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 [email protected]. Alice Nakamura is wih he Uiversiy of Albera School of Busiess ad ca be reached a [email protected]. 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, [email protected], 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

18 W. Erwi Diewer ad Alice O. Nakamura Box 4. A Exposiio of he Repea Sales Mehod As i Diewer (23a), le S(,) deoe he se of housig uis ha are i scope for he idex ad were sold i boh periods ad. Deoe he price for propery sold i period by jus wo ime periods ad, so S(,). Le, P V. Here aeio is cofied o be he real esae price idex goig from period o. For he housig uis i S(,), suppose he sochasic model relaig he propery sales price raio, V / V, o P is:,, (2-6) V / V = P expε,, ε where is assumed o be a idepedely disribued error erm wih mea ad cosa variace. Takig logarihms of boh sides of (2-6) leads o he followig liear regressio model: ],, (2-7) l[ V / V =π + ε,,,, where π l P. The leas squares esimaor for π is he arihmeic average of he logarihms of he sales price raios. Expoeiaig his esimaor yields a prelimiary mached model propery price idex goig from period o :,* S(,) / N(,) (2-8) P [V / V ], where N(,) is he umber of houses i he se S(,). This idex is see o be he equally weighed geomeric mea of sales price raios V / V for all he properies ha chaged hads i boh periods ad : a ypical mached model esimaor for a elemeary price idex. Nex cosider he se S(,2) of houses ha sold i boh periods ad 2. Now he resulig prelimiary mached model propery price idex goig from period o 2 ca be show o be: (2-9) P,2* S(,2) [V 2 / V / N(,2) ] where N(,2) is he umber of sales of houses i he se S(,2). Usig he above resuls, he levels of he propery price idex,,*,*,2* (2-2) P ; P P ; P P P. P 2 P,, for periods =,,2 ca be defied as: Thus he price idex is se equal o i he base period ; i period, i equals he esimaed mached model price idex goig from period o, ad i period 2, i equals he produc of he prelimiary mached model price idexes give i (2-8) ad (2-9). The Bailey, Muh ad Nourse (BMN) iovaio was o reparameerize he model described above ad o add a addiioal se of esimaig equaios for repea sales pairs i periods ad 2: i.e., for housig properies i S(,2). The BMN esimaig equaios wih hree periods of daa o repea sales are he followig oes: ], (2-2) l[ V / V =π π + ε for S(,), 2 ] 2,2 (2-22) l[ V / V =π π + ε for S(,2), 2 ] 2,2 (2-23) l[ V / V =π π + ε for S(,2), where ow we have 2 2 (2-24) π l P, π l P, ad π lp, wih he followig ormalizaio imposed (where addig a cosa o each π leaves he regressio uchaged): (2-25) π = or P =. This leads o a model ha ca be esimaed usig leas squares regressio. Expoeiaig he leas squares esimaes 2 * 2 * * for he parameers π ad π, deoed here by π a d π, leads o esimaes for he prelimiary idexes P a d 2* P. The BMN esimaes for he housig price levels i he hree periods are: (2-26) P, P expπ, P expπ. * * 2* 2* The hree period model geeralizes readily o he T period case cosidered by Bailey, Muh ad Nourse (963). 3

19 W. Erwi Diewer ad Alice O. Nakamura Box 5. The CPD Model wih Complee Mached Model Daa Cosider a sample of N houses ( =,2, K, N ) each of which sold i each of he hree periods ( =,, 2 ): S (,,2). A sochasic model for he house prices, V, i each period ca be specified as follows: (2-27) V =α P expε, where P is he housig price idex level for period, ε =, K,N, α is a parameer ha reflecs he qualiy of housig ui relaive o average qualiy ad is a idepedely disribued, mea zero, cosa variace error erm. Takig logarihms of boh sides of (2-27) leads o he followig sysem of esimaig equaios for he N houses: V (2-28) l =β +π + ε, =, K,N, =,, 2. where β lα ad π l P. Diewer (23a) shows ha, for he model defied by (2-28) ad he ormalizaio (2-25), he leas squares (LS) esimaors for he model parameers saisfy he followig N+2 equaios: N N * = = N (2-29) l V = β + π, N 2 N * = = N (2-3) l V = β + π, ad 2 3 * * 2* * 2* (2-3) l V + l V + l V = β +π + π, =, K, N. Usig equaios (2-3) o elimiae he (2-32) = (/ N) l[v / V ], π = (/ N) l[v / V ]. β * * 2* π N N = = from (2-29) ad (2-3) yields he followig soluios for he ukows: Afer expoeiaig hese esimaes, his complee iformaio CPD model leads o he followig geomeric mea of he period relaive o he correspodig period values as he esimae for he period housig price level, P, ad he geomeric mea of he period 2 values relaive o he correspodig period values as he esimae for P : * N / N 2* = N = = / N (2-33) P [V / V ], P = [V / V ] * * A firs glace, i seems ha he CPD mehod (ad by exesio, uweighed hedoic regressio mehods) for comparig prices bewee couries (or ime periods) are oally urelaed o radiioal idex umber mehods for makig price comparisos. However, i a series of relaed papers, Diewer (22, 23a, 23b, 24, 25b, 26a, 26b) ad Diewer, Heravi ad Silver (27) show how aleraive specificaios ad weighs ca be used wihi he CPD framework o derive a umber of kow idex umber formulae. 3 Also, some homes rasac wice i a period of mohs ad ohers do o rasac for decades. 32 Sellers of properies ofe uderake reovaios ad repairs jus before puig heir properies o he marke For example, expoeiaig (2-42) i box 6 reveals ha his simple hedoic regressio model, where each housig ui has oly a sigle dummy variable characerisic, leads o a period o price idex ha is equal o he equally weighed geomeric mea of he sellig prices i period divided by he geomeric mea of he correspodig sellig prices of he mached models i period. See also de Haa (23), Silver (23) ad Silver ad Hervari (25). Diewer (25b) shows ha he uweighed idexes ca be very far from heir weighed couerpars. Thus i is impora o ru appropriaely weighed regressios for obaiig esimaes of price idexes. 32 See, for example, Case ad Quigley (99). 33 Dreima ad Peigo-Cross prese evidece of his, ad show ha he house price variace differs by price ier ad he legh of ime bewee successive sales of a propery. 3

20 W. Erwi Diewer ad Alice O. Nakamura Box 6. The CPD Model wih Icomplee Mached Model Daa Nex a model is cosidered where o every house mus rade i each period for iformaio abou he house o be icluded i he aalysis daa se. I order o miimize oaioal complexiies, Diewer (23a) provides he followig deails for he case of wo periods. Le S(,) be he se of housig uis ha sold i boh periods ad. Takig io accou he ormalizaio (2-25), he esimaig equaios correspodig o hese houses are: (2-34) l V = β + u, for S(, ), (2-35) l V = β +π + u for S(, ). Le S(, ) deoe he se of housig uis i he arge populaio ha sold i period bu o i period. The esimaig equaios for hese observaios are: m (2-36) l V m = γ + u, for m S(,~ ), m where γ m is he logarihm of he qualiy adjusme facor for he mh housig ui ha sold i period bu o i period. Similarly, le S(, ) deoe he se of housig uis i he arge populaio ha sold i period bu o i period. The esimaig equaios for hese observaios are: k (2-37) l V k = δ + u for k S(,~ ), k where is he logarihm of he qualiy adjusme facor for he kh housig ui ha sold i period bu o. δ k * * * * Le π, β, γ m ad δk deoe he LS esimaes of he parameers π, β, γ m ad δk ha appear i (2-34)-(2-37). The sacked vecor of depede variables for equaios (2-34)-(2-37) ca be wrie as he sum of he vecors of exogeous variables imes heir correspodig leas squares esimaes plus he vecor of leas squares residuals. As oed above, he ier produc of each exogeous vecor wih he vecor of LS residuals is zero. Thus he LS esimaors for he ukow parameers i he regressio model mus saisfy he followig equaios: S(,) k S(,~ ) k (2-38) l V + l V β + N(,) π + δ + N(, ~ π ; 2 * * * * * = S(,) k S(~) k ) (2-39) l V + l V = β + π, for S(, ) (2-4) l V m = γ * m, for m S(,~ ), (2-4) l V k = δ * k, for k S(,~ ), where N(,) is he umber of dwelligs ha raded i boh periods ad N(, ) is he umber ha sold i bu o * δ k. Equaios (2-4) ca be used o elimiae he i equaio (2-38), ad equaios (2-39) ca be used o * β elimiae he from equaio (2-38). The resulig equaio for π is: * (2-42) π = [/ N(,)] l[v / V ], S(,) which is he arihmeic average of he logarihms of he sales price raios for he mached models i he wo periods. For he housig uis ha sold (or were reed) i period, a more geeral hedoic regressio model is: K k k (2-43) l V = π + = z β + ε, S(). k ε is a idepedely disribued error erm wih mea ad cosa variace, (or re) of housig ui i period, z k * V * is he observed sellig price is he amou of characerisic k ha housig ui possesses, ad equals he logarihm of he cosa qualiy price idex for period, P ; i.e., π =l P for =,,,T. The parameer β rasforms amous of he kh characerisic z io cosa qualiy uiliy uis for k =,,K. k k π To correc for qualiy chage coamiaio whe usig he repea sales mehod o measure OOH price chage, oe way is o remove all observaios where available iformaio 32

21 W. Erwi Diewer ad Alice O. Nakamura suggess here have bee reovaios ha go beyod ormal upkeep. 34 Aoher aleraive is o use iformaio, whe available, abou dwellig characerisics o correc for reovaio relaed chages usig a geeral hedoic regressio model. 35 Diewer (23a; see box 5 for deails) shows how he repea sales approach ca be modified o icorporae hedoic regressio correcios for chages i observed characerisics of dwelligs sice hey were las o sold. The resulig liear regressio model (equaios (2-34)- (2-37) i box 6) is he same as he wo coury versio of Summers (973) coury produc dummy model (wih icomplee iformaio); i is also ideical o he wo period case of he Aizcorbe, Corrado ad Doms (2) dummy produc hedoic regressio model. 36 I is basic form, he hedoic mehod usually ivolves regressig he logarihm of he propery sale price o he characerisics of he propery ad a ime dummy variable for each period spaed by he esimaio daa se (excep he omied base period). Oce he esimaio has bee compleed, he ime dummy coefficies ca be expoeiaed o creae a idex. A aleraive approach o he hedoic mehod is o esimae separae hedoic regressios for boh of he periods compared; i.e., for he base ad curre period. Usig iformaio o he characerisics of he properies sold, he daa could also be sraified ad a separae regressio ca be ru for specified classes of resideial properies. Thus he hedoic regressio mehod could be used o produce a family of idexes. 37 Diewer, Heravi ad Silver (27) oulie aleraive formulaios ad esablish he relaioships amog hem. 38 A poeial advaage of he geeral hedoic regressio model is ha i uses all available observaios o housig sales i each period i a orivial way whereas he repea sales model does o use ay iformaio a all o sales ha ake place i oly oe of he sample periods. 39 I is iuiively obvious ha whe a observaio has is very ow dummy variable i a liear 34 For example, Case ad Shiller (989, pp ) use a varia of he repea sales mehod wih U.S. daa o house sales i four major ciies over he years of They aemped o deal wih he depreciaio ad reovaio problems by removig houses wih qualiy chages from he daa se. 35 A umber of hybrid approaches have bee developed over he years ha aemp o icorporae he bes of boh worlds for hedoic ad repea sales idexes. The mai obsacle o widespread accepace is usually lack of daa, bu for cusomized purposes hese iovaios ca be useful. Gazlaff ad Lig (994) esed a assessed value echique. The idea is o broade he repea sales sample o iclude sigle-sale properies by usig a assessed value i place of a secod sales value. The assessed value comes from propery ax records, ad he uderlyig assumpio is ha hose assessmes are ubiased. The OFHEO idexes are available olie a: hp:// The Freddie Mac idex is foud a: hp:// 36 See also Aizcorbe ad Pho (28) i his volume. 37 I is worh oig ha a perceived advaage of he sraificaio mehod is ha media price chages ca be measured. However, regressio esimaes ca also be derived from robus esimaors from which he parameer esimaes for he price chage will be similar o a media. 38 The coecios bewee weighed hedoic regressios ad weighed idex umber formulae are esablished i a vas lieraure icludig Diewer (23c, 24, 25b), de Haa (23), Silver (23) ad Silver ad Heravi (25). Prediced prices ca he be geeraed i each period usig he esimaed hedoic regressios based o a cosa characerisics se, such as he characerisics of he base period. A raio of he geomeric meas of he esimaed prices i each period would yield a pure price compariso based o a cosa base period se of characerisics. A hedoic idex based o cosa curre period characerisics could also be compiled, as could such idexes based o a symmeric use of base ad curre period iformaio. 39 The laer is also a feaure of he CPD model, as origially developed for ieraioal price level comparisos. 33

22 W. Erwi Diewer ad Alice O. Nakamura regressio model, he his observaio is o used o deermie ay of he oher parameers i he model. If he umached prices i he sample of housig prices behave differely ha he mached prices, he a geeral hedoic regressio model ca geerae quie differe price idexes ha models ha rely oly o mached prices. Deermiig which dwellig characerisics should be icluded is a challege whe applyig he geeral hedoic regressio model. Some variables migh be icluded as well for he household ype sice here is evidece of sysemaic dwellig maieace differeces by household characerisics such as wheher he ower occupier(s) are over 75 years of age. 4 For may daa ses, here are lierally hudreds of poeial housig ad ower/household characerisics ha could be icluded o he righ had side. 4 The variable ad fucioal form ad pre-esimaio daa poolig or sraificaio choices cosiue, i effec, he crieria uder which properies will be judged o be comparable for he measureme of he housig price level ad price level chage The Srucures ad Lad Decomposiio Problem 43 Usually he logarihm of he purchase price is ake as he depede variable i real esae price models. While his specificaio accords wih he direcly observable propery price iformaio, i is icosise wih cerai aspecs of he srucure ad lad compoes of he price of a propery. As Diewer (23a, 26a) explais, resideial real esae is ypically a composie good; i.e., wo disic commodiies are budled ogeher ad sold (or reed) a a sigle price. The wo disic commodiies are: () he srucure, ad (2) he lad ha he srucure sis o (he sie). To model his composie, cosider a sample of dwellig uis 4 The Federal Housig Admiisraio (FHA) isures reverse morgages, called Home Equiy Coversio Morgages (HECM), which allow older owers o cover house equiy io cash. The owers do o eed o pay off he reverse morgages uil hey move or permaely leave heir homes, ad he he propery is sold o pay off he loa. These morgages help older owers afford o say o i heir homes. Privae leders had bee reluca o offer reverse morgages a affordable raes due o he uceraiy of repayme. Wihou a reverse morgage beig ivolved, a ower has a fiacial iceive o sped o maieace whe ha spedig ca be expeced o icrease he house value ad ower equiy. However, if he ower has a reverse morgage, he ower cao beefi fiacially uless hey are allowed o icrease heir borrowig agais he house value if reovaios cause he house o appreciae. I fac, he ower s fiacial iceives are o miimize maieace spedig uless his hreaes o shore how log hey ca say i he home. See Davidoff ad Welke (24). Also, based o esimaios from he Healh ad Reireme Survey (HRS), Rodda ad Parabash (25) repor ha he house values of elderly (75 years or more) owers appreciae i real erms a. o.2 perceage pois less per year ha he houses of middle-aged (5 o 74 year old) owers. These esimaes are smaller ha he fidigs by Davidoff (24) who used he America Housig Survey o show 3 perceage poi slower appreciaio for owers aged more ha 75 relaive o all oher owers. The mos direc explaaio for he older ages discou is ha he homes of older owers are ouof-dae i syle ad frequely poorly maiaied. Wihou regular maieace ad occasioal remodellig, a house ges discoued i he marke compared o ewer homes ha mach buyers prefereces. 4 Buler (982) ad Ozae ad Malpezzi (985) demosrae ha coefficie esimaes are o ormally robus wih respec o omied variables, bu he idex oucomes may be more robus. See Li, Prud homme ad Yu (27), ad also Diewer, Heravi ad Silver (27). 42 Aoher problem ha has o bee discussed is he possibiliy ha house sale prices migh exhibi seasoal flucuaios. The geeral hedoic regressio model could be modified o iclude seasoal dummy variables. 43 Discussios bewee Erwi Diewer ad Ae Laferrère helped improve he preseaio of he model here. 34

23 W. Erwi Diewer ad Alice O. Nakamura purchased a he begiig of period. Suppose he purchase price of propery is p, where here ad i box 7 we absrac from depreciaio ad propery age issues (so here is o sub v). The value for propery ca be regarded as he sum of he (ofe uobserved) cos per square meer for he srucure, imes he floor space of he srucure i square meers (deoed by A i box 7), plus he price per square meer of lad (ofe o direcly observed) imes he area of he sie i square meers (deoed by B i box 7). For period, he propery value ca be represeed as i equaio (2-45) i box 7, ad for period, he value for his propery ca be represeed as i equaio (2-46). The srucure ad lad compoes are usually subjec o differe raes of iflaio, ad he depreciaio raes will usually differ oo sice lad depreciaes lile if a all (hough here ca be depreciaio of sie ifrasrucure such as draiage works). The asse iflaio ad depreciaio effecs are embedded i he coefficies of A ad B. 44 Esimaig equaios are give by (2-47) ad (2-48) i box 7. If daa are available for he characerisics of he srucure ad he lad, he he pair of equaios show i (2-49) ad (2-5) ca be esimaed isead. This model is flexible ad provides a meas of decomposig a propery price idex io srucural ad lad compoes (hough he model is highly oliear). 6. Furher Thoughs o User Coss versus Real Equivalece Doughery ad va Order (982), who helped popularize he user cos approach i he real esae lieraure, sae ha, i a compeiive ecoomy, he per period user cos should be equal o he per period real price charged for a dwellig by a profi maximizig ladlord. Thus, he observable real value is assered o equal he user cos. Ad Cecchei (27) wries ha: [Ower equivale re] really is he curre opporuiy cos of he house. I measures he icome I could receive if I were o vacae my curre livig space ad re i o someoe else. However, we argued i secio 2.5 ha he usual user cos referred o above by Cecchei is o quie he full opporuiy cos of he house; he full opporuiy cos is he maximum of he user cos ad he marke re ha he house could fech. We also saw earlier ha here is a cosiderable amou of empirical evidece ha he usual user coss ad marke res do o always closely approximae each oher. I fac, Garer ad Verbrugge (28) claim o show ha res ad propery values someimes move quie differely: 45 Wha is he per period cos of owig a durable good? For log lived durable goods, here are wo commoly proposed measures: re, ad user coss. I simple fricioless heory, hese measures are equivale. Ye here ad i Verbrugge (26) we demosrae ha, i he U.S. housig daa, hese measures diverge markedly, over exeded periods of ime Muliplicaive errors wih cosa variaces are more plausible ha addiive errors wih cosa variaces; i.e., i is more likely ha expesive properies have relaively large errors compared o very iexpesive properies. 45 See Verbrugge (26) who discussed (ad dismissed) a possible aleraive explaaio for his divergece. 35

24 W. Erwi Diewer ad Alice O. Nakamura Box 7. Srucure ad Lad Decomposiio Suppose he oal cos, p, of a propery afer he srucure is compleed will equal he floor space area of he srucure, say A square meers, imes he buildig cos per square meer, α say, plus he cos of he lad, which will equal he cos per square meer, β say, imes he area of he lad sie, B. Now hik of a sample of properies of he p same geeral ype, wih prices,, i period ad srucure areas ad lad areas B for =, K,N(), ad A where hese prices are equal o coss of he above ype imes error erms η which have mea. This leads o a hedoic regressio model for period where α ad β are he parameers o be esimaed i he regressio: ] (2-45) p = [ αa +βb η. Takig logarihms of boh sides of (2-45) leads o he followig radiioal addiive errors regressio model: ] (2-46) l p = l[ αa +βb + ε, where he ew error erms, ε lη for =, K,N(), are assumed o have meas ad cosa variaces. For a subseque period, he price per square meer for he give ype of srucure will have chaged from α o αγ ad he lad cos per square meer will have chaged from β o βδ where γ is he period o price idex for he ype of srucure ad δ as he period o price idex for he lad ha is associaed wih his ype of srucure. For =, K,N(), he period couerpars o (2-45) ad (2-46) are: ] (2-47) p = [ αγ A +βδ B η ad (2-48) l p = l[ αγ A +βδ B + ε, ] p where ε lη, he period propery prices are, ad he srucure ad lad areas are ad. Diewer (26a) suggess ha equaios (2-46) ad (2-48) ca be ru as a sysem of oliear hedoic regressios. The mai parameers of ieres are γ ad δ, which ca be ierpreed as period price idexes (relaive o he correspodig period price levels of ) for he price of a square meer of his ype of srucure ad he price per meer squared of he uderlyig lad. This framework ca be geeralized o ecompass he radiioal array of characerisics used i real esae hedoic regressios. Suppose ha we ca associae wih each propery ha is rasaced i a lis of K price deermiig characerisics characerisics X,X 2, K, XK Y,Y 2, K, YM A B for he srucure ad a similar lis of M price deermiig for he ype of lad. The equaios ha geeralize (2-46) ad (2-48) are: K M = k = k k m = m m }, K,N() (2-49) l p l{[ α + X α ]A + [ β + Y β ]B + ε, = ad K M = k = k k m = m m } ) (2-5) l p l{ γ [ α + X α ]A +δ [ β + Y β ]B + ε, =, K,N(, where he parameers o be esimaed are ow he K+ qualiy of srucure parameers, α, α, K α, he M+, qualiy of lad parameers, β, β, K β, he period price idex for srucures parameer γ ad he period price, M idex for he lad uderlyig he srucures parameer δ. Noe ha [ K + X ] i (2-49) ad (2-5) α k = k αk replaces he sigle srucures qualiy parameer α i (2-46) ad (2-48) ad [ + M Y β m ] i (2-49) ad (2-5) replaces he sigle lad qualiy parameer β i (2-46) ad (2-48). β m = m K 36

25 W. Erwi Diewer ad Alice O. Nakamura How do Garer ad Verbrugge (28) ad Verbrugge (26) arrive a he above coclusios? The key is he user cos forecasig equaio from Verbrugge s 26 paper. He 46 sars off wih he followig expressio for he user cos u i of home i: (2-6) ui = Pi (i + δ Eπi ) where P i is he price of home i i period ; i is a omial ieres rae; 47 δ is he sum of aual depreciaio, maieace ad repair, isurace, propery axes ad poeially a risk premium; ad Eπ i is he period expeced aual (cosa qualiy) home appreciaio rae for home i. Thus he resulig user cos ca be viewed as a opporuiy cos measure for he aual cos of owig a home sarig a he begiig of he quarer idexed by ime. Presumably, ladlords, whe hey se a aual re for a dwellig ui, would use a formula similar o (2-6) i order o deermie he re for a ea. 5 So far, here is ohig paricularly coroversial abou Verbrugge s aalysis. Wha is coroversial is his deermiaio of he expeced house price appreciaio erm, Eπ i. Verbrugge (26, p. 2) wries ha: Raher ha usig a crude proxy, I will cosruc a forecas for Eπ i... Verbrugge goes o o use various ecoomeric echiques o forecas expeced price appreciaio for his oe year horizo. He isers hese forecass io he user cos formula (2-6) above ad obais remedously volaile ex ae user coss, ad he res of his coclusios follow. Diewer (26a, pp ) gives wo reasos why i is ulikely ha ladlords se heir real raes based o shor erm forecass of housig price appreciaio. His firs reaso is ha housig eure daa reveal ha a ypical ower occupier holds heir propery for 6 o 2 years. Give his ad he kow coss for households of movig (icludig o moeary coss such as disrupig he friedship ad school siuaios of childre), he argues ha owers ca be expeced o pla usig i erms of a aualized average rae of price appreciaio averaged over a leas 6 years. I coras, he Verbrugge (26) ad Garer ad Verbrugge (28) sudies esimae a propery appreciaio rae based o a oe year ime horizo. Diewer (23a) suggess ha oe mehod for reducig he volailiy i he user cos formula is o replace he omial ieres rae less expeced price appreciaio erm ( i log ru average real ieres rae, r say. This is wha is doe i Icelad. 5 Eπ i ) by a cosa or a slowly chagig 46 See formula () i Verbrugge (26, p. ). His oaio is o followed exacly here. 47 Verbrugge (26, p. ) used eiher he curre 3 year morgage rae or he average oe year Treasury bill rae ad oed ha he choice of ieres rae ured ou o be icosequeial for his aalysis. 48 Verbrugge (26, p. 3) assumed ha δ was approximaely equal o 7 %. 49 π i is he acual 4 quarer (cosa qualiy) home price appreciaio bewee he begiig of period ad oe year from his period. 5 Diewer (23a) oed ha here would be a few differeces bewee a user cos formula for a ower occupier as compared o a ladlord bu hese differeces are o impora for Verbrugge s aalysis. 5 See Guðaso ad Jósdóir (28, chaper 5, his volume). 37

26 W. Erwi Diewer ad Alice O. Nakamura Diewer also argues ha i is ulikely ha ladlords use ecoomeric forecass of housig price appreciaio oe year away ad adjus res for heir eas every year based o hese forecass. Teas do o like remedous volailiy i heir res, wries Diewer (23a). 52 I is however possible ha ladlords may have some idea of he log ru average rae of propery iflaio for he ype of propery ha hey maage ad his log ru average aual rae of price appreciaio could be isered io he user cos formula (2-6). Gordo ad va Goehem (24) oe ha real rae sickiess has bee show o be paricularly grea for eas coiuig o from he previous year, which is he case for he majoriy of eas. 53 Gordo ad va Goehem (24) argue oo ha socieal ad poliical forces have resuled i ax laws ha rasfer he beefis of capial gais o ladlords, a leas i he shor ru. 54 They muse ha we migh expec, i he log ru, ha capial gais o real properies, as well as ax deducios available o ladlords, would raslae io icreasig supplies ad fallig real real raes. Ye Gordo ad va Goehem (24) cie evidece ha his raslaio has bee akig place slowly, whe a all, i mos localiies i he Uied Saes. Gordo ad va Goehem (24) go o o sae ha hey have, everheless, fially foud a covicig explaaio i a paper by Díaz ad Luego-Prado (23) for sicky re behaviour. The basic hesis of he Díaz ad Luego-Prado paper is ha adjusme coss, uceraiy, ax deducibiliy, dow payme perceages, ad discou raes preve mos Americas who are reers from swichig o owed accommodaios, hereby makig i uecessary for ladlords o reduce heir res o hold hese eas. 55 This coclusio is referred o by Gordo ad va Goehem (24) as a covicig explaaio of a fudameal puzzle Diewer (26a, p. 24) wries ha i is everheless also possible ha ladlords may have some idea of he log ru average rae of propery iflaio for he ype of propery ha hey maage ad his log ru average aual rae of price appreciaio could be isered io he user cos formula. 53 See, for example, he fidigs of Geesove (999). Also, Hoffma ad Kurz-Kim (26, p. 5) repor he followig: I Germay, as i oher euro area couries, prices of mos producs chage ifrequely, bu o icremeally... I our sample, prices las o average more ha wo years... bu he chage by early %. The loges price duraios are foud for housig res, which, o average, are for more ha four years. Ad also, Hoffma ad Kurz-Kim (26, p.5) fid ha Germa res are chaged oly oce every 4 years o average: I Germay, as i oher euro area couries, prices of mos producs chage ifrequely, bu o icremeally. Pricig seems o be eiher coiuous or margial. I our sample, prices las o average more ha wo years -- if price chages wihi a moh are o cosidered -- bu he chage by early %. The loges price duraios are foud for housig res, which, o average, are for more ha four years. 54 Siai ad Souleles (23) argue ha re risk is aoher reaso why mos households idicae by heir choices ad o surveys ha hey would prefer o be i owed housig. The uderlyig model is a eure choice model i which he reer faces ucerai re chages each year bu o risk of capial loss whe he reer moves. Owers, o he oher had, ca avoid ucerai aual icreases by purchasig a house wih a fixed rae morgage. There is sill he risk of capial loss whe he ower fially sells he propery, bu he loger he holdig period he more ha fuure risk is discoued. Moreover, he ower oly faces ha risk a he ed of he holdig period, whereas he reer faces some ogoig risk of re icreases, wih he aure of his risk beig loosely bouded by formal real agreemes, cusoms, ad ladlord fears of re corols. The reer s risk is ha res will go up ad he ower s risk is ha prices will go dow. Siai ad Souleles (23) claim o show ha re risk domiaes house price risk, which meas households use owership o shield agais re icreases. I fiace laguage, households ca hedge agais re risk by buyig heir home. The demad for homeowership icreases wih he expeced holdig period ad he cumulaive re volailiy (i.e., re volailiy durig he holdig period), bu decreases wih house price volailiy. 55 Gordo ad va Goehem (24) remid us ha a large proporio of reers are youg, have o ye saved he dow payme ecessary for home owership, move oo ofe o allow he advaages of home owership o offse rasiio coss, ad are subjec o capial marke cosrais based o heir curre icomes ad poor credi hisories. 38

27 W. Erwi Diewer ad Alice O. Nakamura As we udersad heir resuls, however, he Díaz ad Luego-Prado coclusios, if correc, oly provide a explaaio for dowward re sickiess; heir resuls do o provide a aswer o he quesio of wha keeps ladlords from raisig res much more, ad more frequely, ha hey are geerally observed o do. We sugges wo possible fear facors ha migh explai upward re sickiess. Oe is ha, whe real markes become igh ad res sar o rise, he possibiliy of re corols beig eaced or sregheed is a ever prese hrea for ladlords. Oce re corols are brough i, i ca ake years or eve decades for oppoes o ge rid of hem agai. A secod is ha he ofe ivisible had of reer rage could be a ifluece o ladlords i seig real raes, eve for icumbe eas How We See he Opios For official saisicias who are persuaded ha sheler should be icluded i a CPI, icludig ower occupied sheler, ad who are persuaded of he meris of pricig he use of sheler services raher ha he acquisiio or purchase of properies, he evidece ad argumes covered i his paper sugges he followig choices, depedig o he measureme objecives. For a aio ieresed i producig a sigle aioal CPI ha reflecs he cosumpio price experiece for a represeaive (e.g., a media) household, i seems o us ha he opporuiy cos approach is he mos saisfacory oe. There are wo disic opporuiy coss associaed wih home owership, amely () he fiacial opporuiy cos which is he radiioal user cos cocep ad (2) he opporuiy cos of reig ou he dwellig ui which is he marke equivale re cocep. Aleraively, i recogiio of he large role ha housig owership saus plays i shapig oher household cosumpio opios ad paers, he kow barriers o moveme io owed housig for may reers, ad he low raes of rasiio from reig o owig or from owig o reig for mos demographic groupigs of aduls, a aio could produce separae CPI idexes for households, depedig o heir real or ower occupier saus i he previous ime period. The compoe for reers would simply follow res as he mai sheler price iformaio. For ower occupiers, our preferred reame is he opporuiy cos approach, reaig he effecive opporuiy cos of OOH as he maximum of he fiacial ad real opporuiies coss. I addiio, of course, i would be useful for saisical agecies o also produce series based o he radiioal user cos ad real equivalece approach as well as o he acquisiios approach for ieraioal comparabiliy purposes, i he spiri of he Saisics Caada aalyic 56 Empirical evidece suggess ha real properies depreciae faser ha ower occupied dwelligs. The damage deposis ladlords demad are o sufficie o cover he damages ha some eas iflic, ad ea grievace procedures ofe make i difficul for ladlords o keep he damage deposis eve whe here is damage. I is well documeed ha ladlords are more likely o icrease res, ad more likely o isiue bigger re icreases, for ew eas. However, ladlords may face some of he same resrais as employers ieresed i isiuig lower wage scales for ewly hired workers. Whe he ew eas move i, if he propery has icumbe eas as well, he ew oes will soo lear wha he real codiios are for hose who came earlier. Tea rage ca ake may forms ha ladlords may fid difficul o preve or obai compesaio for. 39

28 W. Erwi Diewer ad Alice O. Nakamura series program described by Baldwi, Nakamura ad Prud homme (28). Daa permiig, boh he reer ad he ower occupier CPI compoes should be qualiy adjused usig hedoic mehods. Appedix A. Early Developmes i he Accouig Treame of Depreciaio The earlies accouig professio approaches o depreciaio were based o appraisals. I he early 9s, Middledich (98) devised a mehod for cosrucig a curre value a he ed of a accouig period. Suppose a asse was purchased ew a he begiig of accouig period a he price p, ad ha his asse is subjec o a period depreciaio rae of δ ad a geeral rae of price iflaio over period of r ; i.e., he geeral price level a he ed of he period divided by he geeral price level a he begiig of he period is + r. The he hisorical cos accouig value of he asse a he ed of he period is ( + r )p, bu he Geeral Price Level Adjused (GPLA) value is: V GPLA ( δ )( + r ) p. Noe he differece bewee r, a ex pos geeral iflaio rae, ad he asse specific aicipaed iflaio rae i defied as ( + i ) p / p where p ad p are he price of he same asse a he begiig ad ed of he accouig period. I geeral, r will o equal i ad hece he GPLA value for he asse will o equal is ed of period marke value (uless he geeral iflaio rae r is equal o he asse specific iflaio rae i ). This is he mai weakess of Geeral Price Level Adjused accouig. However, is sregh is ha i will adjus for he effecs of geeral iflaio. There is also he issue of how o choose he geeral iflaio rae r. Oe of he simples choices is o use he iflaio rae for a widely raded commodiy (such as gold) as he idex of geeral iflaio. Aoher aleraive is o use he rae of icrease i he exchage rae of he coury agais a sable currecy. Isead of usig he price of gold or ay sigle commodiy as he idicaor of iflaio, he geeral iflaio bewee he begiig ad he ed of he accouig period migh be beer capured by lookig a he price chage of a represeaive baske of goods. As a furher refieme, we could replace a fixed baske price idex by a more geeral idex such as he Fisher (922), which allows for subsiuio i respose o price chages. The specific price level mehod for cosrucig curre values for a asse held by a busiess ui hrough successive accouig periods was suggesed by Daies (929, p. ), Sweeey (934, p. ) ad may oher accouas. 57 The mehod works as follows. Firs, 57 Iasmuch as he price level is o sable for ay grea legh of ime, ad sice his calculaio is coemplaed for each fiscal period, he oly feasible procedure for a compay wih housads of asses is he use of price idex umbers Bell (953, p. 49). Where o marke exiss for ew fixed asses of he ype used by he firm, wo meas of measurig curre coss are available: () appraisal, ad (2) he use of price idex umbers for like fixed asses o adjus he origial cos base o he level which would ow have o be paid o purchase he asse i quesio. 4

29 W. Erwi Diewer ad Alice O. Nakamura asses held by he busiess ui a he begiig of period are classified io a fiie umber of disic asse classes. Secodly, i is supposed ha idex umbers ha perai o each asse class are available a he begiig ad ed of each accouig period. Fially, suppose ha a asse 58 was purchased a he begiig of accouig period a he price p, he period depreciaio rae is δ ad he asse iflaio rae for he releva asse class over period is i (i.e., he specific asse idex umber a he ed of he period divided by he specific asse idex umber a he begiig of he period is ( + i ) ). The he Specific Price Level Adjused (SPLA) value of he asse a he ed of period is defied as: VSPLA ( δ )( + i ) P. The prese specific price idex umber mehod for cosrucig a ed of period esimaed asse value is very similar o he Geeral Price Level Adjused asse value; he oly differece is ha ow a presumably more releva specific price idex is used for revaluaio purposes. Appedix B. The Use of Assessme Iformaio Mos couries ax real esae propery. Hece, mos couries have some sor of official valuaio office ha provides periodic appraisals of all axable real esae propery. Va der Wal, er Seege ad Kroese (26) describe how Saisics Neherlads uses appraisal iformaio i order o cosruc a propery price idex. The SPAR (Sales Price Appraisal Raio) Mehod has also bee used i New Zealad sice he early 96s. 59 I makes use of mached pairs, bu ulike he repea sales mehod, he SPAR mehod uilizes early all he available rasacios daa, ad hece should be less proe o sample selecio bias. (See box 8 for deails.) The firs measure i each pair is he official goverme appraisal of he propery, while he secod measure is he machig rasacio price. The raio of he sale price ad he appraisal of all sold dwelligs i he base period, =, serves as he deomiaor. The umeraor is he raio of he sellig price of he referece period, =, ad he appraisal for he base period of all dwelligs ha have bee sold i he referece period. Oher varias of a SPAR ype idex ca be defied. Diewer (26a) defies he (regular) Duo, Carli ad Jevos Marke Value o Appraisal idexes ad discusses heir aleraive meris. These appraisal mehods rely o assessme iformaio i he base period ad sales iformaio i he curre period. The assessme mehods use much more iformaio ha he repea sales mehod. The aalys eed o have separae iformaio o housig or srucure characerisics i order o impleme his mehod. Raher, he iformaio qualiy of hese mehods ress o he qualiy of he iformaio ad mehods of he assessme auhoriy. Edwards ad Bell (96, p. 86). See also Chambers (965). For moder mehods, see Chiloy (98) ad Chiloy ad Megbolugbe (997). 58 More geerally, p ca be he esimaed begiig of period curre value for he asse. 59 For more deail, see Bourassa, Hoesli ad Su (26). For maerial o appraisal qualiy, see Leveis (26). 4

30 W. Erwi Diewer ad Alice O. Nakamura Box 8. A Mehod for Makig Use of Assessme Daa Deoe he umber of sales of a give ype of real esae i he base period by N(), he sales prices by,p 2,,pN() ] p 2 N() A [ p K, ad he correspodig official appraisal prices by [ A,A, K,A ]. The umber of sales of he same ype of propery i he curre period is deoed by N(), he sales prices are deoed as,p2,,pn() ] p 2 AN() [ p K, ad he correspodig official appraisal prices are deoed by [ A,A, K, ] A. The value weighed SPAR idex (va der Wal, er Seege ad Kroese 26, p. 4) ca be wrie as: N() N() N() N = = = = () DSPAR i i i i i i i (2-5) P [ p / A ]/[ p / A. I he subscrip for he idex defied by (2-5), he D sads for Duo, sice he idex formula o he righ had side is closely relaed o he Duo formula ha occurs i elemeary idex umber heory. More specifically, if N() N() i= i= he erm A / A equals, he he idex reduces o a Duo idex (see ILO e al. 24, chaper 2.). Diewer (26a) suggess ha oe way o jusify (2-5) is o suppose ha he value p for each propery rasaced i period equals a commo price level for ha propery ype, P say, imes a qualiy adjusme facor, ha: Q (2-52) p = P, =,2, K,N()., so Q Nex, we assume ha he period assessed value for rasaced propery =,2, K,N(), deoed by, is equal o he commo price level P imes he qualiy adjusme facor imes a idepedely disribued error erm, wrie as + ε, where i is likely ha he expeced value for each of he error erms is. This sochasic specificaio reflecs he fac ha he errors are more likely muliplicaive raher ha addiive. Thus: (2-53) A = P Q (+ ε ), wih he error erms havig zero expecaios; i.e.: (2-54) ε =. E Suppose ow ha he value p Q he propery ype, P say, imes a qualiy adjusme facor, say, so ha: i i (2-55) p =P Q. A for each propery rasacio i period equals a commo price level for Q Nex, suppose ha he period assessed value for propery i i period, A i, equals he period price level imes he qualiy adjusme facor, Q i, imes a idepedely disribued error erm, deoed by + ε i. I is o loger likely ha he expeced value of he error erm is equal o sice he base period assessmes cao pick up ay depreciaio ad reovaio biases ha migh have occurred bewee periods ad. Thus: i i (2-56) A = P Q (+ ε ). i Our goal is o obai a esimaor for he level of propery prices i period relaive o period, which is P / P. Defie he share for propery i oal value of properies rasaced i period, s, as follows: k N = ( ) p k (2-57) s p /. Similarly, defie he share of propery i i period o he oal value of properies rasaced i period, i i k N = ( ) k (2-58) s p / p i=,2, K,N() Now subsiue (2-52)-(2-56) io defiiio (2-5), use defiiios (2-57) ad (2-58), ad we obai: P [ N() P Q / N() P Q ( )]/[ N() P Q / N() DSPAR = i = i i = i +εi = k = P Q (+ ε )] N() N() = k = k = (2-59) [P / P ][+ s ε ]/[+ s ε ]. s i, as: P 42

31 W. Erwi Diewer ad Alice O. Nakamura Refereces Aizcorbe, A., C. Corrado ad M. Doms (2), Cosrucig Price ad Quaiy Idexes for High Techology Goods, Idusrial Oupu Secio, Divisio of Research ad Saisics, Board of Goverors of he Federal Reserve Sysem, July. Aizcorbe, A. ad Y. Pho (28), Differeces i Hedoic ad Mached-Model Price Idexes: Do he Weighs Maer? i W.E. Diewer, B.M. Balk, D. Fixler, K.J. Fox ad A.O. Nakamura (eds.) (28), Price ad Produciviy Measureme, Volume 5: Hedoics, Trafford Press. Ae, B. ad T.A. Meezes (22), Povery Price Levels: A Applicaio o Brazilia Meropolia Areas, Coferece o he Ieraioal Compariso Program, -5 March, 22, Washigo DC, World Bak. Bailey, M.J., R.F. Muh ad H.O. Nourse (963), A Regressio Mehod for Real Esae Price Cosrucio, Joural of he America Saisical Associaio 58, Baldwi, A., A.O. Nakamura ad M. Prud homme (28), Differe Coceps for Measurig Ower Occupied Housig Coss i a CPI: Saisics Caada s Aalyical Series, chaper 9 i W.E. Diewer, B.M. Balk, D. Fixler, K.J. Fox ad A.O. Nakamura (eds.) (28), Price ad Produciviy Measureme, Volume : Housig, Trafford Press. Beay, T.K.M., E.R. Larse, ad D.E. Sommervoll (27), The Price of Housig: Measurig he Price of Housig Cosumpio for Self-Owers i he CPI, workig paper, hp:// Becker, G.S. (964), Huma Capial: A Theoreical ad Empirical Aalysis wih Special Referece o Educaio, Naioal Bureau of Ecoomic Research. Becker, G.S. (976), The Ecoomic Approach o Huma Behavior, Uiversiy of Chicago Press. Beidelma, C.R. (973), Valuaio of Used Capial Asses, America Accouig Associaio. Bell, A.L. (953), Fixed Asses ad Curre Coss, Accouig Review 28, Böhm-Bawerk, E. V. (89), The Posiive Theory of Capial, W. Smar (raslaor of he origial Germa book published i 888), G.E. Secher. Bourassa, S.C., M. Hoesli ad J. Su (26), A Simple Aleraive House Price Idex, Joural of Housig Ecoomics 5, Buler, R.V. (982), The Specificaio of Hedoic Idexes for Urba Housig, Lad Ecoomics 58 () Feb., Caig, J.B. (929), The Ecoomics of Accouacy, Roald Press Compay. Capozza, D.R., R.D. Israelse ad T.A. Thomso (25), Appraisal, Agecy ad Aypicaliy: Evidece from Maufacured Homes, Real Esae Ecoomics, 33(3), Case, B. ad J.M. Quigley (99), The Dyamics of Real Esae Prices, Review of Ecoomics ad Saisics 73 (), Case, K.E. ad R.J. Shiller (989), The Efficiecy of he Marke for Sigle Family Homes, America Ecoomic Review 79, Cecchei, S. (27), Housig i Iflaio Measureme, hp:// Ceral Saisics Office Irelad (23), House Prices ad he Cosumer Price Idex: Explaaory Noe, hp:// Chambers, R.J. (965), Edwards ad Bell o Busiess Icome, Accouig Review 4, Chiloy, P. (98), The Effec of Maieace o he Measureme of Depreciaio o Housig, Joural of Urba Ecoomics 7, Chiloy, P., M. Cho ad I.F. Megbolugbe (997), Appraisals, Trasacios Iceives ad Smoohig, Joural of Real Esae Fiace ad Ecoomics 4(), Chrisese, A.-K., J. Dupo ad P. Schreyer (25), Ieraioal Comparabiliy of he Cosumer Price Idex: Ower-Occupied Housig, preseed a he OECD Semiar, Iflaio Measures: Too High -- Too Low -- Ieraioally Comparable? Paris 2-22 Jue. Chrisese, L.R. ad D.W. Jorgeso (969), The Measureme of U.S. Real Capial Ipu, , Review of Icome ad Wealh 5,

32 W. Erwi Diewer ad Alice O. Nakamura Chrisese, L.R. ad D.W. Jorgeso (973), Measurig he Performace of he Privae Secor of he U.S. Ecoomy, , i M. Moss (ed.), Measurig Ecoomic ad Social Performace, Columbia Uiversiy Press, Corrado, C., C. Hule ad D Sichel (25), Measurig Capial ad Techology: A Expaded Framework, i C. Corrado, J. Haliwager ad D. Sichel (eds.), Measurig Capial i he New Ecoomy, Uiversiy of Chicago Press, -45. Cour, A.T. (939), Hedoic Price Idexes wih Auomoive Examples, i The Dyamics of Auomobile Demad, Geeral Moors Corporaio, Croe T.M., L.I. Nakamura ad R. Voih (2), Measurig Housig Services Iflaio, Joural of Ecoomic ad Social Measureme 26, Croe, T.M., L.I. Nakamura ad R.P. Voih (28), Hedoic Esimaes of he Cos of Housig Services: Real ad Ower Occupied Uis, chaper 4 i W.E. Diewer, B.M. Balk, D. Fixler, K.J. Fox ad A.O. Nakamura (eds.) (28), Price ad Produciviy Measureme, Volume : Housig, Trafford Press. Daies, H.C. (929), The Chagig Objecives of Accouig, Accouig Review 4, 94-. Daiels, M.B. (933), The Valuaio of Fixed Asses, Accouig Review 8, Davidoff, T. (24), Maieace ad he Home Equiy of he Elderly, Haas School of Busiess Workig Paper, UC Berkeley, February 25. Davidoff, T. ad G. Welke (24), Selecio ad Moral Hazard i he Reverse Morgage Idusry, Haas School of Busiess, UC Berkeley, July 5. Deao, A, J. Friedma ad V. Alaas (24), Purchasig power pariy exchage raes from household survey daa: Idia ad Idoesia, paper preseed a he World Bak Semiar o Global Povery Measureme, Jauary, 24, Washigo DC. de Haa, J. (23), Direc ad Idirec Time Dummy Approaches o Hedoic Price Measureme, paper preseed a he 7 h Oawa Group Meeig, Paris, May hp:// Diaz, A. ad M.J. Luego-Prado (26), Durable Goods ad he Wealh Disribuio, workig paper. hp:// Diewer, W.E. (974), Ieremporal Cosumer Theory ad he Demad for Durables, Ecoomerica 42, Diewer, W.E. (98), Aggregaio Problems i he Measureme of Capial, i D. Usher (ed.), The Measureme of Capial, Uiversiy of Chicago Press, Diewer, W.E. (22), Harmoized Idexes of Cosumer Prices: Their Cocepual Foudaios, Swiss Joural of Ecoomics ad Saisics 38, hp:// Diewer, W.E. (23a), The Treame of Ower Occupied Housig ad Oher Durables i a Cosumer Price Idex, Discussio Paper 3-8, Deparme of Ecoomics, Uiversiy of Briish Columbia. hp:// Forhcomig i W.E. Diewer, J. Greeless ad C. Hule (eds.), Price Idex Coceps ad Measureme, NBER Sudies i Icome ad Wealh, Uiversiy of Chicago Press. Diewer, W.E. (23b), Hedoic Regressios: A Cosumer Theory Approach, i R.C. Feesra ad M.D. Shapiro (eds.), Scaer Daa ad Price Idexes, Sudies i Icome ad Wealh, Volume 64, NBER ad Uiversiy of Chicago Press, hp:// Diewer, W.E. (23c), Hedoic Regressios: A Review of Some Uresolved Issues, paper preseed a he 7 h Meeig of he Oawa Group, Paris, May hp:// Diewer, W.E. (24), O he Sochasic Approach o Likig he Regios i he ICP, Discussio Paper 4-6, Deparme of Ecoomics, Uiversiy of Briish Columbia, November. hp:// Diewer, W.E. (25a), The Measureme of Busiess Capial, Icome ad Performace, a uorial preseed a he Uiversiy Auooma of Barceloa, Spai, Sepember 2-22, 25. hp:// Diewer, W.E. (25b), Weighed Coury Produc Dummy Variable Regressios ad Idex Number Formulae, Review of Icome ad Wealh 5(4), hp:// 44

33 W. Erwi Diewer ad Alice O. Nakamura Diewer, W.E. (25c), Issues i he Measureme of Capial Services, Depreciaio, Asse Price Chages ad Ieres Raes, pp i Measurig Capial i he New Ecoomy, C. Corrado, J. Haliwager ad D. Sichel (eds.), Chicago: Uiversiy of Chicago Press. Diewer, W.E., (26a), The Paris OECD-IMF Workshop o Real Esae Price Idexes: Coclusios ad fuure Direcios. Paper preseed a he OECD-IMF Workshop o Real Esae Price Idexes held i Paris, 6-7 November 26. hp:// Diewer, W.E. (26b), Adjace Period Dummy Variable Hedoic Regressios ad Bilaeral Idex Number Theory, Aales d écoomie e de saisique 79/8, -28. hp:// Diewer, W.E., S. Heravi ad M. Silver (27), Hedoic Impuaio Idexes versus Time Dummy Hedoic Idexes, forhcomig i W.E. Diewer, J. Greeless ad C. Hule (eds.), Price Idex Coceps ad Measureme, NBER Sudies i Icome ad Wealh, forhcomig Uiversiy of Chicago Press. Diewer, W.E. ad D.A. Lawrece (2), Progress i Measurig he Price ad Quaiy of Capial, i L. J. Lau (ed.), Ecoomerics Volume 2: Ecoomerics ad he cos of Capial: Essays i Hoor of Dale W. Jorgeso, MIT Press, Diewer, W.E. ad F.C. Wykoff (28), Depreciaio, Deerioraio ad Obsolescece whe here is Embodied or Disembodied Techical Chage, forhcomig i W.E. Diewer, B.M. Balk, D. Fixler, K.J. Fox ad A.O. Nakamura (eds.) (28), Price ad Produciviy Measureme, Volume 9: Capial, Trafford Press. Also available a hp:// Doughery, A. ad R. Va Order (982), Iflaio, housig cos ad he cosumer price idex, America Ecoomic Review, 72, Dreima, M.H. ad A. Peigo-Cross (24), Aleraive Mehods of Icreasig he Precisio of Weighed Repea Sales House Prices Idices, Joural of Real Esae, Fiace ad Ecoomics 28 (4), Edwards, E.O. ad P.W. Bell (96), The Theory ad Measureme of Busiess Icome, Uiversiy of Califoria Press. Eiglsperger, M. (26), The Treame of Ower-Occupied Housig i he Harmoised Idex of Cosumer Prices, preseed a he workshop o CPI Measureme: Ceral Baks Views ad Cocers, Bak for Ieraioal Selemes i Basel, Swizerlad. Europea Commuiies (24), HARMONIZED INDICES OF CONSUMER PRICES (HICPs): A SHORT GUIDE. hp://epp.eurosa.ec.europa.eu/poral/page?_pageid=274,,274_658299&_dad=poral&_schema=po RTAL#GUIDE Europea Parliame (996), Housig Policy i he EU Member Saes, Direcorae Geeral for Research, Workig Docume, Social Affairs Series, W 4. hp:// Eurosa (2), Hadbook o Price ad Volume Measures i Naioal Accous. Eurosa (27), 6ST MEETING OF THE STATISTICAL PROGRAMME COMMITTEE, Iem of he Ageda, Progress repor o Ower-Occupied Housig, Theme 55, LUXEMBOURG, 5 FEBRUARY 27. hp://epp.eurosa.ec.europa.eu/pls/poral/docs/page/pgp_ds_hicp/tab658298/cps% EN%2-%2OOH%2PROGRESS%2REPORT-REVTABLE.PDF Fisher, I. (897), The Role of Capial i Ecoomic Theory, Ecoomic Joural 7, Fisher, I. (922), The Makig of Idex Numbers, Hougho-Miffli. Fisher, I. (93), The Theory of Ieres, Macmilla Co. Flavi, M. ad T. Yamashia (22), Ower-Occupied Housig ad he Composiio of he Household Porfolio over he Life Cycle, America Ecoomic Review 92, Garer, T.I. ad R. Verbrugge (28), The Puzzlig Divergece of Res ad User Coss, 98-24: Summary ad Exesios, chaper 8 i W.E. Diewer, B.M. Balk, D. Fixler, K.J. Fox ad A.O. Nakamura (eds.) (28), Price ad Produciviy Measureme, Volume : Housig, Trafford Press. Gazlaff, D.H., ad D.C. Lig (994), Measurig Chages i Local House Prices: A Empirical Ivesigaio of Aleraive Mehodologies, Joural of Urba Ecoomics 35 (2), Geesove, D. (999), The Nomial Rigidiy of Aparme Res, NBER Workig Paper 737, Naioal Bureau of Ecoomic Research. Gordo, R.J. ad T. va Goehem (24), A Ceury of Dowward Bias i he Mos Impora Compoe of he CPI: The Case of Real Sheler, 94-23, forhcomig i E.R. Berd ad C.R. Hule (eds.), Hard-o- 45

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