Chapter 2 ACCOUNTING FOR HOUSING IN A CPI

Transcription

1 Chaper 2 ACCOUNTING FOR HOUSING IN A CPI W. Erwi Diewer ad Alice O. Nakamura Cosrucio of he U.S. CPI mirrors he aioal icome accous reame of ower occupied housig. Owers are assumed o re heir homes from hemselves, creaig a caegory called Ower Equivale Re (OER). Ad because more ha wo-hirds of U.S. households ow he house ha hey live i, OER s weigh i he CPI is subsaial; i accous for 23.8% of he headlie CPI ad 3.8% of he radiioal core CPI ha excludes food ad eergy. No surprisigly, how you measure somehig his impora is a very big deal. (Sephe Cecchei, 3 Jue 27, hp:// Iroducio Sephe Cecchei, a former Execuive Vice Preside ad Direcor of Research a he U.S. Federal Reserve Bak of New York, argues i he lead quoaio ha he reame of ower occupied housig (OOH) i a aio s CPI is a very big deal. Judged by he household expediure budge share of sheler for virually every aio, Cecchei is surely righ. Ye, his is a measureme area where he developme of harmoized official pracices has bee a elusive objecive. 2 The differig reames of OOH i aioal CPIs udermie effors o udersad he iflaio ad ecoomic growh experieces of aios. I secio 2, we provide a overview of he four mai approaches i curre use for dealig wih housig i a CPI: () he real equivalece, (2) user cos, (3) acquisiios ad (4) paymes approaches. 3 A fifh approach origially proposed by Diewer (26a) is also Erwi Diewer is wih he Deparme of Ecoomics a he Uiversiy of Briish Columbia. He ca be reached a diewer@eco.ubc.ca. Alice Nakamura is wih he Uiversiy of Albera School of Busiess ad ca be reached a alice.akamura@ualbera.ca. The fiacial assisace of he OECD, he Ausralia Research Coucil, ad he Caadia SSHRC are graefully ackowledged, as is he hospialiy of he Cere for Applied Ecoomic Research a he Uiversiy of New Souh Wales. The auhors hak Sepha Arhur, Deis Capozza, Johaes Hoffma, Ae Laferrère, David Robers, Mick Silver ad Paul Schreyer for helpful commes o he ogoig research o which his paper repors. Noe of he above idividuals or orgaizaios is resposible for ay errors or opiios. 2 Eiglsperger (26) of he Europea Ceral Bak made he followig observaios: The Harmoised Idex of Cosumer Prices (HICP) plays a promie role i he moeary policy sraegy of he Europea Ceral Bak (ECB)... A very impora ad difficul cocepual issue which has o bee fially decided upo is he reame of expediure o housig by homeowers. While he HICP already covers he expediure of eas (maily res), mos of he expediure of ower-occupiers o housig (OOH)... are o icluded i he HICP a prese. This ca be raced back o he differe pracices of reaig OOH i aioal cosumer price idices (CPIs)... 3 We use he ermiology of he 24 Ieraioal CPI Maual (ILO e al., 24), followed as well i he reviews of ieraioal pracice of Eiglsperger (26) ad Chrisese, Dupo ad Schreyer (25). PRICE AND PRODUCTIVITY MEASUREMENT, Volume : Housig, Chaper 2, pp Ediors: W. Erwi Diewer, Ber M. Balk, Deis Fixler, Kevi J. Fox ad Alice O. Nakamura Trafford Press (hp:// Also available for dowload of he eire volume or idividual chapers wihou cos a ad a Alice Nakamura, Caada, alice.akamura@ualbera.ca, 28. Permissio o repri graed wih credi o auhors ad ediors.

2 W. Erwi Diewer ad Alice O. Nakamura meioed: he opporuiy cos approach, which icorporaes elemes of boh he real equivalece ad he user cos approaches. Three of hese approaches -- he real equivalece, user cos ad opporuiy cos approaches -- aim o price he use (i.e., he cosumpio) of housig services as his occurs, moh by moh, over ime. These hree approaches ca be derived from he same heoreical foudaios: 4 a model ha has origis i he ecoomics ad accouig lieraures o busiess ivesme. 5 Secio 3 oulies hese foudaios, ad he user cos is defied ad relaed o depreciaio ad boh geeral ad asse class specific iflaio rae parameers. All dwelligs are uique i some ways, icludig heir locaios. 6 Measureme challeges ha arise wih uique asses are discussed i secio 4. I secio 5, we sugges mehods for dealig wih complicaios due o he budled lad ad srucure compoes of resideial properies. Verbrugge (26), Garer ad Verbrugge (28), ad Gordo ad Goehem (24) raise some seemigly fudameal, ad very differe, cocers abou he user cos ad real equivalece approaches. These cocers are cosidered i secio 6. For issues fraugh wih aio specific deails where ieraioal agreeme is eeded, he way forward is ofe o focus o broad sroke differeces amog he various cocepual approaches i hopes ha agreeme o deails will follow oce he cocepual differeces are clarified. However, he secio 6 maerials sugges ha, for OOH, he way forward may ivolve lookig more carefully a applicaio specific deails. Secio 7 cocludes. 2. Differe Coceps of he Cos of Ower Occupied Housig (OOH) We begi our overview of aleraive approaches for dealig wih OOH wih he real equivalece approach. Examples of he implemeaio of each approach are give, wih he excepio of he ew opporuiy cos approach. 2. The Real Equivalece Approach 4 Thus, Kaz (27) wries: The user cos of capial measure is based o he fudameal equaio of capial heory. This equaio, which applies equally o boh fiacial ad o-fiacial asses, has bee kow sice a leas he middle of he 9h ceury. I saes ha i equilibrium, he price of a asse will equal he prese discoued value of he fuure e icome ha is expeced o be derived from owig i. The view ha he appropriae value for a asse is he discoued sream of he expeced fuure e reveue flow from he asse was acively advocaed by Irvig Fisher (897, 93). Böhm-Bawerk (89, p. 342) was perhaps he firs o oice his priciple. There has also bee some ieres i he accouig lieraure i evaluaig a asse value by he discoued sream of is fuure expeced reurs. For example, Maessich (25, p. 28) oes ha: Durig he secod half of he ceury he ifluece of ecoomics ad he emergece of fiace (as a subjec idepede of accouig) gave a decisive boos o he furher exploraio of he prese value approach for accouig (icludig saeme preseaio). See also Wagehofer (24) ad Beidelma (973). 5 See Diewer (23a) (25a). 6 Capozza, Israelse ad Thomso (25) refer o he aypicaliy of a house ha has acquired uusual feaures as i aged. Appraisers may have a difficul ime fidig comparable houses i he eighbourhood ad may discou he appraisal value because of his. 4

3 W. Erwi Diewer ad Alice O. Nakamura The real equivalece approach values he services yielded by he use of a dwellig by he correspodig marke real value for he same sor of dwellig for he same period of ime (if such a real value exiss). Two aios ha use his approach for heir CPIs are he Uied Saes ad Germay. 7 Our summary descripios ha follow of he CPI reame of OOH i he Uied Saes ad Germay ecessarily iclude some maerial abou reer occupied housig (ROH) as well. (Alhough he focus i he lieraure has bee o he CPI reame of OOH raher ha ROH, here are issues deservig of aeio for ROH as well, ad wha is doe wih ROH ieviably carries over io he reame of OOH whe he real equivalece approach is used for OOH.) 2.. The U.S. case 8 The sheler idex i he CPI for he Uied Saes is he expediure weighed average of several compoe idexes. The Re of Primary Residece Idex (hereafer referred o as he re idex) ad he Owers Equivale Re of Primary Residece Idex (hereafer referred o as he real equivalece idex) beig he wo mai compoes of he CPI. The CPI Housig Survey is he source of he daa o resideial res used o compile he re idex. Iiiaio is he erm he BLS uses o refer o he iiial collecio of re daa for a seleced dwellig. Afer iiiaio, he re for he dwellig ui is priced o a coiuig basis while i remais i he pael. The iiial re is he basis for all calculaios of re chage ha occur durig he life of a real ui i he sample. The BLS compiles daa o he mohly ecoomic re for each reer occupied dwellig icluded i he CPI Housig Survey. The ecoomic re for a dwellig is he corac re (icludig he value of cerai re reducios) adjused by he value of ay chages i he services he ladlord provides. The BLS also derives daa o he mohly pure re for use i OOH real equivalece compuaios. For compaibiliy wih he expediures ower occupiers face, pure res exclude he cos of ay uiliies icluded i real coracs. Expediure weighs are used for combiig he ecoomic re daa ad he pure re daa (all colleced from reers i he CPI Housig Survey) io he re idex ad he real equivale idex compoes of he CPI sheler idex. 9 The expediure daa are from 7 Real equivalece is also he approach ake i he Sysem of Naioal Accous: 993 (Eurosa e al. 993, p. 34) for ower occupied housig. Eurosa s (2, p. 99) Hadbook o Price ad Volume Measures i Naioal Accous also recommeds he real equivalece approach for he reame of he dwellig services for ower occupied housig. To impleme he real equivalece approach, he releva real or leasig markes exis. 8 This secio draws o he U.S. Bureau of Labor Saisics (BLS) (27). 9 Whe a ower occupied housig compoe was firs iroduced io he CPI of he Uied Saes, he real equivalece idex was calculaed by reweighig he re sample o represe ower occupied uis. The owig o cocers ha he mix of ypes of real uis ad also where hey are locaed are differe from OOH, from , he BLS ried oher mehods for implemeig a real equivalece approach for ower occupied housig. However, i Jauary 999, he agecy reured o he mehod used for he real equivalece idex whe i was firs iroduced. See also Croe, L.I. Nakamura ad Voih (2, 28) ad Heso ad Nakamura (28) for more o he BLS mehods, ad he associaed mehods used by he U.S. Bureau of Ecoomic Aalysis (BEA) for he reame of ower occupied housig i he aioal accous for he Uied Saes. 5

4 W. Erwi Diewer ad Alice O. Nakamura households i he Cosumer Expediure (CE) Ierview Survey. Boh reers ad homeowers are icluded i he CE sample. For reers, he expediure weigh iformaio is obaied by askig sampled cesus ui (CU) reer households he followig quesio: Wha is he real charge o your CU for his ui icludig ay exra charges for garage & parkig faciliies? Do o iclude direc paymes by local, sae or federal agecies. Wha period of ime does his cover? For ower occupiers, he expediure weigh iformaio is obaied by askig sampled ower households he followig quesio: If someoe were o re your home oday, how much do you hik i would re for mohly, ufurished ad wihou uiliies? BLS he uses he ecoomic res ad he reer expediure weighs o esimae he chages for he re idex. Fially, he BLS uses he pure res ad he correspodig ower expediure weighs o esimae he chage for he OOH real equivalece idex. For reasos oed i secio 6, i is easier o impleme real equivalece i he Uied Saes ha i mos oher aios. I some respecs, herefore, he U.S. implemeaio of real equivalece ca appropriaely be viewed as boh a bes pracice example, ad he bes aaiable applicaio, of he real equivalece approach The Germa case Kurz ad Hoffma (24) repor ha i he Germa Cosumer Price Idex (CPI), as i he CPI for he Uied Saes, res are used for he impuaio of he coss of ower occupied housig, which is achieved by alerig he expediure weighs for he real daa. Approximaig OOH coss by meas of he re idex is said o be valid for Germay because he Germa housig marke is lighly regulaed, he ax sysem is o severely disorig, ad he share of real housig is quie subsaial. However, he srucure of ower occupied housig differs subsaially from ha of real housig. Real housig ypically akes he form of flas i aparme houses, whereas sigle family houses ad erraced houses predomiae i he ower occupied segme. Furhermore, oly res for a resriced sample of dwelligs are recorded for he CPI purposes. The poeial cosequeces of hese real housig versus ower occupied housig mix differeces are examied by Kurz ad Hoffma (28). 2.2 The User Cos Approach The user cos for ower occupied housig ca be heoreically derived, ad could poeially be compued, as he coss bore by a household for purchasig a home a he begiig of he ui ime period, livig i i durig he period, ad re-sellig i a he ed of he period. Morgage ieres paymes, maieace ad repair, isurace premiums, ad axes are ypical recurrig cos iems for homeowers of livig i heir ow dwelligs: wha we will refer o someimes as housekeepig coss. The full ex ae user cos cosiss of he housekeepig coss plus aicipaed ormal physical depreciaio, plus he waiig coss (he coss of forgoe 6

5 W. Erwi Diewer ad Alice O. Nakamura ieres due o he fuds ied up i he owed dwellig) ad aicipaed capial gais (or losses) due o housig marke specific iflaio over he give ime period. The full ex pos user cos has he same compoes as he correspodig ex ae user cos excep ha ex pos or acual capial gais or losses are used i place of aicipaed gais or losses. I imes whe housig prices are risig seeply, ex pos user coss ca be egaive. If we wa he user cos o approximae a marke re, he ex ae cocep mus be used: ladlords who have a ex pos egaive user cos will geerally o re heir properies a a egaive price! The issue of egaive user coss is addressed i subseque secios. Official saisics isiues ha have adoped user cos approaches have geerally o adoped he full user cos approach; hey have adoped various modified user cos approaches. We review he Caadia ad Iceladic cases below The Caadia case For ower occupied accommodaio, Saisics Caada produces a modified user cos measure ha icludes six elemes of homeower expese: a) Morgage ieres cos; b) The cos of regular ogoig maieace ad repairs ad oher owed accommodaio upkeep expeses; c) The cos of homeowers isurace; d) Propery axes; ad e) Replaceme cos (i.e., depreciaio). Noe, however, ha he Saisics Caada CPI reame of OOH omis he waiig cos iems of he full user cos: foregoe ieres o fuds ied up i a owed dwellig ad capial appreciaio or depreciaio. I fac, if he depreciaio erm were dropped from he Caadia reame, he resulig price of housig services would be a varia of he paymes approach o OOH, discussed below The Iceladic case The real raes repored by eas (abou 8% of households, based o Saisics Icelad s cosumer survey) form he basis for a re compoe i he Iceladic CPI. The sheler idex for he Iceladic CPI has wo mai compoes. The firs is a housekeepig ype expediures idex ha akes io accou mior maieace as well as The iformaio i his secio is mosly from Saisics Caada (27) ad Saisics Caada (995). For more o he reame of OOH i he Caadia CPI, see also Baldwi, A. Nakamura ad Prud homme (28) i his volume. Maerial i his secio is based o Guðaso (25a, 25b), as well as Guðaso ad Jósdóir (28) i his volume. Privae commuicaios wih Rósmudur Guðaso of Saisics Icelad ad Jó Seisso, ow wih Columbia Uiversiy bu formerly wih he Bak of Icelad, have also bee of grea help o udersadig he specifics of he Iceladic user cos calculaios. 7

6 W. Erwi Diewer ad Alice O. Nakamura charges for sewerage, refuse collecio ad waer supplies. 2 The oher compoe is a ower equivale re, referred o by Saisics Icelad as a simplified user cos. 3 Wha follows is a brief explaaio of Icelad s ower equivale re compoe. For furher deails o he Iceladic approach, see Guðaso (25a, 25b) ad Guðaso ad Jósdóir (28). Copies of all sales deeds for resideial housig mus be filed wih he Lad Regisry. The deeds sae he purchase price of he propery ogeher wih he provisios for buyer liabiliies. These liabiliies ake four forms:. The buyer makes a cash payme o sigig he deed of sale. If he buyer has ake a loa from a pesio fud or a bak for he cash dow payme, i is classified here. So are supplemeary loas from he Iceladic Housig Fiacig Fud (he HFF), which are paid ou i cash. 2. The buyer commis o make paymes. 3. The buyer rasfers bods o he seller: geerally swappable housig bods. Whe he buyer akes a loa from he HFF, he HFF issues he seller housig bods i reur. 4. The buyer assumes he seller s fiacial obligaios i coecio wih he propery. The Lad Regisry of Icelad deermies he prese value of each regisered propery. Accordig o he deed of sale, he purchase price is equivale o he oal omial value of paymes accordig o iems ad 2 above, he omial value of he housig bods received by he seller uder iem 3, ad he oal curre value of he pricipal of he fiacial obligaios ake over by he buyer accordig o iem 4. For a realisic picure of he cos of ower occupied housig, i is o eough o cosider merely he buyig price. The cos also depeds o he schedulig of paymes uder iem 2, he discou o housig bods paid accordig o iem 3, ad he ieres erms for he buyer obligaios uder iem 4. The Lad Regisry evaluaes all hese paymes, accordig o he deails i he deed of sale, ad compues he prese discoued value for he sale. 4 Ower equivale re is ieded o reflec chages i marke prices of housig ad also fiacig coss ad depreciaio. The Lad Regisry calculaes he cash price per square mere for several caegories of resideial housig ad muliple regios. More specifically, deeds of sale are classified accordig o wheher he housig is i he Greaer Reykjavík Area or i oher regios, ad wheher i is deached or muli resideial (i.e., a aparme). Each caegory is divided io four subcaegories by size. The average price per square mere is calculaed for each subcaegory. Saisics Icelad uses he Lad Regisry s daa for average price per square mere i is calculaios of ower equivale re. Three-moh averages are used. Thus he housig price i he Greaer Reykjavík Area ha is used for calculaig he May CPI is he average price of 2 This housekeepig compoe was abou 3.6% of oal expediure i he CPI base for March This compoe amoued o abou.% of oal expediure i he CPI base for March Sice paymes uder iem are made i cash, hey do o eed o be revalued a prese discoued value. The Lad Regisry uses overdraf ieres raes o calculae he prese discoued value of paymes accordig o iem 2. The Lad Regisry uses he marke yield o housig bods plus a premium of.35% whe i calculaes he prese discoued value of paymes accordig o iems 3 ad 4. See Igvarsso (22, p. 26). 8

7 W. Erwi Diewer ad Alice O. Nakamura housig sold i he period of Jauary o March. Saisics Icelad weighs he average price i each caegory by he umber of rasacios i ha caegory over a hree-year period. The ieres cos o ower occupied housig is a share weighed average of he ieres calculaed i wo ways: usig real raes of ieres o collaeral loas, ad 3 perce real ieres o he par of he value of he housig which is classified as ower s equiy. Thus, for he laer ieres compoe, he ieres rae is o allowed o chage, bu he ieres rae for he firs compoe does chage i lie wih he erms of he loas specified i he housig sale agreemes. Recely, owers equiy has accoued for jus over half he value of housig, ad average real ieres raes have bee jus over 5 perce. 5 Saisics Icelad assumes ha housig srucures have a lifeime of 67 years (wih a depreciaio rae of.5 perce per year) ad wih he real value of he plo of lad reaed as remaiig uchaged. For he sake of simplificaio, he combied value of he housig ad plo of lad are reaed like a asse wih a lifeime of 8 years (depreciaed by.25 perce per year). Thus N equals 8 i he user cos formula used by Saisics Icelad, ad he user cos for a propery is compued as he produc of he prese value of he propery sale imes he erm N r /[ ( + r) ] where r is he real ieres rae (deermied each period as explaied above). 2.3 The Acquisiios Approach The acquisiios approach ca be applied o OOH, jus as i is o all oher goods ad services covered by a CPI. The objecive is o measure he average chage i prices of he goods ad services acquired by households each period, irrespecive of wheher hey were wholly or eve parially paid for (e.g., purchases o credi), ad irrespecive of wheher he purchased asses were used, ha period. For he acquisiios approach, oly goods ha he household secor purchases from oher secors of he ecoomy are i scope. For ay propery ha is fully i scope because owership was acquired i he give ime period ad i was purchased from ouside he household secor (e.g., properies beig sold by a developme compay), he full sales price is coued i he period of he sale. Also, he e acquisiios approach icludes i-period coss of services relaig o he buyig ad sellig of secod had houses such as real esae age fees ad asse rasfer axes. For mos sors of goods i idusrialized aios, he direc sales by households o oher households are a very small proporio of oal sales. 6 Thus, limiig he CPI coverage o 5 I Icelad, a prese, a large par of housig loas are a raes which are o deermied direcly i he marke. This applies, for example, o loas from he Housig Fiacig Fud (HFF) ad some pesio fud ledig o homebuyers. Uder hese codiios, a geeral rise i he real ieres rae has relaively lile impac o he ieres raes used o calculae ower equivale re. O he oher had, a geeral icrease i ieres raes which raises he yield o housig bods ca lower he cash price of he housig by reducig he prese discoued value of loas bearig fixed real ieres. Head o compeiio bewee he baks ad he HFF has bee viewed as a problem by he goverme. 6 This is sill he case eve if household-o-household sales faciliaed by iermediaries such as cosigme compaies ad mach makig services such as E-Bay are reaed as household-o-household. 9

8 W. Erwi Diewer ad Alice O. Nakamura purchases from oher secors makes lile differece for mos goods ad services. However, whe he acquisiios approach is used for OOH, wha eers he CPI for housig are mosly expediures o ew dwelligs excludig lad, wih almos all secod had dwelligs ad eve mos of he lad used for ew home cosrucio beig excluded due o prior owership wihi he household secor. For example, if he lad o which a ew house sis was previously owed by aoher household, he he cos of his lad is excluded from a acquisiios ype house price idex eve hough he house srucure is ew ad is coued. The acquisiios approach is used by Ausralia ad New Zealad. This is also he approach ha has bee eaively seled o for he Europea Uio s Harmoized Idices of Cosumer Prices (HICPs) The New Zealad case The New Zealad CPI (like he Ausralia CPI) is compiled usig a acquisiios framework. The expediure weigh allocaed o he purchase of housig represes he value of he e icrease i he sock of ower occupied housig durig he weigh referece period. Expediure o ewly cosruced dwelligs by ower occupiers is icluded, as are aleraios ad addiios o esablished ower occupied dwelligs. Sales wihi he household secor of esablished ower occupied dwelligs are viewed as o addig o he sock ad are o coued. 2.4 The Paymes Approach The paymes approach oly measures acual cash ouflows associaed wih owig ad occupyig a home. Thus he cosumpio of OOH services ges lile or o weigh for dwelligs already fully paid for The Irish case The Ceral Saisics Office of Irelad (23) uses he paymes approach for OOH i heir CPI. For ower occupiers, he Irish CPI covers he followig cos iems: a) Morgage ieres, b) Repairs ad decoraios, ad house maieace services; c) House (dwellig ad coes) isurace; ad d) Local auhoriy charges. Morgage ieres paymes are measured usig a fixed baske profile of morgages up o wey years i duraio. Morgage capial repaymes ad dow paymes o dwellig purchases are o covered i he CPI as hey are cosidered o be ivesme. 7 The HICPs are he official measure of cosumer price iflaio for he purposes of moeary policy i he euro area ad for assessig iflaio covergece as required uder he Maasrich crieria. See he Europea Commuiies (24). 2

9 W. Erwi Diewer ad Alice O. Nakamura 2.5 Diewer s Opporuiy Cos Approach The opporuiy cos approach o he reame of OOH is oo ew o have bee implemeed by ay saisical agecy. Diewer (26a, p. 27) explais his approach as follows: [P]erhaps he correc opporuiy cos of housig for a ower occupier is o his or her ieral user cos bu he maximum of he ieral user cos, which is he fiacial opporuiy cos of housig, ad wha he propery could re for o he real marke. Afer all, he cocep of opporuiy cos is supposed o represe he maximum sacrifice ha oe makes i order o cosume or use some objec ad so he above poi would seem o follow. The home ower s ieral user cos is he fiacial opporuiy cos of owig he dwellig ui; i.e., i focuses o he fiacial capial ha is ied up whe oe ows he home. This is he user cos cocep discussed i he followig secio. Diewer, i he above quoaio, oes ha he home ower faces aoher opporuiy cos; amely he re ha he homeower could receive if he dwellig ui was reed ou o a ea. Thus he effecive opporuiy cos of OOH is o he fiacial user cos or he real opporuiy coss bu he maximum of hese wo. Diewer goes o o observe ha: If his poi of view is acceped, he a cerai pois i he propery cycle, user coss would replace marke res as he correc pricig cocep for ower occupied housig, which would dramaically affec Cosumer Price Idexes ad he coduc of moeary policy. The empirical resuls obaied by Heso ad Nakamura (28) ad heir suggesed explaaios for hese resuls raise he possibiliy also ha, for some groups of homeowers, he fiacial opporuiy cos may sysemaically domiae he real opporuiy cos of OOH, ad vice versa. Noe ha he opporuiy cos approach o OOH resolves poeial problems associaed wih egaive ex pos or ex ae user coss. The opporuiy cos price for OOH ca ever be egaive. 3. The Theory of Household User Coss Diewer (974, p. 54) ses ou he user cos priciples for cosumer durables: To form he real price (or user cos) for he services of oe ui of he h good durig period, we imagie ha he cosumer purchases he good durig period ad he sells i durig he followig period (possibly o himself). The he discoued expeced real price for he h cosumer good durig period is give by he discoued cos of he purchase of he h good durig period mius he discoued resale value of he depreciaed good durig period +. The resale value of he depreciaed good durig period +, referred o i he above quoaio from Diewer (974), icludes he loss i poeial resale value due o physical depreciaio ad 2

10 W. Erwi Diewer ad Alice O. Nakamura ay aicipaed or expeced holdig gais or losses for ha ype of asse. This user cos approach is wha price saisicias refer o as he full user cos approach. 8 Uforuaely, here is ofe a large divergece bewee user coss ad he correspodig marke res. This ca be see, for example, from able 4 i Heso ad Nakamura (28) which shows ha as dwellig uis become more valuable, he raio of he esimaed marke real price o he asse value of he ui drops raher seeply o abou oe half of he iiial raio. 9 The re o value raio should be approximaely equal o he sum of he housig depreciaio rae plus he propery ax rae plus he omial opporuiy cos of capial less he aicipaed rae of propery price iflaio. All of hese raes should be approximaely cosa as he value of he propery icreases. 2 The evidece preseed by Heso ad Nakamura (28) suggess ha he real equivalece approach o OOH will give a subsaially lower share o OOH i a CPI compared o a user cos approach or o a opporuiy cos approach. Diewer (22, p. 69) oed ha expediure weighs usig he user cos approach o OOH were likely o be cosiderably higher ha he correspodig weighs obaied usig he acquisiios (also someimes called he moey oulays) approach. If he empirical resuls of Heso ad Nakamura (28) are applicable o oher couries, he user cos expediures are likely o exceed he correspodig real equivalece expediures which i ur are likely o be greaer ha acquisiios expediures. Thus, aleraive reames of OOH are likely o give rise o differe movemes i he CPI. Girouard, Keedy, va de Noord ad Adré (26) also prese evidece ha he raio of marke res o he uderlyig asse value of he dwellig ui varies subsaially over ime. This empirical evidece, alog wih ha preseed by Heso ad Nakamura (28), suggess ha he subsaial rasacios coss associaed wih a chage i housig saus ca coribue o a divergece of he usual fiacial user coss from he correspodig marke res. The issues surroudig he choice of approach o OOH o ake for a CPI are discussed furher i secio 6. The res of his secio is devoed o he radiioal fiacial user cos approach. I box, he derivaios are show for aleraive expressios for he full user cos for a dwellig, measured as of he begiig of period. 2 The ime period is idicaed by he superscrip ad he umber of periods a dwellig has bee used as of he begiig of he desigaed ime period is deoed by he subscrip v. Thus, p is he price of a ew dwellig a he begiig of period, ad p is he price of a dwellig used for oe period as of he sar of period. The expressios i box absrac from housekeepig expeses. 8 Diewer (974, 98; pp , 23a) followed Fisher (897; p. 527) ad Hicks (939; 22) ad derived his user coss usig a discree ime approach as opposed o he coiuous ime approaches used by Jorgeso (963, 967), Griliches (963), Jorgeso ad Griliches (967, 972) ad Chrisese ad Jorgeso (969, 973). For more rece research o user coss ad capial measureme, see Hule ad Wykoff (98a, 98b, 996), T.P. Hill (999, 2, 25), Diewer ad Lawrece (2), R.J. Hill ad T.P. Hill (23), Corrado, Hule ad Sichel (25), Diewer (25a, 25c) ad Diewer ad Wykoff (28). 9 For example, i he Washigo D.C. area, he re o value raio is i he 8.8 o 8.9 perce rage for a $5, ui which drops o 4.2 o 4.3 perce for a $5, ui. 2 Oe could make he case ha more expesive properies have a higher lad compoe ad hus he overall depreciaio rae for he dwellig ui ad he lad associaed wih i should be higher for he less expesive properies. O he oher had, properies wih more lad geerally have more expesive srucures buil o hem. 2 We are absracig i his secio from housekeepig expeses icurred by livig i he dwellig, as well as from issues of reovaio ad lad/srucure/equipme dwellig composiio complicaios: issues ake up i secio 6. 22

11 W. Erwi Diewer ad Alice O. Nakamura Box. Begiig of Period User Coss Evaluaed Ex Pos As i Diewer (23a) ad absracig here from direc operaig homeower coss for exposiioal p v simpliciy, le deoe he price paid for a dwellig ha is v periods old a he begiig of period. To deermie he e cos of usig he dwellig durig period, we begi wih he purchase price a he begiig of he period: p. Suppose he dwellig ca be sold a he ed of period (which we ake o be he same poi i ime as he begiig of period ) a he price of p. If here is posiive iflaio, moey is less valuable whe received a he ed versus he begiig of a period. For period, he ed of period value ca be covered o is equivale a he begiig of ha same (o he ex) period by discouig by he erm + r where r is he begiig of period omial ieres rae. Le u v deoe he oe period user cos, as of he begiig of period, for usig a dwellig ha is v periods old; ha is, his is he price of usig he a dwellig for he period ime ierval. The period user cos for he ew dwellig is defied, usig price daa for his same dwellig from he begiigs of periods ad, as: + (2-) u p p /( r ). The secod erm i (2-) is he price for he oe period old dwellig discoued o he begiig of period. Suppose he cosumer purchases he ew dwellig a he begiig of period a he price p, charges he self imposed real price of u, ad views he remaider of he purchase price as a ivesme: (2-2) I p u. The rae of reur ha could poeially be realized o he ivesme defied by (2-2) is he ieres rae r ha he cosumer faces a he sar of period. Fiacial capial heory implies ha, he sellig price ha could be realized for he dwellig a he ed of period, should saisfy he followig equaio: (2-3) I (+ r ) = p. The user cos formula (2-) ca be pu io a more familiar form usig he ecoomic depreciaio ad housig specific iflaio raes. The depreciaio rae for a ew dwellig (i.e., a dwellig wih v=) over oe ime period, deoed by δ, reflecs he loss of ecoomic value wih ormal use ad maieace, ad is defied by: p (2-4) ( δ ) p /. The housig specific iflaio rae for a ew dwellig over period is deoed by (2-5) + i p / p. p i ad is defied by: Thus he depreciaio rae is defied by he raio of he same period prices for dwelligs ha have bee used for differe leghs of ime whereas he iflaio rae is defied by he raio of he prices a differe pois i ime for iems used he same legh of ime. Elimiaig p from (2-4) ad (2-5) leads o he followig expressio for he ed of period used dwellig price as a fucio of he cos a he begiig of period : p (2-6) p = ( δ )(+ i ). Subsiuig (2-6) io (2-) yields aoher expressio for he begiig of period user cos of a ew dwellig: (2-7) where r * r i u = [( + r ) ( δ )( + i )]p /( + r ) = [(r i ) +δ (+ i )]p /(+ r ) * * = (r + δ )p /( + r ). * + = is a period real ieres rae ad δ =δ ( i ) is a iflaio adjused depreciaio rae. 23

12 W. Erwi Diewer ad Alice O. Nakamura Suppose, for he mome, we also igore iflaio; hece r = i box for =,. 22 Wihou iflaio, we see from (2-) ha he user cos is defied simply as he purchase price of he ew dwellig mius is resale price oe period laer. From (2-6) i box, we see ha he resale price equals he origial purchase price imes wo erms. The firs of he erms o he righ had side of (2-6) reflecs he oe period loss i dwellig value due o physical depreciaio. This erm is defied i (2-4) as he raio of he resale price of he dwellig a he ed of period (which is he begiig of period ), ad he price a he ed of period of a hypoheical comparable home ha is ew he. The secod erm o he righ had side of (2-6) is a housig specific iflaio rae, which ca be measured (as i (2-5)) as he raio of he price a he ed of period of a hypoheical comparable ew home o he ew price a he begiig of period for he give home. Expressios like (2-6) i box have bee preseed i he accouig lieraure goig back, a leas, o he early 9s whe Daies (929) ad Sweeey (934) wroe. (For more o his opic, see appedix A ad also Diewer 25a, chapers 2, 3 ad 7.) Aeio o imig maers for udersadig he aleraive ways i which user coss ca be defied. Realized prices are deermied a pois i ime. Raes of ieres are also regarded as fixed a pois i ime. I coras, raes of iflaio are defied for ime iervals. I box, he user cos is expressed i erms of prices discoued o he begiig of period. The coveios used i fiacial accouig sugges ha flow rasacios wihi a accouig period should be regarded as akig place a he ed of he period. This would sugges ha a ed of period, raher ha a begiig of period, user cos should be used. The user cos ca be mechaically recas i a ed of period forma by reverse discouig. (See he op secio of box 2.) There is o way of kowig a acual iflaio rae uil he ed of he period for which i is defied. However, his rae could be esimaed ad aicipaed, as hose decidig o he purchase of asses like owed housig mus do i real life. I he boom porio of box 2, begiig of he period user coss are defied usig a aicipaed iflaio rae. The Saisics Icelad simplified user cos mehod for icludig OOH services coss i heir CPI (see secio 2.2.2) makes use of equaio (2-9) i box This mehod requires some way of deermiig: The curre period sale prices for homes, The aicipaed real ieres rae ( r The home depreciaio rae, * = r i ), The rae of value loss due o he physical depreciaio of homes, ad The value of he housig sock. 22 The equaios i Diewer s (23a) paper are formulaed for he illusory case of a household durable bough ew i period ad used for oe period (i.e., used o he ed of period which is he begiig of period. For may cosumer durables, from clohes o couches, mos of he iems purchased by households are ew. However, his is less he case for cars, ad mosly o he case for dwelligs. Price developmes over he firs few years followig a chage of owership are o he same for homes purchased ew as for homes already a few years old a he ime of he mos rece chage of owership. This is why aios like Caada have a separae price idex for ew home sales. I acual applicaio, ay wo periods could be subsiued for periods ad i box, ad v (which deoes he dwellig age a he begiig of he firs period) could ake o oher values oo. 23 See he remarks followig equaio (9) o pages 2-3, ad also (54) ad (55) o pages i Diewer (23a). 24

13 W. Erwi Diewer ad Alice O. Nakamura Box 2. Oher Ways of Defiig User Coss Ed of Period User Coss For a ew dwellig a he ed of period, we ca defie a ed of period user cos equivale o he begiig of period user cos give i (2-7) i box, which Diewer (23a) erms a approximae real cos, as: (2-8) ϕ ( + r = [(r i ) +δ (+ i )]p = (r )u * * + δ )p. If he real ieres rae small erm, δ i, is igored, he he ed of period user cos give by (2-8) reduces o: (2-9) ϕ ( r + δ ). * r is defied as he omial ieres rae, r, less he dwellig iflaio rae, * p i, ad he Thus he user cos (wheher begiig or ed of period) is deermied primarily by he (real) opporuiy cos of he * capial ied up, give by r p Begiig of Period Aicipaed User Coss Diewer (23a) suggess ha he acual asse iflaio rae, aicipaed housig iflaio rae, deoed by (2-) The erm r *a, plus he declie i value of he dwellig over he period due o depreciaio. a i a a u = [(r i ) + δ ( + i )]p /( + r ) = (r i *a *a = (r + δ )p /( + r ). a ) i. Thus, (2-7) becomes:, i (2-5)-(2-7) ca be replaced by a esimaed or ca ow be loosely ierpreed as a housig specific aicipaed real rae of ieres. Also, * a a he iflaio adjused depreciaio rae mus be replaced by a aicipaed iflaio adjused rae: δ =δ(+ i ). Saisics Icelad icorporaes a asse specific iflaio rae io heir user cos calculaio, wih his beig muliplied by he propery value figure, hereby reflecig resideial propery appreciaio. Depreciaio is allowed for, bu he reame is largely by assumpio. The same rae is applied, period afer period. The raioale for his approach has bee widely used for reasos ariculaed more ha years ago by Ewig Maheso (9/884, p. 35): The pla of valuig every year isead of adopig a depreciaio rae, hough i migh appear he more perfec, is oo edious ad expesive o be adoped... he ex bes pla, which is ha geerally followed... is o esablish average raes which ca wihou much rouble be wrie off every year, o check he resul by complee or parial valuaio a loger iervals, ad o adjus he depreciaio rae if required. May ohers have held similar views. For isace, Daiels (933) wries: The fucio of depreciaio is recogized by mos accouas as he provisio of a meas for spreadig equiably he cos of comparaively log lived asses. Thus, if a buildig will be of use durig wey years of operaios, is cos should be recogized as operaig expese, o of he firs year, or he las, bu of all wey years...the impora maer is ha a he ime of abadome he cos of he asse shall as early as possible have bee charged off as expese... 25

14 W. Erwi Diewer ad Alice O. Nakamura Box 3. Depreciaio for Durables wih Log Service Lives Le δ v be he depreciaio rae for a dwellig ha is v periods old a he begiig of he give period. Depreciaio raes ca be defied recursively, sarig wih he rae for a brad ew dwellig. Followig Diewer (23a), ad applyig he same defiiio as is used for period ad prices i (2-4), is defied here by ( δ ) p / p 2, so ( δ )( δ ) p / p, where p 2, he begiig of period price for a ui of a dwellig ha is 2 periods old, is compared o he price of a brad ew dwellig a he begiig of period. Similarly, if we have values for he cross secioal depreciaio raes for dwelligs ha are,,2, K,v periods old (i.e., if we kow he values of δ, δ, δ2,, δ v ), he he period cross secioal depreciaio rae for a ui of dwellig ha is v periods old a he begiig of period, ( v v +, is defied by: δ v (2-) δ ) K( δ )( δ ) p / p. Noe ha here, as is cusomary i he depreciaio lieraure, he sequece of viage depreciaio raes is idepede of he period, so δv = δv for all ad v. Thus a sequece of viage (i.e., of used) dwellig prices a a poi i ime ca be used o esimae he sequece of depreciaio raes ha apply for all ime periods. Recall he user cos formula for a ew ui of a dwellig give by (2-). The same approach leads o he followig begiig of period sequece of viage user coss: ( δ δ δ +δ + + = (2-2) = )( ) ( )[(r i ) ( i )]p /( r ) for v,2, u v v 2 K v v K v [(r i ) +δ (+ i )]p /(+ r ) for v= Whe v =, defie δ ; i.e., he erms i fro of he square brackes o he righ side of (7) are se equal o. Noe ha if v =, he (2-2) reduces o (2-7). I his case, all he cross secioal viage depreciaio raes i (2-2) are assumed o be equal o he same rae δ, where δ is a posiive umber less ha oe; i.e., for all ime periods ad all viages v, i is assumed ha (2-3) δ v =δ. Subsiuio of (2-3) io (2-2) yields he followig for he sequece v =,,2, of period viage user coss: v v v + (2-4) u = ( δ ) [(r i ) +δ (+ i )]p /( r ). From (2-4) we see ha, give geomeric depreciaio, all of he viage user coss are proporioal o he user cos for a ew dwellig. Noe ha his proporioaliy meas i is o ecessary o use a idex umber formula o aggregae over viages whe formig a dwellig services aggregae. If he aicipaed ieres rae is subsiued for a acual oe, his defies a aicipaed sequece of user coss as of he begiig of period. δ Oe way of aempig o deermie a sequece of depreciaio raes for a durable capial ipu as i ages was suggesed by Böhm-Bawerk (89): esimae he expeced umber of accouig periods ha he ipu is likely o be used i producio ad assume ha he sigle period depreciaio rae is δ = /. This sraigh lie mehod of depreciaio ca be used o allocae he iiial purchase cos of he asse across he periods of is life. Aoher commoly used mehod for he deermiaio of depreciaio raes ress o he assumpio ha depreciaio occurs o he udepreciaed value of he asse a a cosa geomeric rae δ where < δ <. This mehod, someimes called he reducig balace mehod or he decliig balace mehod i he accouig lieraure, is very coveie o apply. Ye, Caig (929, pp ) cauios ha: Obviously he umber of periods of coemplaed use of a asse ca seldom be ielligely esimaed wihou referece o he aicipaed codiios of use. If he formula is o be respecable a all, he value of mus be he mos probable umber of periods ha will yield he mos ecoomical use. 26

15 W. Erwi Diewer ad Alice O. Nakamura The accouig professio primarily works for busiesses. Hisorically, busiesses self produced or bough mos of heir machiery ad equipme ew ad he used i uil i was ready o be scrapped. I ha coex, i may ofe make sese o represe depreciaio, ad also he user cos of capial, usig oly he price for he asse whe ew ad he plaed o umber of periods uil he asse will be scraped. I hese siuaios, i may also make sese o focus o a user cos formulaio ha oly coais price iformaio for he durable good before i is used for he desigaed legh of ime, as i (2-7) i box. The user cos expressios i boxes ad 2 are show, for exposiioal coveiece, i a wo ime period coex. The formulas preseed ivolve a depreciaio parameer: δ. Box 3 shows assumpios uder which a sequece of depreciaio raes for houses buil a differe pois i ime -- i.e., for houses of differe viages -- ca be summarized i erms of a sigle depreciaio parameer. 24 However, for houses, whe here is acive resale, i seems desirable o use his iformaio o empirically deermie he depreciaio rae (or raes). The resale housig marke is far larger ad wider i is coverage of he rage of differe ypes of dwelligs ha are he resale markes for mos sors of busiess machiery ad equipme. 4. Dealig wih he Uique Aspecs of Dwelligs The depreciaio paer for a durable ca be deermied empirically whe here are muliple resale, or real price, observaios for dwelligs ha have bee used for differe umbers of periods bewee he pois i ime whe price iformaio was colleced. Large umbers of dwelligs of differe viages are sold each year i eve a aio as small as Icelad. Of course, all dwelligs are uique i some respecs, icludig heir exac locaios. If dwelligs are regarded as uique for price measureme purposes, i will o be possible o empirically sor ou he separae effecs of depreciaio ad asse iflaio: his is wha Diewer (23a) erms a fudameal ideificaio problem. 25 Moreover, if he depreciaio rae is deermied by assumpio or simplisic proxies, his imposes a allocaio bewee dwellig deerioraio ad housig iflaio effecs. However, he prospecs for learig from empirical observaio improve grealy if dwelligs ca be viewed as he same provided hey have cerai shared characerisics. This is he basis of he repea sales ad hedoic approaches. 24 For more o depreciaio ad some worked examples, see Diewer ad Lawrece (2) ad Diewer (23c). Addiioal examples ad discussio ca be foud i OECD (2a, 2b). 25 Special cases of his fudameal ideificaio problem have bee oed i he coex of various ecoomeric housig models: For some purposes oe migh wa o adjus he price idex for depreciaio. Uforuaely, a depreciaio adjusme cao be readily esimaed alog wih he price idex usig our regressio mehod. I applyig our mehod, herefore, addiioal iformaio would be eeded i order o adjus he price idex for depreciaio, Bailey, Muh ad Nourse (963, p. 936). The price idex ad depreciaio are perfecly colliear, so if oe cares abou he price idex, i is ecessary o use exeral iformaio o he geomeric depreciaio rae of houses, Palmquis (23, p. 43). 27

16 W. Erwi Diewer ad Alice O. Nakamura 4. The Repea Sales ad Characerisics Period Dummy (CPD) Mehods Cosider a dwellig which is ew a he sar of period wih price. From (2-6) i box, he price, p, ha his dwellig could be sold for a he begiig of period, whe i has bee used for period, is: p = ( δ)( + i ) p. Thus he poeially observable period used asse price ew home, p is equal o he period price of he p, imes he produc of wo facors: δ ), a qualiy adjusme facor ha akes ( io accou he effecs of agig o he dwellig, ad ( + i ), a period o period pure price chage facor holdig qualiy cosa. The problem wih uique asses is ha cross secioal iformaio o used asse prices a ay oe poi i ime will o allow us o separae ou he effecs of hese wo facors. However, his separaio ca be based o empirical evidece if some way ca be foud for decidig whe differe dwelligs, ha have bee used differe umbers of periods, ca be viewed as comparable for depreciaio measureme purposes. The repea sales mehod compares he price observaios for housig properies ha rade more ha oce over a give ime ierval. 26 Trasacio daa ca be liked, so ha we ca compare he sales price for he same house a differe imes. The differece i hose sales prices is a esimae of how much prices have icreased for a paricular budle of aribues. We do o eed o kow he aribues o deermie how much he price has chaged. By akig he average icrease i prices, he repea-sales house price idex ca deermie average house price appreciaio raes wihou havig o measure all he aribue characerisics of he properies sold. The uderlyig assumpio is ha, wih ormal wear ad ear ad ormal maieace, mos owers of housig properies maage o maiai heir properies i uchaged codiio. I oher words, his mehod deals wih he fudameal ideificaio problem for uique asses largely by assumig away depreciaio ad oher sors of qualiy chage for exisig homes. The origiaors were well aware of his limiaio. 27 p 26 The repea sales procedure, ow i widespread use, daes back o Bailey, Muh, ad Nourse (963). See also Dreima ad Peigo-Cross (24) for he uses of his mehod ad see Gree ad Malpezzi (23, pp. 32-6) for a review of he repea sales idex lieraure. Case ad Shiller (989) refied he mehodology o corol for heeroskedasic errors. The problem is ha he size of he errors is relaed o he ime i bewee sales, ad his violaes he assumpio of equal error variaces i leas squares regressio. 27 Aoher assumpio implici i he repea sales mehod is ha aribue prices remai cosa bewee sales so ha he aribue prices cacel ou i he cosrucio of he house price idex. The repea sales approach has become pracically he idusry sadard. Faie Mae ad Freddie Mac have combied heir rasacio daa, ad OFHEO publishes he resulig house price idexes a he aioal, regioal, sae ad large meropolia levels o a quarerly basis. Eve if he OFHEO idex or he closely relaed Freddie Mac idex do o perfecly corol for qualiy chages, he fac ha hey are updaed every quarer for such a wide rage of geographies (ad are free) has made hem he house price idexes of choice i research. Wolvero ad Seeza (2) oe here are problems wih he repea sales mehod wih respec o corollig for aypical maieace ad capial improvemes. Usig he U.S. Naioal Associaio of Realors (NAR) daa ha iclude iformaio o sale prices, locaios ad 28

17 W. Erwi Diewer ad Alice O. Nakamura As origially proposed, he repea sales mehod ca oly be used o measure price level chage over ime. No iformaio o price levels ca be derived from he pure repea sales mehod as origially developed, makig spaial comparisos of housig price levels impossible by his meas. I he lieraure o spaial price level comparisos, Summers (973) proposed a simple ype of hedoic regressio model where he oly explaaory variables are dummy variables for he coury ad he commodiy. As preseed i he lieraure, he repea sales ad CPD mehods appear very differe, bu Diewer (23a) shows hey are closely relaed. Hedoic regressio models work wih price levels raher ha price raios as depede variables, as is he case for he repea sales mehod. For relaig he Bailey-Muh-Nourse repea sales procedure o hedoic approaches, Diewer (23a) explais ha i is helpful o iroduce he mehod as i arose hisorically: as a geeralizaio of he chaied mached model mehodology ha was used by he early pioeers 28 i he cosrucio of real esae price idexes. (See box 4.) Diewer (23a) shows ha he repea sales mehod ca be recas i a CPD framework. He he goes o o show he relaioships o a geeral hedoic regressio model 29 for housig. Thus all ha has bee leared abou he CPD mehod applies for he repea sales mehod. The much broader applicabiliy of his mehod is esablished by Diewer (23a) More Geeral Hedoic Models The weighed repea sales house price mehod is aracive parly because differe aalyss should produce he same resuls if give he same daa. The accepace of his mehodology ress, secodly, o he presumpio ha repea sales price idexes do a beer job of holdig qualiy cosa ha aleraive approaches. Ad, Malpezzi (22) ad ohers oe ha his mehod is popular wih real esae researchers ad praciioers because i uses oly he iformaio readily available i all localiies for a coury like he Uied Saes: he sale price, locaio, ad legal propery ideificaio iformaio eeded o regiser he sale. However, whe iformaio is available abou dwellig characerisics such as floor space, umber of bahrooms, umber of bedrooms, ad so o, here is obvious ieres i uilizig he iformaio. characerisics of 558 dwelligs sold i he years , Mills ad Simeauer (996) esimae ha more ha half of dwellig price icreases durig heir aalysis period resuled from qualiy improvemes. 28 See Wygarde (927) ad Wezlick (952). 29 The mai feaures of a geeral hedoic regressio model were laid ou i Cour (939). This publicaio was o readily available o researchers ad so he echique was o used widely uil he work of Griliches (97a, 97b) popularized he echique. See Triple (24) for a sysemaic review of hedoic regressio mehods. 3 Rao (28) oes ha he CPD mehod, he weighed versio i paricular, is beig icreasigly used i derivig spaial comparisos due o is abiliy o hadle price quoaios. See, for example, Ae ad Meezes (22), Heso ad Ae (22), Rao (23, 25), ad Deao, Friedma ad Alaas (24). 29