The Effect of Monetary Policy on Housing Tenure Choice as an Explanation for the Price Puzzle

K.7 The Effect of Monetary Policy on Housing Tenure Choice as an Explanation for the Price Puzzle Dias, Daniel A. and João B. Duarte Please cite paper as: Dias, Daniel A. and João B. Duarte (2016). The Effect of Monetary Policy on Housing Tenure Choice as an Explanation for the Price Puzzle. International Finance Discussion Papers 1171. http://dx.doi.org/10.17016/IFDP.2016.1171 International Finance Discussion Papers Board of Governors of the Federal Reserve System Number 1171 June 2016

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1171 June 2016 The Effect of Monetary Policy on Housing Tenure Choice as an Explanation for the Price Puzzle Daniel A. Dias 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 References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.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.

The effect of monetary policy on housing tenure choice as an ∗ explanation for the price puzzle DanielA.Dias† Joa˜oB.Duarte‡ June 23, 2016 Abstract Inthispaperweprovideanalternativeexplanationforthepricepuzzle(Sims1992)basedon theeffectofmonetarypolicyonhousingtenurechoiceandtheweightofthesheltercomponent inoverallCPI.Inthepresenceofnominalorfinancialfrictions,wheninterestratesincrease,the real cost of owning a house increases, and this increase may make some people prefer to rent insteadofbuying. Thischangeinconsumptionbehaviorincreasesthepriceofrentsrelativeto other goods. Starting in 1983, homeownership costs are based on a measure of implied owner equivalent rent, which is calculated using observed house rents. This change implies that, directlyandindirectly,pricesintherentalmarketalmostentirelycommandthesheltercomponent ofCPI,whichweighsaround30%intheoverallindex. WhenwetakethesetwopiecesintoaccountanduseCPInetofshelterservicesasameasureofinflation,weobtainimpulseresponses ofpricestoamonetarycontractionshockmoreinlinewithwhatispredictedbytheory. Inaddition, our results also suggest that inflation is much less persistent than what is implied by analysesusingameasureofinflationthatincludesshelterservices. Ourresultspassalonglist ofrobustnesscheckexercisesandcomparewellagainstotherexplanationsofthepricepuzzle. JELclassificationcodes: E31,E43,R21. KeyWords: Pricepuzzle,housingtenurechoice,monetarypolicy,SVAR. ∗The authors thank, without implicating, Chris Sims, Harald Uhlig, Stephen Parente, Dan Bernhardt, Antonella Tutino, Rui Zhao, Anne Villamil, Woong Yong Park, Igor Ezio, Mark Wright, Alejandro Justiniano, Leonardo Melosi, andvariousparticipantsattheChicagoFedseminar,FederalReserveBoardseminar,theBankofPortugalresearchseminar series, theGeorgetown Center forEconomic Research BiennialConference, Interaction between Housingand the Economyworkshop,the2015EconometricSocietyWorldCongress,andthemacroreadinggroupatUIUCforhelpful suggestionsanddiscussions. ThisresearchwassupportedbythePaulBoltzFellowshipandtheUIUCcampusresearch boardwithanArnoldO.BeckmanResearchAward. Theviewsinthispaperaresolelytheresponsibilityoftheauthors andshouldnotbeinterpretedasreflectingtheviewsoftheBoardofGovernorsoftheFederalReserveSystemorofany otherpersonassociatedwiththeFederalReserveSystem.Allerrorsareourown. †BoardofGovernorsoftheFederalReserveSystemandCEMAPRE.Email:daniel.dias@frb.gov. ‡DepartmentofEconomics,UniversityofIllinoisatUrbana-Champaign.Email:aurelio2@illinois.edu.

1 Introduction Using structural vector autoregression (SVAR) analysis, Sims (1992) noted that inflation responded positively and persistently to a contractionary monetary policy shock. This result is puzzling because a central tenet of monetary policy is the ability to control prices by contracting or expandingmonetarysupply(vis-a-visincreasingordecreasinginterestrates)whenpricesareabove or below the desired level, respectively. Since this result was first found, and starting with the paperwhereitwasfirstshown(Sims(1992),severalexplanationshavebeenproposed. Inthispaper, we contribute to this literature by proposing an alternative explanation of the price puzzle based on the effects of monetary policy on housing tenure choice and the weight of shelter in the overall consumerpriceindex(CPI). InDuarteandDias(2015)weshowthat,inresponsetoanexpansionarymonetarypolicyshock, house rents decrease while house prices increase. We use the effects of monetary policy on housingtenurechoicedecisionstogetherwithheterogeneousvaluationofhomeownershipbyagentsto explain this result. When interest rates change, the marginal home buyer may change, which may make house and rent prices change. Because with a higher interest rate the cost of homeownership may increase, more people may prefer to rent instead of buying. This shift in consumption behavior makes house prices decrease and rents increase. This mechanism, together with the fact thatshelter, directlyandindirectly, accountsforabout30%oftheoverallCPI,canhelpexplainthe price puzzle. When interest rates increase (a contractionary monetary policy shock), the nominal priceleveldecreases,butrentswillincreaseiftheshareofbuyersdeclinesandtheshareofrenters increases. If the increase of rents is sufficiently larger than the decrease of the nominal price level, then it can be expected that, after a contractionary monetary policy shock, inflation, measured by CPI, will increase. We test this idea using structural vector autoregression analysis, similar Sims (1992). Our empirical results strongly support our idea, and when we take into account the effect of monetary policy on rents and the weight of shelter in CPI, we find that after a contractionary monetary policy shock, the price puzzle is substantially reduced or even disappears. Our results are robust to alternative shocks identification strategies, measures of the price level, sample periods, and identification strategies. Exogenous changes in the construction of CPI allowed us to test ourtheoryfurther. Inaddition,usingdifferentmeasuresofinflation,likethepersonalconsumption expenditure (PCE) and the deflator of gross domestic product (GDP), in which the weight of shelter/housingislowerthanintheCPI,permittedustoconductadditionalrobustnesscheckexercises. 1

As already mentioned, Sims (1992) proposes the first solution to the price puzzle. The author argues that the puzzle is due to model misspecification and that, when a commodity price index variable is included in the SVAR model, most of the puzzle disappears. Hanson (2004) shows that this solution is sensitive to the sample period. In particular, the inclusion of commodity prices solvesthepuzzleforsampleperiodsbefore1980butnotforposteriorsampleperiods. Inlinewith theexplanationofSims(1992),severalotherpapersjustifythepuzzlewithmodelmisspecification. Giordani (2004) argues that the price puzzle is mostly a spurious result due to not including a measureoftheoutputgapintheempiricalmodel. OncethisvariableisincludedintheSVARmodel, the effect of a contractionary monetary policy shock on prices is still positive in the first periods but then becomes negative. Bernanke, Boivin, and Eliasz (2005) also argue that the SVAR model used by Sims (1992) was misspecified and suggest the utilization of a factor augmented vector autoregressive (FAVAR) model to correct for the misspecification. Using the suggested model, the authorsobtainaresponseofinflationtoacontractionarymonetarypolicyshockthatisclosertothe expectedresponse. BrissimisandMagginas(2006)alsoarguethatthemodelusedbySims(1992)is misspecified and the source of misspecification is the lack of forward-looking variables to account for expectations at the time of the change of interest rates. To fix this problem, the authors added thefedfundsfuturesratesandacompositeleadingindicatorofeconomicactivitytotheempirical model. Withthenewspecification,theseauthorsobtainaresponseofinflationtomonetaryshocks thatismuchmoreinlinewithwhatwouldbeexpected. An alternative line of research that also aims to explain the price puzzle tries to produce theoretical models in which prices increase after a contractionary monetary policy shock. One theory that could deliver such a result is the so-called channel cost of monetary policy (Barth and Ramey (2001)). Totestthishypothesis,Rabanal(2006)estimatesaNewKeynesianmodelofthebusinesscycleandteststheconditionsunderwhichacostchannelofmonetarypolicycouldgenerateapositive response of prices to a contractionary monetary policy shock. This author finds that demand side effects always dominate supply-side effects in prices and, therefore, there is no evidence that the costchannelofmonetarypolicycanexplainthepricepuzzle. Ourresultsprovidesomeinsightson the type of demand shocks that drive the response of prices. In contrast to Rabanal (2006), Henzel etal. (2009)estimateaNewKeynesianDSGEmodelfortheeuroareaandarguethat,undercertain parameter restrictions, which are not rejected by the data, the channel cost of monetary policy can explainthepricepuzzle. Our contribution combines both types of explanations and adds to them. We also find that the 2

SVAR model in Sims (1992) is misspecified, and suggest a way to improve the specification of the model. Inaddition,weprovideatheoreticalexplanation(theeffectofmonetarypolicyonhousing tenurechoice)forwhy(some)pricesmayincreaseafteracontractionarymonetarypolicyshock. The rest of the paper is organized as follows: in section 2 we discuss some practical issues regarding the calculation of the CPI; in section 3 we present a simple conceptual framework to guideourempiricalimplementation;insection4wedescribeourdataanddatasources;insection 5 we present our main empirical results; in section 6 we perform several robustness checks; in section7wecompareourexplanationofthepricepuzzletootherexplanations;andinsection8we conclude. 2 Housing in the CPI In this section we present some information regarding the construction of the CPI and discuss how some of the methodologies used in the construction of the CPI can help in understanding the price puzzle. The first aspect about the CPI that we note is that total housing expenses have a 46% weight in the index. This component has two sub-components, shelter and other housing related expenses, with the former currently weighing 31% in total CPI and the latter 15%.1 This information suggests that the overall CPI may be very sensitive to what happens in the housing componentgivenhowlargeitsweightis. A second aspect to note is that, although the price of most of the sub-components of housing (e.g., utilities or insurance) are relatively easy to measure, the price of shelter is not. The price of shelteriseasytomeasurewhensomeonelivesinahousethatdoesnotbelongtoher,butveryhard tomeasureinthecaseofsomeonelivinginahousethatbelongstoher. Whensomeonelivesinher own house, thereis noestablished pricefor therent that thisperson wouldhave topay if she was renting that same house. Over time, there have been different methods to address this problem, andthesedifferentmethodscanattenuateorexacerbatethepricepuzzle. BeforeFebruary1983,theCPIcalculatedsheltercostsdifferentlythanwhatisdonetoday.2 The costofhousingshelterforhomeownerswasbasedonhousingprices,mortgageinterestrates,prop- 1Inthispaper,sheltercostsonlycorrespondstorentsandtheowners’equivalentrent. Thesheltersub-componentof CPIalsoincludesotheritemswhicharenotrelevanttothediscussionofthepaper.Theseotheritemsonlyweigh1.1%in totalCPI.Hence,totalshelterisaround31%andrentplusowners’equivalentrentisalmost30%. 2ForamoredetaileddiscussionaboutthechangesintheCPImethodology, pleaseseeGillinghamandLane(1982) andtheBLSdocumentonCPImethodology,“HowtheCPImeasurespricechangeofOwner’sequivalentrentofprimary residence(OER)andRentofprimaryresidence(Rent).” 3

erty taxes, insurance, and maintenance costs. Hence, it included the asset as well as the service characteristics of housing when estimating the costs of shelter for homeowners. Some problems withthemethodologyandwiththetechnicalmeasurementitselfwerepointedoutbytheBureauof LaborandStatistics(BLS)andtheresearchcommunity. Themainconcernsraisedwerethefollowing: thedifficultyfacedbytheBLSincorrectlyestimatingthemortgageinterestratecostbecauseof the new financial contracts involving variable interest rates and specific special arrangements; the difficulty in estimating housing prices given the small sample and the low frequency with which housesaretraded;thegeneralconcernoftheBLSthatCPIshouldhaveastrongcredibilityandthe possibility that the way housing shelter was being estimated together with its importance in the CPI could be negatively affecting the credibility of the index; and lastly, the idea that CPI should beascloseaspossibleasagoodmeasureofconsumptionexpenditureand,hence,homeownership costsshouldbecomputedascloselyaspossibletoaconsumptiongoodandnottoanasset. Given the dissatisfaction with how the cost of shelter for homeowners was computed and the necessityforamorepurelyconsumption-orientedindex,theBLSsuggestedanalternativemeasure calledowner’sequivalentrent(OER)ofprimaryresidence. Theideabehindthisnewmeasurewas toaskhowmuchrentwouldthehomeownerhavetopayifshehadtorentherownhouse. Inorder to answer this question, the BLS defined small geographic areas, called segments, within each of the87CPIpricingareas. AsegmentcorrespondstooneormoreCensusblocks. Foreachsegment, the BLS collects prices from the rental market of houses that are representative of that segment. This approach allows the BLS to get an implicit rent for owners by comparing houses that have similarcharacteristicsastherepresentativeonesintherentalmarketinthesamesegment. Inother words, theBLSuseshedonicpricingmethodstoestimatetheOER.Hence, theOERisveryclosely relatedtotherentalpricesobserved–thecorrelationbetweenthelevelofrentalpricesandOERis 0.996whilethecorrelationbetweentheyear-on-yeargrowthratesis0.842. Therefore,theOERcan essentiallybeseenasameasureofsheltercostsfacedbyhomeownersthatisbasedalmostsolelyon thepriceofrentsfromtherentalmarket. TheCPIbasedonthisnewmeasurewasfirstintroduced inFebruary1983, andduringaperiodofsixmonths, untilJuly1983, theCPIwascalculatedusing thetwomeasuresofsheltercosts. Thischangeinmethodologyallowsustocomparethesizeofthe pricepuzzlewhentwoalternativemeasuresofsheltercostsareusedintheconstructionoftheCPI. In our baseline empirical estimation we consider a sample starting in January 1983 and ending in December2006.3 3Wetruncatethesampleattheendof2006toavoidthefinancialcrisisperiodbecauseduringthisperiod,therewere 4

40 35 30 25 20 15 10 5 0 1985 1990 1995 2000 2005 2010 Years )stniopegatnecrepni(IPCnithgieW Shelter OER Rent Totalrent Figure 1: Weight of rent, owners’ equivalent rent, and total shelter costs in CPI between 1982 and 2012. Source: BLS. Finally,wepresenthowtherelativeimportanceofhousingtotalrent(rentofprimaryresidency plustheowners’equivalentrent)evolvedbetween1982and2006. Figure1showstheevolutionof selected items’ weights in CPI. It is clear that almost all of the increase in the relative importance inCPIofhousingrentsisdrivenbytheOER.TheinitialincreaseintheOERshareintheCPIfrom 13.5%to19%wasdrivenbyare-weightin1981-82. Theinitialweightof13.5%wasbasedon1971- 72 expenditure information. This lag in the re-weighting process of the CPI created a data blip in the OER. After 2000, when the weight started being estimated every two years, this lag problem was reduced. However, for the OER, the revision took place in 1982 and, at the time, the weights werestillgivenbythe1971-72period,whichexplainsthelargeincreaseoftheshelterweightinthe first years of the OER implementation. The increase of the share of the OER did not restrict itself to the beginning of the 1980s. After that, the OER share increased from 19% to 24% in 2012. The changein2012wasmostlyduetoanincreaseinthequantitydemandedofOER.4 Atthesametime, theshareofrentsdidnotchangemuch. Thereweresomesmallvariations,butoveralltheshareof severalshocksaffectingtheusualmonetarytransmissionmechanism,whichcouldaffectouranalysisforreasonsbeyond thescopeofthispaper. 4Fordetails,seeChurch(2014). 5

rentsremainedfairlystable. Onepossibleexplanationisthatthehousingsizesforrentalunitsdid not increase as much as the size of the houses that are owned by its occupants. Also, there was a largeincreaseofhomeownership,especiallyduringthe2000-2006period. Thisfactseemsrelevant inexplainingtheslightdecreaseoftheweightofrentandtheincreaseoftheweightofOERinthe overallCPIinthisperiod. Before proceeding to the discussion of the conceptual framework, an important remark is in place. Although all the previous discussion was only about the construction of the CPI, similar problems are faced by other alternative measures of inflation such as the the PCE and the deflator of GDP. The problem of estimating the price of shelter is also present in these two indexes, but it islessimportantforexplainingthepricepuzzlebecausetheweightofshelterissignificantlylower thanintheCPI(15%inthePCEand13%inthedeflatorofGDP). 3 The effect of interest rates on the nominal state of the economy and the CPI It is well known that the CPI as a measure of monetary inflation has several problems for the conduct of monetary policy. One of these problems is that the CPI is not able to separate price changes caused by changes in the nominal state of the economy from price changes caused by supply and/or demand shocks (relative price changes). The usual way to solve this problem is to construct measures of core inflation. These can be as simple as removing the more volatile components of CPI like energy and unprocessed food, or they can be more elaborate and come out of econometric models (see Clark (2001) for a survey of core inflation measures). The measurement issuethatwepointoutinthispaperaddstothelistofproblemswithusingCPI(orothermeasures like the PCE or the deflator of GDP) as a measure of monetary inflation, but it has important differences from the other problems previously identified because, according to our idea, the relative pricechangeisduetochangesininterestratesvis-a-vismonetarypolicy. Inordertomakeourpoint clearer,wewritetheCPIastheproductoftwocomponents. CPI(t) = P(t)(αC(t)+(1−α)R(t)) (1) Thefirstcomponentinequation1correspondstothenominalstateoftheeconomyattimet–P(t)– whilethesecondcomponentcorrespondstotherealpricesofnonshelterandshelterconsumption 6

–(αC(t)+(1−α)R(t)). Inthisexampleweonlyconsidertwogoods/services,consumptionnetof shelter–C(t)–andshelter–R(t)–becausewewanttofocusourdiscussiononthedifferentbehavior of the two groups of goods/services in response to a monetary shock. In the same equation, α representstheweightofnon-shelterconsumptionintotalconsumption. In Duarte and Dias (2015) we argue that monetary policy affects the choice between housing tenure(rentvs. own)andthereforetherelativepricesofthetwochangewheninterestrateschange. Fromourdiscussionintheprevioussection,forthepurposeofcomputingthecostsofshelter,most of the information used in these calculations comes from the shelter rental market, which leads to the shelter component of CPI behaving almost identically to shelter rents. With this in mind, and with equation 1, we can now discuss when we expect to observe a price puzzle based on our mechanism. Whenthecentralbankincreasesinterestratesitisnormallyforthepurposeofreducinginflation, that is, to reduce the growth rate of P(t). If the change in interest rates had no effect on real prices of shelter and non-shelter goods then it should be expected that, after a contractionary monetary policyshock,theimpulseresponsefunction(IRF)ofCPIwouldbenegativebecausetherealprices of both goods would not change. According to our mechanism, after a contractionary monetary policyshock,notonlywouldP(t),thenominalleveloftheeconomy,change,butpossiblyalsoR(t), thepriceofshelterservices. Inorderforthiseffecttogenerateapricepuzzleitwouldbenecessary thattheeffectofinterestratesonR(t),weighedby(1−α),belargerthantheeffectofinterestrates onP(t): ∆P(t) ∆R(t) ∆CPI(t) If < (1−α) =⇒ > 0 (2) ∆i ∆i ∆i Fromequation2itisstraightforwardtoseethatthesmallertheweightofnon-sheltergoodsin total CPI – α – or the larger the response of shelter prices to interest rates, the more likely it is that theoverallCPIwillincreaseafteracontractionarymonetaryshock.5 Thisconsiderationimpliesthat the”size”ofthepricepuzzlemaybetimevarying,whichisconsistentwiththefindingsofHanson (2004). Importantly, and regardless of the overall effect of interest rates changes on total CPI being positive or negative, based on this discussion, for monetary policy conduct and evaluation, the shelter component of the CPI (or PCE, or deflator of GDP) should be excluded if the goal is to 5Althoughourdiscussionhereisinformal,inDuarteandDias(2015)weaddanendogenoushousingtenurechoice toastandardNewKeynesianmodel,whichallowsustohaveamoreformalandprecisediscussionofthismechanism. 7

measurethenominalstateoftheeconomy. Inaddition,thisresultalsohighlightstheimportanceof usingdatathataremodelconsistent(orvice-versa). 4 Data The data that we use in this paper come from multiple sources. The data used in the main results were collected from the St. Louis Fed Fred economic database. We collected the same four variables used in Sims (1992) – the federal funds rate (FFR), M1 money stock (M1SL), industrial production (INDPRO), and CPI index (CPIAUCSL). In addition, we also collected information for theconsumerpriceindexofrentofprimaryresidence(CUSR0000SEHA)andconsumerpriceindex of owners’ equivalent rent of residence (CUSR0000SEHC), which we use to construct the variable CPI net of shelter. With the exception of the monetary variables (M1SL and FFR), all series were seasonallyadjustedandallvariablesbutthefederalfundsrateareinloglevels. Althoughmostof ourdatarangesfrom1960to2006,ourmainempiricalresultsconcerntheperiodfrom1983to2006. We restrict the sample to this period because, as explained in section 2, the CPI suffered a major revision in 1983 that changed the way shelter costs were estimated. In the same methodological revision,housingpriceswereexcludedfromtheCPI. Because we perform various robustness checks of our main results and also show how our resultscomparetopreviousexplanationsofthepricepuzzle,wehadtocollectseveralotherdata. As alternativeinflationmeasuresweusethepersonalconsumptionpriceindex(PCE)andthedeflator of GDP. The former is observed at a monthly frequency, while the latter is observed at a quarterly frequency. BothwereobtainedfromtheSt. LouisFedFredeconomicdatabaseandcovertheperiod 1960 to 2006. As an alternative measure of monetary policy shocks we use the Romer and Romer (2004)monetarypolicyshocksmeasure,whichwasupdatedtoamorerecentperiodbyCoibionet al. (2012). ToreplicatetheresultsofGiordani(2004)weusedtheFederalReserveBoardmeasureof capacityutilization,whichweobtainedfromtheSt. LouisFedFredeconomicdatabase. Toreplicate the results of Brissimis and Magginas (2006) we used the composite index of leading indicators variable that is published by the Conference Board and the expected federal funds rate for the current month.6 Finally, in order to implement the FAVAR methodology of Bernanke, Boivin, and Eliasz (2005), we used an updated version of the original dataset covering the period 1960 to 2007 atamonthlyfrequency.7 6ThisvariablewaskindlyprovidedbyTradeNavigator.com. 7WethankDaliborStevanovicforsharingthesedatawithus. 8

5 Empirical Results 5.1 SVARModelandIdentificationStrategy TheSVARmodelweestimateaswellastheshockidentificationstrategyweuseinourbaseline results, correspond exactly to Sims (1992). That is, we estimate a SVAR model with four variables: federal funds rate, industrial production index, M1 money stock, and some measure of the price level. Intheoriginalpaper,theauthorusedtheCPIasameasureofthepricelevel. Inourapplication,weusetheCPI,sub-componentsoftheCPI,andalternativemeasuresofinflationlikethePCE andtheGDPdeflator. The identification of shocks in the SVAR model used to obtain the baseline results is based on a Cholesky decomposition with the variables ordered as in Sims (1992): federal funds rate, M1 money stock, price variable and industrial production index. In this shock identification strategy, thefirstvariablecontemporaneouslyaffectsallothervariables;thesecondvariableaffectsallother variables contemporaneously but the first one; the third variable only affects the fourth variable contemporaneously;andthefourthvariablehasnocontemporaneouseffectsontheothervariables. Insection6wepresentresultswithalternativeidentificationstrategiestoshowthatourmainresult doesnotdependonusingaparticularidentificationstrategy. 5.2 MainResults Figure2summarizesourmainresult. Inthisfigureweshowtheimpulseresponsetoapositive federalfundsrateshockofoverallCPIandCPInetofshelter. TheimpulseresponseofoverallCPItoanincreaseofthefederalfundsratecorrespondstowhat is perceived as being puzzling and at odds with economic theory. After an increase of the interest rate,CPIisabovethebaselinelevelformorethan30months. InthethecasewhereweuseCPInet ofshelter,westillobserveaperiodofaround14monthswhereCPIisstillabovezero,butafter4to 5 months the level is significantly lower than overall CPI and after 14 months it actually becomes negative, as would be expected. The reason why even when we use CPI net of shelter we still observeaninitialperiodwhereCPIisabovezeroafteracontractionarymonetaryshockisnoteasy to explain. This initial behavior could be explained by the theory of the cost channel of monetary policy. Itisalsopossiblethatthereareotherproductsforwhichdemandincreasesafteranegative interest rate shock. In order to test the first hypothesis we would need some information about the evolution of marginal costs of production, while to test the second hypothesis we would have 9

0.15 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsRFFotlevelecirpfoesnopseR CPI CPInetofshelter Figure2: ImpulseresponseofCPIandCPInetofsheltertoafederalfundsrateshockfor1983:01to 2006:12period. Shelteronlyincludesprimaryrentandownerequivalentrent. to search for products for which prices vary in the same direction as interest rates. Unfortunately, informationonmarginalcostsofproductionisnoteasilyavailable,andestimatingpriceelasticities of different product categories to interest rates is something we plan to do in future research. An alternativeexplanationisthattheidentificationstrategyisnotthemostadequateoneandanother shouldbeconsidered. Inthenextsectionweperformseveralrobustnesscheckexercises,including usingdifferentidentificationstrategies. NoteinFigure2that, forthefirst6months, theimpulseresponseofbothseriesisverysimilar, butaround7months, whiletheresponseofCPInetofshelterstartsdeclining, theresponseofCPI starts increasing and only stops increasing around 11 months. This behavior is consistent with our story but could also be due to some other factor. In order to provide some evidence that this behaviorisduetotheincreaseinshelterpricesafterthecontractionarymonetaryshock,weestimate afour-variableSVARmodelwhere,alongwiththefederalfundsrate,industrialproductionindex, and the M1 money stock, we include the shelter price index.8 In Figure 3 we show the impulse responsesoftheshelterpriceindextoacontractionarymonetaryshock. 8The shelter price index is the same index that we exclude from the overall CPI to construct the CPI net of shelter series. Thisseriesthatwecallshelterpriceindexdoesnotcorrespondexactlytowhatisdenominatedasshelterbythe BLS. 10

0.3 0.25 0.2 0.15 0.1 0.05 0 −0.05 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsRFFotxedniecirpretlehS Figure3: Impulseresponseofsheltertoafederalfundsrateshockfor1983:01to2006:12period. TheresultsshowninFigure3areinlinewithourinterpretationofthebehavioroftheimpulse responseofCPI.9 Theresponseofshelterpricesincreasesinthreedistinctperiods,around3,7and 15 months. The increase around 3 months does not show in the response of CPI, but the increase around6monthscoincideswiththeinversionofdirectionoftheimpulseresponsefunctionofCPI. In Figure 3 the response of shelter prices continues to increase for almost 3 years while in Figure 2 the response of CPI peaks at 11 months. Because the impulse response function is not linear, and because it depends on the behavior of all variables in the system, the impulse response of CPI and shelter do not need to be fully consistent with our story. Yet, in our view, both variables show a behavior in the first periods of the response that is consistent with our story and with our interpretationoftheinversionofdirectionoftheimpulseresponseforCPI. Two important questions that we have not addressed so far are whether the two impulse response functions in Figure 2 are statistically different from each other and whether the responses of the other variables in the model are similar when CPI or CPI net of shelter are used. To answer these questions properly we would need to be able to compare impulse response functions from non-nested models in a statistical way. Unfortunately, to the best of our knowledge, there are no 9TheresultshowninFigure3isbasicallythesameresultshowninDuarteandDias(2015),whichledustowritethe presentpaper. 11

suchtestsandthereforethebestwecandoisshowthevariousimpulseresponsesandletthereader judge for him/herself. In Figure 4 we show the impulse responses with corresponding 68% confidence bands of all the variables included in the SVAR model to a contractionary monetary policy shock. 0.4 0.2 0 −0.2 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsRFFotRFF 0.2 0 −0.2 CPI CPInetofshelter −0.4 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsRFFotlevelecirP 0.6 0.4 0.2 0 −0.2 −0.4 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsRFFotORPDNI 0 −0.5 −1 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsRFFot1M Figure4: Impulseresponsestoafederalfundsrateshockfor1983:1to2006:12period. Bothshaded areasrepresentthe68%confidenceintervals. ThelightareaisassociatedwiththeCPI,themedium areawiththeCPInetofshelter,andthedarkerareawiththeintersectionofthetwo. WiththeexceptionoftheresponsesofCPIandCPInetofshelter,theresponsesoftheotherthree variablesarequalitativelysimilarinbothspecifications. Weinterpretthissimilarityasevidencethat our result is not driven by some strange response of one or more variables included in the model. Also interesting to note is that only in the cases of CPI and CPI net of shelter the 68% confidence bands of the two impulse response functions do not overlap for most of the response horizon. We acknowledge that comparing the confidence bands of two impulse response functions is not a formaltest, butthefactthatforCPIand CPInetofshelterthetwo impulse responsebandsdonot overlapisconsistentwithourinterpretationoftheresults. Thatis,theresponsesofCPIandCPInet ofsheltertoacontractionarymonetarypolicyshockareeconomicallydifferent. An additional interesting result regards the forecast error variance decomposition of the two variables(CPIandCPInetofshelter). InTable1weshowtheforecasterrorvariancedecomposition up to 48 periods. Although the two decompositions are not too different from each other, the de- 12

Forecasterrorvariancedecomposition CPI Step StdError FF M1 CPI INDPRO 1 0.173 0.6 1.1 98.3 0.0 8 0.585 7.7 1.5 85.3 5.5 16 0.976 7.1 2.1 80.1 10.7 24 1.275 5.4 3.4 79.1 12.1 32 1.482 4.1 4.9 78.7 12.3 40 1.629 3.5 6.2 78.2 12.1 48 1.737 3.6 7.2 77.6 11.6 CPInetofshelter Step StdError FF M1 NETCPI INDPRO 1 0.246 0.0 1.4 98.6 0.0 8 0.804 2.8 1.8 90.8 4.6 16 1.328 1.2 4.0 85.3 9.5 24 1.709 1.5 7.3 81.4 9.8 32 1.951 3.5 10.6 77.5 8.4 40 2.123 6.7 12.9 73.2 7.2 48 2.264 10.6 13.8 69.0 6.6 Table1: ForecasterrorvariancedecompositionofCPIandCPInetofshelter. compositionofCPInetofshelterputsasmallerweightinthecontributionofindustrialproduction, and more on the other three variables – 11.6% after 48 periods in the case of CPI and only 6.6% in the case of CPI net of shelter. Since inflation is inherently a nominal variable, it is sensible that in thelongrunitismostlydrivenbynominalshocksandnotbyrealshocks. 6 Robustness Checks 6.1 AlternativeIdentificationStrategies Asmentionedpreviously,theidentificationstrategythatweusetoobtainthemainresultsisnot unique and other strategies could be justified. We do not have a strong preference for a particular identification strategy. Instead, we are mostly concerned about showing that our results do not dependontheidentificationstrategythatisused. Inthisregard, wetrytwodifferentorderingsof variablesintheSVARmodel. Itisdifficulttoarguethatthemonetaryauthorityknowsthepricelevelandindustrialproduction when using monthly data. Still, the monetary authority has weekly and daily information on variablesthatcangiveanideaofwhatishappeningwiththepricelevelandindustrialproduction in any given month. In particular, the BLS typically collects price data in the middle of the month 13

whiletheFederalOpenMarketCommittee(FOMC)meetseitherinthemiddleorattheendofthe month. We present here two different orderings: one where the monetary authority observes contemporaneously industrial production and the price level, as in Christiano et al. (1996), and one where it just observes the price level. Results of the these two alternative identification strategies arepresentedinFigures5and6,respectively. 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsRFFotlevelecirpfoesnopseR CPI CPInetofshelter Figure5: ImpulseresponseofCPIandCPInetofsheltertoafederalfundsrateshockfrom1983:01to 2006:12periodforalternativeordering: industrialproduction,pricelevel,interestrate,andmoney aggregate. From Figures 5 and 6 we conclude that our baseline results do not depend on the ordering of the variables in the VAR since alternative variable orderings generate results that are qualitatively similar. Thatis,notonlydoestheresponseofCPInetofshelterbecomenegativemuchfasterthan the response of CPI, but we also observe that the response of CPI inverts the direction around 7 months. Giventherecursiveidentificationapproach,itcanbearguedthattheidentificationofthemonetary policy shock is different when using CPI net of shelter instead of CPI. The monetary policy authoritycertainlyrespondstoCPIbutthesamecannotbeclaimedforCPInetofshelter. Oneway ofaccommodatingthiscriticismistousetheRomerandRomer(2004)measureofmonetarypolicy shocks (updated to a more recent time period by Coibion et al. 2012). As argued by Romer and Romer(2004),thismeasureofmonetaryshocksisrobusttoanticipatoryandendogenousactionsof themonetarypolicyauthority. Inthisway,wecancompareresponsesofCPIandCPInetofshelter 14

0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 −0.25 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsRFFotlevelecirpfoesnopseR CPI CPInetofshelter Figure6: ImpulseResponseofCPIandCPInetofsheltertoafederalfundsrateshockfrom1983:01 to2006:12periodforalternativeordering: pricelevel,interestrate,moneyaggregate,andindustrial production. thatusethesameidentification. ThecorrespondingresultsareshowninFigure7. Thesamequalitativeresultsareobtainedonceagain. However,somedifferencesareobserved. Thepricepuzzleis”smaller”forCPIthanwhenarecursiveidentificationisused. Thisresultisnot new;ithasalreadybeenreportedinRomerandRomer(2004). Withthisidentification,nevertheless, we still see the same ordering of impulse responses we saw previously. The response of CPI stays positive for a longer period than the response of CPI net of shelter – approximately 15 months for theformerandapproximately5 monthsforthelatter. Hence, thereisadifferenceofalmostayear betweenthetwodifferentmeasuresintermsofpositiveresponseandofapproximately0.1standard deviationsintermsofquantitativedifferencefrom15monthsforward. 6.2 AlternativeMeasuresofInflation Toshowthatourresultsdonotdependonthemeasureofthepricelevelthatisused,weestimate thesamemodelusedtoobtainourbaselineresults,butinsteadofusingCPI,weusethePCEandthe GDPdeflator. Figures8and9showtheresultswhenthePCEandtheGDPdeflatorareconsidered, respectively. SimilartowhatwasobservedinFigure2,weseeinFigures8and9thatwhenweexcludeshelter 15

0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 −0.25 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsycilopyratenomotlevelecirpfoesnopseR CPI CPInetofshelter Figure 7: Impulse response of CPI and CPI net of shelter to a monetary policy shock (Romer and Romer(2004)andCoibionetal. (2012))1983:01to2006:12period. 0.05 0 −0.05 −0.1 −0.15 −0.2 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsRFFotlevelecirpfoesnopseR PCE PCEnetofshelter Figure8: ImpulseresponseofPCEandPCEnetofsheltertoafederalfundsrateshockfrom1983:01 to2006:12period. Shelteronlyincludesprimaryrentandownerequivalentrent. from the price index (PCE or GDP deflator) the response of prices to a contractionary monetary policyshockbecomesnegativemuchfasterthanwhenshelterisincluded. In the case of the PCE, the result based on overall PCE is already quite satisfactory, as after 16

0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 −0.25 −0.3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Steps kcohsRFFotlevelecirpfoesnopseR GDPdeflator GDPdeflatornetofshelter Figure9: ImpulseresponseofGDPdeflatorandGDPdeflatornetofsheltertoafederalfundsrate shock from 1983:01 to 2006:4 period for quarterly data. Shelter only includes primary rent and ownerequivalentrent. 15 months the impulse response crosses the zero line and becomes negative. However, despite the initial result not being as strange as in the case of the CPI, when we use PCE net of shelter a measure of the price level the impulse response becomes negative after 6 months, which is much quickerthaninthecaseofoverallPCE.Itisimportanttonoticethattheinitialresultisnotasstrange as in the case of CPI because the weight of shelter in the PCE is only 15% while it is close to 30% inCPI.Besidesthedifferenceintheweightofshelter,thePCEalsodiffersfromtheCPIintermsof howtheweightsusedinthecomputationoftheindexchangeovertime. IntheCPI,theseweights are fixed for a fairly long period of time (more than 1 year). In the PCE, the weights used in its computationadjusteverymonthbasedonthequantitiesconsumedofeachgoodorservice. For the GDP deflator, we also obtain a similar result. When we exclude shelter from this price index,theimpulseresponsebecomesnegativemorequickly(betweenthreeandfourquarters)than whenshelterisincluded. 6.3 TheOriginalPuzzleDissected Asexplainedpreviously,in1983therewasamajorrevisioninthemethodologyusedintheconstructionoftheCPI.Amongotherchanges,theconceptofowners’equivalentrentwasintroduced 17

and the cost of home ownership item was removed from the index. This change brings naturally theinvestigationofthepre-1983periodasarobustnesscheck. Figure10showsresultsbasedonthe sample used in the original article as well as results for two sub-samples – before and after 1983. Given our previous discussion, it would be expected that the price puzzle would be ”worse” after 1983 because that corresponds to the period with a higher weight of shelter. This hypothesis is confirmed in Figure 10, where it can be seen that the CPI impulse response function is positive for more than 48 months. Also interesting is that only in the post-1983 sample is a change of direction of the impulse response function observed. This inversion of direction also takes place at around8months,andtheimpulseresponsestabilizesaroundmonth13/14. Regardingthepre-1983 sub-periodweobserveaslightly”smaller”puzzlethantheoriginal. 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsRFFotIPCfoesnopseR 1960:1-1992:12originalpuzzle 1983:1-1992:12 1960:1-1982:12 Figure 10: The original price puzzle presented in Sims (1992) and its breakdown in the before and after1983sub-periods. Ifwecomparetheoriginalpuzzlewiththepuzzlepresentedinourmainresults,itispossibleto seehowsimilartheyare. Bothbecomenegativearound35months. However,thepositiveresponse isstrongerintheoriginalpuzzlethantheresponseofCPIshowninFigure2. Intheoriginalpuzzle, thepositiveresponsepeaksatmorethan0.2%whileinourbaselineresultpeaksatlessthan0.1%. Thisresultseemstobeatoddswithourmechanismsincetheoriginalpuzzlewasbasedonasample where housing shelter had less weight (around 6%) and housing prices were part of the CPI. This motivatesbreakingdowntheperiodpre-1983toinvestigatewhatdynamicsareinplace. 18

·10−3 3 2 1 0 −1 −2 −3 −4 −5 −6 −7 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsRFFotIPCfoesnopseR 1960:1-1969:12 1970:1-1982:12 1970:1-1982:12withcomm.price Figure11: The1960-1982periodanditsbreakdownbetweenthepre-andstagflationdecades. Figure 11 shows the breakdown in two sub-samples. From 1960:1 to 1969:12 the result is what would be expected if the mechanism proposed in this paper was relevant. That is, in a period wherehouserentshadaverysmallweightinoverallCPI,theresponseofpricestoacontractionary monetaryshockisnegative,astheorywouldpredict. TheresultspresentedinFigures10and11seemtosuggestthattheoriginalpuzzlewasmainly driven by the 1970:1 to 1982:12 period and the change in the calculation of shelter costs. It is well known that the 1970s was a turbulent period in economic terms with the occurrence of oil shocks, high inflation, and experimentation with monetary policy. The fact that the original puzzle is partiallydrivenbythe1970:1to1982:12periodhelpsinunderstandingwhytheinclusionofcommodity prices helped explaining the puzzle, but this link disappeared in more recent periods, as was pointedoutbyHanson(2004). However,inFigure11wecanseehowusingthecommodityprices did not correct much of the puzzle even for the 1970:1 to 1982:12 period. This finding is similar to Romer and Romer (2004), who show how small the response of the price level is to monetary policy shocks (their own measure and actual federal funds rate) when commodity prices are included. OnefinalremarkabouttheresultsinFigures10and11isthatforallcaseswhereapre-1983 sample was used, we do not observe an inversion of the CPI impulse response function. That is, inthesecases,therearenoinstancesinwhichtheimpulseresponsestartsdecliningandthenstarts 19

increasingagain,aswasthecaseforimpulseresponsesbasedonpost-1983samples. 7 Alternative Explanations of the Price Puzzle As discussed in the introduction, there are several explanations for the price puzzle, each with itsownmerits. Wedonotwanttodiscusswhetherourexplanationisbetterthanexistingonesnor takeastandonwhichexplanationisourpreferredone. Instead,wewanttoseehowourexplanation fits with existing ones. To do so, we replicate some of the leading explanations of the price puzzle incorporatingouridea. Wechoosefouralternativeexplanations: 1)exclusionofameasureofoutput gap-Giordani(2004);2)exclusionofforwardlookingvariables-BrissimisandMagginas(2006);3) insufficientcontrollingforothervariablesusedintheinformationsetofthecentralbanker-FAVAR model of Bernanke, Boiving and Eliasz (2005); 4) theory based sign restriction method of Uhligh (2005).10 7.1 OutputGap Giordani (2004) argues that the SVAR model used by Sims (1992) is misspecified, and this misspecificationleadtoaspuriouspricepuzzle. Thesourceofthemisspecificationistheinclusionofa measure of GDP (or industrial production) instead of using a measure of output gap. In Figure 12 weshowtheimpulseresponsefunctionofCPIandCPInetofasheltertoacontractionarymonetary policyshockinthecontextofamodelwithoutputgap(leftpanel)andwithGDP(rightpanel). As is visible in Figure 12, the SVAR model with output gap delivers results where there is almost no price puzzle for both CPI and CPI net of shelter, but it also shows that CPI net of shelter responds more negatively than CPI to the same monetary shock. In the case of the SVAR model that uses GDP, the response of CPI is always positive for the first four years, while the response of CPI net of shelter becomes negative after two years. These results make it very clear that the point made by Giordani (2004) is important, but the results also show that using the response of inflation to monetary shocks is quicker than what is implied by the response of CPI. From our discussion in section2, thefactthatrentsincreaseafteracontractionarymonetarypolicyshockdoesnotalways lead to a price puzzle, but the response of CPI is always a combination of two distinct responses: theresponseoftheshelterandthenon-sheltercomponentsofCPI. 10Tobefairtotheauthor,themaingoalofUhligh(2005)istostudytheeffectsofmonetarypolicyshocksonoutput, andinordertobetteridentifymonetarypolicyshocks,theauthorimposesrestrictionsontheresponseofprices. 20

0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 −0.25 −0.3 −0.35 −0.4 0 2 4 6 8 10 12 14 16 Steps kcohsRFFotlevelecirpfoesnopseR Withoutputgap 0.1 0.08 0.06 0.04 0.02 0 −0.02 −0.04 −0.06 −0.08 −0.1 −0.12 −0.14 −0.16 CPI −0.18 CPInetofshelter −0.2 0 2 4 6 8 10 12 14 16 Steps kcohsRFFotlevelecirpfoesnopseR WithGDP CPI CPInetofshelter Figure 12: Impulse responses to a federal funds rate shock for 1983:1 to 2006:4 period with an output gap measure as in Giordani (2004). The left panel reports the response of price level to the fullspecificationwithoutputgapandtheleftpanelwithGDPinsteadofoutputgap. 7.2 Forward-LookingVariables Brissimis and Magginas (2006) also argue that the original SVAR model used by Sims (1992) is misspecified. According to these authors, the Sims (1992) SVAR model is misspecified because it doesnotincludeanyforward-lookingvariabletohelpwiththeidentificationofshocks. Tocorrect thismisspecification,theauthorsaddtotheSVARmodelofSims(1992)ameasureofexpectedeconomicactivityandameasureofexpectedinterestrates. Themeasureofexpectedeconomicactivity is treated as endogenous, while the second is treated as exogenous. We replicate this approach with both CPI and CPI net of shelter (Figure 13). We consider the cases of adding both variables to the empirical, and only adding the expected economic activity variable. Similar to Giordani (2004), the new model specification defended by Brissimis and Magginas (2006) improves the resultssignificantly. Atthesametime,wealsofindasimilarresulttowhatweshowedintheprevious sub-section. Thatis,theresponseofCPInetofshelterismuchquickerthantheresponseofCPIand, 21

inthecaseofjustusingtheexpectedeconomicactivityindicator,theresponseofCPInetofshelter becomesnegativebeforetheresponseofCPI. 0.1 0 −0.1 −0.2 −0.3 −0.4 −0.5 −0.6 0 10 20 30 40 Steps kcohsRFFotlevelecirpfoesnopseR WithFFFandLCOM 0.2 0.1 0 −0.1 −0.2 −0.3 −0.4 −0.5 −0.6 CPI CPInetofshelter −0.7 0 10 20 30 40 Steps kcohsRFFotlevelecirpfoesnopseR WithLCOMonly CPI CPInetofshelter Figure13: Impulseresponsestoafederalfundsrateshockfor1989:1to2006:12periodwithforwardlooking information variables as in Brissimis and Magginas (2006). The left panel reports the response of price level to the full specification with federal funds futures rate (FFF) and composite leadingindicatorofeconomicactivity(LCOM).TherightpanelonlyincludesLCOM. 7.3 FAVAR Bernanke, Boivin, and Eliasz (2005) propose a new econometric method that allows for richer informationenvironmentswhilekeepingthemodeilfairlyparsimonious. Thismodelisknownasa factoraugmentedvectorautoregressive(FAVAR)model. Thebasicideaistocondensealargesetof variablesintojustafewnumberoffactorsandthenusethesefactorsandothervariablesofinterest inaSVARmodel. OneofthebyproductsofthisnewapproachisthattheimpulseresponseofCPI toacontractionarymonetarypolicyshockismuchmoreinlinewitheconomictheory. Toshowthat ourresultstillholds,wereplicatetheresultsofBernanke,BoivingandEliasz(2005)usingdatafrom 22

1959:01 to 2006:12 together with the variable CPI net of shelter, which only covers the period from 1983:01 to 2006:12. The impulse responses to a contractionary monetary policy shock of CPI and CPInetofshelterbasedonaFAVARmodelareshowninFigure14.11 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 −1.2 −1.4 0 5 10 15 20 25 30 35 40 45 Steps kcohsRFFotlevelecirpfoesnopseR FAVAR CPI CPInetofshelter Figure14: ImpulseresponsesofCPIandCPInetofsheltertoafederalfundsrateshockfor1959:01 to2006:12periodusingathreefactorsFAVARmodelasinBernanke,BoivinandEliasz(2005)while addingCPInetofSheltertothesample. The results could not be clearer. In the case of the response of CPI, although it turns negative morequicklythaninourbaselinecase(Figure2),itstilltakesabout18monthstobecomenegative. At the same time, the response of CPI net of shelter is never positive and it corresponds to what theorypredicts. Despitethisresultbeingveryfavorabletoourmainpoint,wemustacknowledgethatthecomparison of the two responses is somewhat unfair because the two variables cover different time periods. In the case of CPI it includes the period of the 1970s which is known to be a conturbated period. InFigure15,weshowtheimpulseresponseofCPInetofashelterandofCPIpre-1983and post-1983. 11CPInetofshelterisonlydefinedfortheperiodfrom1983:01to2006:12becausetheconceptofownerequivalentrent wasonlyintroducedin1983.However,themethodallowsustousevariableswithdifferenttimeperiods. 23

0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 −1.2 0 5 10 15 20 25 30 35 40 45 Steps kcohsRFFotlevelecirpfoesnopseR FAVAR CPIpre-1983 CPInetofshelter CPIpost-1983 Figure 15: Impulse responses of CPI pre-1983, CPI post-1983 and CPI net of shelter to a federal FundsRateShockfor1959:01to2006:12periodusingFAVARwiththreefactorsandsamplejustas inBernanke,BoivinandEliasz(2005)whileaddingCPInetofsheltertothesample. Inthiscase, theresponseofCPIpre-1983takesmorethantwoyearstobecomenegative, while the response of CPI post-1983 is always negative. In the case of CPI net of shelter, the result is basically the same as in Figure 14. We would like to highlight the fact that, once again, there is a considerable difference in the responses of CPI and CPI net of shelter, with the latter being more responsivethantheformer. 7.4 SignRestriction Finally,weshowhowtheresultschangewhenapuresignrestrictionisusedasanidentification strategy. In this case, the monetary policy shock is identified by restricting the signs of selected impulse functions for a fixed number of periods. We follow Uhlig (2005) and eliminate the price puzzle by construction by restricting the interest rate response to be positive, the price level to be negative, andmoneyaggregatetobenegativeforfivemonths. Weleavetheindustrialproduction response unrestricted. Hence, this is an agnostic identification with respect to output. This alternativeidentificationisimportanttohelpseparatethemisspecificationproblemofourmechanism. Figure16showstheresults. 24

0 −0.05 −0.1 −0.15 −0.2 −0.25 −0.3 −0.35 −0.4 −0.45 −0.5 0 5 10 15 20 25 30 35 40 45 50 Steps kcohsRFFotlevelecirpfoesnopseR CPI CPInetofshelter Figure 16: Pure sign restriction agnostic with respect to output. Impulse response functions sign restricted for five months (k = 5). The variables restricted are the same as in Uhlig (2005) with interestratebeingpositive,moneyaggregatenegative,andCPInegativefortherestrictedperiods. 1983:01to2006:12period. We see once again a sharp difference in the response of CPI net of shelter in comparison to the response of CPI. These results are not directly comparable to the ones presented previously, but they share at least one important common feature: CPI net of shelter responds more quickly to a monetaryshockthanoverallCPI. When some variable is not model consistent and a pure sign restriction is used the results obtainedmaybehidingsomeimportantissues. Bydiggingdeeper,wewereabletounveilanimportantfeatureoftheCPIthatwebelievetobeveryimportantformonetarypolicy. 8 Conclusion In this paper we take into account the effects of monetary policy on housing tenure choice and the weight of shelter in the CPI to explain the price puzzle. After an increase in interest rates, morepeoplewillwanttorentinsteadofownandthisshiftinconsumptionbehaviorincreasesthe price of rents in comparison to all other goods. We provide a simple theoretical framework (the effect of monetary policy on housing tenure choice) for why housing rents may increase after a contractionarymonetarypolicyshock. Thismechanismisdifferentfromthecostchannelliterature, 25

and our empirical results suggest that it is relevant in explaining the price puzzle. Our results are qualitativelyrobusttodifferentidentificationstrategies,measuresofinflation,sampleperiods,and theycomparewellagainstalternativeexplanations. In our opinion, these results would be interesting on their own, but they may be significantly more far-reaching than just explaining the price puzzle. While providing a possible explanation for the price puzzle, we showed that, when we exclude shelter from the CPI, inflation seems to be muchlesspersistentthanpreviouslythought. Moregenerally,theresultsofthispaperhighlightthe importanceofmeasuringinflationinatheoreticallyconsistentwaytobetterseparatepricechanges causebyinflationfrompricechangescausedbyrelativepricechanges. References Barth,MarvinJ.,andRamey,ValerieA.,2001,“TheCostChannelofMonetaryTransmission,” NBERMacroeconomicsAnnual. Bernanke, Ben S., Boivin, Jean, and Eliasz, Piotr, 2005, “Measuring the Effects of MonetaryPolicy: AFactor-AugmentedVectorAutoregressive(FAVAR)Approach,”TheQuarterly JournalofEconomics,Volume120(1),387-422. BLS, 2009, “How the CPI measures price change of Owner’s equivalent rent of primary residence(OER)andRentofprimaryresidence(Rent),”BureauofLaborStatistics. Brissimis,SophoclesN.,andMagginas,NicholasS.,2006,“Forward-LookingInformationin VAR Models and the Price Puzzle,” Journal of Monetary Economics, Volume 53(6), pp. 1225- 1234. Christiano,LawrenceJ.,Eichenbaum,Martin,andEvans,Charles,1996,“TheEffectsofMonetary Policy Shocks: Evidence from the Flow of Funds,” Review of Economics and Statistics, Volume78(1),pp.16-34. Church,JonathanD.,2014,“Explainingthe30-yearshiftinconsumerexpendituresfromcommoditiestoservices,1982-2012.,”MonthlyLaborReview,April. Clark,ToddE.,2001,“ComparingMeasuresofCoreInflation,”EconomicReview,secondquarter,pp.5-31. 26

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