Measuring Aggregate Housing Wealth: New Insights from Machine Learning

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Measuring Aggregate Housing Wealth: New Insights from Machine Learning Joshua H. Gallin, Raven Molloy, Eric Nielsen, Paul Smith, and Kamila Sommer 2018-064 Please cite this paper as: Gallin, Joshua H., Raven Molloy, Eric Nielsen, Paul Smith, and Kamila Sommer (2018). “Measuring Aggregate Housing Wealth: New Insights from Machine Learning,” Finance and Economics Discussion Series 2018-064. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2018.064r1. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Measuring Aggregate Housing Wealth: New Insights from Machine Learning (cid:42) Joshua Gallin, Raven Molloy, Eric Nielsen, Paul Smith, Kamila Sommer July 26, 2019 Abstract WeconstructanewmeasureofaggregatehousingwealthfortheU.S.basedon(1)homevalue estimates derived from machine learning algorithms applied to detailed information onpropertycharacteristicsandrecenttransactionprices,and(2)Censushousingunitcounts. Accordingtoournewmeasure,thetimingandamplitudeoftherecenthouse-pricecyclediffers materiallybutplausiblyfromcommonly-usedmeasures,whicharebasedonsurveydataor repeat-salespriceindexes. Thus,ourmethodologygeneratesestimatesthatshouldbeofconsiderablevaluetoresearchersandpolicymakersinterestedinthedynamicsofaggregatehousing wealth. JELCodes: C82,E21,R31. Keywords: Residentialrealestate,Consumereconomicsandfinance, Datacollectionandestimation,Flowoffunds. (cid:42) Pleasedonotcitewithoutthepermissionoftheauthors.Earlierversionsofthispaperwerecirculatedunderthe title“MeasuringAggregateHousingWealth:NewInsightsfromAutomatedValuationModels.” WethankZillowforprovidingthedataandforveryhelpfuldiscussionsaboutitsconstruction,andwethankMaxMiller andHannahHallforexcellentresearchassistance.Allerrorsremainourown. Theanalysisandconclusionssetforthherearethoseoftheauthorsanddonotindicateconcurrencebyothermembers oftheresearchstaff,theBoardofGovernors,ortheFederalReserveSystem. Ourevaluationoftheadvantagesand disadvantagesoftheZillowAutomatedValuationModel(AVM)aremadeinthecontextofestimatingtheaggregate valueofown-useresidentialrealestate.ItisnotanevaluationorendorsementofZillow’sAVMorwebsiteforvaluinga particularhomeorportfolioofhomes. 1

1 Introduction Owner-occupiedhousingisamajorcomponentofhouseholds’balancesheets.1 Asaresult,changes in aggregate housing wealth can affect aggregate consumption and savings and, by extension, macroeconomicoutcomessuchaseconomicgrowthandbusinesscycles. However,housingwealth isquitedifficulttomeasure(aswewilldiscussbelow),whichhasmadeitdifficultforresearchers toreliablyobserveitsdynamics. Inanefforttoimprovethemeasurementofhousingwealth,this paperintroducesanewmethodtomakeuseoflocalpropertyvalueestimatesthatarederivedfrom machinelearningalgorithmsappliedtodetaileddataonpropertysalesandcharacteristicsfrom publicrecordsandothersources. Wecombinethesepropertyvalueestimateswithhousingunit counts from the Census to derive new estimates of aggregate U.S. housing wealth from 2001 to 2018. Ourestimatesshowconsiderablymoreresponsivenesstochangingmarketconditionsthan surveymeasuresandsomewhatlessvolatilitythanrepeat-salesmeasures,highlightingsomeofthe keybiasesplaguingthesecommonlyusedestimatesofhousingwealth. Thus,ourmethodology generatesestimatesthatshouldbeofconsiderablevaluetoresearchersandpolicymakersinterested inthedynamicsofhousingwealthandtherolethatitplaysineconomicoutcomes. The difficulty in measuring aggregate housing wealth stems from the inherent difficulty in measuringindividualpropertyvalues. Transactionprices,whicharethebestmeasureofahome’s value, are relatively infrequent for a given property, with years or even decades between sales. Consequently, commonly used measures of individual house values have typically been based on homeowners’ reports from surveys or extrapolated from previous sales using changes in a repeat-salespriceindex. Researchhasfoundbothofthesemethodstobeflawedindistinctways. Forexample,studieshavefoundthatowner-reportedestimatesofhousevaluesarebiasedupon average,perhapsbecauseownersareoverlyoptimistic. Moreover,ownersappeartohavedifficulty identifying market turning points, causing the bias to fluctuate over the housing cycle.2 Other studieshaveshownproblemswithusingrepeat-salespriceindexes,dueinparttothefactthatthe propertiesthataresoldarenotalwaysrepresentativeofthosethatarenotsold. Thisbiasmayalso 1Accordingtothe2018q4DistributionalFinancialAccounts,owner-occupiedrealestateaccountedfor53percentof theassetsofthebottomhalfofthewealthdistribution,and32percentoftheassetsofthoseinthe50th-90thpercentile ofwealth.Seehttps://www.federalreserve.gov/releases/efa/efa-distributional-financial-accounts.htm. 2See, forexampleGoodmanandIttner(1992);KielandZabel(1999);BucksandPence(2006);Kuzmenkoand Timmins(2011);Henriques(2013);Chanetal.(2016). 2

becyclical,asthedegreeofdifferencebetweentransactingandnon-transactinghomesmayshift systematicallyoverthehousingcycle.3 Byextension,aggregatehousingvaluesconstructeddirectly fromsurveydataorbyextrapolatingfromagivenbaseusingarepeat-saleshousepriceindexwill alsobeaffectedbythesesamebiases. The method of measuring housing wealth that we develop in this paper uses an automated valuationmodel(AVM),whichcanbelooselythoughtofasanalgorithmthatcombinesinformation on a home’s characteristics, neighborhood features, nearby sales, and homes listed for sale to produceanestimateofthehome’scurrentmarketvalue. AlthoughversionsofAVMshavebeen in use for decades, private tech companies have recently created much more sophisticated and comprehensiveAVMsbycombiningverylargeanddetailedproperty-leveldatasetswithmachinelearningalgorithmstoimputevaluesofindividualhousingunitstolargeswathsofresidentialreal estateintheU.S.Thiscombinationofbigdataandmachinelearningtechniquesoffersthepotential formoreaccurateestimatesofhousingvalues–especiallyduringmarketturningpoints–than thosebasedonsurveysorrepeat-salesindexes. TheestimatesofaggregatehousingwealththatweconstructarebasedonanAVMcreatedby Zillow,aprivaterealestateanddataanalyticsfirmthatprovidesestimatedhomevaluesforover 100millionpropertiesintheU.S.Constructingourmeasureofaggregatehousingwealthisnotas simpleasaddingupthevalueestimatesofallpropertiesintheZillowdata. Zillow’sAVMcoverage, whileextensive,isnotuniversal. Moreover,Zillow’sestimatesincludesomerentalpropertiesthat wedonotwanttoincludeinourmeasureofaggregatehousingwealthandthatwecannoteasily identify. WeaddresstheseissuesbycombiningtheAVMdatawithdatafromtheCensusBureau’s American Community Survey (ACS). Specifically, we calculate the quantity of owner-occupied housing units by property type and county from the ACS and multiply these quantities by the average value of homes in each market segment (county and property type) as determined by Zillow’sAVM.InSections4and5,wevalidateourmethodbycarefullyinvestigatingtheproperties oftheAVMestimatesandtherepresentativenessofthesampleonwhichtheseestimatesarebased. Wherewecan,wetestforpotentialbiasinournewmeasure. Our method yields new high-frequency (monthly) estimates of aggregate owner-occupied 3See,forexampleandCaseetal.(1997);GatzlaffandHaurin(1997);DreimanandPennington-Cross(2004);Glennon etal.(2018). 3

housingwealthfrom2001to2018,therebyofferingafreshlookatthedynamicsovertherecent housingcycle. Wefindthatfrom2001to2006,theAVMestimatesarelargelyinlinewithestimates based on owners’ reported values in surveys such as the annual ACS, the biennial American Housing Survey (AHS), or the triennial Survey of Consumer Finances (SCF). By contrast, our measuredivergesnotablyfromsurveymeasuresfrom2006to2012,atimeperiodthatincluded anenormoushousingbustandagradualrecovery. Inparticular,theAVM-basedmeasureturns down earlier and falls by much more than a measure based on owner reports. This result is consistent with prior research suggesting that survey respondents were either unaware of the marketfluctuationsinrealtime,ortheybelievedthattheirhomevaluesweredifferentthanthose inthesurroundingmarket. Totheextentthatownersdidacknowledgechangesinthemarketin theirsurveyresponses,itappearsthattheywerelatetodoso. The AVM-based measure also differs from the measure of housing wealth reported in the FederalReserve’sFinancialAccountsoftheUnitedStates,whichislargelydrivenbychangesina repeat-saleshousepriceindexfrom2005onward. Specifically,whilethecontractioninwealthand subsequentrecoveryintheAVMmeasureismorepronouncedthanitisinthesurveymeasures, thecycleislesspronouncedintheAVMmeasurethanintheFinancialAccounts. Weinterpretthis resultasillustratingthepossibilitythatrepeat-salesindexesoverstatetheeffectofmarketchanges onaggregatehousingwealthbecausetheyinaccuratelyextrapolatethehousepricedynamicsof transactinghomestoallhomes. Weviewoneofthecontributionsofthispaperasshowinghowdatathatarecollectedinthe privatedomainforotherpurposescanbecombinedwithsurveydatatoproduceanaggregatetime seriesforuseinnationalstatistics. Researchersarecurrentlyengagedinapplicationsthatattempt to make use ofsuch datato measure a variety of aggregateoutcomes includingretail spending, servicesconsumption,employment,andbusinessformation.4 Consistentwiththesestudies,one lessonfromouranalysisisthatprivatelygenerateddatamaystillneedtobeaugmentedwithother datasourcesinordertoconstructnationallyrepresentativestatistics. Anothercontributionisshowinghowmachinelearningtechniques(asusedinZillow’sAVM) can be used to improve estimates of aggregate housing wealth.5 Perhaps most importantly, our 4Forexamples,seeAladangadyetal.(2019);Batchetal.(2019);Cajneretal.(2019);Gindelskyetal.(2019);Glaeser etal.(2019). 5Machinelearninghasbeenusedinavarietyofapplicationsfrompredictiontocausalestimation.Notablerecent 4

findingssuggestthatstudiesthatuseself-reportedvaluesfromsurveysliketheSCFtoexamine fluctuationsinhousevaluesorhousingwealthcouldbeunderstatingquiteseverelythecyclical changesinaggregatewealth. Sincehousingwealthissuchabigpartoftotalhouseholdwealth,any biasinowner-reportedhomevaluesinturnaffectsmeasurementofcyclicaldynamicsofhousehold networth. Ourresultsalsosuggestthateconomistsandpolicy-makersusingtheFinancialAccounts orrepeat-salespriceindexestomeasureaggregatewealthmightoverstatethesizeofthehousing wealthcycle. Especiallybecausehousingwealthmeasurementhasthepotentialtoaffectresultsina widerangeofstudies,thediscussionandfindingsinthispapershouldbeofinteresttoresearchers andpolicymakersinterestedinquantifyingtheeconomiceffectsofcyclicalfluctuationsinwealth. Therestofthepaperisorganizedasfollows. Section2providesasummaryofthedifficulties inmeasuringhousingwealth. Section3describesthebasicsofZillow’sAVMmethodology. Section 4describeshowweuseZillow’sAVMtoproduceanationallyrepresentativemeasureofaggregate housingwealth. Sections5,6and6discusspossiblebiasesinourmethodaswellascorrectionswe developtoaddressthesebiases. Section7describesourestimatesofhousingwealthfortheUnited States and how these measures compare to the Financial Accounts and aggregated survey data. Section8concludeswithadiscussionoftheimplicationsofourpaperforotherstudiesandfuture usesoflarge-scaleAVMsineconomicresearch. 2 Measuring Housing Wealth As with any other economic statistic, the best measure of aggregate housing wealth would be unbiased, precise, and available at a high frequency and with a short reporting lag. Ideally, we would observe the currentmarketvalue ofevery homeat all times, and simply add themup to measuretheaggregate. Inreality,currentmarketvaluesexistonlyforhomesthathavesoldrecently, which make up a minority of the stock of homes. For example, in the 2017 American Housing Survey,only10percentofowner-occupiedpropertieshadtransactedintheprevioustwoyears;for morethanonethird,thelasttransactionwasin2000orearlier. As noted above, measurements of housing wealth have typically derived from surveys of homeowners who are asked to estimate the value of their homes, or repeat-sales price indexes examplesaresummarizedinKleinbergetal.(2015);Athey(2018);AtheyandLuca(2019). 5

derivedfromrecentmarkettransactions. Alongliteratureexplorestheissuesassociatedwitheach approach. Regardingtheimplicationsofusinghousepriceindexestoestimatechangesinaggregate homevalues,severalpapershavefoundthatthesamplesofhousingunitsusedtoformrepeat-sales indexesarenotrepresentativeofabroadersetofhomes. Homesthattrademorefrequentlytend tohavesystematicallyhigherhousepriceappreciation(KortewegandSorensen,2016;Caseetal., 1997). Moreover,theselectionbiasassociatedwithtransactingmorefrequentlyiscorrelatedwith economic conditions and the housing cycle (Gatzlaff and Haurin, 1997; Malone and Redfearn, 2009),complicatingtheinferenceofcyclicalchangesinhousingwealthfromarepeat-saleshouse price index. Likely because of these biases and selection issues, Glennon et al. (2018) find very large differences between value estimates based on repeat-sales indexes and transaction prices duringthehousingcrisis. Afurthercomplicationwithusinghousepriceindexestomeasureaggregatehousingwealthis thefactthatextrapolationusingapriceindexrequiresstartingfromanationally-representative baseatsomepointintime–theindexonitsowncannotspeaktothelevelofhousingwealth. Such abase–whichisfrequentlyconstructedfromavailablesurveydata–isinitselfquitedifficultto accuratelymeasure,forreasonswewilldiscussbelow. Moreover,extrapolatingforwardfromany baseusingapriceindexintroducestheproblemthatpriceindexesaredesignedtoabstractfrom changesinthequantityandqualityofthehousingstock.6 Butchangesintheaggregatevalueof housingshouldincludechangesinquantityandquality,soattemptstoextrapolatewealthusing apriceindexmustsomehowaccountforthesefactorsusingotherdatasources.7 Thisissuemay notbesoimportantforextrapolatinghousingwealthoverafewquarterssincethehousingstock changesslowlyovertime. Butthelongerthetimeperiod,themorelikelythelackofinformation onqualitywillmatter. Measurementofhousingwealthdirectlyfromsurveysaddressestheproblemsassociatedwith theuseofhousepriceindexes,whileintroducingnewissuesrelatedtotheaccuracyofhomeowner reporting. Ontheonehand,nationallyrepresentativesurveyscontainvalueestimatesrepresenting 6Specifically,arepeat-salesindexassumesthatthequalityofahousingunitisconstantbetweentransactionpairs, nomatterhowmuchtimehaselapsedbetweenthetwosalesdates. 7IntheFinancialAccountsafter2005,quantityandqualityadjustmentscomeonlyintheformofestimatesofnet fixedinvestmentfromtheBureauofEconomicAnalysis.Thatis,theFinancialAccountsemploysaperpetualinventory approachinwhichchangesinhousingwealthcomefromcapitalgains,estimatedusingarepeat-salesindex,andnet fixedinvestment,whichincludesestimatesofthevalueofadditions,renovations,andconstructionofnewunits. 6

all owner-occupied homes. The sum of these survey responses thus yields a straightforward estimateofaggregatevalueforeverysurveyyear. Sincethesereportedvaluesinprinciplereflect the changing characteristics of the housing stock over time, the resulting aggregate estimates shouldaccountforchangesinquality. Ontheotherhand,thisapproachtomeasuringaggregate housing wealth will only work if owner valuations are unbiased. A long line of research finds evidenceofsystematicbiasinowner-reportedhousevalues,althoughtheprecisemagnitudeofthis biasisdifficulttoassess. Some studies assess the bias of owner valuations by comparing owner-occupant estimates directly with subsequent sale prices. Goodman and Ittner (1992) compare survey respondents’ housevaluationstosubsequentsalesprices(overthenexttwoyears)usingdatafromthe1985and 1987wavesoftheAHSandfindthat,onaverage,ownersoverestimatethevalueoftheirhomes by about 8 percent. More recently, Molloy and Nielsen (2018) compare owner estimates in the 2014ACSwithsalepricesin2016andfindthattheaverageowneroverestimatesthevalueoftheir homeby6percent. Thisgeneralapproachtoassessingbiasinself-reportsisnotfoolproof,however. Typically, ahousepriceindexmustbeusedtoextrapolatetheowner-reportedvalueforwardin timetothesaledate.8 Whilefocusingontransactionswithintwoyearsofthesurveydatemitigates potential bias from the use of price indexes (discussed above), the resulting transaction/survey pairsarefewinnumberandmaynotberepresentativeofthefullsurveysample. Forexample,in anticipationofafuturemove,homeownerswhoareonlyafewyearsfromsellingmaybebetter informedabouttheirlocalhousingmarket,suggestingasmallerbiasthanwhatwouldbetypical forrespondentswhodonotintendtosell. Otherstudiesattempttoassessbiasinownerreportsbycomparingthemtoahomevaluethat is extrapolated from a previous sale price, also using a house price index. The degree of owner overvaluation estimated in this manner can be quite large, ranging between 3 and 16 percent (Ihlanfeldt and Martinez-Vazquez, 1986; Kiel and Zabel, 1999; Benitez-Silva et al., 2015; Chan etal.,2016;vanderCruijsenetal.,2018). Moreover,theovervaluationappearstoincreaseduring marketdownturnswhenownervaluationsdonotfallasmuchaspriceindexes(Henriques,2013; 8GoodmanandIttner(1992)inflatetheownervaluationsusingametropolitanareahousepriceindexwhileMolloy andNielsen(2018)adjustforthetimedifferencebetweentheownervaluationandthesaleusingacounty-levelZillow HomeValueIndex. Neitheradjustmentisaccurateifthetruevalueofthehomedoesnotappreciateinlinewiththe associatedpriceindex. 7

Chan et al., 2016; Davis and Quintin, 2017). In these studies, there is usually a fairly long gap betweenthesurveydateandtheprevioussaledate,soanybiasfromextrapolationusingaprice indexwouldbegreatlyamplified. Insummary,priorliteraturehasdocumentedthepotentialforconsiderablebiasesinexisting measuresofhousingwealth,althoughtheestimatedsizesofthesebiasesrangewidely. 3 Automated Valuation Models While issues inherent to the house price index and owner-report methodologies have been recognizedbyresearchersforyears,nogoodalternativeshaveexistedforconstructingestimatesof aggregatehousingwealth. Recently,however,AVMscreatedbyprivatefirmshaveemergedasa promisingcontender. AlthoughfinancialinstitutionshaveusedversionsofAVMsfordecadesto value mortgage portfolios, the models and data have only recently reached the point where, in ourview,theycanplausiblyprovideaviablemethodformeasuringaggregatehousingwealth. In particular,companiessuchasZillowhaveassembledverylargeproperty-leveldatasetscontaining tens of millions of records and combined them with sophisticated machine learning models to imputevaluesofindividualhousingunitsforlargeswathsofresidentialrealestateintheU.S.This combinationofextensive,detaileddataandmachinelearningoffersthepotentialformoreaccurate andmorerepresentativeestimatesofhousingvaluesthanthosebasedonsurveysorpriceindexes. Zillow’sAVMattemptstoassignvaluestoallsingle-familyhomes,aswellasco-opandcondominiumapartments.9 Asafirstpass,onecanthinkoftheAVMasresemblingahedonicregression relatinghousevaluestoarichsetofpropertyandneighborhoodcharacteristics,estimatedfrom comprehensivedataonobservedsalepricesinthelocalareaaroundeachhome. Theestimated modelisthenappliedtopropertiesthatdonothavearecentsalepricetoproducevalueestimates for the full stock of homes for which sufficient data on characteristics are available or can be imputed.10 Inpractice, Zillow’sAVMisnotasinglehedonicmodel, butaverylargenumberofdistinct models that work together to produce a value estimate for each property. The individual sub- 9Zillowdoesnotattempttovalueapartmentsinrentalbuildingsbecausesuchbuildingsareboughtandsoldasa singleproperty.Therefore,anAVMapproachbasedontransactionpricesforindividualhomeswouldnotbeavalid. 10ForverygeneralbackgroundinformationonZillow’sAVM,seehttps://www.zillow.com/zestimate/. 8

modelsareestimatedusingstandardmachinelearningtechniquesthatusetheunderlyingdatain differentways. Theresultingestimatesfromthesub-modelsarethencombinedintoasinglefinal estimatebasedonout-of-samplepredictiveperformanceanddataqualityfilters. Whiletheexact detailsofZillow’sestimationareproprietary,theirAVMisanensemblemodel,thetypeofmodel that has been shown to outperform other common machine learning approaches in predicting houseprices(MullainathanandSpiess,2017).11 TheAVMwillnotassignavaluetoapropertyin theeventoftoomuchuncertaintyabouttheestimatedvalue,e.g.,frommissingdataorunusual propertycharacteristics. Thepropertiesexcludedforthesereasonstendtobeinlesspopulated areaswheretransactionsaresparseanddataqualityispoor. Zillow’sAVMusesawidevarietyofdatasources. Deedsrecordsandpropertytaxrecordsarethe backboneoftheirdata,astheserecordsarenearlyuniversaland,whencombined,typicallyinclude bothpropertycharacteristicsandtransactiondetailssuchassalespricesanddates. However,deeds andpropertytaxrecordsarenotperfect. Forexample,“non-disclosure”statesdonotrequirethat sales prices be disclosed in deeds records, and property tax records do not always capture the myriad property characteristics that affect a home’s value.12 To add additional information on propertycharacteristics,ZillowsupplementsthedeedsrecordswithdatafromMultipleListing Service(MLS)registries,mortgageservicers,andothersources. Forexample,Zillow’sdataincludes informationaboutwaterviews,localschoolquality,andotherlocalamenitiesthatwouldbevery difficult to assemble through other means. In addition, the Zillow website invites homeowners to update or correct the characteristics of their property that might be missing or inaccurate in Zillow’sdatabase. Zillowupdatesandre-estimatestheirmodelsdailytoonboardnewdataasitbecomesavailable. ThesedailyrunsallowZillowtocontinuallyassesstheirmodelerrorsforbiasandupdatetheir algorithmstomaximizetheaccuracyofthepredictionatanypointintime. The available (albeit limited) information to date suggests that AVMs are at least somewhat 11MullainathanandSpiess(2017)alsoprovideaveryhelpfulsummaryofmachinelearningtechniques.Theyargue thatensemblemodels,suchasZillow’s,tendtoperformverywellinvirtuallyallpredictionexercises.Ingeneral,the machinelearningtechniquesemployedbyZillowfollowbestpracticesasoutlinedinMullainathanandSpiess(2017) andAthey(2018). 12Thenon-disclosurestatesareAlaska,Idaho,Kansas,Louisiana,Mississippi,Montana,NewMexico,NorthDakota, Texas,Utah,andWyoming. Inaddition,somecountiesinMissouridonotrequirethatthatsalespricesbedisclosed indeedsrecords. Eveninnon-disclosurestates,mortgageloanamountsareoftendisclosedatrecorders’offices. See http://www.zillowgroup.com/news/chronicles-of-data-collection-ii-non-disclosure-states/. 9

betterthanothermethodsofhousingvaluationduringnormaltimes,andcanbeconsiderablybetter duringmarketdownturns. Glennonetal.(2018)evaluaterepeatsalesindexesbyextrapolating priorsalespriceswitharepeat-salesindexandcomparethesevaluationstosalesprices. Across the four counties that they examine, they report average errors ranging from 3 to 7 percent in 2005,andfrom26to113percentin2010.13 Bycomparison,usingdataprovidedbyZillowthat wewilldiscussbelow,forthosesamefourcountieswecalculateaverageAVMerrorsrangingfrom -7 to 2 percent in 2005 and from 9 to 19 percent in 2010. Molloy and Nielsen (2018) analyze a sample of homes with a different AVM and owner valuations in 2014 that subsequently sold in 2016. Although the average errors were about 6 percent using either valuation method, the distribution of AVM errors was centered very close to zero, whereas the distribution of owner valuationerrorswascenteredaround2percent(i.e. thevaluationwas2percenthigherthanthe salesprice).14 Onthewhole,itseemsthatAVMshavethepotentialtomateriallyimproveestimates ofaggregatehousingwealthduringmarketdownturns,andmaybeanimprovementoverother existingmethodsevenduringnormaltimes. 4 UsingZillow’sAVMtoMeasureAggregateOwn-UseHousingWealth WeuseZillow’sAVMtoconstructameasureoftheaggregatehousingwealthheldbyhouseholds fortheirownuse; i.e.,excludingrentalunits.15 Ourmeasureisthusdirectlycomparabletothe mostcommonlyusedmeasuresofaggregatehousingwealth,whichalsoexcluderentalproperty. OnesuchmeasureisthewidelycitedseriesfromtheFederalReserve’sFinancialAccountsofthe UnitedStates,whichisahybridbetweensurveydata(through2005)andarepeat-saleshouseprice indexafter2005.16 Anothercommonmethodtomeasureaggregatehousingwealthistoaggregate estimates directly from surveys; since most surveys only ask owner occupants to report house 13Apositiveerrormeansthevaluationwashigherthanthesalesprice. 14The AVM accuracy tends to improve over time with better data and model improvements. See https://www. zillow.com/zestimate/#accforup-to-dateinformationabouttheaccuracyofZillow’sAVM. 15Wefocusonthetotalvalueofrealestateassetsratherthanhomeequity,whichwouldsubtractmortgagedebt. 16TheseriesweconstructinthispaperisdirectlycomparabletotheFinancialAccountsseriesFL155035013,the component of total housing wealth that excludes vacant land and mobile homes. Over the period 2001-present, FL155035013representsabout93percentto95percentoftotalhouseholdhousingwealthreportedinTableB.101.hof theFinancialAccounts. 10

values,thesesurveysdonotprovidedataonthevalueofrentalunits.17 4.1 RepresentativenessofZillow’sData AkeyconsiderationinusingZillowtoconstructanaggregatetimeseriesisthatZillow’scoverage maynotbebroadenoughtobenationallyrepresentative. AnotherconsiderationisthatZillow’s universe includes some rental properties (held by businesses or households), which we do not want to include in our measure of aggregate own-use housing wealth, and which cannot be straightforwardlyidentifiedintheZillowdata. Table1: PropertyCountsin2017(millions) ACS Zillow Total Own-use Total Single-Family 92.9 76.4 78.7 Multi-Family 35.9 5.8 7.7 Total 128.8 82.1 86.3 Table 1 illustrates how the Zillow data compare with the universe of own-use properties in 2017asmeasuredinthenationally-representativeACS.AccordingtotheACS,therewereabout93 millionsingle-familyhomesintheU.S.in2017,about76millionofwhichwereforhouseholds’ own use and 17 million of which were for rental use.18 Zillow’s AVM is able to provide value estimatesforabout79millionsingle-familyhomesin2017(includingbothown-useandrental). Thus, Zillow’s overall coverage of the single-family market, at about 85 percent, is fairly high. However,becauseowner-occupiedhomesarenotidentifiedassuchintheZillowdata,wecannot knowexactlyhowmanysingle-familyhomesmeantforownusearemissedbyZilloworhowmany single-familyrentalhomesareincluded. Turning to the multifamily market, there were about 36 million multifamily homes in 2017 ACS,butonlyabout6millionwereforownuse. Zillow’ssamplefor2017includesabout8million multifamilyhousingunits,includingbothown-useandrentalproperties. Zillow’soverallcoverage 17OnenotableexceptionistheSurveyofConsumerFinances,inwhichsurveyrespondentsreportthevalueofrental propertyownedbyahousehold. 18ConsistentwiththeFinancialAccountsdefinition,wedefinepropertiesintheACSas“own-use”iftheyare(1) owner-occupiedorvacantand(2)likelyintendedforown-use.Thelattercategoryincludesunitsthatareforsaleanda fractionofallothervacantunitsthatarenotforrent. Thisfractionisdeterminedbytheratioofowner-occupiedto renter-occupiedunitsbystateandpropertytype.Seebelowfordetails. 11

rate(about20percent)ismuchlowerformultifamilypropertiesbyconstruction,becauseZillow doesnotattempttovalueapartmentsinrentalbuildings(definedasbuildingsinwhichasingle property-taxparcelcontainsmultipleunits);rather,theirfocusisonmultifamilyhousingunits thataresoldindividually,likecondosandco-ops. TheexclusionofrentalbuildingsfromZillow’s valuation universe is a helpful feature for our purpose, as we do not include these units in our wealthmeasure.19 Fortheunitsinmultifamilybuildingsthatwedowanttoinclude(i.e.,condos andco-ops),theavailableevidencesuggeststhattheZillow’scoverageisactuallyquitehigh. In particular, using the Census Bureau’s 2012 Rental Housing Finance Survey, we estimate that roughly25percentofrentalmultifamilyhousingunitswerecondos. Ifweapplythissharetothe 2017ACSdata, theestimatedtotalnumberofcondoandco-opunitswouldbeabout8million, veryclosetothetotalnumbervaluedbyZillow(seeTable1).20 However,theZillowmultifamily sample of 8 million is still larger than the ACS count of own-use multifamily homes, which is about6millionunits. ThisdifferenceindicatesthattheZillowmultifamilysamplestillincludesa significantnumberofrentalunitsthatwewouldliketoexclude. Inaddition,itlikelyalsomisses someown-usepropertiesthatwewouldliketoinclude. Finally,inconstructinganaggregatemeasure,itisimportanttoassesswhetherZillow’scoverage variessystematicallyacrossdifferentpartsoftheU.S.Towardthatend,Figure1showsZillow’s coverageatthestatelevel. Specifically,itshowstherelationshipbetweenthenumberofproperties covered by Zillow in 2017 in a given state and the number of own-use properties in the ACS for that state. The closer the state is to the dashed 45-degree line, the better the alignment of housing counts between Zillow and the ACS. Zillow’s coverage of single-family own-use units (upperpanel)isalittlelowerforsmallerand/orlessdenselypopulatedstates(suchasAlaskaand NorthDakota),buttherelativelycloseproximityofmoststatestothe45-degreelineindicatesthat Zillow’suniverseisgenerallyquiterepresentativeoftheACSown-useuniverse. Zillow’scoverage ofmultifamilyunits(lowerpanel)variesmoreacrossstates,butisstillgenerallyhigh. 19Theseunitsaregenerallyheldbyhouseholdsonlyindirectly,throughtheirholdingsofcorporateandnon-corporate equity.Assuch,wedonotclassifythemasdirecthouseholdholdingsofown-usehousingwealth. 20WecannotestimateZillow’soverallcoverageofcondoandco-opunitsdirectlyfromtheACSdatabecausetheACS doesnotincludeinformationthatwouldallowustoreliablyidentifywhichoftheunitsinmultifamilybuildingsare condosorco-ops. 12

Figure1: RatioofZillowtoACSPropertyCountsin2017byState Single Family, ACS Own−use v. Zillow 16 16 TlX ClA FlL 15 GlA NlC lI M L lOlIHNlY PlA 15 14 lIAO Ol l R K LKllAY Sl AlC L ClO Ml Ml D A MlMAW ll N T Wl l l ZO N I A IlN NlVJ lA 14 NlV UlT Ml A S l KlR SClT IlD NlNMlWE lV 13 13 NlH Hl RlI I DlE MlT MlE 12 WlY AlK NlD VlT SlD 12 DlC 12 13 14 15 16 stinU deulav−wolliZ fo goL Log of ACS Units Multifamily, ACS Own−Use v. Zillow FlL 14 ClA 14 NlY lIL 13 13 MlI Nl MlJA 12 UlT TlN NlV AlZ NG Hl llSClWA I lCI WlV O C l l lAA H T Pl MCl A lDOTlX 12 11 lIA NlHIlN DlC Ml M N lO 11 KlY AlL OlR 10 MlE RlI 10 AlK OlKIlDNlMDlE LlA 9 9 MlNS lENlMl DT KlS VlT 8 WlY WlV AlR 8 8 9 10 11 12 13 14 stinU deulav−wolliZ fo goL Log of ACS Units Bolded red denotes non−disclosure states. 13

4.2 OurNewMethod AlthoughZillow’scoverageappearshighenoughandbroadenoughtobenationallyrepresentative, thenumberofunitsinZillow’sdatacanchangediscontinuouslyovertimeasnewdatasourcesare integratedintotheirestimationframework. Forexample,thenumberofhousingunitsinZillow’s samplejumpedby3.5percentfromMay2009toJune2009astheircoverageexpanded. Whilewe wanttotakeadvantageofthepotentialfortheadditionofnewunitstoimprovethequalityofthe Zillowestimates,wedonotwantourmeasureofaggregatehousingwealthtojumpdiscontinuously becauseZillowimprovedtheirsamplebyaddingunitsthatalreadyexisted. Moreover,wewould notwantourmeasuretobeaffectedbytheinclusionofrentalproperties,whicharenotpartofour definitionofown-usehousingwealth. Togetaroundtheseissues, wedividetheaggregateU.S.housingmarketintosegmentsand calculate the wealth in each segment by multiplying the average value from Zillow’s AVM by thenumberofown-usehousingunitsderivedfromthenationallyrepresentativeACS.Wedefine market segments as a combination of property type (single-family or multi-family) and county. Thus,foreachcountycandpropertytypep,weestimatethevalueofown-usehousingattimet as: Vˆ(p,c,t)=NACS(p,c,t)V¯Z(p,c,t), whereNACS(p,c,t)isanestimateofthenumberofpropertiesintendedforownusefromtheACS andV¯Z(p,c,t)istheaverageAVMvalueforresidentialproperties. ToconstructthecountsofpropertiesintendedforownusefromtheACSineachcounty,wesplit allhousingunitsreportedinthesurveyintothreemutuallyexclusiveandexhaustivecategories: units that are unambiguously for own use (owner-occupied plus vacant-for-sale), units that are unambiguouslyforrentaluse(renter-occupiedplusvacant-for-rent),andunitsthatarevacantbut are not for sale or for rent. Consistent with the Financial Accounts concepts, we define the total numberofpropertiesintendedforownuseasthesumofunitsintendedforownuseplusashare (φ)ofvacantpropertiesthatarenotforsaleorrent: NACS(p,c,t)=NACS(p,c,t|ownuse)+NACS(p,c,t|vacant)φ(p,c,t). Weassumethattheshareofvacantpropertiesthatareintendedforpersonaluse,φ,isthesameas 14

theshareofoccupiedpropertiesforownusesothat: NACS(p,c,t|ownuse) φ(p,c,t)= . NACS(p,c,t|ownuse)+NACS(p,c,t|rentaluse) If we had accurate housing counts of all own-use units (NACS) and unbiased average home values (V¯Z) for each property type and county, then the above method would yield unbiased estimates of aggregate housing wealth in each county. These county-level estimates could then be straightforwardly summed to produce an estimate of the national aggregate. However, this theoreticalframeworksuffersfromtwosetsofpracticallimitations. Thefirstsetofissuesrelates topotentialbiasintheaveragehomevalue. Mostobviously,anybiasintheproperty-levelAVM estimates could result in biased county-level averages. Another source of bias comes from the factthatZillowisunabletoproducereliableestimatesforsomepropertiesintheirsample,and the average value of these omitted properties might differ from the average value of included properties. Finally,Zillow’sinclusionofsomerentalpropertiesintheirsamplewilltendtobias downourestimateofaveragevaluetotheextentthatrentalpropertieshaveloweraveragevalues that own-use units. In Section 5, we examine each of these potential biases in more detail. The secondsetofpracticallimitationsresultsfromissuesrelatedtogeographiccoverage. Neitherthe ACSnorZillowprovidecompletecoverageofallcountiesintheU.S.–botharemissingdatafor somecounties,ofteninruralareas. WediscussthesecoverageissuesinSection6. 5 Testing for Bias in County-Level Average Home Values Thissectionexaminesthreeconditionsthatarerequiredforthecounty-levelaverageAVMestimates (V¯Z)tobeunbiasedestimatesofthecounty-levelown-useaveragevalues. 5.1 Property-LevelBias Ouraggregatewealthestimateswillbebiasediftheproperty-levelAVMestimatesarebiased. On several levels, assessing the bias for an AVM is considerably more straightforward than it is for surveys. Aspropertysalesoccur,ZillowcomparesthesalespriceagainsttheAVMestimatemade attheendofthemonthpriortothesaletogenerateadistributionofout-of-samplemodelerrors.21 21Similartosurveys,AVMestimatescanonlybecomparedtosalespricesofpropertiesthattransact.Onepotential criticismsofanysucherroranalysisisthathomesthattransactmaynotberepresentativeofallhomesinthemarket. 15

Thenear-contemporaneousnessoftheAVMmeasurementandthehome’ssaleeliminatestheneed forahousepriceindextocomparetheAVMvaluationwiththeactualsalesprice. Moreover,since ZillowhasAVMestimatesfornearlyallsalesinthedeedsrecords,therearemanymoreAVM-sales pairsthanthenumberofownervaluation-salespairsavailableinsurveys. ToassesstheimportanceofanyAVMbiasonouraggregatemeasureofhousingwealth,Zillow has provided us with average errors by county, property type, and house value from 2001 to 2017.22 Because our ultimate goal is to estimate aggregate housing wealth and because highervaluepropertieshavealargerinfluenceonaggregatewealth,wecalculatevalue-weightedaverage errorsbycountyandyearbasedontheerrordistributionsprovidedbyZillow;seetheAppendixfor details. Formostcounties,thesevalue-weightederrorsarefairlyclosetozero,suggestingaccurate AVMpredictionsonaverage.23 However, insome(especiallysmallerandsparser)counties, the averagevalue-weightederrorcanbenotablydifferentfromzero. Moreover,thesizeofthebiasina typicalcountryappearstofluctuateovertime. Figure2showstheevolutionofthemodelerrors overtime,averagingacrosscounties,wheretheerrorisdefinedastheAVMestimateminusthesale price,asapercentofthesaleprice. Thisvalue-weightedaveragewasabout-0.5percentintheearly 2000s,thendippedtoabout-2percentin2004and2005asmarketpriceswererisingsobriskly thattheAVMdidnotfullykeepup. In2006,theaverageerrorturnedpositiveandsubsequently widenedtoabout5percentasmarketpricesfellmorequicklythanestimatedbytheAVM.Asthe marketstabilized,theerrorratedeclinedtoabout2percent,andremainedinthe2-3percentrange through2017. Toreducethebiasimpartedbytheseaverageerrors,webias-adjustthecountyaverageproperty valuesbymultiplyingtheaverageAVMestimateforeachcountyandpropertytypebytheinverseof oneplusthevalue-weightedaverageerrorinthatcountyandyear. Thisbiasadjustment,described intheAppendix,hasonlyamutedeffectonthelevelandtrajectoryofhousingwealth.24 Thisissueherediffersfromtheoneaffectingtherepresentativenessofrepeat-salespriceindexesforvaluingaggregate housingwealth.Inthatcase,theissueiswhetherpricechangesforhomesthattransactaresimilartopricesforhomes thatdonottransact.Here,theissueiswhethermodelerrorsforhomesthattransactcanbeusedtoassesstheaccuracy ofthemodelforhomesthatdonottransact. 22TheaveragevaluedatathatweobtainfromZilloware“raw”estimates,inthattheyarenotadjustedforanymodel bias.ThevalueestimatesthatZillowpublishesonitswebsiteareadjustedformodelbias. 23However,theAVMaccuracytendstobelowerinthetailsofthepricedistribution.Especiallyforveryinexpensive homes,theAVMismorelikelytohaveapositivebias(i.e.theAVMestimateishigherthantheactualsaleprice),while forveryexpensivehomes,thereversetendstobetrue. 24ConsistentwithFigure2,thisisbecauselargererrorstendtobeconcentratedinsmaller,less-denselypopulated 16

Figure2: Value-WeightedAverageCounty-levelAVMErrors(U.S.Average) Percent 6 6 4 4 2 2 0 0 −2 −2 −4 −4 2001 2003 2005 2007 2009 2011 2013 2015 2017 Source: Zillow and Federal Reserve calculations. 5.2 BiasfromMissingAVMEstimates HomesmightnothaveanAVMestimateforavarietyofreasons,includingalackofinformation aboutpropertycharacteristicsoralackofsalesofcomparablehomes. OnereasonwerelyonACS property counts as a benchmark is to overcome this challenge. But by applying average AVM values to ACS property counts, we are implicitly assuming that the average value of properties with and without an AVM are the same, conditional on county and property type. As such, a key consideration is whether properties with and without an AVM estimate are sufficiently homogeneousincharacteristicstobesimilarlyvaluedonaverage. Wesuspectthatthisassumption isrelativelybenignforthepurposeofcalculatingaggregatehousingwealth,sinceZillow’scoverage ofown-usehousingunitstendstobefairlyhigh. To investigate this issue further, we examine property-level data from the 2014 ACS that were merged by address with a property-specific AVM estimate from another data provider.25 countieswithfewerproperties.Moreover,thedistributionofaveragevalue-weightederrorsacrosscountiesatanygiven periodisroughlysymmetric,sothatthecountieswithoutsizedpositivebiasesareroughlycounterbalancedbycounties withoutsizednegativebiases. 25TheCensusBureaupurchasedAVMestimatesfromanotherdataprovider,sowewereabletoconductthisanalysis usingtheconfidentialmicrodataavailableattheCensusBureau. 17

AlthoughthismergeddatasetdoesnotallowustodirectlyevaluateZillow’sAVM,itdoesallowus tocomparetheowner-reportedvaluesofhomesthathaveestimatesfromthisalternativeAVMto owner-reported values for homes that do not have estimates from the same AVM. To the extent thatthealternativeAVMisrepresentativeofZillow’sAVM,thisexercisecanhelpusunderstand thevaluedifferencesbetweenthepropertieswithaZillowAVMestimateandthosewithout. To thisend,foreachpropertytype(single-ormultifamily),weregressthenaturallogarithmofthe owner-reported value on an indicator for whether the AVM estimate is missing, controlling for geographiclocationusingfixedeffects. AsshowninTable2,thecoefficientonthemissingAVMindicatorforsingle-familyhomesis about1.2percent,meaningthat,onaverage,homesthatdonothaveanAVMestimatearevalued bytheirownersabout1.2percenthigherthanhomeswithanAVMinthesamecounty–arelatively smalldifference. However,whentheregressionexcludeslocationfixedeffects,wefindthatsinglefamily homes with a missing AVM have a 19 percent lower average owner-reported value than homesthathaveanAVMestimate,andinaregressionwithstate-level(ratherthancounty-level) fixedeffectsthehomeswithamissingAVMarevaluedabout10percentless. Theseresultsillustrate thenon-randomgeographicdistributionofthemissingAVMvaluesandthustheimportanceof aggregatingproperty-levelAVMestimatesatgranular(county)levelforsingle-familyhomes. Formultifamilyhousingunits(i.e.,co-opsandcondos),propertieswithoutanAVMareestimatedtobe6.8percentlowerinvaluethanthosewithanAVM.However,unlikewithsingle-family homes, the within-county value difference is actually larger than (and opposite in sign to) the difference unconditional on geography. These results suggest that our county-up aggregation mightoverstatetheaggregatevaluebyasmallamountformultifamilyhomes. However,because multifamilyhomesaresuchasmallshareoftheaggregatehousingstock–intheACS,theyaccount for only 7 percent of all own-use units in 2017 (Table 1) – the degree of overstatement for the aggregatehousingstockwillbeverysmall.26 26ConservativelyassumingthatZillow’scoverageofcondoandco-opunitsis80percent,the7percentdifference betweenvaluedandunvaluedpropertieswouldtranslatetoanoverallbiasformultifamilyofabout1.4percent.Since multifamilyunitsaccountonlyabout7percentofallown-useunitsintheU.S.,thetotalcontributionofthisbiastothe aggregatewealthlevelwouldbenegligibleat1.4percent(0.2*0.07=0.014). 18

Table2: DifferencesinOwner-ReportedValuesbyAVMMissingStatus AVMMissing (1) (2) (3) Indicator CountyFE StateFE NoControls Single-Family 0.012*** -0.10*** -0.19*** (N=1,416,264) (0.0014) (0.0014) (0.0014) Multi-Family -0.068*** -0.055*** 0.029*** (N=63,838) (0.0063) (0.0068) (0.0072) Note: Standarderrorsinparentheses. Dataaretrimmedbyexcludingvalueslessthan$10,000or morethan$4million. ***p<0.01,**p<0.05,*p<0.1. 5.3 BiasfromtheInclusionofRentalUnitsinZillow’sUniverse A key reason we rely on ACS property counts is that we would like to focus on own-use units, and, as indicated in Table 1, Zillow’s data includes some rental units. By applying the average Zillow values to the ACS property counts, we are implicitly assuming that the Zillow averages are not biased by the inclusion of rental properties. Ideally, we would remove the rental units fromtheZillowdata,butpublicdeedsrecordsdonotallowonetoeasilyidentifywhichhomesare heldforownuseandwhichhomesareintendedasrentalunits.27 Consequently,theZillowAVM averageswillincludethevaluesofsomerentalunits,andwillnotaccuratelyrepresentown-use propertiesifrentalunitshavesystematicallylowerorhighervalues. Inprinciple,thisrentalbias could go either way. On the one hand, rental units are likely to be smaller and of lower quality thanowner-occupiedunits,draggingtheaverageAVMestimatedown. Ontheotherhand,rental units may be in more desirable locations, and hence be located on more valuable land, thereby boostingtheaverageAVMestimate. WeevaluatethisissueusingthesamemergedACS/AVMproperty-leveldatafrom2014that wasdescribedabove. Inthiscase,weregressthenaturallogarithmoftheAVMforeachpropertyon anindicatorforwhethertheACSidentifiesthepropertyasarentalunit,conditionalongeographic location. Table2showsthatonaverage,single-familyrentalunitsarevalued34percentlowerthan owner-occupiedunitswithinthesamecounty(column1). Formultifamilyunits,thisdifferentialis alittlesmaller,withrentalunitsvaluedabout17percentlowerthanowner-occupiedmultifamily 27Onemightbeabletoinferownershipofthepropertiesbymatchingtheaddressofthepropertytotheaddress oftheownerinthetaxassessors’records. Whilethisiscurrentlybeyondourcapability,suchinferencemaybecome feasibleinthefuture. 19

unitswithinthesamecounty.28 Theaveragevaluedifferencesconditionalonstate(column2)or unconditionalongeography(column3)aremodestlylargerforbothsinglefamilyandmultifamily homes. Table3: DifferencesinAVMValuebyRentalStatus (1) (2) (3) RentalIndicator CountyFE StateFE NoControls Single-Family -0.34*** -0.39*** -0.37*** (N=1,417,726) (0.0013) (0.0016) (0.0018) Multi-Family -0.17*** -0.21*** -0.25*** (N=65,998) (0.0046) (0.0052) (0.0064) Note: Standarderrorsinparentheses. Dataaretrimmedbyexcludingvalueslessthan$10,000or morethan$4million. ***p<0.01,**p<0.05,*p<0.1. Thelargedifferenceofthenon-ZillowAVMbetweenrentalunitsandowner-occupiedsuggests that Zillow’s inclusion of some rental properties could pull down the average AVM value that we apply to the ACS property counts. We estimate the effect that this could have on aggregate housingwealthvaluebasedontheaveragevaluedifferentialbetweenowner-occupiedandrental unitsreportedinTable2andtheshareofrentalunitsthatweestimatetobeincludedinZillow’s AVMdata;theAppendixdescribesourapproachindetail. Thisanalysissuggeststhatadjusting thevaluesfortheunintendedinclusionofrentalunitswouldincreaseourestimateofaggregate housing wealth in 2014 by about 6 percent. It seems quite plausible that the value differential betweenowner-occupiedandrentalunitscouldhavechangedmateriallyovertime,butweonly have the ACS/AVM merged data for 2014. Because we want to evaluate the fluctuations in the AVM-basedmeasureofhousingwealthoverthehousingcycleandwehavenoideahowthisbias may have evolved, and because the result comes from a non-Zillow AVM, we do not adjust our timeseriesofaggregatewealthbasedontheestimatedbiasfor2014. Weleavethisissueforfuture studyasmethodsforidentifyingandseparatingrentalpropertiesindeedsrecordsmaybecome availableinthefuture. 28ItisworthkeepinginmindthatmostofthemultifamilyrentalunitswithanAVMestimatearelikelycondominium unitsthatarerentedout. TheseresultswouldlikelybequitedifferentiftheAVMwereavailableforrentalunitsin buildingswheretheentirebuildinghasasingleowner. 20

6 AVM and ACS Coverage Issues 6.1 AvailabilityofAverageAVMvaluesbyCounty Due to data limitations, Zillow does not provide average AVM values for all counties, property types, and time periods. For the missing market segments, we impute the average value as the averagevalueinthestateforthatpropertytype. Apotentialproblemwiththisapproachisthat thesecountiesaremorelikelytohavethinhousingmarkets(e.g.,inruralareas),andtheycould havealoweraveragevaluethanothercountiesinthesamestate,assuggestedbyTable2. However, the bias imparted by this assumption on aggregate housing wealth is likely quite small, as the countieswithoutaZillowAVMaveragecoveronlyasmallfractionofhousingunits–lessthanone percentofallACShousingunitsin2017.29 6.2 AvailabilityofACSCountsbyCounty Wecomputethenumberofown-usehousingunitsbycountyandpropertytypeusingthepublicusemicrodatafromtheACS.Weusethesedataratherthanpublishedcountsbecauseitistheonly waytocalculatethenumberofvacantpropertiesthatareintendedforown-use. Thedrawbackof thisapproachisthattheACSonlyidentifies480countiesinthepublic-usedata,coveringabout60 percentofalloccupiedunits. TocalculatetheaggregatehousingwealthinthecountiesthatarenotobservedintheACS,we needtoknowthenumberofown-useunitsinthesecountiesandtheaveragevalue. Weestimate thenumberofhousingunitsasthedifferencebetweenthenumberofown-useunitsinthestate andthesumofthecounty-levelunitcountsinthatstate.30 Thus,onecanthinkofourapproach asaggregatingalloftheunobservedcountiesintoasingle“restofthestate”market. Weimpute theaveragevaluesfortheseresidualmarketsusingtheaverageAVMofcountiesthatareincluded in these residual markets. Since the average AVM values are missing for so few counties, we thinkthisapproachshouldyieldafairlycloseapproximationtotheaveragevalueinthe“restof state”segment. Amodifiedbutcloselyrelatedversionofouraggregationmethodthatemploys 29Weexploredtheuseofalternateassumptionsthatestimatetheaveragevaluefor“missing”countiesbasedon characteristicsofthecounty.Buttheeffectsonaggregatevaluearetrivial,soforsimplicitywemaintaintheassumption thatcountieswithamissingAVMhavethesameaverageasthestate-wideaverage. 30Statesareidentifiedforallhousingunitsinthepublicusedata. 21

county-levelpropertycountsfrompublishedACStablesandaccountsforabout80percentofall housingunitsyieldsestimatesthatarecomparabletoourbaselinemethod.31 TwoadditionalissuesrelatedtotheACScoveragebearmentioning. First,thefullimplementationofsurveydidnotbeginuntil2005. Toestimatehousingunitcountsfor2001to2004,we estimatethenumberofhousingunitsbymarketsegmentinthe2000Censusandassumeaconstant growth rate between 2000 and 2005. Second, in order to obtain timely estimates of aggregate housingwealth,wemustestimatethenumberofhousingunitsafter2017(thelastavailableyear oftheACS).Sincehousingcountsaregenerallyveryslowmoving,weassumethatgrowthin2018 wasequaltotheaveragegrowthratefrom2015to2017. 7 New Estimates of Aggregate Own-Use Housing Wealth Figure3offersafreshlookattheevolutionofaggregateown-usehousingwealthsince2001by plottingournewmeasureconstructedfromZillow’sAVMalongwithmeasuresfromtheFinancial Accountsandfromowner-reportedvaluationsinsurveys(i.e.,ACSandSCF).TheFinancialAccounts isausefulpointofcomparisonbecauseitisoftenusedinmacroeconomicmodelsandmoveslargely withahouse-priceindexafter2005.32 From2001to2005,theFinancialAccountsisbenchmarkedto aweightedsumofownervaluationsreportedintheAmericanHousingSurvey. TheACSprovides ourbaselinecomparisonwithowner-reportedvaluationsbecauseitisavailableannually. Tocreate a measure of aggregate house value from the ACS, we multiply average owner-reported values from the ACS by county and property type by the total own-use housing unit counts that were used to construct the AVM-based wealth estimate.33 Thus, the ACS measure accounts for the aggregatevalueofvacantown-usehousingwealthforwhichowner-reportedvalueestimatesare notdirectlyavailable. Forcompleteness,theSCFtriennialestimatesprovideanothermeasureof 31ThepublishedACStablescovermorecountiesthanthepublic-usemicrodata,accountingforabout80percentof housingunits.However,thepublishedtablesarenotdetailedenoughtoallowustoestimatethenumberofown-use vacantunitsbycounty.Inanalternativeapproach,weusedthenumberofowner-occupiedunitsbycountyfromthe tablesandestimatedthenumberofown-usevacantunitsineachcountyfromthestate-wideratioofown-usevacant unitstoowner-occupiedunits.Thisalternativeestimateisquitesimilartoourbaselineestimatefrom2001to2004,and isabout3percenthigherthanthebaselinefrom2005to2017. 32Forobservationsafter2005,theaggregatelevelisextrapolatedusingtheCoreLogicrepeat-salespriceindex(to estimatecapitalgainsonexistingproperties)andanestimateofnetinvestmentinresidentialstructures(basedon estimatesofthevalueofnewconstruction,renovation,anddepreciation)fromtheBureauofEconomicAnalysis. 33InaccordancewithourdiscussioninSection6,wecalculatetheaverageACSestimatesfromthepropertylevel, publicusedata,whichonlyprovideacountyidentifierforlargercounties.ForcountiesnotidentifiedintheACS,we usetheaveragevalueofpropertiesthatareidentifiedasbeinginthesamestatebutthatarenotinanidentifiedcounty. 22

Figure3: AlternativeMeasuresofAggregateOwn-UseHousingWealth Trillions of chained (2012) dollars l 26 26 l SCF ACS AVM 24 24 FAUS l l 22 l 22 l 20 20 18 18 l 16 16 2001 2003 2005 2007 2009 2011 2013 2015 2017 Source: American Community Survey (U.S. Census Bureau), Financial Accounts of the United States, Survey of Consumer Finance (triennial), and Zillow. Note: Nominal values have been adjusted for inflation using the chain price index for personal consumption expenditures published by the Bureau of Economic Analysis. value-weightedaggregatewealthconstructedfromowner-reportedhousevalues.34 Allthewealth seriesarereportedin2012-constantdollars. Figure3showsthattheAVM,owner-reportedmeasuresfromtheACSandSCF,andFinancial Accountsmeasurestrackeachotherquitecloselyfrom2001to2006. TheAVMandACSmeasures arenearlyontopofoneanotherfrom2001to2004,withtheAVMmeasurerisingslightlyfaster than the ACS from 2004 to 2006. Although the Financial Accounts measure lies a little below the other two, this difference owes to the fact that the AHS estimates in the Financial Accounts between2001and2005areadjusteddownwardby5.5percenttoreflecttheupwardbiasinowner valuations reported in Goodman and Ittner (1992) and Kiel and Zabel (1999). Figure 4 shows that removing this adjustment causes the Financial Accounts to be almost exactly equal to the AVM-basedmeasurefrom2001to2006.35 ThealignmentofournewAVM-basedmeasurewiththe survey-basedmeasuresfromACS,AHS,andSCFinthe2001-2005periodisconsistentwiththe 34TheSCFestimatesincludethevalueofsecondandthirdhomesthatarenotusedasrentalproperty. 35RemovingthisadjustmentmakestheFinancialAccountsmorecomparabletotheACS,whichisnotadjustedfor biasinownervaluations.Moreover,the5.5%adjustmentisprobablytoolargebecauseitisbasedonasimpleaverageof ownervaluationerrors,andMolloyandNielsen(2018)findthaterrorsinownervaluationstendtobesmallerforhigher valueproperties,causingthevalue-weightedaveragetobeabouthalfaslargeasthesimpleaverage. 23

Figure4: AlternativeMeasuresofAggregateOwn-UseHousingWealth,NoOptimismAdjustment Trillions of chained (2012) dollars l 26 26 l SCF ACS AVM 24 24 FAUS l l 22 l 22 l 20 20 18 18 l 16 16 2001 2003 2005 2007 2009 2011 2013 2015 2017 Source: American Community Survey (U.S. Census Bureau), Financial Accounts of the United States, Survey of Consumer Finance (triennial), and Zillow. Note: Nominal values have been adjusted for inflation using the chain price index for personal consumption expenditures published by the Bureau of Economic Analysis. ideaowner-reportedvaluesarequiteclosetomarket-basedvaluationsduringaperiodofrising houseprices,asfoundbyMolloyandNielsen(2018). After2005,thethreemeasuresdivergesubstantially. First,themeasuresdifferonthetiming ofthemarketturningpoints. Mostnotably,theAVMandtheFinancialAccounts(whichareboth informedbymarketpricesoverthisperiod)estimateaclearpeakin2006,whiletheACSmeasure startstodeclinenoticeablyonlymuchlaterin2009.36 Thetimingofthetroughalsodiffersacross thesemeasures,withtheFinancialAccountsturningupin2011andtheAVMandACSturningup in2012. Second,thethreemeasuresdisagreeontheseverityofthehousingcycle. Between2006and 2011,theFinancialAccountsmeasuredropsby35percent,whereastheACSmeasuredeclinesby only15percent. OurnewAVMmeasureismoresimilartotheFinancialAccountsoverthisperiod, falling30percentfrompeaktotrough. Thus,eachmeasureprovidesadifferentassessmentofthe amountofhousingwealthlostbyhouseholdsduringthecrisis. OurnewAVMmeasureindicates thathouseholdslostabout$7.4trillionoverthisperiod,whiletheFinancialAccountssuggestslosses 36Thedifferencesinthetimingofthepeakbetweenowner-reportedandmarket-basedmeasuresisthemainreason whytheFinancialAccountsmethodologyswitchesfromasurvey-basedmeasuretoahousepriceindexin2005. 24

of$8.4trillionandtheACSsuggestsonly$3.7trillion. Thegrowthratesofthesethreemeasures werefairlysimilarduringtherecovery. Onnet,whereastheAVMandFinancialAccountsmeasures werestill8percentand10percentbelowtheir2006valuesin2017,theACSmeasurewas2percent aboveits2006value. ThedifferencesbetweentheAVM-basedmeasureandtheACS-basedmeasureareconsistent withmanyoftheconcernsaboutownervaluationsthathavebeenraisedintheliterature.37 Specifically,ourresultssuggestthatsurveyrespondentswereeitherunawareofthemarketfluctuations inrealtime,ortheybelieved–correctlyornot–thattheirhomevaluesweredifferentfromwhat salesinthesurroundingmarketwouldimply. Inparticular,theACSmeasureindicatesthatsurvey respondentsthoughtthattheirhomesweremaintainingtheirvaluesevenasthehousingmarket andthefinancialsystemwereexperiencingseverestrain. TotheextentthatACSrespondentsdid eventuallyacknowledgeadecliningmarket,itappearsthattheydidnottakethedeclinefullyon board. ThedifferencesbetweentheAVMandtheFinancialAccountspost-2006arealsoconsistentwith someoftheconcernsaboutrepeat-salesindexesraisedinpriorstudies.38 WhiletheAVMmeasure andtheFinancialAccountsshowmuchmoreresponsivenesstochangingmarketconditionsthan surveys,theAVMmeasureshowssomewhatlesscyclicalitythantheFinancialAccountsmeasure. SincetheFinancialAccountsmeasureisconstructedusingarepeat-salespriceindexduringand aftertheGreatRecession,itsmovementsarebasedonthepricechangesexperiencedbytransacting homes. If non-transacting homes experienced different price dynamics, as might be the case duringperiodsofmarketturmoilwhen“motivated”homeownersexperiencingfinancialstrain makeupanelevatedshareoftransactions,thenapplyingrepeat-salespriceindexmovementsto non-transactinghomescouldoverstatefluctuationsintheaggregatevalue. Toshedmorelightonthisissue,thetopandbottompanelsofFigure5comparethelevelsand annualgrowthratesoftheAVMaveragehomevaluestotheCoreLogicrepeat-salespriceindex.39 TheindexrisesmorethantheaverageAVMvaluesduringthehousingboomandfallsmoreduring 37HousingwealthestimatesfromtheSCFestimates(notshown)liefairlyclosetothosefromtheACS,illustrating thatthemovementsintheACSarerepresentativeofownervaluationsmoregenerally. 38ThenetinvestmentcomponentoftheFinancialAccountsmeasureincreasesovertimebutdoesnotcontributemuch cyclicalitytoaggregatewealth. 39Source:CoreLogic,Inc.,Private-LabelLoan,HomeEquityServicing,andHPIdata.Thisindexcorrespondstoseries FI075035243intheFinancialAccounts. 25

Figure5: LevelandGrowthRateofAverageValueofOwn-UseHousingUnits Level of Average Value Thousands of chained (2012) dollars 340 340 AVM CoreLogic House Price Index 320 320 300 300 280 280 260 260 240 240 220 220 2001 2003 2005 2007 2009 2011 2013 2015 2017 Source: CoreLogic and Zillow. Note: Nominal values have been adjusted for inflation using the chain price index for personal consumption expenditures published by the Bureau of Economic Analysis. Growth Rate of Average Value Percent AVM 10 10 CoreLogic House Price Index 5 5 0 0 −5 −5 −10 −10 −15 −15 2001 2003 2005 2007 2009 2011 2013 2015 2017 Source: CoreLogic and Zillow. Note: Nominal values have been adjusted for inflation using the chain price index for personal consumption expenditures published by the Bureau of Economic Analysis. 26

thecontraction,suggestingthatthattheselectionbiasesintherepeat-salesindexmightindeedbe present. Finally,Figures3and4plotannualdatainordertoallowustomakeconsistentcomparisons acrossallthreedataseries,astheACSprovidesonlyannualaverages. Twoadditionaladvantages oftheAVM-basedmeasureoverowner-reportsarethattheycanbecomputedatahigherfrequency andtheyaremoretimely. Wearenotawareofanysurveysthatprovideowner-basedvaluations atahigherfrequencythanannually,likelybecausesurveysarequitecostlyandtime-intensiveto conduct. Bycontrast,wecancomputequarterlyormonthlyestimatesoftheAVM-basedmeasure quiteeasilybecausetheAVMisre-estimatedandupdatedwithnewdataeveryday.40 8 Conclusion In this paper, we develop a detailed, high-frequency, and timely measure of aggregate housing wealthusingcounty-levelaveragehomevaluesfromZillow’sAVM,whichisbasedonmachinelearningtechniquesanddetailedinformationonrecenttransactionpricesandpropertycharacteristics. To create our measure, we combine the average home values from Zillow’s AVM with county-levelpropertycountsfromCensus,whileadjustingfortheaveragecounty-levelbiasofthe particularAVMthatweuse. Usingthismethod,wepresentnewestimatesofaggregateU.S.housingwealthfrom2001to2018. Ourworkdemonstrateshowdatathatarecollectedfromaprivate sourceforanentirelydifferentpurposecanbeusedtocreateanationallyrepresentativeaggregate timeserieswhencombinedwithotherdata. Policymakersaroundtheworldhavebeenincreasingly interestedintheuseofsuchdatainordertoimproveaggregatestatisticsandreducethecostof production. Whileourapplicationprovidesanexampleofhowthiscanwork,itisworthbearingin mindthatinalmosteveryapplicationthatusesprivate-firmdatatoconstructaggregatestatistics therewillbearoleforsurveysorotherdatasourcestoprovideawaytoaggregateappropriately. OurAVM-basedestimatesshowconsiderablymoreresponsivenesstochangingmarketconditionsthansurvey-basedmeasuresandsomewhatlessvolatilitythanrepeat-salesmeasures. The findingthatownervaluations(asreportedinsurveys)appeartounderestimatetheamplitudeofthe cyclecouldaffectthefindingsofstudiesthatuseownervaluations,suchasthosethatinvestigate 40AlthoughweonlyhaveannualhousingstockestimatesfromtheACS,welinearlyinterpolatetheseannualestimates. Webelievethisinterpolationtobefairlyaccuratebecausethequantityofhousingchangesfairlyslowlyovertime. 27

changesinthedistributionofhouseholdwealthovertheGreatRecession(see,forexample,Bricker etal.(2011);Hur(2018),orPetermanandSommer(ming)). Moreover,thefindingthattheFinancial Accountsseriesappearstoamplifytherecenthousingboomandbustisalsoworthbearinginmind, asvariousmacroeconomicframeworksusethisseries(orrelyonrepeat-salesindexesinotherways) toestimatethemarginalpropensitytoconsume(e.g., Carrolletal.2011)andotherparameters (Iacoviello and Neri, 2010; Saez and Zucman, 2016; Favilukis et al., 2017; Glover et al., 2019). However,ourresultsalsosuggestthatthebiasfromrepeat-salesindexesisnotaslargeasthebias inowner-valuations,andsoduringhousingbustsandrecoveriestheuseofhousepriceindexesto extrapolatehousingwealthmightnotbeabadapproximation. Onesimpleextensionofouranalysiswouldbetocalculateameasureofaggregatehousehold housing wealth that includes rental property. Such a measure could prove more useful than own-usehousingwealthforunderstandinghouseholdconsumptiondecisions. Additionally,since our measure is constructed from county-level estimates, it can naturally be decomposed across states,metropolitanareas,orcounties. Thistypeofanalysiswouldaddtothegrowingliterature onvariationinincomeandothereconomicoutcomesacrosslocations(MianandSufi,2014;Chetty etal.,2014;ChettyandHendren,2018a,b). Finally,whileourworkhasfocusedonaggregatingAVMestimatestocreateanaggregatetime series,furtherresearchshouldconsidermergingproperty-levelAVMestimateswithnationallyrepresentativesurveydata. Thismergeddatamightimproveourabilitytoassesstheaggregate distributionofhousingwealth,atopicthathasreceivedmuchattentionoflate(Carrolletal.,2014; Pikettyetal.,2018;Battyetal.,2019). MergedAVM/surveydatacouldalsobeusedtostudythe connectionbetweenhousingwealthandothereconomicoutcomesatthehouseholdlevel. Weview suchanalysisasanimportantavenueforfuturework. 28

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9 Appendix This appendix discusses some aspects of our methodology in greater detail. In particular, we describehereourmethodsforadjustingtheZillowaveragevaluesformodelbiasandcalculating theeffectsofrentalbias. 9.1 ModelBiasAdjustment As discussed in the text, Zillow’s AVM estimates are biased, in the sense that they have a timevaryingnon-zeroaverageerrorratewhencomparedtosubsequenttransactions. Thisisparticularly trueforpropertiesinthebottom30percentofthevaluedistribution. Toaccountforthisbias,Zillow adjuststheir“raw”estimatesusingthemedianobservederrorwithinagivengeography/property type/time.41 Zillow reports to us both the median-adjusted and “raw” average value estimates. Sinceourgoalistocalculateanaggregate,weareconcernedwithaveragebias,ratherthanmedian, andweusetherawZillownumberstoadjustforaveragebiasusingaproceduredescribedbelow. Ideally,wewouldadjusttheZillowaveragestoaccountfortheexpectedvalue-weightedmodel error. We cannot directly observe the value-weighted average errors for two reasons. First, the errorsareonlycalculableagainstobservedtransactions. Second,wedonothavethefullpropertyby-propertyerrordistributionsfromZillow. Rather,Zillowreportstoustheaveragepercenterror by transaction decile, along with each decile’s upper and lower bounds, by quarter and county, separatelyforsingle-familyandmultifamilyproperties. Wethereforeconstructourvalue-weighted adjustmentsusingthefollowingprocedure: 1. LetVu(p,c,t,i)bethevaluedefiningtheupperlimitofdecilei forpropertytypep,county c,andyeart.42 Wedefinethevalueshareofdecileiasw(p,c,t,i)= (cid:80) (V (V u( u p ( , p c , , c t , , t i , ) j + )+ V V u( u p ( , p c , , c t , , t i− ,j 1 − ) 1 )/ )) 2 /2 , j where Vu(p,c,t,0) is set to 0 and Vu(p,c,t,10) is set equal to 1.5Vu(p,c,t,9). The upper boundonthevaluedistribution(50percentabovethe90th percentile)isanarbitrarylimit intendedtoavoidgivingtoomuchweighttotheverytopofthevaluedistribution, which typically has a very long tail. Our results are not sensitive to this particular choice; e.g., weobtainquantitativelysimilarresultsusingeither1.2Vu(p,c,t,9)or2.0Vu(p,c,t,9)asthe upperbound. (cid:80) 2. Weestimatethevalue-weightedaverageerrorasE(p,c,t)=( w(p,c,t,i)APE(p,c,t,i)),where i APE(p,c,t,i)istheaveragepercenterrorinvaluedecilei. Someoftheerrordistributionsare based on very few transactions and are therefore likely estimated with considerable error. In response, we set E(p,c,t) to missing if the number of transactions in (p,c,t) is less than 20. Wealsodrop(p,c,t)observationsifoneormoreofthedecileaverageerrorsismissing. For counties not covered by Zillow’s model or set to missing due to one of the above two exclusion criteria, we use the average value-weighted error for counties in the same state 41Pleaserefertohttps://www.zillow.com/research/zhvi-methodology-6032/formoredetailsaboutZillow’s biasadjustmentprocedure.Itshouldbenotedalsothatbiasmaypermitgreateraccuracyinameansquarederrorsense. Sinceourfocusisonconstructinganaggregatemeasure,ourobjectivesaredifferentthanZillow’s,aswecareaboutbias muchmorethanvariance.AdjustmentswhicharesensibleforusmaynotbesensibleforZillow. 42Theerrors-by-percentiledatacometousataquarterlyfrequency.Theproblemthatsomegeographieshavetoofew transactionstoaccuratelyestimateavalue-weightedadjustmentismoreextremeatthequarterlyfrequency.Therefore, weaggregatetoayearlylevelbysummingtransactionswithinageographyseparatelyacrosseachdecilebucket.This procedureisnotexactlyrightbecausetheupperandlowerboundsofthedecilebucketschangefromquartertoquarter. However,theseboundsinpracticechangeverylittlebecausetheyaredefinedrelativetothefulldistributionofZillow AVMestimates,ratherthanrelativetothedistributionofobservedtransactions. 32

whichdohaveerrordistributiondata. LetE˜(p,c,t)denotetheaverageerrorsincludingthese imputations. E˜(p,c,t) 3. We define the adjustment factor γ(p,c,t) = , where APE(p,c,t) is the unadjusted APE(p,c,t) average error regardless of the number of transactions (i.e., the floor of 20 is dropped). If the county is not covered by Zillow, we set APE(p,c,t) equal to the statewide average error prior to computing γ(p,c,t). Note that (γ(p,c,t)APE(p,c,t)) is the estimated valueweightedaverageerrorfor(p,c,t). TheonlyreasontogofromE˜(p,c,t)toγ(p,c,t)andback to (γ(p,c,t)APE(p,c,t)) instead of using E˜(p,c,t) directly is to make use of the unweighted averageerrorsofcountieswithfewerthan20observations. 4. We define the combined (sf and mf) value weighted error Eˆ(c,t) as the weighted sum of (γ(p,c,t)APE(p,c,t))forsingle-familyandmultifamilyproperties,wheretheweightsareeach propertytype’sshareofthetotalobservedtransactionsincountycandyeart. 5. Weadjusttheaverageerrorsby(1+Eˆ(c,t)) −1. Wecombinethemultifamilyandsingle-family errorsintoonecounty-levelseriesfortworeasons. First,theshareofcountieswithsufficiently manymultifamilytransactionstoaccuratelyestimatevalue-weightederrorsisquitesmall. Second, the value-weighted errors do not appear to be very different for multifamily and single-familyproperties. Figure 6 below shows that the bias adjustment changes the aggregate series very little from 2001-2005. After2005,theeffectofthebiasadjustmentistoslightlylowertheaggregateseries. Figure6: Bias-AdjustedandUnadjustedAggregateWealthSeries Trillions of chained (2012) dollars AVM, unadjusted AVM, bias adjusted 24 24 22 22 20 20 18 18 16 16 2001 2003 2005 2007 2009 2011 2013 2015 2017 Source: American Community Survey (U.S. Census Bureau) and Zillow. Note: Nominal values have been adjusted for inflation using the chain price index for personal consumption expenditures published by the Bureau of Economic Analysis. 33

9.2 RentalBias As noted in the main text, since Zillow’s data do not distinguish between rental properties and own-useproperties,andweareinterestedinown-useproperties,largedifferencesinaveragevalue byownershipstatuswilltendtobiasourresults. Asdiscussedabove,itappearsthatrentalhomes areonaveragesubstantiallylessvaluablethanowner-occupiedproperties. Asaresult,estimates of the aggregate value of own-use housing will be biased downwards by the inclusion of rental propertiesinZillow’saverages. Weimplementthefollowingproceduretoestimatetheeffectoftheinclusionofrentalproperties onouraggregatemeasure. Ourproceduremakesuseofaproperty-levelmatchbetweenadifferent (thoughbroadlysimilar)AVMandACSmicrodata. Thismatcheddataallowsustoestimatethe averageAVMvaluesseparatelyforowner-occupiedandrental-occupiedpropertiesasindicated in the ACS. (Such a calculation is not possible using the Zillow data because we do not have property-levelestimates). Inparticular,ourprocedureconsistsofthefollowingsteps: 1. Wematchthe2014ACStothe2014alternativeAVMestimatesatthepropertylevel. 2. Foreachgeographyg andpropertytypep,wecalculatetheratioofAVMvaluesforrental propertiestoowner-occupiedproperties: V¯(p,g,rental) δ(p,g)= . V¯(p,g,owner) 3. Foreachcountyc,propertytypep,andtimeperiodt,letβ(p,c,t)betheestimatedshareof propertiesinZillow’sdatathatareowner-occupied. Wecalculatethesesharesdifferentlyfor single-familyandmultifamilyproperties. Thesingle-familysplitsarecalculatedusingthe sameowner-occupied/rentalsplitsfromtheACSthatweusetocalculatethesingle-family aggregatevalues. WedonotusetheACSsplitsformultifamilybecausewedonotthinkthat thefulluniverseofmultifamilypropertiescoveredintheACSislikelytoberepresentative ofthesetofmultifamilypropertiesinZillow’saveragevalueestimates. Instead,weusethe CensusBureau’s2012RentalHousingFinanceSurveytoestimatethenumberofnon-condo rental units in 2+ buildings at 20,799,737. The 2012 ACS has 25,354,734 occupied rental units,suggestingthatroughly82percentoftheACSuniverseisnon-condos(andtherefore likelytonotbeinZillow’sdeeds-basedpropertyrecords). This82percentestimatedoesnot accountforvacantunits,however. TheCensusHousingVacancySurveyreportsa9.3percent vacancy rate on all 2+ multifamily units in 2012. We therefore estimate the total number ofmultifamilyrentalsincludedintheZillowaveragebyadjustingdowntherelevantACS multifamilyrentaltotalsbyafactorof1-0.907*0.820=0.256. Theeffectofthisadjustment factorof0.256istomodestlydecreasethemultifamilyinflationfactors. 4. Let g(c) denote the geography g from the 2014ACS/AVMmatched data corresponding to countyc. Forexample,ifg arestatestheng(c)isthestatecontainingc. Usingβ(p,c,t)and δ(p,g(c)),thepropertytype/county/timeperiodadjustmentfactorisconstructedas 1 λ(p,c,t)= . β(p,c,t)+(1−β(p,c,t))δ(p,g(c)) Usingtheλ(p,c,t)toadjusttheaveragevaluesfromZillowresultsinanalternateaggregate estimatethatisroughly6percenthigherin2014thanwhatwereportinourbaselineresults. 34