputedusingamovingblockbootstrapmethod.Thefirst-stageregression F-testhasavalueof18.29,anditsrobustR2is5.27%. Figure 1 shows the IRFs of a 25 basis point (bps) monetary policy shock on the four core variables and on housing rents. The IRFs of industrial production, CPI, one-year Treasury rate, and excess bond premium are standard and well known.6 The novel result pertains to the response of nominal housing rents to a monetary policy shock. In contrast to the prices of goods or other 6InthecaseoftheCPI,theresultisstandardforthisidentificationofmonetarypolicyshocks;however,asweshow inthenextsection,withotheridentificationsofmonetarypolicyshocks,itisstillcommontoobserveaslightincreaseof pricesbeforetheystarttodecline,aresultknownintheliteratureasthe“pricepuzzle”(Sims(1992)). 6

services, nominal housing rents increase in response to a contractionary monetary policy shock.7 Note that this result implies that real housing rents (defined as the ratio of nominal housing rents to consumer prices) also increase in response to a contractionary monetary policy shock, but by more than nominal housing rents.8 This finding is surprising because nominal housing rents are the price of a service — shelter — and, from standard monetary theory, it would be expected that all nominal prices should decline (or at least not increase) after a contractionary monetary policy shock. Forinstance,ifrentswereverysticky,itwouldfollowthatnominalrentswouldnotchange (orwouldchangeatalowerratethanothergoods)andthat,asothernominalconsumerpricesfall, real housing rents would increase. Our results show, however, that this mechanism cannot be at playbecausenominalrentsreactquickly,whichinturnimpliesthattheremustbeastrongreaction inrealtermsofthehousingrentalmarket. Onepossibleexplanationforthisresultisthatthemonetaryshocksarenotwellidentified,and therefore the response of housing rents to monetary policy shocks shown in Figure 1 is spurious. This explanation seems implausible because the IRFs of the other four variables included in the SVAR model behave as expected.9 Moreover, the identification of monetary policy shocks that we followisthesameasthatusedinGertlerandKaradi(2015),whichisawell-establishedmethodin thisliterature. Analternativeexplanationisthatmonetarypolicyaffectshousingtenuredecisions—ownversus rent. If both the supply of housing for rental and of housing for ownership are inelastic in theshortrun, andthereislimitedconvertibilitybetweenhomesforsaleandhomesforrent, when interest rates go up, mortgage rates rise and the cost of homeownership increases. As homeownership costs rise, the demand for rental housing also increases, and, as a result, housing rents rise. TotestthishypothesisweusetheSVARmodeldescribedintheprevioussectiontoestimatetheresponse of housing prices, the housing stock for renting vacancy rate, and the homeownership rate to a contractionary monetary policy shock. The results of this exercise are shown in Figure 2 and areallbasedonquarterlydata,becausethehomeownershiprateandthehousingstockforrenting vacancy rate data are only available at that frequency. We also re-estimated the response of hous- 7FollowingtheresultsofGertlerandKaradi(2015),wechosetousethethree-month-aheadforwardfederalfundsrate astheinstrumentformonetarypolicy,asithasthebeststatisticalpropertiesamongtheinstrumentsanalyzedinGertler andKaradi(2015).However,wealsoexperimentedwithotherinstrumentsandourmainresultsheld. 8InFigure8intheAppendix, weshowthatindeedrealhousingrentsalsoincreaseinresponsetoacontractionary monetarypolicyshock,butwedonotformallytestwhethertheresponseofnominalhousingrentsisstatisticallydifferent fromthatofrealhousingrents. 9Wenotethatourresultswithrespecttotheresponseofrentstomonetarypolicyshocksare,overall,robusttousing differentapproachestoidentifymonetarypolicyshocksandtodifferentsampleperiods. 7

ing rents using quarterly data.10 In line with our hypothesis that monetary policy affects housing tenuredecisions,theresultsinFigure2showthat,inresponsetoacontractionarymonetarypolicy shock, housing rents increase and housing prices, the homeownership rate, and the housing stock availableforrentdecline. HousingPrices HousingRents 0.05 0.08 0 0.06 0.05 0.04 − 0.1 0.02 − 0.15 0 − 0.2 0.02 − 0 6 12 18 − 0 6 12 18 HousingStockforRentingVacancyRate HomeownershipRate 0.02 0 0.02 0 − 0.04 0.02 − − 0.06 − 0.04 − 0.08 − 0.06 0.1 − − 0.08 0.12 − 0 6 12 18 − 0 6 12 18 Figure 2: Testing the housing tenure choice channel: percentage responses of selected variables of the proxy svar model to a 25 bps shock in the federal funds rate. The red line corresponds to the median response and the shaded areas correspond to 68% confidence bands, which were computed using a movingblockbootstrapmethod. Sofar,wehaveshownonlythathousingrentsincreaseinresponsetoacontractionarymonetary policy shock; however, housing rents are only a small portion of the total consumer consumption bundle and the overall CPI. A natural question is whether other components of the CPI behave 10Each panel in Figure 2 is obtained by estimating an SVAR model with a common set of four variables (industrial production,CPI,one-yearTreasuryrate,andexcessbondpremium)andanadditionalvariable(eitherhousingprices, housingrents,housingstockforrentingvacancyrate,orthehomeownershiprate). 8

similarly to housing rents. In Figure 3, we show the IRFs of the main components of the CPI. The first three variables — rent of primary residence (same as housing rent), owners’ equivalent rent (OER),andshelter(thecombinationofrentsandtheOER)—areallpartofthehousingcomponent of the CPI, while the other six variables — food and beverages, transportation, apparel, medical care, education and communication, and recreation — are the remaining major components of the CPI.11,12 ThefirstrowofFigure3showsthatnotonlyhousingrentsriseafteracontractionarymonetary policy shock, but also the OER, and, consequently, shelter, which we define as the combination of housing rents and the OER. As for the other major components of the CPI, the results show that prices either decrease (food and beverages and transportation) or have no reaction to a monetary policyshock(apparel,medicalcare,educationandcommunication,andrecreation).13 The fact that the OER behaves similarly to housing rents should not be surprising, as the OER is an estimate of homeowners’ rents that uses housing rents as an input. However, the fact that two sub-components of the CPI that account for about one-third of the total CPI increase after a contractionarymonetarypolicyshockraisesthequestionoftheimportanceofhousingforinflation dynamics. Wetacklethisquestioninthenextsection. 4 Shelter Costs and Inflation Dynamics In this section, we study the implications of the dynamics of shelter costs (rents and the OER) for inflation dynamics. We start by describing how the shelter costs component of the CPI or PCE is constructed, compare some of the statistical properties of the widely used measures of inflation (the CPI and the PCE) with those of alternative measures of inflation that exclude shelter costs, compare the responses to monetary policy shocks of inflation measures including and excluding shelter costs, and end by evaluating the importance of the response of shelter to monetary shocks forthe“pricepuzzle”. 11Inthenextsectionwediscussinsomedetailtheconceptofowners’equivalentrentandhowitisconstructedbythe BLS. 12Our definition of shelter costs is slightly different from that of the BLS, as we consider only the rent of primary residenceandtheOERcomponents,whiletheBLSalsoincludescostsforlodgingawayfromhome. Becausetheweight ofsuchcostsisonlyabout1%,forpracticalpurposes,thereisnorelevantdifferencebetweenourmeasureofsheltercosts andthatoftheBLS. 13Wenotethat,whentheDeltaandtheparametricbootstrapmethodsareusedtoestimatethedistributionofIRFs,the responsesofrents,OER,andshelterarestatisticallysignificantformosttimehorizons.Atthesametime,similartowhat weshowinFigure3,fortheothercomponentsoftheCPIwefindthattheresponseoftheseitemstoamonetaryshockis notstatisticallysignificantforalltimehorizons. 9

HousingRents Owners’EquivalentRent Shelter 0.4 0.2 0.4 0.1 0.2 0.2 0 0 0 0.1 − 0.2 0.2 0.2 − 0 6 12 18 24 30 36 42 − 0 6 12 18 24 30 36 42 − 0 6 12 18 24 30 36 42 FoodandBeverages Transportation Apparel 0.2 1 0.4 0.5 0.2 0 0 0 0.2 − 0.5 0.2 − − 0.4 1 0.4 − 0 6 12 18 24 30 36 42 − 0 6 12 18 24 30 36 42 − 0 6 12 18 24 30 36 42 MedicalCare Recreation EducationandCommunication 0.4 1 1.5 0.5 1 0.2 0 0.5 0 0.5 0 − 0.2 1 0.5 − 0 6 12 18 24 30 36 42 − 0 6 12 18 24 30 36 42 − 0 6 12 18 24 30 36 42 Figure3:ResponseofthemaincomponentsoftheCPItoamonetarypolicyshock:percentageresponses of selected variables of the proxy svar model to a 25 bps shock in the federal funds rate. The red line correspondstothemedianresponseandtheshadedareascorrespondto68%confidencebands,which werecomputedusingamovingblockbootstrapmethod. 4.1 ShelterCostsinMeasuresofInflation HousingexpensesarethelargestcomponentoftheCPI,withatotalweightof42%intheindex. This component has two sub-components: shelter and other housing-related expenses, with the formercurrentlyweighingaround33%inthetotalCPIandthelatterabout9%. Thefactthatshelter costs have such a large weight in the overall CPI suggests that the index will be very sensitive to whathappensinthiscomponent. AsforthePCE,housingexpensesarealsoitslargestcomponent; 10

however, the weight is smaller than in the CPI, as such expenses account for only close to 24% of the index, and shelter is only 16% of the overall index — about half of the weight of shelter in the CPI. Given the lower weight of shelter costs, we expect the PCE to be less sensitive to changes in sheltercoststhantheCPI. Althoughthepricesofmostofthesub-componentsofhousing(e.g., rentofprimaryresidence, utilities, or insurance) are relatively easy to measure, the price of shelter for homeowners is not, because it is not a market price. Before 1983, the BLS used house prices, mortgage interest rates, propertytaxes,insurance,andmaintenancecoststoestimatesheltercostsforhomeowners. Because not all of these items represent costs for a homeowner, in 1983, the BLS changed its approach and beganusingtheconceptofOERtoestimatetherentalcostforhomeowners. TheOERisanestimate of the rent that a homeowner would have to pay if he or she was renting that same home. To computetheOER,theBLSusesobservedrentsandthecharacteristicsofthehomesbeingrentedas inputstothemethod.14 Asaresult,thecorrelationbetweentheyear-on-yeargrowthrateofthetwo series is very high — close to 85%. For this reason, we consider rent of primary residence and the OERtobebasicallythesame,and,fromhereon,weanalyzeonlysheltercosts. 4.2 InflationMeasuresNetofShelterCosts Onewaytounderstandtheimportanceofsheltercostsforinflationdynamicsisbyconsidering alternative measures of inflation that exclude shelter costs. In Figures 4 and 5, we show the level andthemonth-to-monthgrowthratesof(1)theCPIandtheCPInetofshelterand(2)thePCEand thePCEnetofshelter,whileinTable1,weprovidesomedescriptivestatistics. Table1: Inflationindexesdescriptivestatistics. mean s.d. ρ : x ,x ρ : x ,x ADFa 1 t t−1 2 t t−2 CPI 0.22 0.25 0.44 0.06 -7.35 CPInetofshelter 0.19 0.39 0.44 0.08 -7.37 PCE 0.19 0.19 0.43 0.14 -6.70 PCEnetofshelter 0.17 0.23 0.44 0.15 -6.90 aADFisAugmentedDicky-Fuller 14FormoredetailsonhowtheBLSconstructstherentofprimaryresidenceandtheOER,seeBureauofLaborStatistics (2009) 11

CPIvsCPInetofshelter PCEvsPCEnetofshelter 260 120 240 110 220 100 200 90 180 160 80 140 70 120 60 100 CPI PCE CPInetofshelter PCEnetofshelter 80 50 Jan. 1983 Dec. 2017 Jan. 1983 Dec. 2017 Figure4: MonthlyindextimeseriesofCPIvs. CPInetofshelter, andPCEvs. PCEnetofshelterfrom January1983toDecember2017. ThevisualinspectionofFigures4and5suggeststhatthepriceindexeswithandwithoutshelter costsarenottoodifferentfromeachother. Themostnoticeabledifferenceisthatthepricemeasures including shelter costs increased at a slightly faster pace than those excluding such costs, as the blue lines in Figure 4, corresponding to the overall price indexes, are always above the red lines, corresponding to the price indexes excluding shelter costs. In addition, Figure 5 suggests that the overall price indexes are less volatile than the price indexes excluding shelter costs. The entries in Table1confirmthatindeedthepriceindexeswithandwithoutsheltercostshavesimilarstatistical characteristics, but the measures including shelter increased more on average between 1983 and 2017 and that they are less volatile. Despite some small differences in the mean and the standard deviation,thetwopairsofinflationmeasuresshowremarkablysimilarautocorrelationstructures— thefirst-andsecond-orderautocorrelationtermsarealmostidentical,andallseriesarestationary. Althoughthetwopairsofvariablesareverysimilarinseveraldimensions(asshowninFigures 4 and 5 and Table 1), we are interested in knowing whether these variables respond differently to monetary shocks. The left-hand panels of Figure 6 show the IRFs of (1) the CPI and the CPI net of shelter and (2) the PCE and the PCE net of shelter; while the right-hand panels of the same figure 12

CPIvsCPInetofshelterInflation PCEvsPCEnetofshelterInflation 2 2 1.5 1.5 1 1 0.5 0.5 0 0 0.5 0.5 − − 1 1 − − 1.5 1.5 − − 2 2 − − 2.5 CPI 2.5 PCE − − CPInetofshelter PCEnetofshelter 3 3 Ja−n. 1983 Dec. 2017 Ja−n. 1983 Dec. 2017 Figure5: MonthlyinflationtimeseriesofCPIvs. CPInetofshelter,andPCEvs. PCEnetofshelterfrom January1983toDecember2017. showthedifferencebetweentheimpulseresponsesof(1)theCPIandCPInetofshelterand(2)the PCE and the PCE net of shelter.15 The results in Figure 6 show that the measures of inflation that excludeshelterreactmoretoamonetarypolicyshockthanthemeasuresofinflationthatincludeall items. Moreover,asshownintheright-sidepanelsofFigure6,thedifferencebetweentheimpulse responses of the two inflation measures is statistically significant. As expected, given the larger weight of shelter in the CPI, the difference is larger for the CPI than for the PCE; however, the differenceisstatisticallysignificantinbothcases. A natural question is, why do these findings matter? First, by not taking into account the responseofrents(vis-a`-visshelter)tomonetarypolicy,monetarymodelswillbemissinganimportant element of the effect of monetary policy on prices, and therefore theory and data will not be well 15The results in Figure 6 are based on a proxy SVAR model with five variables — industrial production, one-year Treasuryrate,excessbondpremium,CPI(PCE),andCPI(PCE)netofshelter. WesimultaneouslyincludetheCPI(PCE) andtheCPI(PCE)netofshelterinthemodeltotestiftheimpulseresponsesofthetwoinflationmeasuresarestatistically different.TocomputetheWald-statisticofthehypothesisthattheimpulseresponsesoftheCPI(PCE)andtheCPI(PCE) netofshelterarestatisticallydifferent,webootstrapthedifferencebetweentheimpulseresponsestothesamemonetary policyshockusingamovingblockbootstrapmethod. 13

CPIvs. CPInetofshelter Difference: CPIvs. CPInetofshelter 0.2 0.2 0 0.1 0.2 0 − CPI CPInetofshelter 0.4 0.1 − 0 6 12 18 24 30 36 42 − 0 6 12 18 24 30 36 42 PCEvs. PCEnetofshelter Difference: PCEvs. PCEnetofshelter 0.2 0.2 0 0.1 0.2 0 − PCE PCEnetofshelter 0.4 0.1 − 0 6 12 18 24 30 36 42 − 0 6 12 18 24 30 36 42 Figure6: All-itemsinflationmeasuresvs. net-of-sheltermeasures: percentageresponsesofthebaseline modelvariablestoa25bpsmonetarypolicyshockidentifiedwithhigh-frequencysurprisesonfederal funds3-monthfuturesaroundpolicymeetings.Thesolidredandthedashedbluelinescorrespondtothe medianresponses,whiletheshadedareascorrespondto68%confidencebands,whichwerecomputed usingamovingblockbootstrapmethod. mapped. Second and more important, when monetary policy authorities target a measure of inflation like the CPI or the PCE, to produce the same change in inflation, monetary authorities will need larger monetary policy shocks, with resulting larger real effects and nominal price volatility. Giventheresultsofthispaper, lookingatthetotalCPIorPCEreactionstomonetarypolicymasks important heterogeneity in consumer price variation. We find that low responses of overall consumer prices to monetary policy shocks are the result of strong opposing movements in nominal housingrentsandthenominalpricesofallothergoodsandservicesintheeconomy. 14

Inaddition,basedonourresults,theresponseofrentstomonetarypolicyshocksislikelytobe theresultofashiftindemandbetweenrentalandowner-occupiedhomes. Therefore,thechangein rents as a result of monetary policy shocks is a relative price movement and not a change in trend (or the underlying inflation rate). Monetary policy should react to changes in the trend of prices (inflation) but not to relative price changes. A measure of inflation that includes rents/shelter will likely lead monetary authorities that follow a monetary policy rule, such as the Taylor rule, to respondbothtochangesininflationandtorelativepricemovements. 4.3 HousingRentsandthe“PricePuzzle” One argument in favor of using the high-frequency instrument approach, as in Gertler and Karadi (2015), to identify monetary policy shocks is that, when this approach is used, there is no “pricepuzzle”—pricesrisingafteracontractionarymonetarypolicyshock. Ourempiricalresults basedonthehigh-frequencyinstrumentapproachconfirmthisfinding. However,aswementioned previously,theGertlerandKaradi(2015)shockisnotcriticismfree,andsomeauthorspreferusing the Romer and Romer (2004) shock. One critique of Romer and Romer (2004) is that the response of prices to a contractionary monetary policy shock still exhibits a “price puzzle”. In Figure 7, we compare the responses of prices including and excluding shelter for different methods of identifyingmonetarypolicyshocks;inadditiontothehigh-frequencyapproach,weuseaFAVARmodelas inBernankeetal.(2005)andtheRomerandRomer(2004)monetarypolicyshocksasaninstrument for the proxy SVAR described in section 2.16 We find that, for the high-frequency instrument case, the response of prices excluding shelter costs to a contractionary monetary policy shock is larger than that of price measures including shelter costs, and of the and Romer and Romer instrument case it turns negative much earlier in comparison to price measures including shelter costs. In the case of the FAVAR model, both the all-items CPI and PCE response show a large and positive responsetoacontractionarymonetarypolicyshock,whilethesamepricemeasuresexcludingshelter eitherdonotshowanyresponse(thecaseoftheCPInetofshelter)orhaveaverymoderatepositive response(thecaseofthePCEnetofshelter). Although we cannot claim that excluding shelter costs from price measures solves the “price puzzle”,itgreatlyamelioratesthepuzzle. Inotherwords,theresponseofhousingrentstomonetary policyshocksdoesnotfullyaccountforthe“pricepuzzle”,butitgoesalongwayinexplainingit. 16IntheAppendix,weprovideabriefdescriptionoftheFAVARmodelanddetailsoftheimplementationofthemodel. 15

0.2 0 0.2 − 0.4 − 0 10 20 30 40 50 skcohSycneuqerF-hgiH CPIvsCPInetofshelter PCEvsPCEnetofshelter 0.2 0 0.2 − CPI PCE CPInetofshelter PCEnetofshelter 0.4 − 0 10 20 30 40 50 0.4 0.2 0 0 10 20 30 40 50 skcohSRAVAF 0.4 0.2 0 0 10 20 30 40 50 0.2 0 0.2 − 0.4 − 0 10 20 30 40 50 skcohSremoRdnaremoR 0.2 0 0.2 − 0.4 − 0 10 20 30 40 50 Figure7:All-itemsinflationmeasuresvsnet-of-sheltermeasures:percentageresponsesoftheconsumer priceindexestoa25bpsmonetarypolicyshockidentifiedwithhigh-frequency,FAVAR,andRomerand Romer(2004)shocks.Thesolidredandthedashedbluelinescorrespondtothemedianresponses,while the shaded areas correspond to 68% confidence bands, which were computed using a moving block bootstrap for the high-frequency shocks, a two-step bootstrap for the FAVAR shocks, and a standard bootstrapfortheRomerandRomershocks. 5 Concluding Remarks Inthispaper, weshowthathousingrents, incontrasttothepricesofotherservicesandgoods, increase in response to a contractionary monetary policy shock. In addition, we show that this result extends to the shelter component of the CPI and the PCE, and that the responses of these 16

priceindexestomonetaryshocksareattenuatedbytheresponseofsheltercosts. Wearguethatitis importanttotakeintoaccounttheresponseofsheltercostsforthreereasons: first,forthepurposeof linkingthemeasuresofinflationintheoreticalmonetarymodelstothesamemeasuresinthedata; second, toenablemonetaryauthoritiestoavoidexcessconsumerpricevariationwhenconducting monetarypolicy;andthird,toexplaintoalargeextentthe“pricepuzzle”foundintheliterature. In future research, we plan to analyze the welfare effects of monetary policy in the context of housing tenure choice. In particular, we are interested in understanding whether monetary policy has different welfare effects on homeowners and renters and whether the monetary authority shouldconsidertheseeffectswhensettingmonetarypolicy. References Bernanke,B.S.,Boivin,J.,andEliasz,P.(2005).Measuringtheeffectsofmonetarypolicy:Afactor-augmented vectorautoregressive(FAVAR)approach. QuarterlyJournalofEconomics,120(1):387–422. Bru¨ggemann,R.,Jentsch,C.,andTrenkler,C.(2016). Inferenceinvarswithconditionalheteroskedasticityof unknownform. JournalofEconometrics,191(1):69–85. BureauofLaborStatistics(2009). HowtheCPImeasurespricechangeofowner’sequivalentrentofprimary residence(OER)andrentofprimaryresidence(Rent). Technicalreport. Calza,A.,Monacelli,T.,andStracca,L.(2013). Housingfinanceandmonetarypolicy. JournaloftheEuropean EconomicAssociation,11(s1):101–122. Campbell,J.R.,Evans,C.L.,Fisher,J.D.,andJustiniano,A.(2012). Macroeconomiceffectsoffederalreserve forwardguidance. BrookingsPapersonEconomicActivity,2012(1):1–80. Debortoli,D.,Kim,M.J.,Linde´,J.,andNunes,M.R.C.(2017). Designingasimplelossfunctionforcentralbanks: Doesadualmandatemakesense? InternationalMonetaryFund. DelNegro,M.andOtrok,C.(2007). 99Luftballons: MonetarypolicyandthehousepriceboomacrossU.S. states. JournalofMonetaryEconomics,54(7):1962–1985. Erceg, C.J., Henderson, D.W., andLevin, A.T.(2000). Optimalmonetarypolicywithstaggeredwageand pricecontracts. JournalofMonetaryEconomics,46(2):281–313. Forni,M.,Giannone,D.,Lippi,M.,andReichlin,L.(2009). Openingtheblackbox: Structuralfactormodels withlargecrosssections. EconometricTheory,25(5):1319–1347. 17

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A Additional Figures IndustrialProduction RealHousingRents 0.5 0.6 0 0.4 0.5 0.2 − 1 0 − 1.5 0.2 − 0 6 12 18 24 30 36 42 − 0 6 12 18 24 30 36 42 PriceLevel One-YearRate 0.1 0.4 0 0.2 0.1 − 0 0.2 − 0.3 0.2 − 0 6 12 18 24 30 36 42 − 0 6 12 18 24 30 36 42 ExcessBondPremium 0.4 0.2 0 0.2 − 0 6 12 18 24 30 36 42 Figure8: Additionalresults: percentageresponsesofthebaselinemodelvariablestoa25bpsmonetary policy shock identified with high-frequency surprises on federal funds 3-month futures around policy meetings. The red line corresponds to the median response and the shaded areas correspond to 68% confidencebands,whichwerecomputedusingamovingblockbootstrapmethod. Weusetheall-items CPI to deflate the nominal housing rents. The first-stage regression F-test has a value of 18.29, and its robustR2is5.27%. 20

B Data Used Table2: MonthlyDataDescription Series Source SeriesDescription Sample IndustrialProduction(INDPRO) FRED Index2012=100,SeasonallyAdjusted 1983:M1-2017:M12 HousingRents(CUSR0000SEHA) FRED Consumer Price Index for All Urban Con- 1983:M1-2017:M12 sumers:Rentofprimaryresidence,Index1982- 1984=100,SeasonallyAdjusted PriceLevel(CPIAUCSL) FRED Consumer Price Index for All Urban Con- 1983:M1-2017:M12 sumers: All Items, Index 1982-1984=100, SeasonallyAdjusted One-YearRate(GS1) FRED 1-Year Treasury Constant Maturity Rate, Per- 1983:M1-2017:M12 cent,NotSeasonallyAdjusted ExcessBondPremium Jarocinski and GilchristandZakrajek(2012) 1983:M1-2017:M12 Karadi(2018) Owners’ Equivalent Rent FRED Consumer Price Index for All Urban Con- 1983:M1-2017:M12 (CUSR0000SEHC) sumers:Owners’equivalentrentofresidences, IndexDec1982=100,SeasonallyAdjusted Shelter Owncalculation Average of rents and owners’ equivalent rent 1983:M1-2017:M12 appropriately weighted by the corresponding CPI weights, Index Dec 1982=100, Seasonally Adjusted FoodandBeverages(CPIFABSL) FRED Consumer Price Index for All Urban Con- 1983:M1-2017:M12 sumers: Food and Beverages, Index 1982- 1984=100,SeasonallyAdjusted Transportation(CPITRNSL) FRED Consumer Price Index for All Urban Con- 1983:M1-2017:M12 sumers: Transportation, Index 1982-1984=100, SeasonallyAdjusted Apparel(CPIAPPSL) FRED Consumer Price Index for All Urban Con- 1983:M1-2017:M12 sumers: Apparel, Index 1982-1984=100, SeasonallyAdjusted MedicalCare(CPIMEDSL) FRED Consumer Price Index for All Urban Con- 1983:M1-2017:M12 sumers: Medical Care, Index 1982-1984=100, SeasonallyAdjusted Recreation(CPIRECNS) FRED Consumer Price Index for All Urban Con- 1993:M1-2017:M12 sumers:Recreation,SeasonallyAdjusted Education and Communication FRED Consumer Price Index for All Urban Con- 1993:M1-2017:M12 (CPIEDUSL) sumers:EducationandCommunication,Index Dec1997=100,SeasonallyAdjusted 21

CPINetofShelter Owncalculation CPI excluding shelter, 1982-1984=100, Season- 1983:M1-2017:M12 allyAdjusted PCE(PCEPI) FRED Personal Consumption Expenditures: Chain- 1983:M1-2017:M12 typePriceIndex PCENetofShelter Owncalculation PCEexcludingshelter,Chain-typePriceIndex, 1983:M1-2017:M12 SeasonallyAdjusted Table3: QuarterlyDataDescription Series Source SeriesDescription Sample IndustrialProduction Owncalculation Quarterlyaverageoftheindustrialproduction 1981:Q1-2017:Q4 monthlydata,SeasonallyAdjusted One-YearRate Owncalculation Quarterlyaverageoftheone-yearratemonthly 1981:Q1-2017:Q4 data,SeasonallyAdjusted HousingPrices(USSTHPI) FRED All-Transactions House Price Index for the 1981:Q1-2017:Q4 UnitedStates,Index1980:Q1=100,NotSeasonallyAdjusted HousingRents Owncalculation Quarterlyaverageofthehousingrentsmonthly 1981:Q1-2017:Q4 data,SeasonallyAdjusted HousingStockforRentingVacancy FRED RentalVacancyRatefortheUnitedStates,Per- 1981:Q1-2017:Q4 Rate(RRVRUSQ156N) cent,NotSeasonallyAdjusted Homeownership Rate (RSAHO- FRED Homeownership Rate for the United States, 1981:Q1-2017:Q4 RUSQ156SN) Percent,SeasonallyAdjusted C FAVAR Model ThedistinguishingfeatureoftheFAVARrelativetoasmallscaleSVARmodelistheinformation structure assumed by the econometrician.17 In the FAVAR model, we relax the assumption that both the central bank and the econometrician observe perfectly all of the variables that enter the dynamic system 1. Instead, we assume that we observe perfectly only a subset of Y . All other t variables, denoted by F with dimensions r < n 1, are assumed to not be observed perfectly t × by the econometrician but are, nevertheless, strongly correlated with a large number, N >> n, of observableeconomicandfinancialtimeseries,X . LettingY bethesetofobservablefactorsandF t t t thesetofunobservablefactors,wehavethataFAVARsystemwithplagsisgivenby 17ForseminalcontributionsotherthanBernankeetal.(2005),seeGiannoneetal.(2004),StockandWatson(2005),and Fornietal.(2009).Foraformaltreatmentofthemodel,seeFornietal.(2009)andStockandWatson(2016). 22

    Y Y t t−1   = A(L) +Hε t (4) F F t t−1 X = Λ F +Λ Y +ν (5) t F t Y t t whereΛ isanN r matrixoffactorloadingsrelatedtotheunobservedfactors,Λ isanN F Y × × (n r)matrixoffactorloadingsrelatedtotheobservablefactors,A(L)isamatrixlagpolynomial, − and H is an r r matrix. The common shocks and the idiosyncratic components are assumed to × be uncorrelated at all leads and lags. We estimate 4 and 5 using a two-step principal components procedureandidentifythestructuralshocksthrougharecursiveassumption(asinBernankeetal. (2005), we assume that factors respond with a lag to changes in the monetary policy indicator). In theFAVARmodelthatwasusedinsub-section4.3,weassumethatthefederalfundsrateistheonly factorthatisperfectlyobservable. TodeterminethenumberofunobservablefactorsintheFAVAR model,weusedtheeigenvaluedifferencemethodproposedbyOnatski(2010). Thismethodledus to select 3 unobservable factors. Finally, we used the Akaike information criterion approach and selected 12 lags for the FAVAR model. We estimated the model with different combinations of the numbers of factors and lags, and the results remained unchanged. Finally, we used the FRED-MD database(McCrackenandNg(2016))thatismaintainedbytheFederalReserveBankofSt. Louisto estimatetheFAVARmodelunderlyingtheresultsinFigure7. 23