Handbook on Residential Property Prices Indices (RPPIs)

Transcription

1 M e h o d o l o g i e s & W o r k i g p a p e r s Hadbook o Resideial Propery Prices Idices (RPPIs) 23 ediio

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3 M e h o d o l o g i e s & W o r k i g p a p e r s Hadbook o Resideial Propery Prices Idices (RPPIs) 23 ediio

4 Europe Direc is a service o help you fid aswers o your quesios abou he Europea Uio. Freephoe umber (*): (*) Cerai mobile elephoe operaors do o allow access o 8 umbers or hese calls may be billed. More iformaio o he Europea Uio is available o he Iere (hp://europa.eu). Caaloguig daa ca be foud a he ed of his publicaio. Luxembourg: Publicaios Office of he Europea Uio, 23 ISBN doi:.2785/347 Ca. No KS-RA-2-22-EN-N Theme: Ecoomy ad fiace Collecio: Mehodologies & Workig papers Europea Uio, Ieraioal Labour Orgaizaio, Ieraioal Moeary Fud, Orgaisaio for Ecoomic Co-operaio ad Developme, Uied Naios Ecoomic Commissio for Europe, The World Bak, 23 Reproducio is auhorised provided he source is ackowledged. Phoo credis: Phovoir Reproducio of phoos is allowed for o-commercial purposes ad wihi he sole coex of his publicaio. Pried i Belgium Pried o elemeal chlorie-free bleached paper (ECF) Also available uder he ile Hadbook o Resideial Propery Prices Idices (RPPIs), ILO ISBN (paperback) ISBN (PDF) OECD ISBN (PDF) The opiios expressed ad argumes employed herei do o ecessarily reflec he official views of he ILO, IMF, OECD, UNECE, he World Bak or of he govermes of heir member couries or hose of Eurosa or he Europea Commissio.

5 Table of coes Table of coes Foreword Rppi 7 Preface 9. Iroducio 2. Uses of Resideial Propery Price Idices 5 3. Elemes for a Cocepual Framework 2 4. Sraificaio or Mix Adjusme Mehods Hedoic Regressio Mehods Repea Sales Mehods Appraisal-Based Mehods Decomposig a RPPI io Lad ad Srucures Compoes 8 9. Daa Sources. Mehods Currely Used 3. Empirical Examples Recommedaios 55 Glossary 6 Bibliography 67 Idex 77 Hadbook o Resideial Propery Prices Idices (RPPIs) 3

6 Table of coes Lis of ables 3.. Esimaed Re o Value Raios as Perceages (Capializaio Raios) Sample Probabiliy of a Sale i Each Cell Mached Model Fisher Chaied ad Fixed Base Price Idices, Mea, Media ad Represeaive Model Price Idices Rollig Year Fixed Base Fisher, Fisher Chaied Movig Average ad Fisher Fixed Base Movig Average Price Idices Log-Liear Time Dummy Price Idices ad he Chaied Sraified Sample Mea Fisher Price Idex Liear Time Dummy Price Idices, he Log Log Time Dummy Price Idex ad he Chaied Sraified Sample Mea Fisher Price Idex Chaied Laspeyres, Paasche ad Fisher Hedoic Impuaio Price Idices Repea Sales Price Idex, Chaied Sraified Sample Mea Fisher Price Idex ad Hedoic Impuaio Fisher Price Idex SPAR Idex, Hedoic Impuaio Fisher Price Idex ad Repea Sales Idex The Price of Lad (P L ), he Price of Qualiy Adjused Srucures (P S ), he Overall Cos of Producio House Price Idex (P ) ad he Fisher Hedoic Impuaio House Price Idex The Price of Lad (P L2 ), he Price of Srucures (P S2 ), he Overall Price Idex Usig Splies o Lad (P 2 ) ad he Fisher Hedoic Impuaio Price Idex The Price of Lad (P L3 ), he Price of Qualiy Adjused Srucures (P S3 ), he Overall House Price Idex wih Moooiciy Resricios o Srucures (P 3 ) ad he Overall House Price Idex Usig Splies o Lad (P 2 ) The Price of Lad (P L4 ), he Price of Qualiy Adjused Srucures (P S4 ) ad he Overall House Price Idex usig Exogeous Iformaio o he Price of Srucures (P 4 ) House Price Idices Usig Exogeous Iformaio (P 4 ) ad Usig Moooiciy Resricios (P 3 ), he Chaied Fisher Hedoic Impuaio Idex ad he Chaied Fisher Sraified Sample Idex The Price of Lad (P L4 ), he Price of Qualiy Adjused Srucures (P S4 ), he Overall House Price Idex usig Exogeous Iformaio o he Price of Srucures (P 4 ) ad heir Rollig Widow Couerpars (P RWL ) ad (P RW ) Approximae Sock Price Idices ad Based o Hedoic Impuaio (P Sock ) ad Sraificaio (P Sock2 ) ad he Fisher Hedoic Impuaio Sales Price Idex Approximae Price Idices for he Sock of Houses (P Sock ), he Sock of Lad (P LSock ), he Sock of Srucures (P SSock ) ad he Correspodig Sales Idices (P L4 ad P 4 ) Idices of Propery Prices Published i Japa Idices of Resideial Propery Prices Published i he UK Teure Saus All Housig i Souh Africa (Accordig o Cesus 2) Disribuio of Number of Rooms i Iformal Dwelligs Price Deermias Perceage of Maerials Used i he Cosrucio of Iformal ad Tradiioal Dwelligs i Souh Africa Evaluaio of Barriers Meas, Medias, Perce Chages, Sadard Deviaios, ad Skewess Regioal Expediures, Prices ad Volumes (Implici Quaiies) Usig Media Prices as he Regioal Prices Overall House Price Idices usig Media Prices ad Aleraive Formulae o Aggregae over Regios A, B ad C Hadbook o Resideial Propery Prices Idices (RPPIs)

7 Table of coes.4. Regioal Expediures, Prices ad Volumes (Implici Quaiies) Usig Mea Prices as he Regioal Prices Overall House Price Idices usig Mea Prices ad Aleraive Formulae o Aggregae over Regios A, B ad C Log-liear Regressio Resuls for a Simple Example Resuls from a Pooled Regressio for Years 26 ad Resuls from a Pooled Regressio for Years 26 o Resuls from a Pooled Regressio for Years 27 ad Resuls from a Regressio for Resuls from a Regressio for Mea Values of he Characerisics for he Base Period (26) Repea Sales Daa Dummy Variables for Repea Sales Uweighed Repea Sales Regressio Weighed Repea Sales Regressio Repea Sales Price Idices (22 = ) Growh Raes i Perce for he Various House Price Idices (27)...54 Hadbook o Resideial Propery Prices Idices (RPPIs) 5

8 Table of coes Lis of figures 4.. Mached Model Fisher Chaied ad Fixed Base Price Idices, Mea, Media ad Represeaive Model Price Idices Rollig Year Fixed Base Fisher, Fisher Chaied Movig Average ad Fisher Fixed Base Movig Average Price Idices Log-Liear Time Dummy Price Idices ad he Chaied Sraified Sample Mea Fisher Price Idex Liear Time Dummy Price Idices, he Log Log Time Dummy Price Idex ad he Chaied Sraified Sample Mea Fisher Price Idex Chaied Laspeyres, Paasche ad Fisher Hedoic Impuaio Price Idices The Fisher Impuaio Price Idex, he Chaied Sraified Sample Mea Fisher Price Idex, he Liear Time Dummy Price Idex ad he Log Log Time Dummy Price Idex Repea Sales Price Idex, Chaied Sraified Sample Fisher Price Idex ad Hedoic Impuaio Fisher Price Idex SPAR Idex, Hedoic Impuaio Fisher Price Idex ad Repea Sales Idex The Price of Lad (P L ), he Price of Qualiy Adjused Srucures (P S ), he Overall Cos of Producio House Price Idex (P ) ad he Fisher Hedoic Impuaio House Price Idex The Price of Lad (P L2 ), he Price of Srucures (P S2 ), he Overall Price Idex Usig Splies o Lad (P 2 ) ad he Fisher Hedoic Impuaio Price Idex The Price of Lad (P L3 ), he Price of Qualiy Adjused Srucures (P S3 ), he Overall House Price Idex wih Moooiciy Resricios o Srucures (P 3 ) ad he Overall House Price Idex Usig Splies o Lad (P 2 ) The Price of Lad (P L4 ), he Price of Qualiy Adjused Srucures (P S4 ) ad he Overall House Price Idex usig Exogeous Iformaio o he Price of Srucures (P 4 ) House Price Idices Usig Exogeous Iformaio (P 4 ) ad Usig Moooiciy Resricios (P 3 ), he Chaied Fisher Hedoic Impuaio Idex ad he Chaied Fisher Sraified Sample Idex Approximae Sock Price Idices ad Based o Hedoic Impuaio (P Sock ) ad Sraificaio (P Sock2 ) ad he Fisher Hedoic Impuaio Sales Price Idex Approximae Price Idices for he Sock of Houses (P Sock ), he Sock of Lad (P LSock ), he Sock of Srucures (P SSock ) ad he Correspodig Sales Idices (P L4 ad P 4 ) Diagram: House purchase imelie ad house price idices Four Resideial Propery Price Idices for Caada Propery Iformaio Flow Four Resideial Price Idices for Japa (Jauary 999=) House Purchase Time-lie NHB RESIDEX Idices Idia Ciywise idex Quarerly Naioal House Price Idex for Exisig Uis Nomial ad Real Quarerly Naioal Real House Price Idex for Exisig Uis Aual Perceage Chages Aual Naioal House Price Idex for Exisig Uis ( ) Aual Real House Price Idex for Exisig Uis Pricipal meropolia areas Aual Real House Price Idex for Exisig uis: Houses wih Subsidies (VIS) ad Houses wihou (NOVIS)...33.: Disribuio of House Prices i Hadbook o Resideial Propery Prices Idices (RPPIs)

9 Foreword - RPPI Foreword RPPI This Hadbook o Resideial Propery Prices Idices (RPPIs) represes he firs comprehesive overview of cocepual ad pracical issues relaed o he compilaio of price idexes for resideial properies. The developme of he RPPI Hadbook has bee co-ordiaed by he Saisical Office of he Europea Uio (Eurosa), uder he joi resposibiliy of six orgaizaios - Ieraioal Labour Orgaizaio (ILO), Ieraioal Moeary Fud (IMF), Orgaisaio for Ecoomic Co-operaio ad Developme (OECD), Saisical Office of he Europea Uio (Eurosa), Uied Naios Ecoomic Commissio for Europe (UNECE) ad World Bak - hrough he mechaism of a Ier-Secrearia Workig Group o Price Saisics (IWGPS). The Hadbook is published joily by hese orgaizaios. The aim of he RPPI Hadbook is o give pracical guidace o he compilaio of house price idexes ad o icrease ieraioal comparabiliy of resideial propery price idexes. The Hadbook oulies he differe user eeds, gives deails o daa eeds ad mehods, ad provides recommedaios. The primary purpose of he Hadbook is o assis producers of resideial propery price idexes, paricularly i couries ha are revisig or seig up heir RPPIs. The Hadbook draws o a wide rage of experiece ad experise i a aemp o describe pracical ad suiable measureme mehods. I should also help couries o produce heir RPPIs i a more comparable maer. As i brigs ogeher a large body of kowledge o he subjec, he Hadbook may be used for self-learig, or as a eachig ool for raiig courses o resideial propery price idexes. Oher RPPI users, such as busiesses, policy-makers or researchers may also fid he Hadbook useful as a source of iformaio, o oly abou he differe mehods ha are employed i collecig daa ad compilig such idexes, bu also abou heir limiaios. I his respec, i may faciliae he ierpreaio of he resuls. The drafig ad revisio have eailed may meeigs over a hree-year period, i which RPPI expers from aioal saisical offices, ieraioal ad regioal orgaisaios, uiversiies ad research isiues have paricipaed. Their collecive advice ad wisdom were idispesable for he compilaio of his Hadbook. A elecroic versio of he Hadbook is available o he Iere a hp://epp.eurosa.ec.europa.eu. The IWGPS views he Hadbook as a livig docume ha will be ameded ad updaed o address paricular pois i more deail. Commes o he Hadbook are welcomed by he IWGPS, ad should be se o Eurosa ( ESTAT-hicp-mehods@ ec.europa.eu). They will be ake io accou i ay fuure revisios. Waler Radermacher Chief Saisicia of he Europea Uio Direcor Geeral Eurosa - Saisical Office of he Europea Uio Alfredo M. Leoe Acig Direcor Saisics Deparme Ieraioal Moeary Fud Lidia Braaova Direcor of Saisical Divisio Uied Naios Ecoomic Commissio for Europe Rafael Diez de Media Chief Saisicia Direcor of he Deparme of Saisics Ieraioal Labour Orgaisaio Marie Durad Chief Saisicia Direcor of Saisics Direcorae Orgaisaio for Ecoomic Co-operaio ad Developme Shaida Badiee Direcor, Developme Daa Group World Bak Hadbook o Resideial Propery Prices Idices (RPPIs) 7

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11 Preface Preface Iroducio The aim of his Hadbook is o faciliae he seig-up of resideial propery price idices i couries where hese are sill missig ad he improveme of exisig price idices where his is deemed ecessary. I is desiged o give pracical guidace o he compilaio of house price idices, boh i developed ad less developed couries, ad o icrease ieraioal comparabiliy of resideial propery price idices. I explais he differe user eeds, gives deails o daa ad mehods ha ca be used o compile resideial propery price idices ad provides recommedaios. The producio of he Hadbook was fuded ad suppored by Eurosa. Backgroud The eed for propery price idices ha are fi-for-purpose was recogised a a coferece orgaised joily by he Ieraioal Moeary Fud (IMF) ad he Bak for Ieraioal Selemes (BIS) i Washigo DC, Ocober 23. As a resul, a chaper o resideial propery price idices was added o he IMF s Compilaio Guide of Fiacial Soudess Idicaors. The idea of a more deailed Hadbook daes back o a workshop orgaised by he Orgaisaio for Ecoomic Co-operaio ad Developme (OECD) ad he IMF o Real Esae Price Idices i Paris, November 26. The Hadbook would compleme he exisig ieraioal mauals o cosumer price idices, producer price idices ad impor-expor price idices ha were produced uder he auspices of he Ier-Secrearia Workig Group o Price Saisics. Eurosa agreed o ake his iiiaive forward by supporig ad fudig he preparaio of he Hadbook, give he srog liks o is ogoig work o he iclusio of ower-occupied housig i he Harmoized Idex of Cosumer Prices (HICP) ad he role ha house price idices have i he se of Pricipal Europea Ecoomic Idicaors. A he Eurosa-IAOS-IFC coferece o resideial propery price idices, held i Basel, -2 November 29, he Hadbook pla was discussed. Prelimiary versios of he Hadbook were preseed ad discussed a several occasios, i paricular a he UNECE-ILO Meeig o Cosumer Price Idices i Geeva, -2 May 2, a workshop held i The Hague, - February 2, ad he welfh Oawa Group meeig i Welligo, 4-6 May 2. A Guide o Readers Alhough o all of he chapers are self-coaied, he Hadbook is o desiged o be read from cover o cover. For example, some of he chapers ca easily be skipped by compilers who are paricularly ieresed i mehodological issues. Furher deails o he coes of he Hadbook are give i Chaper. The Hadbook cao be oo prescripive for wo reasos. Firsly, i is o always possible o give pracical guidace as some of he soluios o cocepual problems are o always clear-cu ad here are choices o be made abou precisely how a pracical soluio is implemeed. Secodly, wha is applicable ad wha ca be achieved will deped o he daa ad resources available o he idividual aioal saisical isiue (or oher compilig isiue). Ackowledgemes The wriig of he Hadbook was led by Saisics Neherlads; Ber M. Balk co-ordiaed he projec aciviies. Ja de Haa ad W. Erwi Diewer aced as mai ediors. The auhors of he idividual chapers are as follows: Preface Ber Balk, Ja de Haa ad David Fewick. Iroducio Ber Balk 2. Uses of Resideial Propery Price Idices David Fewick 3. Elemes for a Cocepual Framework Erwi Diewer 4. Sraificaio or Mix Adjusme Mehods Ja de Haa ad Erwi Diewer Hadbook o Resideial Propery Prices Idices (RPPIs) 9

12 Preface 5. Hedoic Regressio Mehods Ja de Haa ad Erwi Diewer 6. Repea Sales Mehods Ja de Haa 7. Appraisal-Based Mehods Ja de Haa 8. Decomposig a RPPI io Lad ad Srucures Compoes Erwi Diewer 9. Daa Sources David Fewick. Mehods Currely Used David Fewick. Empirical Examples Marc Prud homme ad Erwi Diewer 2. Recommedaios David Fewick, Erwi Diewer ad Ja de Haa Glossary Ja de Haa The qualiy of he Hadbook was icreased by he valuable coribuios of may idividuals ad orgaisaios, icludig ipu from boh compilers ad users of resideial propery price idices i differe pars of he world. The umber of coribuors is, of course, oo grea o meio hem all by ame. The BIS (ad i paricular Paul Va de Bergh) have bee excelle hoss for he Basel workshop i 29. May haks go o UNECE (ad i paricular Carse Boldse) who were also heavily ivolved i he orgaisaio of he Basel workshop, ad of he special sessio o he RPPI Hadbook durig he joi UNECE/ILO CPI meeig i 2. Special haks are due o Irmraud Beuerlei, Simo Coé, Lee Evers, Gregory Klump, Jose Vicee Romero, Parick Sabouri, A.P. Saxea, ad Chihiro Shimizu for coribuig o he coury-based case sudies ad o Emily Carless, Preechaya Chavaliumroy, Ali Hepşe, Marissa Gozalez Guzma ad Hecor Zarae, who provided oher backgroud iformaio o published idices. Useful commes o prelimiary drafs of he Hadbook were received from Carlos Brás, Morris Davis, Mari Eiglsperger, Timohy Erickso, Rui Evagelisa, Deis Fixler, Joh Greelees, Bria Graf, Vada Guerreiro, Roald Johso, Marcel va Kis, Adrew Leveis, Bogda Marola, Daiel Saos, Mick Silver, Leo Sveidkauskas, Radall Verbrugge, David Wasshause, ad paricipas a he workshop i The Hague, i paricular Marc Fracke ad Ja Walschos. Eurosa, he BIS, he IMF ad he ECB also provided helpful commes. Thaks are also due o Res Hedriks ad Nig Huag for commes ad compuaioal assisace. Hadbook o Resideial Propery Prices Idices (RPPIs)

13 Iroducio

14 Iroducio. Resideial propery is boh a source of wealh ad, isofar as propery owers live i or o heir propery, a impora deermiig facor i heir cos of livig. The price of a house is somehig differe from he cos of dwellig services i provides, hough he wo coceps are obviously ierliked..2 Moiorig he developme of house prices is cosidered impora, especially i imes of ecoomic urbulece. Ye he way house price developme is measured varies per coury, ad eve wihi a coury here are someimes wo or more compeig mehods i use. This siuaio is of course o favourable for he desig of cosise policy measures based o solid ieraioal comparisos..3 Agais his backgroud i is udersadable ha i was proposed ha a hadbook be prepared o housig, or broader resideial propery, price idices. ( ) The primary goals of he hadbook are o provide guidace for hose wishig o se up resideial propery price idices or modify exisig idices i view of ieraioal harmoisaio; o provide a discussio ad compariso of he various arges ad heir correspodig cocepual frameworks; o provide a iveory of exisig pracices. The coes of he hadbook are briefly oulied below..4 Chaper 2 reviews a umber of areas where resideial propery price idices (RPPIs) play a role. The followig applicaios are cosidered: as a macro-ecoomic idicaor of ecoomic aciviy; for use i moeary policy ad iflaio argeig; as a ool for esimaig he value of a compoe of real wealh; as a fiacial sabiliy or soudess idicaor o measure risk exposure; as a deflaor i he Naioal Accous; as a ipu io ciizes decisio makig o wheher o buy or sell resideial propery; as a ipu io he Cosumer Price Idex; ad for use i makig ier-area ad ieraioal comparisos..5 I Chaper 3 o he uses of a RPPI, he focus will be o fill i gaps i he Sysem of Naioal Accous ad i he compilaio of a Cosumer Price Idex. I is likely ha if appropriae RPPIs ca be cosruced o fill i hese gaps, he he resulig family of RPPIs will mee he eeds of mos users. ( ) Acually, his was oe of he coclusios of he OECD-IMF Workshop o Real Esae Price Idices (Paris, 6-7 November 26)..6 Broadly speakig, wo separae ypes of RPPI ca be disiguished: a cosa qualiy price idex for he sock of resideial housig a a paricular mome i ime ad a cosa qualiy price idex for resideial propery sales ha ook place durig a paricular period of ime. The cosrucio of hese wo ypes of idex will be differe; mos paricularly, he weighig associaed wih he wo ypes will differ..7 Chaper 3 coiues by summarizig he four mai approaches o cosrucig a RPPI. I he fial secios a umber of miscellaeous opics are addressed, such as he frequecy of a RPPI, he cosisecy of mohly wih quarerly esimaes ad he cosisecy of quarerly wih aual esimaes, revisio policies, ad seasoal adjusme..8 Chapers 4-7 review i deph he mai mehods for compilig RPPIs. The simples mehods are based o some measure of ceral edecy of he disribuio of rasacio prices i a period, i paricular he mea or he media. Sice house price disribuios are geerally posiively skewed (predomialy reflecig he heerogeeous aure of housig, he posiive skew i icome disribuios, ad he zero lower boud o rasacio prices), he media raher ha he mea is ofe used. As o daa o housig characerisics are required o calculae he media, a price idex ha racks chages i he price of he media house sold from oe period o he ex ca be easily cosruced. Aoher aracio of media idices is ha hey are easy o udersad..9 Oe major drawback of simple media based idices is ha hey provide very oisy esimaes of price chage. The se of houses acually raded i a period, or a sample hereof, is ypically small ad o ecessarily represeaive of he oal sock of houses. Chages i he mix of properies sold will herefore affec he sample media price more ha he media price of he housig sock. A perhaps bigger problem ha shor-erm oise is sysemaic error, or bias. A media idex will be subjec o bias whe he qualiy of he housig sock chages over ime. Bias ca also arise if cerai ypes of houses are sold more frequely ha oher ypes of houses ad a he same ime exhibi differe price chages.. A geeral echique for reducig sample selecio bias is (pos-) sraificaio. This echique, which is also kow as mix adjusme, is discussed i Chaper 4.. Chaper 5 reviews he hedoic regressio approach. This approach recogizes ha heerogeeous goods ca be described by heir aribues or characerisics. Tha is, each good is esseially a budle of performace characerisics. I he housig coex, his budle may coai aribues of boh he srucure ad he locaio of he properies. Alhough here is o marke for 2 Hadbook o Resideial Propery Prices Idices (RPPIs)

15 Iroducio characerisics, sice hey cao be sold separaely, he demad ad supply for he properies implicily deermie he characerisics margial coribuios o he prices of he properies. Regressio echiques ca be used o esimae hose margial coribuios or implici prices..2 This chaper discusses, i a o-echical way, he mai models used as well as he mehods o form RPPIs from esimaio of such models. The overall evaluaio of he hedoic regressio mehod is ha i is probably he bes mehod ha could be used i order o cosruc cosa qualiy RPPIs for various ypes of resideial propery. However, i is also he mos daa-iesive mehod..3 The repea sales mehod, reviewed i Chaper 6, uilizes iformaio o he same properies which have bee sold more ha oce. Because oly mached models are used, here is o chage i he qualiy mix o corol for. I is basic form, he oly iformaio required is price, sales dae ad address of he propery. So he repea sales mehod is much less daa- iesive ha hedoic mehods. Also, he repea sales mehod will auomaically corol for micro locaio (address), somehig which hedoic mehods are uable o do..4 The mached model mehodology, where prices of exacly he same iem are compared over ime, is he aural sarig poi for he cosrucio of ay price idex. Because of he low icidece of rasacios, ad because he qualiy of houses coiually chages, he sadard mached model mehodology cao be applied sraighforwardly. The repea sales mehod aemps o deal wih his issue by lookig oly a properies ha have bee sold more ha oce over a sample period. This, however, ca lead o a relaively low umber of observaios ad o sample selecio bias. To overcome such problems, assessed values of he properies could be used..5 I may couries, official goverme assessmes are available for all properies, because such daa are eeded for axaio. If he assessmes perai o some referece dae, a RPPI ca be cosruced by relaig acual sale prices o assessed values. This cosiues a varia of he mached model mehodology, he disic feaure beig ha composiioal chage is accoued for. I his case, here is o eed o use ecoomeric echiques. The various assessme-based mehods, ad i paricular he sale-price appraisal raio (SPAR) mehod, are reviewed i Chaper 7..6 Chapers 4-7 all ed wih empirical examples esed o acual daa i order o illusrae he mehods discussed ad o provide addiioal backgroud maerial. The daa se covers 4 quarers of resideial propery sales for a relaively small ow i he Neherlads. As will become clear i Chapers 4-7, mos mehods are uable o decompose a RPPI io a lad ad a srucures compoe. Chaper 8 discusses how hedoic regressio mehods ca be used o obai such a decomposiio ad cosiders how o cosruc a RPPI for he sock of housig whe hedoic regressio mehods are used. Usig he acual daa, his chaper also suggess ways o overcome several pracical problems ha are ofe ecouered i empirical work of his aure, such as a high correlaio bewee he size of he srucure ad he size of he lad..7 I pracice, because of he high cos of uderakig purpose-desiged surveys of house prices, he approaches adoped by saisical agecies ad ohers o cosruc RPPIs have bee maily a fucio of he house price daa ses geeraed by he legal ad oher processes associaed wih buyig a house. The idices so cosruced ca vary accordig o he poi i he house purchasig process a which he price is measured, for isace wheher he fial rasacio price or he earlier valuaio used for securig a loa is ake. Also, he amou of deailed iformaio available o he characerisics of he properies sold will affec idex compilaio mehods, ofe acig as a cosrai o he echiques available o qualiy adjus for houses of differe sizes ad locaios. Thus, daa availabiliy has hisorically bee a cosrai o he approach used for idex cosrucio..8 Chaper 9 qualiaively examies he differe daa sources ha ca be used for cosrucig RPPIs, such as pried ews media, real esae ages, morgage compaies, propery regisers ad ax offices. I he fial secio, aeio is paid o he siuaio i may developig couries where daa are scarce ad he issue of propery owership is ambiguous..9 Chaper caalogues he availabiliy of RPPIs i differe couries ad also preses some case sudies. I relies o mea-daa gahered by various orgaisaios, icludig he Europea Ceral Bak ad he Bak for Ieraioal Selemes, ad more recely a fac-fidig exercise coduced by Eurosa i coecio wih he iclusio of ower-occupied housig coss i he Europea Uio s Harmoised Idex of Cosumer Prices, which was exeded o cover some o-eu couries..2 Chaper provides addiioal pracical guidace by demosraig he workig of he RPPI cosrucio mehods (excludig he SPAR mehod) ha were oulied i Chapers 4, 5 ad 6 o simple examples usig small daa ses..2 Chaper 2 cocludes by providig recommedaios. Hadbook o Resideial Propery Prices Idices (RPPIs) 3

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17 Uses of Resideial Propery Price Idices 2

18 2 Uses of Resideial Propery Price Idices Iroducio 2. There are may areas of sociey where idividuals or orgaisaios use resideial propery price idices (RPPIs) direcly or idirecly eiher o ifluece pracical decisio makig or o iform he formulaio ad coduc of ecoomic policy. Differe uses ca have a sigifica impac o he preferred coverage of he idex ad also o he appropriae mehodology applied for is cosrucio. 2.2 From a idividual household s perspecive, real esae ofe represes he sigle larges ivesme i heir porfolio. I also accous for he larges share of wealh i mos aios balace shees. Chages i house prices ca have far-reachig implicaios for idividuals. For example, chages i housig equiy ad household deb levels ca permeae hrough o he overall ecoomy. I fac, cosumer spedig is ofe affeced by chages i house prices as a resul of wealh effecs ad is effec o cosumer cofidece. House prices ifluece home improveme ad reovaios expediures, which i may couries are higher ha overall spedig o ew house cosrucio. House prices play a major role i he measureme of he affordabiliy of home-owership, a key housig policy objecive i some couries. House price chages also ifluece he decisio o build ew houses (he supply side) as well as he decisio o become a homeower (he demad side). ( ) Ivesors ur o house price idices o o oly measure wealh bu also o help i assessig curre ad fuure raes of reur. ( 2 ) 2.3 From a broader perspecive, aalyss, policymakers, ad fiacial isiuios follow reds i house prices o expad heir udersadig of real esae ad credi marke codiios as well as o moior he impac o ecoomic aciviy, ad fiacial sabiliy ad soudess. ( 3 ) For isace, morgage leders will use iformaio o house price iflaio o gauge defaul risk. Ceral baks ofe rely o movemes i house price idices o moior households borrowig capaciy ad deb burde ( 4 ) ad heir effecs o aggregae cosumpio. ( 5 ) 2.4 I his coex i should be emphasised ha he differe uses of resideial propery price idices may require differe cocepual bases ad mehodology, alhough i pracice, oher facors someimes come io play, such as daa availabiliy. ( 6 ) I geeral, o sigle idicaor of house price chage ca saisfy every purpose. For isace, he price dyamics of he housig marke for ( ) See Duffy (29). ( 2 ) Resideial cosrucio ivesme accous for abou 5% of GDP i he euro area. ( 3 ) See Case ad Wacher (25). ( 4 ) See Fiocchiaro ad vo Heideke (27). ( 5 ) See Case e al. (2), Phag (24) ad Belsky ad Prakke (24). ( 6 ) See Fewick (26) ad also Chaper 9. moiorig house iflaio, as experieced by purchasers, may bes be esimaed by collecig iformaio o curre rasacio prices ad usig his iformaio o cosruc a price idex for he sales of housig uis. I coras, o esimae a ecoomy s (real) sock of wealh, iformaio o he sample of rasaced dwelligs mus ideally be supplemeed by iformaio o he sock of o-rasaced dwelligs i order o cosruc a price idex for he housig sock. This may be doe by re-weighig o reflec he differe mix of houses i he housig sock compared wih rasacios bu he adequacy of his mehod depeds o wheher he dwelligs ha are acually rasaced ca ac as a proxy for he oes ha have o bee subjec o a chage of owership. If he price of houses ha have o chaged owership is o available ad iformaio o heir umbers ad characerisics is limied or eve o-exise, he user eeds o be assured ha he profile of he rasacios is represeaive of he overall housig sock. I pracice, he laer codiio may o be fully me as differe secors of he housig marke ca be iflueced by differe facors ad he limied umber of rasacios may lead o ureliable or eve o-exise daa o prices for some of hese differe sraa. 2.5 The (price deermiig) aribues of idividual houses ofe chage over ime. These chages iclude improvemes o he dwellig i he form of reovaios o kiches ad bahrooms, replaceme widows wih isulaed glazig, or he isallaio of eergy efficie heaig or air-codiioig sysems, ad also exesios of he srucure which reflec he rece red i may couries owards larger houses. Improvemes ad exesios will be parially offse by depreciaio of he srucures. Irrespecive of he purpose of he idex, a ideal RPPI should be adjused for all of hose chages. To pu i differely, he idex should represe chages i he prices of properies ha are comparable i qualiy over ime. 2.6 The eed for qualiy adjusme exeds beyod corollig for home improvemes ad depreciaio, however. The mix of dwelligs ha are sold i oe period is likely o be differe from ha i he ex period whe, say, he sample of houses sold cosiss of more larger houses compared o he previous period. Such composiioal or mix chages may have a cyclical paer because sales of larger houses will ypically declie as a ecoomy eers a recessio. Composiioal chages of he sample over ime, jus like qualiy chages of he idividual dwelligs, should o be ierpreed as price chages measureme echiques are required o adjus he price chages for qualiy mix chages. A shor overview of he various mehods ha are available o solve he problems of qualiy (mix) chage will be provided i Chaper 3. A deailed discussio of hese mehods will follow i Chapers Hadbook o Resideial Propery Prices Idices (RPPIs)

19 Uses of Resideial Propery Price Idices 2 A Review of he Differe Uses of Resideial Propery Price Idices 2.7 Resideial propery price idices have a umber of impora uses: as a macro-ecoomic idicaor of ecoomic growh; for use i moeary policy ad iflaio argeig; as a ipu io esimaig he value of housig as a compoe of wealh; as a fiacial sabiliy or soudess idicaor o measure risk exposure; as a deflaor i he aioal accous; as a ipu io a idividual ciize s decisio makig o wheher o buy (or sell) a resideial propery; as a ipu io he cosumer price idex, which i ur is used for wage bargaiig ad idexaio purposes; ( 7 ) for use i makig ier-area ad ieraioal comparisos. Each use is cosidered i ur. As a Macro-Ecoomic Idicaor of Ecoomic Growh 2.8 Risig house prices are ofe associaed wih periods of ecoomic expasio while fallig house prices ofe correspod wih a slowig ecoomy. Goodhar ad Hofma (26) show ha for 6 idusrialised couries here exiss a srog correlaio bewee house prices ad ecoomic aciviy. I fac he six major bakig crises i advaced couries sice he mid 97s were all associaed wih he bursig of a housig bubble (Reihar ad Rogoff, 29). ( 8 ) I he mai, house prices are reaed as a leadig idicaor alhough here is some debae abou wheher house price chage is a leadig, laggig or coicide ecoomic idicaor. 2.9 Wha is clear is ha risig house prices are ofe associaed wih ecoomic growh hrough a leas hree chaels: Higher (relaive) house prices ed o simulae icreased cosrucio aciviy, which i ur leads o higher ( 7 ) The iclusio of a house price idex i he calculaio of a CPI depeds o he objecives of he CPI ad, i paricular, wheher a acquisiios, paymes or user cos approach is adoped. Furher discussio of hese issues is give i he Cosumer Price Idex Maual (ILO e al., 24) ad he Pracical Guide o Producig Cosumer Price Idices (Uied Naios, 29). ( 8 ) Claesses, Kose ad Terroes (28; 25) fid ha... recessios associaed wih house price buss are o average over a quarer loger ha hose wihou buss. Moreover, oupu declies (ad correspodig cumulaive losses) are ypically much larger i recessios wih buss, 2.2 (3.7) perce versus.5 (2.3) perce i hose wihou buss. These sizeable differeces also exed o he oher macroecoomic variables, icludig cosumpio, ivesme ad he uemployme rae. employme ad higher icomes for a wide rage of workers ivolved i he housig marke, such as real esae ages, cosrucio workers ad professioals i he fiacial ad he legal professios. Expecaios of higher fuure reurs o propery ivesme lead builders o sar ew cosrucio ad his is accompaied by higher marke demad i propery-relaed secors from ower-occupiers ad propery ivesors. ( 9 ) I addiio, buildig aciviy will ed o icrease from more home reovaios. Higher house prices ed o lead o icreased sales of exisig housig uis ad his i ur ca lead o addiioal ax reveues i he form of propery rasfer axes geeraed from he higher volume ad value of propery sales. These icreased ax reveues ca lead o icreased goverme spedig which i ur provides addiioal ecoomic simulus. Risig real esae prices will lead o improvemes i he household secor s balace shee (he wealh effec) ad his i ur will geerally lead o icreased household spedig o cosumpio ad ivesme. ( ) Accordig o a repor by he U.S. Cogressioal Budge Office (27), whe house prices surged i he 99s ad 2s, cosumer spedig grew faser ha icomes. This household wealh effec geerally leads o icreases i spedig by cosumers o home reovaios ad repairs i addiio o icreased spedig o oher goods ad services. 2. Of course, he above simulaive effecs of icreasig house prices go io reverse whe (real) house prices fall. I is herefore impora ha he public ad ecoomic policy makers have a heir disposal accurae ad imely iformaio o movemes i real esae prices. 2. Asse prices, icludig real esae prices, are a key idicaor for more fully udersadig he dyamics of he ecoomy. ( ) Accordig o Plosser (27), asse prices coai impora iformaio abou he curre ad fuure sae of he ecoomy ad ca play a impora role i he deliberaios of ceral bakers as hey seek o achieve heir objecives of price sabiliy ad susaiable oupu growh. For Use i Moeary Policy ad Iflaio Targeig 2.2 I addiio o he above geeral ieres i moiorig propery prices, may ceral baks have iflaio arges which ca direcly ivolve idices of propery prices. For isace, ceral baks i some couries uilize a Moeary Codiios Idex (MCI) as a day-o-day ( 9 ) See Zhu (25). ( ) See Campbell ad Cocco (27). ( ) See Turvey (989) ad Goodhar (2). Hadbook o Resideial Propery Prices Idices (RPPIs) 7

20 2 Uses of Resideial Propery Price Idices operaig arge for he coduc of moeary policy. I a expaded versio of his idex, as ha suggesed by Jaroci ski ad Smes (28) ad Goodhar ad Hofma (27), he MCI would iclude some measure of house prices because of he impora role his variable plays i he iflaioary process ad for ecoomic performace. Oher ceral baks who have a iflaio arge based o he Cosumer Price Idex (CPI) will idirecly ake io accou he moveme i house prices whe seig ieres raes, depedig i par o he reame of Ower Occupied Housig (OOH) i heir coury s CPI. This issue is discussed furher i Chaper I ca be argued ha i he fuure, resideial propery prices are likely o play a icreasig role i he coduc of moeary policy. Over rece years a iflaio arge has bee used by a growig umber of couries o defie ad operae heir moeary policy frameworks. The IMF (27) provides a lis of 28 couries classified as iflaio argeers accordig o heir exchage rae arragemes (wihou specifyig he arge or iflaio measure). Carare ad Soe (23) exed his aalysis furher by classifyig couries ha use a iflaio arge for moeary policy, io fully-fledged iflaio argeers, eclecic argeers ad iflaio argeig lie regimes, usig he clariy ad credibiliy ( 2 ) of he commime o he iflaio arge o classify idividual couries. The auhors he ideify 42 medium ad large coury ceral baks who have some form of floaig exchage rae mechaism (i.e. o adopig a fixed exchage rae) leavig heir degree of commime o a iflaio arge as he defiig moeary objecive. They esimaed ha by 2 some 7 idusrial ad emergig markes operaed fully-fledged iflaio argeig, ha is have a medium o high level of credibiliy, clearly commi o heir iflaio arge ad isiuioalize his commime i he form of a raspare moeary framework ha fosers accouabiliy of he ceral bak o he arge. The umber of couries operaig fully-fledged iflaio argeig has bee icreasig over he years. As a Ipu for Esimaig he Value of Housig as a Compoe of Wealh 2.4 House prices are a ipu io he measureme of aggregae wealh i he ecoomy. Exisig dwellig uis are par of he balace shee accous i he Sysem of Naioal Accous (SNA). Thus i is ecessary o have a price idex for his asse class i order o form esimaes of real household wealh. As was meioed i he iroducio o his chaper, risig house prices will geerae a ( 2 ) Clariy is gauged by he public aouceme of he iflaio arge ad by he isiuioal arragemes for accouabiliy. Credibiliy is measured idirecly usig as a proxy he acual iflaio ouur ad by marke raigs of log-erm local currecy goverme deb. wealh effec ha ca lead o icreases i cosumpio ad icreased household borrowig. 2.5 More geerally, idividuals will have a idirec sake i real esae asse prices, icludig resideial propery, hrough pesio fuds ad oher direc ivesmes i real esae. As a Fiacial Sabiliy or Soudess Idicaor o Measure Risk Exposure 2.6 Fiacial Soudess Idicaors (FSIs) are idicaors of he curre healh ad soudess of he fiacial sysem ad isiuios of a coury ad of heir corporae ad household compoes. They iclude boh aggregaed idividual isiuio daa ad idicaors ha are represeaive of he markes i which he fiacial isiuios operae, icludig saisics o real esae prices. FSIs are calculaed ad dissemiaed for he purpose of supporig aioal ad ieraioal surveillace of fiacial sysems. The IMF developed FSIs wih a view o moiorig ad sregheig he global fiacial sysem ad o icreasig sabiliy followig he fiacial marke crises of he lae 99s, ad as a way of combaig he subseque growig umber of bakig crises ha have occurred globally. The compilaio guide for fiacial soudess idicaors provides some advice o compilig house price idices whils ackowledgig he relaive absece of ieraioal experiece ad guidace ad he absece of a comprehesive framework for cosrucig such idices. More recely, he Ocober 29 Repor o he G-2 Fiace Miisers ad Ceral Bak Goverors o he Fiacial Crisis ad Iformaio Gaps ( 3 ) meios ha iformaio o dwelligs ad heir associaed price chages are criical igredies for fiacial sabiliy policy aalysis. 2.7 Sharp falls i real esae prices have a derimeal impac o he healh ad soudess of he fiacial secor ad o he fiacial siuaio of idividuals ad of idividual households, by affecig credi raigs, he value of collaeral, ad he deb o equiy raio. 2.8 I should come as o surprise ha he relaioship bewee real esae cycles ad ecoomic cycles is well documeed ad ha he role of real esae prices i deb fiace ad fiacial crises has log bee recogised. This has led o he use of resideial propery price idices as idicaors of fiacial sabiliy, paricularly i couries where real esae accous for a sigifica proporio of aioal ad household wealh, ad where he propesiy of home owership is relaively high. 2.9 The use of reds i resideial propery prices, ad real esae prices more geerally, as a idicaor of fiacial soudess, has bee suppored by i-deph aalyical ( 3 ) Available a: hp:// 8 Hadbook o Resideial Propery Prices Idices (RPPIs)

21 Uses of Resideial Propery Price Idices 2 sudies. Icluded amogs he vas amou of maerial published o his subjec is a paper by Nabarro ad Key (23) who prese a model for real esae ad ledig cycles, suppored by case sudies. Their paper races he cyclical evoluio from iiial idicaors provided by he real marke, o propery prices ad hrough o balace shees of borrowers ad leders, ad draws aeio o a umber of releva idicaors of he real esae marke. I describes wha he auhors call he dagerous ierdepedece bewee real esae cycles ad fiacial sysems. Whils he auhors ackowledge he highly upredicable aure of he real esae cycle ad is differe characerisics ad properies from oe cycle o he ex, hey discuss he likages bewee real esae cycles ad deb fiace o ideify areas where improved iformaio could suppor effecive coueracig sraegies ad policies. They explai how a reliable ad cos-effecive sysem of performace measureme ad moiorig ca be developed ad implemeed ad sugges how such a sysem ca provide a mechaism for aalyical decisio makig, desiged o impac upo he behaviour of he real esae secor. 2.2 Iformaio o resideial propery ad oher propery prices eeds o be supplemeed by releva ad imely deailed aalyses, ad by oher iformaio such as he proporio of houses beig purchased wih cash raher ha beig fiaced hrough a loa. The average raio of loa o propery price, ad how his is disribued, provides a idicaio of he exposure of he borrower ad he leder, as does he price o earigs raio ad, o a cerai exe, he volume of rasacios. ( 4 ) Similarly, a more deailed aalysis of he ypes of houses beig sold by regio will show wheher aciviy i he housig marke is coceraed i paricular segmes of he marke such as high-ed properies or i cerai geographical locaios such as he capial ciy or large urba areas. As a Deflaor i he Naioal Accous 2.2 Naioal saisical agecies use house price idices i a leas wo ways. Firs, he srucures compoe of a price idex for ewly-buil houses is ofe used o deflae curre price values for resideial cosrucio i he aioal accous; see Bover ad Izquierdo (23). Secod, house price idices may be icluded i he cosrucio of he CPI, depedig o he choice of is cocepual basis. This secod use is cosidered below ad i more deail i Chaper Price idices ad deflaors are seemigly differe eiies wihi a wider group of saisics relaig o prices. ( 5 ) I is perie o oe agais his backgroud ( 4 ) Pas observaio suggess ha whe price-o-earigs raios ge o a ususaiable high level, he adjusme is iiially see i a reducio i he volume of housig urover raher ha i rasacio prices. ( 5 ) However, he uderlyig heory of deflaors ad (direc) price idexes is he same; see Chaper 6 i SNA (993). Samuelso ad Swamy (974) oe he followig: Alhough ha wo of he mos rece ad widely available refereces o he compilaio ad use of aioal accous deflaors, SNA (993) ad he Eurosa (2) Hadbook o Price ad Volume Measures i Naioal Accous, pre-dae he CPI Maual (24) ad PPI Maual (24) The CPI ad PPI Mauals were developed i parallel ad ake advaage of he laes research io idex umber heory ad pracice, which is o fully refleced i he official lieraure o aioal accous. ( 6 ) The wo mauals are esseially based o he same uderlyig ecoomic priciples ad saisical heory. They provide a comprehesive ad cohere overview of he cocepual ad heoreical issues associaed wih cosumer ad producer price idices ad raslae hese io available opios for pracical measureme. The CPI Maual also aced as a caalys for he ew ILO Resoluio o Cosumer Price Idices, which was passed i 23. As a Ipu io a Idividual Ciize s Decisio Makig o Wheher o Buy (or Sell) a Resideial Propery 2.24 The buyig or sellig of a dwellig is ypically he larges fiacial rasacio a household will eer io durig his or her life. Chages i house prices are herefore likely o ifluece subsaially wheher a household purchases a propery ad also he budge plas ad savigs decisios of he prospecive house buyers ad sellers. The purchase of a house is cosidered by may ower-occupiers boh as a meas of obaiig sheler services ad as a capial ivesme, he laer poeially providig a opporuiy for sigifica capial gais i he loger-erm. Curre price levels ad reds, ogeher wih expecaios abou fuure reds i house prices ad morgage ieres raes, ( 7 ) will ifluece a idividual s decisio o wheher o purchase ow or pospoe he purchase. The opporuiy cos associaed wih he sums of moey ivolved will also come io play as prospecive purchasers evaluae he aleraive choices available o hem. For isace, prospecive purchasers will ofe ake io accou he impac of chages i house prices o marke res More geerally, idividuals also have a idirec sake i real esae asse prices hrough pesio fuds ad oher ivesmes for which house prices will likely have a effec. For isace, he porfolios of some pesio fuds iclude aparme blocks whose res provide a mos aeio i he lieraure is devoed o price idices. Oce somehow esimaed, price idices are i fac used, if a all, primarily o deflae omial or moeary oals i order o arrive a esimaes of uderlyig real magiudes. ( 6 ) The CPI ad PPI Mauals are cosise wih he maerial i Chaper 6 of SNA (993) ad also wih he 28 Sysem of Naioal Accous bu delve deeper io he problems associaed wih he cosrucio of price idexes, paricularly a lower levels of aggregaio. ( 7 ) Ieres rae policy will have a impac boh o iflaio ad o e disposable icome afer he payme of ieres. Hadbook o Resideial Propery Prices Idices (RPPIs) 9

22 2 Uses of Resideial Propery Price Idices icome ad where a capial gai is expeced o maerialise from a icrease i he propery value. As a Ipu io he Cosrucio of a Cosumer Price Idex (CPI) 2.26 House prices will direcly affec measured iflaio whe he CPI icludes ower-occupier housig coss ad he mehod of measureme draws o house prices as oe of he ipus. Measured iflaio is idirecly affeced if house prices ifluece marke res, which cosiue aoher eleme of a CPI, ad where addiioally impued res are used as a proxy for ower-occupied housig coss. Reig ad buyig ca be subsiues ad he level of house prices will have a impac o he rae of reur obaied by a ladlord o his or her ivesme ad also o he re charged The reame of Ower Occupied Housig (OOH) is oe of he mos difficul challeges faced by compilers of cosumer price idices. There are a umber of aleraive cocepual reames ad he choice bewee hem ca have a sigifica impac o he overall idex, affecig boh he weigh aribued o OOH (ad by implicaio o a RPPI) ad he measured rae of iflaio. I essece here are four possible mai approaches o icludig OOH i a CPI: he acquisiios approach, he paymes or moey oulays approach, he user cos approach ad he real equivalece approach. The firs hree approaches require he cosrucio of a housig price idex. These various approaches o he reame of OOH are reviewed i more deail i Chaper 3. For Use i Makig Ieraioal ad Ier-area Comparisos 2.28 House price idices are also used i cojucio wih (comparable) bechmark daa o house price levels across regios or couries o geerae ier-area or ieraioal comparisos of livig cos differeials. The problems ha arise i aempig o price he services of OOH i a aioal coex also arise i he coex of ier-area ad ieraioal comparisos. I he laer coex, however, he problems are somewha more difficul ha makig, say, aioal comparisos over ime because ier-area/ieraioal comparisos require comparable ypes of housig across he regios/couries beig compared (or comparable iformaio o he characerisics of housig uis across he regios if a hedoic regressio echique is used) i order o cosruc a cosa qualiy price idex The Europea Ceral Bak (ECB) i co-operaio wih he ceral baks of he idividual couries of he euro-zoe ad he Europea Uio has a ieres i comparaive measureme of chages i resideial propery prices across differe euro-area couries ad for he euro-area as a whole. The raw daa used here come from various aioal sources ad have primarily bee colleced ad documeed by he Bak for Ieraioal Selemes (BIS). ( 8 ) Sice 2, he ECB has compiled a aggregae idex for he euro-area by weighig ogeher chages i prices for houses ad flas for he euro-area couries. ( 9 ) The aioal mehodologies associaed wih he figures available for each idividual coury ad for he euro-area aggregae, have improved over rece years bu perhaps fall shor of he sadards applied o oher ecoomic saisics ad price idicaors for he euro-area. ( 2 ) The BIS has also brough ogeher resideial propery price saisics for he o-euro area couries of he Europea Uio ad has i may cases bee cofroed wih eve more proouced issues cocerig daa comparabiliy ad qualiy. 2.3 Such comparisos ca be cofouded by mehodological ad coverage differeces ad also by differeces i he frequecy ad imeliess of he daa. Some of hese differeces arise from he differe sources of daa used o compile aioal idices. Chaper 9 explores hese daa sources i more deail ad Chaper gives a iveory of he differe mehods used by couries o compile heir idices of resideial propery prices. I ca be observed ha a oable proporio of couries, icludig some developed couries, do o have reliable resideial propery price idices. ( 8 ) The BIS daa se of resideial propery price saisics is available a: hp:// saisics/pp.hm. ( 9 ) See box Prelimiary evidece o developmes i euro area resideial propery prices i he Ocober-2 issue of he ECB Mohly Bullei. ( 2 ) See Eiglsperger (2), page Hadbook o Resideial Propery Prices Idices (RPPIs)

23 Elemes for a Cocepual Framework 3

24 3 Elemes for a Cocepual Framework Iroducio 3. Wha makes he cosrucio of a resideial propery price idex (RPPI) so challegig? This quesio was addressed i Chaper of his Hadbook bu i will be useful o remid readers abou he mai problems, which are as follows: The compilaio of price idices ypically relies o machig he prices for ideical iems over ime. However, i he housig coex, each propery has a uique locaio ad usually a uique se of srucural characerisics. Thus, he mached model mehodology will be difficul or impossible o apply. Trasacios are sporadic. The desired idex umber cocep may o be clear, or pu aoher way, here are several disic purposes for which a RPPI is required ad, broadly speakig, differe purposes require differe idices. For some purposes, oably he cosrucio of aioal balace shees ad he esimaio of user coss of ower occupied housig, a decomposiio of a propery price io lad ad srucures compoes is required bu i is uclear how bes o accomplish such a decomposiio. This issue will be discussed i more deail i Chaper 8 below. 3.2 The firs wo difficulies are well recogized i he housig measureme lieraure as he followig quoaios idicae: The price of housig is harder o measure ha ha of mos oher goods ad asses because of hree key disiguishig characerisics. Firs, ad mos imporaly, dwelligs are heerogeeous. No wo dwelligs are ideical, if oly because hey cao occupy quie he same locaio. This meas ha sampled house prices may be a poor idicaor of all house prices because we cao always reliably predic he sales price of a give dwellig from he price of aoher. Rober Wood (25; 23). The fudameal problem ha price saisicias face whe aempig o cosruc a real esae price idex is ha exac machig of properies over ime is o possible for wo reasos: (i) he propery depreciaes over ime (he depreciaio problem) ad (ii) he propery may have had major repairs, addiios or remodelig doe o i bewee he wo ime periods uder cosideraio (he reovaios problem). Because of he above wo problems, cosrucig cosa qualiy real esae price idices cao be a sraighforward maer; some form of impuaio or idirec esimaio will be required. Erwi Diewer (29b; 92). Such saemes idicae ha he cosrucio of a RPPI will be much more difficul ha he cosrucio of a ormal price idex based o a mached model mehodology. I should be recogized a he ouse ha, because of he difficulies resulig from he uiqueess of each dwellig ui, i would o be possible o cosruc a perfec RPPI; i will oly be possible o cosruc a approximaio o he heoreically ideal idex for each purpose. 3.3 The quesio of wha is he purpose of a RPPI has bee addressed i Chaper 2, where he may uses of a RPPI were cosidered. This chaper focuses o he uses of RPPIs o fill i gaps i he Sysem of Naioal Accous ad i he cosrucio of a CPI. I is likely ha if appropriae RPPIs ca be cosruced o fill i hese gaps, he he resulig family of RPPIs will mee he eeds of mos users. 3.4 Broadly speakig, wo separae RPPIs ca be disiguished: ) a cosa qualiy price idex for he sock of resideial housig a a paricular mome i ime; ad 2) a cosa qualiy price idex for resideial propery sales ha ook place durig a paricular period of ime. The cosrucio of hese wo ypes of idex will be differe; e.g., he weighig associaed wih he wo ypes will differ. I his chaper, he mai approaches o cosrucig a RPPI will be briefly discussed. Deails o hese mehods will be preseed i Chapers 4 o A variey of miscellaeous opics will be addressed i he fial four secios of his chaper. These opics iclude he frequecy of he RPPI ad user eeds, he cosisecy of mohly wih quarerly esimaes ad he cosisecy of quarerly wih aual esimaes, revisio policies, ad seasoal adjusme. Resideial Propery Price Idices ad he Sysem of Naioal Accous 3.6 The Sysem of Naioal Accous (SNA) 993 ad is rece updaig, he Sysem of Naioal Accous 28, ( ) provide a comprehesive accouig framework for a ecoomy. The SNA pariios he value flows i he ecoomy io various meaigful caegories ad provides a recociliaio of he flow accous wih he correspodig sock accous. I is furhermore recommeded o decompose he values i he cells of hese accous io price ad volume (or quaiy) compoes. ( ) See Eurosa, IMF, OECD, UN ad he World Bak (993) ad (29). 22 Hadbook o Resideial Propery Prices Idices (RPPIs)

25 Elemes for a Cocepual Framework There are hree passages i he SNA where resideial propery price idices are required o cover omial values io volumes or real values: he sock of resideial properies ha exis a a paricular locaio i he coury a a paricular poi i ime; he sales of resideial properies ha were sold i a paricular locaio i he coury over a paricular ime period, ad he srucures par of he sales of ew resideial properies ha were sold i a paricular locaio i he coury over a paricular ime period. 3.8 A coury s sock of resideial properies is a compoe of is aioal wealh. Hece, a price idex is required for resideial properies so ha balace shee esimaes of real wealh by compoe ca be formed. ( 2 ) Balace shee esimaes of aioal wealh ypically disiguish bewee he srucures compoe of resideial propery ad he lad compoe. If here is a eed o provide esimaes of he coury s real sock of resideial srucures ad he real sock of resideial lad, i will be ecessary o decompose resideial propery values io separae lad ad srucures compoes ad o cosruc price idices for each of hese compoes. 3.9 I may o be immediaely obvious why a price idex for he sales of resideial properies is required for aioal icome accouig purposes. I is used o esimae he real oupu of he resideial real esae services idusry, i.e., he idusry ha provides services ha faciliae resideial properies rasacios. Some algebra will help udersad why havig a price idex for he sales of resideial properies is esseial i his area. 3. Suppose ha he value of real esae age commissios is V C for some class of propery rasacios i period ad suppose ha he correspodig value of sales for he same group of properies (icludig he commissios) is V S. Furher, suppose ha a cosa qualiy price idex for his ype of sale has bee cosruced ad he period value of his price idex is P S.( 3 ) A esimae of volume of sales for his class of real esae rasacios i period, say Q, ca be calculaed wih he followig relaioship: S Q V / P (3.) S S S ( 2 ) A price idex for he sock of resideial properies is also of some use o ceral bakers who are ieresed i moiorig propery prices for he possibiliy of bubbles i heir couries; see Chaper 2. ( 3 ) Isead of usig a purchaser s price idex, i is also possible o use a seller s price idex. Whe cosrucig a cosa qualiy price idex for housig, should he price deermiig characerisics of he seller or hose of he purchaser be used o do qualiy adjusme? I could be argued ha he qualiy deermiig characerisics of he purchaser should be used i order o qualiy adjus prices for resideial properies, sice if he purchaser does o see eough value i he price of a propery, i will o be purchased. This suggess ha a purchaser s cosa qualiy price idex should be cosruced as opposed o a seller s cosa qualiy price idex. However, oe could also argue ha if he sellig price of a propery (regarded as a fucio of he characerisics of he propery) is o high eough, he producers of ew housig uis will o build a ew ui ad hus i is he price deermiig characerisics of he seller ha should cou, a leas i he coex of valuig ew housig uis. Rose (974) discusses hese issues. I erms of Rose s aalysis of he deermias of he hedoic surface, for he case of ew housig uis, i is likely ha his Case aalysis is releva, where cos codiios are ideical across firms ad hus he hedoic surface is deermied by he supply side of he marke; see Rose (974; 5-5). 3. The real esae idusry ca be reaed as a reailig or wholesalig idusry; i.e., i is a margi idusry ha ca be hough of as buyig a propery a he pre-commissio price ad sellig i a he pos-commissio price. The value of he service is equal o he commissio reveue, V C, ad he quaiy of he service is proporioal o he volume of he sales, Q S. Thus se he volume of he real esae services, Q C, equal o Q S : (3.2) Q Q C S 3.2 Fially, he price idex i period for he subsecor of he real esae idusry associaed wih he propery sales, wih value V S i period, is se equal o he value of he correspodig commissios, V C, divided by he correspodig volume, Q : C C C C P V / Q (3.3) = V /[ V / P ] usig (3.) ad (3.2) C = [ V / V ] P C m P C S S S S S = where m C = VC / VS is he period margi rae for his class of real esae rasacios; i.e., m C is he raio of commissios i period o he correspodig purchaser s oal value of he real esae rasacios. Thus he period price idex for he oupu of his segme of he real esae i- dusry is he produc of he margi rae m C imes he cosa qualiy price idex for he properies sold i period, P S. This demosraio illusraes why cosa qualiy price idices for sales of resideial properies are useful for aioal icome accouig purposes. 3.3 The hird value cell i he aioal accous ha requires a housig price deflaor is he value of ew housig produced i various locaios i he coury over a referece ime period. This value flow is par of gross capial formaio i he coury. Whe a ew propery is produced i he referece period ad if here were o improvemes made o he uderlyig lad ha he ew srucure occupies, he he porio of he sale price ha ca be aribued o he sie lad should be deduced from he sale price ad he residual amou is he par of gross capial formaio ad also par of he cosrucio idusry s oupu. Thus, a RPPI for he srucure compoe of he sales of ew resideial properies is required i he aioal accous. I will be ecessary o decompose sales of ew resideial properies io separae lad ad srucure compoes ad o cosruc a cosa qualiy price idex for he srucure compoe i order o serve he eeds of he aioal accous. 3.4 Recall he above discussio abou modelig he oupu of he real esae idusry. Because he sale of a ew propery will have various rasacios coss associaed wih i (e.g., real esae commissios), his leads o some Hadbook o Resideial Propery Prices Idices (RPPIs) 23

26 3 Elemes for a Cocepual Framework complexiies i he sysem of aioal accous ha have o ye bee defiiively resolved. From he viewpoi of he cosrucio idusry, hese rasacios coss are o par of he reveues ha accrue o he cosrucio secor, so hese coss should o be icluded i he value of he oupu of he cosrucio idusry. However, from he viewpoi of he secor ha purchases he ew housig ui, hese rasacios coss are a real cos ad hey mus be accoued for. There are a umber of ways ha rasacios coss associaed wih he purchase of a ew housig ui could be reaed (from he viewpoi of he purchaser): simply aribue all of he coss o he period of purchase ad rea he rasacios coss as a expediure by he purchaser ( 4 ) (which is a acquisiios approach o hese coss); iclude rasacios coss as par of he srucures compoe of he value of he purchase so ha hese coss would be amorized over ime usig he same depreciaio rae ha was beig used o depreciae he srucure; or separaely amorize he rasacios coss accordig o he average legh of ime a resideial propery of he ype uder cosideraio is beig held before i is resold. Cocepually, he las reame seems preferable ( 5 ) bu he firs ad secod reames will lead o a simpler se of accous. These issues eed o be sudied furher by aioal accouas wih ipu from he broader ecoomics commuiy. Resideial Propery Price Idices ad he Cosumer Price Idex 3.5 Pricig he services of Ower Occupied Housig (OOH) i a Cosumer Price Idex (CPI) is exesively deal wih i he Cosumer Price Idex Maual. ( 6 ) There is o uiversal cosesus o he reame of OOH i a CPI bu he CPI maual suggess four possible approaches. ( 7 ) These approaches rea he uique characer of OOH, which ivolves boh he acquisiio of a house ad he cosumpio over ime of he flow of services of he house, i a differe maer. The moey oulays or paymes approach. I his approach, he ou of pocke expeses of home owership are simply added up. These coss iclude expediures o maieace ad repair, morgage ieres coss, isurace premiums, propery axes ad codomiium charges (if he housig ui is a codomiium). Two impora ypes of implici cos ad oe impora implici beefi of home owership are o icluded. The wo omied coss are depreciaio ad he opporuiy cos of he fuds ha are ied up i he homeower s equiy i he house; he implici omied beefi is ay (e) capial gais ha may accrue o he ower durig he ime period uder cosideraio. ( 8 ) The moey oulays approach is useful if a aalys wishes o focus o he disposable icome of households. However, i is o paricularly useful as a measure of household cosumpio services (because of he omissio of he coss ad beefis meioed above). The (e) acquisiios approach. ( 9 ) I his approach, he services of OOH are igored i he CPI excep whe a ew housig ui is iroduced io he marke place. The purchase price of he ew dwellig ui is charged o he period of purchase so ha a purchase of a ew house is reaed i he same maer as he purchase of a odurable good or service, i.e. he purchase is reaed i he same way as he purchase of oher durable goods. A varia of his approach is o decompose he sellig price of he ewly buil resideial propery io lad ad srucures compoes ad o use jus he srucures compoe as he price which will eer io he CPI. The real equivalece approach. I his approach, a price is impued for he sheler cos of he ower occupied housig ui (boh for ew ad exisig uis), which is equal o he price a which he ui could be reed. ( ) The user cos approach. I his approach, he fiacial opporuiy cos of owig he house ad usig is services durig he referece period is calculaed. ( 4 ) The price idex ha could be used o cover he omial value of rasacio charges io a real amou (or volume) is a composie purchase price idex for he ype of propery uder cosideraio which icludes boh he lad ad srucures compoes. ( 5 ) This is he reame used by he Ausralia Bureau of Saisics. A uresolved issue is he choice of price deflaor i order o form real amorizaio charges. Tha is, should a srucures price idex be used or should a composie srucures ad lad price be used? I he case of real esae he commissios are geerally proporioal o he overall price of he propery (he sum of he lad ad srucures compoes) so i would be appropriae o use a composie propery price idex for he deflaio of his compoe of rasacios coss. Goverme rasacios axes or samp duies may impose differe raes o he lad ad srucures compoes of he sale ad so workig ou a appropriae real price for his compoe of rasacios coss may be raher complicaed. Agai, i may be accepable o avoid all of hese complexiies ad jus use a composie purchase price idex o do he deflaio. ( 6 ) See ILO, IMF, OECD, Eurosa, UN ad World Bak (24), Chaper 23. ( 7 ) Diewer (22) (29a) (29b) provides more discussio of aleraive mehods. ( 8 ) The moey oulays cocep is explaied i some deail i Baldwi, Nakamura ad Prud homme (2). ( 9 ) For a comprehesive pracical reame of he e acquisiios approach, see Eurosa s (22) Techical Maual o Ower Occupied Housig. ( ) This approach is cosise wih he reame of OOH i Naioal Accous. I he SNA, OOH is cosidered a fixed asse, ulike oher durables (such as washig machies, furiure, cars ec). The purchase of a house is cosidered a ivesme ad icluded i gross fixed capial formaio ad hus excluded from household fial cosumpio expediure; he same goes for exesios of he house ad major repairs. However, he owership of a house provides a service which is cosumed over ime by he ower ad he value of his service is icluded i household fial cosumpio expediure. 24 Hadbook o Resideial Propery Prices Idices (RPPIs)

27 Elemes for a Cocepual Framework 3 Sice he CPI Maual (24) was wrie, a fifh cocep for pricig he services of OOH has bee suggesed: ( ) The opporuiy cos approach. I his approach, he price for he services of a owed dwellig ui is se equal o he maximum of is real equivalece ad user cos prices. 3.6 The cocepual differeces bewee hese approaches should be uderlied. The real equivalece approach ad he user cos approach price he services of a ower occupied dwellig. The paymes approach measures he ou of pocke expeses of home owership. The e acquisiios approach akes a compleely differe perspecive, implicily allocaig all he services of he ewly purchased dwellig o he period of purchase. 3.7 I he above approaches excep he paymes ad real equivalece approaches, here is a eed for cosa qualiy price idices for eiher ewly-buil dwellig uis or for he exisig sock of dwellig uis. The user cos ad opporuiy cos approaches o pricig he services of a resideial housig ui are o eirely sraighforward. The Appedix o his chaper oulies he mechaics of hese approaches. 3.8 To summarize, RPPIs are eeded i he cosrucio of a CPI ad o deflae several value flows ad sock holdigs i he aioal accous. For boh CPI ad aioal accous purposes, i will be useful or ecessary o have a decomposiio of he price idices io srucures ad lad compoes. More specifically, i would be useful o be able o cosruc he followig se of RPPIs: ( 2 ) a price idex for he oal sock of resideial housig a a paricular mome i ime, which is eeded for esimaig real chages of he ecoomy s sock of resideial housig, a compoe of a aio s real wealh; a price idex for he ower occupied sock of resideial housig (a subidex of he idex i he bulle poi above), which is eeded o cosruc esimaes for he value of OOH services based o user cos or opporuiy cos priciples; a price idex for resideial propery sales (boh ewlybuil ad exisig dwellig uis) ha ook place durig a give period of ime, which is eeded for esimaig he real oupu of he resideial real esae services secor; a price idex for he sales of ewly-buil resideial properies durig a give period of ime, which is required if a broadly defied e acquisiios approach is used where boh he srucures ad lad compoes would be icluded i he purchase; ( ) See Diewer (29b), Diewer ad Nakamura (29) ad Diewer, Nakamura ad Nakamura (29). ( 2 ) Fewick (25) (26) argued ha i would be useful o develop a cohere cocepual framework for a family of real esae price idexes. I ca be see ha user eeds will vary ad ha i some isaces, more ha oe measure of house price or real esae iflaio may be required. I ca also be see ha coherece bewee differe measures ad wih oher ecoomic saisics is impora ad ha achievig his will be especially difficul as saisicias are ulikely o have a ideal se of price idicaors available o hem. David Fewick (26; 8). a price idex for he srucures compoe of ewly-buil resideial properies ha were sold durig a give period of ime, which is eeded for a arrowly defied e acquisiios approach where oly he srucures compoe would be icluded i he purchase. Mai Mehods 3.9 To measure pure price chage, real esae prices mus be adjused for qualiy chage. I oher words, o compile a cosa qualiy RPPI, i will be ecessary o somehow corol for ay variaios i he amous of he price deermiig characerisics of he properies. The mos impora characerisics are: he area of he srucure (i squared fee or i meers squared); he area of he lad ha he srucure sis o (i squared fee or meers squared); he locaio of he propery; he age of he srucure; he ype of srucure; he srucure ca si eirely i he lo wihou sharig ay walls wih a adjace srucure (deached dwellig ui) or share oe wall wih a eighbourig ui (semi-deached dwellig ui), or he dwellig ui ca be a sigle aparme or ui i a mulifamily residece (aparme or codomiium buildig); he maerials used i he cosrucio of he house (primarily wood, brick, cocree or radiioal maerials; i.e., a shack or shay), ad oher price deermiig characerisics such as he umber of bedrooms, he umber of bahrooms, a garage, a swimmig pool, air codiioig, disace o ameiies, ec. 3.2 Four mai mehods have bee suggesed i he lieraure o corol for chages i he amous of he propery characerisics: sraificaio or mix adjusme, repea sales mehods, hedoic regressio mehods, ad he use of propery assessme iformaio. Below, a brief overview of he four mehods is provided. More deails ca be foud i Chapers Sraificaio of rasacios accordig o some of he price deermiig characerisics is a sraighforward ad compuaioal simple way o adjus for chages i he qualiy mix of he samples i differe ime periods. By defiig a umber of reasoably homogeeous sraa or cells, he average sellig price wihi each cell ca be used as a (proxy o a) cosa qualiy price for ha ype of propery. Regular idex umber heory ca he be applied o aggregae up he average prices by cell io a overall idex. Such sraificaio mehods are also kow as mix adjusme Hadbook o Resideial Propery Prices Idices (RPPIs) 25

28 3 Elemes for a Cocepual Framework mehods. Wood (25) describes his mehod i he followig way: House price observaios are grouped io ses or cells of observaios o houses wih similar locaio ad physical aribues. [..] The mea prices i each cell are weighed ogeher o give a mix adjused price. A chage i he composiio of he sample will aler he umber of observaios i each cell. Bu if he cells are defied sufficiely precisely, so ha all elemes of he cell have similar prices ad price reds, he such composiioal chages will o sysemaically affec he mix adjused house price. Rober Wood (25; 24) The repea sales mehod addresses he qualiy mix problem by comparig properies ha have sold more ha oce over he sample period. Resricig he compariso o uis ha have sold repeaedly esures ha he price relaives compare like wih like, provided ha he qualiy of he houses remaied uchaged. The sadard repea sales mehod is based o a regressio model where he repea sales daa peraiig o all periods are pooled. A poeial drawback of his approach is he issue of revisios : whe ew periods are added o he sample ad he model is re-esimaed, he previously esimaed price idices will chage. A advaage of repea sales mehods is ha, because properies are mached a he address level, locaio, a impora facor affecig real esae prices, is held cosa Oe oher poeial drawback of he repea sales mehod is ha i does o accou for qualiy chages of he sampled houses; over ime a dwellig ui ca udergo reovaios ad be subjec o depreciaio. Cosequely, he qualiy of he propery ca vary wih ime. Hedoic regressio mehods ca i priciple adjus for such qualiy chages i addiio o chages i he qualiy mix of he samples. These mehods uilize iformaio o he releva propery characerisics o esimae qualiy adjused price idices usig regressio echiques, hough i may prove difficul o sufficiely corol for locaio. There are differe ways o esimae hedoic price idices. The ime dummy variable mehod has bee promie i he real esae lieraure. This mehod models he price of a propery as a fucio of is characerisics ad a se of ime dummy variables. Because he daa for all periods are pooled, he resulig idices are subjec o revisios like wih he repea sales mehod. Aoher drawback of he ime dummy mehod is ha i places perhaps uwarraed resricios o variaios i he price of lad ad srucures across ime. These difficulies wih he ime dummy varia of he hedoic regressio approach ca be avoided by usig aoher varia of he mehod kow as he hedoic impuaio mehod May couries ax real esae propery ad are likely o have a official propery valuaio office ha provides periodic appraisals of all axable real esae properies. Assessme-based mehods combie sellig prices wih appraisals o compue price relaives (sale price appraisal raios) ad corol for qualiy mix chages. The Sale Price Appraisal Raio (SPAR) mehod is based o he mached model mehodology. I coras o he repea sales mehod, i relies o all (sigle ad repea) sales daa, ad here is o revisio of previously esimaed idices. Of course he mehod ca oly be applied i couries where reliable assessed values of he properies are available If he referece period is a year, all mehods will ed o geerae similar esimaes of he red i resideial propery price chages for a eire coury. However, as will be see i he examples preseed i Chapers 4-7 ad Chaper, differe mehods do geerae small bu sigifica differeces i reds while for shorer periods hey ca lead o raher differe esimaes of price chage. The various mehods could also produce differe sigals of urig pois As hedoic mehods assume ha iformaio o he characerisics of he properies sold is kow, he samples ca be sraified ad, if a sufficie umber of observaios is available, separae idices ca be esimaed for he sraa. I oher words, hedoic regressio mehods ca provide a se of cosa qualiy price idices for various ypes of propery. Obviously, if daa o some price deermiig characerisics are available, he repea sales ad assessme-based mehods ca also be combied wih sraificaio Sraificaio ca also be used o approximae a sock based RPPI. I his case he sraum weighs will be based o cesus daa peraiig o he value of he ower occupied housig sock. The sraum price idices will sill be based o sample daa of properies sold. Wihi each sraum, he properies raded are ow reaed as a (radom) sample from he sock. Sice log ime iervals bewee wo cesuses is he orm, sock value weighs ca usually oly be updaed very ifrequely As was discussed previously, for various purposes i is ecessary o decompose he overall price of a propery io (addiive) compoes ha reflec he price of he srucure ad he price of he lad he srucure is locaed o. I Chaper 8 i is show how hedoic regressio echiques ca be used o accomplish his decomposiio. 26 Hadbook o Resideial Propery Prices Idices (RPPIs)

29 Elemes for a Cocepual Framework 3 The Frequecy of he RPPI ad User Needs 3.29 For iflaio moiorig purposes, mos ceral baks would prefer a RPPI o a mohly or quarerly basis. For aioal accous purposes quarerly idices will suffice, while for CPI purposes mohly idices are geerally required. Give ha he umber of observaios for a mohly price idex will oly be approximaely oe hird of he umber for a quarerly idex, saisical agecies will have o carefully evaluae he radeoff bewee publicaio frequecy, imeliess ad accuracy. The use of mohly daa may lead o raher oisy figures, whaever mehod used o compile a RPPI. To miigae he oise, a movig average could be compued bu his creaes ew problems, as will be explaied below. ( 3 ) 3.3 I is useful o oulie some of he radeoffs ha saisical agecies may face whe aempig o cosruc house price idices ha mee he eeds of users. Before examiig he radeoffs, i will be ecessary o review he user eeds for a family of resideial propery price idices. The followig lis of user eeds is borrowed from he lis compiled by Emily Carless (2) from he Naioal Saisicia s Office of he UK Saisics Auhoriy. The family of RPPIs should: ( 4 ) be based o he price paid for rasaced properies; be sraified by regio; be sraified by ype of housig (e.g., deached, row, high rise, ype of cosrucio, ec.); be compued o a mohly basis; aggregae up o a cosise aioal idex; be accurae ad imely wih miimal revisios. The fifh requireme, ha he various sub-idices aggregae up o a cosise aioal idex is o oo difficul o saisfy. Wheher he firs requireme, ha he price idices be based o rasacio prices, ca be me, depeds o availabiliy of he daa. I may couries, acual sellig prices are used o compile RPPIs, bu o all saisical agecies may have access o rasacio daa. Eve if rasacio daa are available, here ca be a ime lag ivolved (as will be discussed i Chaper 9), so ha i pracice he firs requireme could be a odds wih he sixh requireme, i.e., ha he idices should be imely. 3.3 There are also coflicig objecives wih some of he oher requiremes: havig may sraa ad askig for mohly idices may lead o a siuaio where some sraa have oly few rasacios, resulig i raher volaile ad iaccurae sub-idices. Alhough akig movig averages of he mohly idices ca reduce volailiy, ( 5 ) such a sraegy will o provide imely sigals of price chage. Tha is, he resulig average idex will be ceered i he middle of he ime period for he movig average ad will o be available uil some mohs have passed. ( 6 ) I paricular, his could give a misleadig picure of he upswigs ad dowurs i he housig marke. So i geeral, i will o be possible o mee wih a sigle price idex all he above lised user eeds, ad saisical agecies will have o make some compromises i heir aemps o mee he differe user eeds. Cosisecy of Mohly wih Quarerly Esimaes 3.32 How ca mohly esimaes of real esae price chages be made cosise wih quarerly esimaes? The aswer o his quesio is reasoably sraighforward if he same average price or ui value mehodology is applied o he quarerly daa as is applied o he mohly daa. Suppose ha a mohly sales RPPI is cosruced usig he sraificaio (or mix adjusme) mehod. As will be explaied i Chaper 4 more horoughly, he mohly price for a paricular cell is he average rasacio price or ui value ad he correspodig quaiy is he oal umber of properies raded. The quarerly RPPI for ha cell would sar ou by calculaig a quarerly ui value, ad he correspodig quaiy is he quarerly oal umber of sraum rasacios. Some algebra will make clearer he relaioship bewee he quarerly cell price ad quaiy daa o he correspodig mohly daa. ( 7 ) 3.33 Suppose ha here are T quarers of mohly daa. Deoe he value of quarerly rasacios i a paricular cell i he sraificaio scheme by V for =,..., T. Wihi each quarer, he value of firs moh rasacios is deoed by V, of secod moh rasacios by V 2 ad of hird moh s rasacios by V 3. The quarer mohly ui value prices are deoed by P, P 2 ad P 3 ( 3 ) Neverheless, movig averages are, for example, used i Icelad. I may also be ecessary o use slighly ou of dae iformaio i a mohly CPI coex; see Gudaso ad Jósdóir (26; 4). ( 4 ) I addiio o he requiremes lised, Carless oed ha users desire a clear explaaio of he mehods used o cosruc he saisics ad idicaors of he qualiy of he measures. Also, some users wa seasoally adjused series i addiio o he uadjused series. ( 5 ) The volailiy may also be miigaed by combiig some sraa, bu he users may lose some of he desired geographical deail or ype of housig coverage hey were expecig. I addiio, he ew combied sraa may o be subjec o he same price red ad hus here is he possibiliy of some resulig ui value bias due o he aggregaio of he sraa. ( 6 ) This umber is equal o half he widow legh of he movig average. ( 7 ) The same ype of aalysis ca be applied o he relaioship bewee a aual (mix adjusme) sales RPPI ad he correspodig quarerly esimaes. Hadbook o Resideial Propery Prices Idices (RPPIs) 27

30 3 Elemes for a Cocepual Framework ad he correspodig mohly umber of rasacios are deoed by Q, Q 2 ad Q 3. Noe ha V m equals P Q m m for m =,2, 3 ad =,..., T. The value of rasacios for quarer, V, is equal o he sum of he mohly rasacios wihi he quarer: V V + V2 + V3 = P Q + P2 Q2 + P3 Q3 = (3.4) =,...,T The quarerly quaiy series, Q, is he sum of he mohly rasacios wihi he quarer ad he quarerly price series, P, is he quarerly ui value for he cell uder cosideraio; i.e.: Q Q + Q2 + Q3 = (3.5) P / =,...,T = V Q (3.6) = [ P Q + P2 Q2 + P3 Q3 ]/[ Q + Q2 + Q3 ] = s P + s2p2 + s3p3 =,...,T where he moh m share of rasacios i quarer, is defied as s / s m, m = Qm Q (3.7) m =,2,3 ; =,..., T Thus, he quarerly price level for he cell uder cosideraio, P, is equal o a rasacio share weighed average of he mohly price levels P for he mohs m i quarer. m 3.34 For RPPI cosrucio mehods oher ha sraificaio (hedoic regressio, repea sales, use of appraisal daa), he relaioship bewee he quarerly esimaes of price chage ad he correspodig mohly esimaes will be more complex. However, i he ed, hese mehods will geerae a price idex, say P for period, ha is associaed wih a cerai group of rasacios (or socks). Geerally, he correspodig period value associaed wih hese socks, say V, will be available ad hus a correspodig period volume, Q = V /P, ca be defied, so he above algebra ca be applied. Revisio Policies 3.35 I would seem ha a RPPI for he sales of properies could be cosruced wihou a eed for revisios bu as i urs ou, i is o always easy o gaher imely daa o propery sales. The cosrucio of a sock ype RPPI is depede o cesus iformaio o housig, which is ofe subjec o log delays. Moreover, whe a ew cesus becomes available, i is geerally desirable o use his iformaio o rerospecively adjus he sock ype RPPI back o he ime of he previous housig cesus. Thus, i will geerally be desirable o allow sock RPPIs o be revised. This should o pose ay major problems for aioal accous purposes, sice hey are rouiely subjec o revisios Revisios do cause problems, however, i he coex of o-revisable saisics such as he CPI. The reame of ower occupied housig i a CPI requires a sock ype RPPI if eiher he user cos or opporuiy cos approach is used. ( 8 ) I may he be ecessary o use prelimiary iformaio o compile he RPPI. Whe addiioal daa become available, a revised CPI could be published as a aalyical series so ha aalyss could form some rough esimaes of he possible bias i usig he uadjused CPI based o a prelimiary esimae of he RPPI for ower occupied housig. Seasoal Adjusme 3.37 Alhough he siuaio may differ somewha across couries, i geeral here are subsaial seasoal flucuaios i he quaiies of properies raded over he year. For he cosrucio of a RPPI, he quesio is wheher seasoaliy i quaiies leads o seasoaliy i prices. The empirical evidece is somewha mixed. Meese ad Wallace (99) fid limied seasoaliy i prices i heir ecoomeric sudy. Prasad ad Richards (28) repor ha media prices i Ausralia ciies are seasoal, bu his seasoaliy vaishes afer corollig for composiioal chage hrough sraificaio. A aggregae levels, ad paricularly a he aio-wide level, i seems herefore ulikely ha RPPI series exhibi srog seasoal flucuaios. However, a lower levels of aggregaio i would be useful o check wheher ay seasoaliy i prices is prese ad adjus for his if seasoally adjused series are required. Some users do wa seasoally adjused series made available o hem (i addiio o he uadjused series) if here is evidece of seasoaliy i prices I Chaper 4, a umerical example is worked ou which shows how seasoaliy ca be reaed usig simple idex umber echiques. Sadard seasoal adjusme mehods could also be used. ( 8 ) The acquisiios approach requires a ew house price idex which probably should exclude he lad compoe of he sellig price of a ew dwellig ui. This ew house price idex could be adequaely approximaed by a suiable ew house cosrucio price idex. 28 Hadbook o Resideial Propery Prices Idices (RPPIs)

31 Elemes for a Cocepual Framework 3 Appedix: The Role of House Price Idices i he Cosrucio of User Coss 3.39 This Appedix shows how user coss ad opporuiy coss ca be cosruced. The firs secio discusses how user coss are cosruced for durable goods i geeral. Nex, addiioal difficulies are brough i which arise from he fac ha properies are uique goods ad are a mixure of lad ad srucures compoes. Fially, he opporuiy cos approach o pricig he services of Ower Occupied Housig (OOH) is discussed. The Cosrucio of User Coss for Durable Goods i Geeral 3.4 I his secio, he elemes of user cos heory for a durable cosumer good are laid ou. The essece of durabiliy is ha i provides some sor of service o he purchaser over may ime periods. For may purposes (icludig he valuaio of household cosumpio expediures o ower occupied housig services) i is o appropriae o apply he eire purchase cos of a durable good o he iiial period of purchase; he purchase cos should be spread over is useful life. The quesio he becomes: how should his ieremporal cos be allocaed over ime? 3.4 There are wo mai approaches o pricig he services of a ower occupied dwellig ui: ( 9 ) he real equivalece approach ad he user cos approach. The user cos approach is impora i is ow righ whe oly few dwellig uis i a coury are reed, i is o realisic o value he services of ower occupied housig usig he real equivalece approach bu i also is impora as a way o explai how ladlords migh se heir res for real dwellig uis. However, pricig sheler services is more difficul ha pricig he services of, say, a sadard model auomobile because housig services are more complex. ( 2 ) Therefore, i his secio he problems of pricig he services of a ordiary durable cosumer good (ha is available i he same form over may periods) will firs be preseed before dealig wih he complexiies associaed wih housig The user cos approach o he reame of durable goods is i some ways very simple: i calculaes he cos of ( 9 ) The acquisiios approach implicily allocaes all of he services of a ewly purchased housig ui o he period of purchase bu he Sysem of Naioal Accous does o recogize his approach as a valid approach o pricig he services of OOH. For oher durable goods, he SNA does recogize he acquisiios approach as a valid approach for pricig he services of a durable good. ( 2 ) I paricular, housig services provide he joi services of he srucure ad he lad ha he srucure sis o ad houses are geerally uique goods. purchasig he durable good a he begiig of he period, usig he services of he durable over may periods ad he eig off from hese coss he beefis ha could be received by sellig he durable good a he ed of he period, akig io accou he ieres foregoe from havig oe s capial ied up i purchasig he durable. However, here are several deails ha are somewha coroversial such as he reame of depreciaio, ieres ad capial gais or holdig gais Aoher complicaig facor wih he user cos approach is ha i makes a disicio bewee curre period purchases wihi he period uder cosideraio ad he holdig of physical socks of he durable a he begiig ad ed of he accouig period. Normally i he sysem of aioal accous, all purchases are hough of as akig place a a sigle poi i ime, say i he middle of he period uder sudy, ad cosumpio is hough of as akig place wihi he period as well. Thus, i his case where he commodiy is eirely cosumed wihi he purchasig period, here is o eed o cosider he valuaio of socks of cosumer durables ha households may have a heir disposal. The complexiy ivolved i accouig for socks ad flows are ufamiliar o may price saisicias, so i may be useful o describe hese problems i some deail here To deermie he e cos of usig a paricular durable good durig say period, assume ha oe ui of he durable good is purchased a he begiig of period a he price P. The used or secod-had durable good ca be sold a he ed of period a he price P S. I migh seem ha a reasoable e cos for he use of oe ui of he cosumer durable durig period would be is iiial purchase price P less is ed of period scrap value or marke opporuiy sellig price, P S. However, moey received a he ed of he period is o as valuable as moey received a he begiig of he period. To cover he ed of period value io is begiig of he period equivale value, i is ecessary o discou he erm P S by he erm +r where r is he begiig of period omial ieres rae ha he household (or purchaser) faces. Hece, he period user cos u for he cosumer durable ( 2 ) is defied as u P - P S /(+r ) (3.A) 3.45 There is aoher way o ierpre he user cos formula (3.A): he cosumer purchases he durable a he begiig of period a he price P ad charges himself or herself he real price u. The remaider of he purchase price, I, defied as I P - u (3.A2) ( 2 ) This approach o he derivaio of a user cos formula was used by Diewer (974) who i ur based i o a approach due o Hicks (946; 326). Noe ha laer, his user cos will be ierpreed as a begiig of he period user cos sice all coss are discoued o he begiig of he period. Hadbook o Resideial Propery Prices Idices (RPPIs) 29

32 3 Elemes for a Cocepual Framework ca be regarded as a ivesme, which is o yield he appropriae opporuiy cos of capial r he cosumer faces. A he ed of period, his rae of reur could be realized provided ha I, r ad he sellig price of he durable a he ed of he period P S saisfy I (+r ) = P S (3.A3) Give P S ad r, (3.A3) deermies I, which i ur, give P, deermies he user cos u via (3.A2). ( 22 ) 3.46 From he above i is clear ha he user cos approach o pricig he services of a durable good for a period ivolves a ivesme aspec. Noe ha he user cos approach is also a fiacial opporuiy cos approach; i.e., he opporuiy cos of he fiacial capial ha is ied up i he purchase (or coiued holdig) of he durable good is ake io accou. Fially, oe ha user coss are o like he prices of odurables or services because he user cos cocep ivolves pricig he durable a wo pois i ime raher ha a a sigle poi i ime. Because he user cos cocep ivolves prices a wo pois i ime, moey received or paid ou a he firs poi i ime is more valuable (assumig prices are goig up i he ecoomy) ha moey paid ou or received a he secod poi i ime ad so ieres raes filer io he user cos formula Also, because he user cos cocep ivolves prices a wo pois i ime, expeced prices ca be ivolved if he user cos is calculaed a he begiig of he period uder cosideraio isead of a he ed. So he price saisicia has wo opios for he choice of P S : Use he expeced price of he durable a he ed of he period from he perspecive of he begiig of he period, or Use he acual marke price of a similar secod had durable a he ed of he period (if such a marke price exiss) The use of a expeced price leads o a ex ae user cos whereas he use of a acual marke price for he used durable a he ed of he period leads o a ex pos user cos. Which cocep should be used i pracice? I he prese coex i is reasoable o favour he ex ae cocep for wo reasos: The ex ae user cos cocep is likely o be closer o a real price of he durable good (if i exiss), ( 23 ) which may price saisicias would view as a preferred price for he services of he durable durig he period, ad The ex ae user cos is closer o he purchaser s expeced cos for usig he durable good durig he period; he purchaser cao kow exacly wha he ed of period price will be ad hece mus form expecaios abou he ed of period price of he durable, which leads o he ( 22 ) This derivaio for he user cos of a cosumer durable was also made by Diewer (974; 54). ( 23 ) If a compay is i he busiess of leasig he services of a auomobile for a cerai period, i has o form expecaios abou he price of is used auos a he ed of he leasig period i order o calculae is schedule of real or leasig prices for is sock of auomobiles. ex ae user cos as he expeced cos for usig he services of he durable durig he period. Thus, he ex ae user cos is likely o be he releva charge for he services of he durable ha moivaes cosumer behavior. The issue of how exacly oe forms expecaios for he sellig price of a used durable will be examied laer whe he pricig of housig services is discussed Wih all of he above complicaios, i is udersadable ha may price saisicias would like o avoid usig user coss as a pricig cocep. However, he use of user coss may be uavoidable i he coex of pricig he services of owed dwelligs uder cerai codiios. The user cos formula (3.A) ca be expressed i a more familiar form usig he ed of period depreciaio rae d ad he period asse iflaio rae i. Defie he ed of period depreciaio rae d by ( - d ) P S /P (3.A4) where P S is he price of a used asse a he ed of period ad P is he price of a ew asse a he ed of period. ( 24 ) The period iflaio rae for he ew asse, i, is defied by +i P /P (3.A5) Elimiaig P from equaios (3.A4) ad (3.A5) leads o he followig formula for he ed of period used asse price: P S = ( - d )( + i )P (3.A6) Subsiuio of (3.A6) io (3.A) yields he followig expressio for he period user cos u : u = [( + r ) - ( - d )( + i )]P /( + r ) (3.A7) Noe ha r - i ca be ierpreed as a period real ieres rae ad ha δ (+i ) ca be ierpreed as a iflaio adjused depreciaio rae. 3.5 I (3.A7), he user cos u is expressed i erms of prices ha are discoued o he begiig of period. However, i is also possible o express he user cos i erms of prices ha are aidiscoued or appreciaed o he ed of period. ( 25 ) The ed of period user cos p is defied as p ( + r )u = [( + r ) - ( - d )( + i )]P = [r - i + d ( + i )]P (3.A8) where he secod equaio follows usig (3.A7). If he real ieres rae r * is defied as he omial ieres rae r less ( 24 ) If he durable ha was purchased (or held) by he household a he begiig of he period was a used durable, he ierpre P as he secod had marke price of a used durable ha is i he same codiio as he iiially held durable. ( 25 ) Thus, he begiig of he period user cos u discous all moeary coss ad beefis io heir dollar equivale a he begiig of period whereas p accumulaes or appreciaes all moeary coss ad beefis io heir dollar equivale a he ed of period. This leaves ope how flow rasacios ha ake place wihi he period should be reaed. Followig he coveios used i fiacial accouig suggess ha flow rasacios akig place wihi he accouig period be regarded as akig place a he ed of he accouig period ad hece followig his coveio, ed of period user coss should probably be used by he price saisicia. For addiioal maerial o begiig ad ed of period user coss, see Diewer (25; 485). 3 Hadbook o Resideial Propery Prices Idices (RPPIs)

33 Elemes for a Cocepual Framework 3 he asse iflaio rae i ad if he geerally small erm d i is egleced, he he ed of he period user cos defied by (3.A8) reduces o ( 26 ) p = (r * + d )P (3.A9) Absracig from rasacios coss, i ca be see ha he ed of he period user cos defied by (3.A9) is a approximae real cos; he real cos for he use of a durable good should equal he (real) opporuiy cos of he capial ied up, r * P, plus he declie i value of a ew asse over he period, d P. Formulae (3.A8) ad (3.A9) hus cas some ligh o he ecoomic deermias of real or leasig prices for cosumer durables. 3.5 If he simplified user cos formula defied by (3.A9) above is used, he formig a price idex for he user cos of a durable good is o very much more difficul ha formig a price idex for he purchase price of he durable good, P. The price saisicia eeds oly o Make a reasoable assumpio as o wha a appropriae mohly or quarerly real ieres rae r * should be; ( 27 ) Make a assumpio as o wha a reasoable mohly, quarerly or aual depreciaio rae d should be; ( 28 ) Collec purchase prices P for he durable ad form he user cos There are some addiioal difficulies associaed wih he user cos approach o measurig he services of a cosumer durable. The above discussio deals oly wih he formaio of a user cos for a ewly purchased cosumer durable. I is ecessary o exed he aalysis o price he services of used uis of he cosumer durable as well. I order o price ou he services of a used durable good, i is ecessary o make assumpios abou he form of depreciaio of he good; does he service flow give o he cosumer remai cosa hroughou he useful life of he durable good or does i declie as he good ages? If he service flow remais cosa, he we have oe hoss shay or ligh bulb depreciaio whereas if he service flow ( 26 ) If oe akes he raio of he approximae real price for he durable good, p, o is asse value, P, he re o value raio p /P = r * + d is obaied, which is equal o he sum of he appropriae real ieres rae r * plus he appropriae depreciaio rae d. Sice real raes of ieres ad depreciaio raes are approximaely cosa over ime, he re o value raio will also be approximaely cosa over ime ad hece a hisorical re o value raio imes a curre asse price idex will geerally give a adequae approximaio o a impued real rae for he cosumer durable. I he housig lieraure, a re o value raio is ofe called a capializaio rae; e.g., see Garer ad Shor (29; 237) or Croe, Nakamura ad Voih (29; 7). ( 27 ) This is o compleely sraighforward. I is difficul o deermie exacly wha he appropriae household omial opporuiy cos of capial should be ad eve if we come o agreeme o his poi, here will be difficulies i esimaig expeced iflaio raes. I he ed, i may boil dow o pickig a somewha arbirary real ieres rae i he 2% o 5% rage (for aual raes), depedig o he rece experiece of he coury uder cosideraio. ( 28 ) The geomeric model for depreciaio requires oly a sigle mohly or quarerly depreciaio rae. Oher models of depreciaio may require he esimaio of a sequece of viage depreciaio raes. If he esimaed aual geomeric depreciaio rae is d a, he he correspodig mohly geomeric depreciaio rae δ ca be obaied by solvig he equaio ( - δ) 2 = - d a. Similarly, if he esimaed aual real ieres rae is r a *, he he correspodig mohly real ieres rae r* ca be obaied by solvig he equaio ( + r*) 2 = + r a *. declies a a cosa liear or geomeric rae, he we have sraigh lie or geomeric depreciaio. ( 29 ) 3.53 How ca oe ell wheher oe hoss shay or geomeric depreciaio is applicable for a cerai cosumer durable? The wo paers of depreciaio (ad user valuaio) ca be disiguished if cross secioal iformaio o reals of he cosumer durable by he age of he reed asse is available. If depreciaio is hough o follow ha of he oe hoss shay, he he real raes for he cosumer durable a a give poi i ime should be approximaely cosa for all ages of he durable good whereas if here is geomeric depreciaio, he real raes for he good should declie a a geomeric rae accordig o he age of he used durable good. Thus, he various paers of depreciaio ca be disiguished if real markes for used durables exis. I a similar fashio, whe cross secioal iformaio o he prices of used uis of he cosumer durable is available, aleraive paers of depreciaio ca be disiguished. ( 3 ) The User Cos of Ower Occupied Housig 3.54 A ower occupied dwellig is differe from a ormal cosumer durable good because of is uique characer. Cosequely, i will be difficul o use iformaio o used asse prices i order o deermie he paer of depreciaio, which is required o measure a user cos for a owed dwellig ui. As was meioed i he iroducio o his chaper, a paricular dwellig ui i a paricular coury is uique for a umber of reasos: The locaio of each dwellig ui is uique ad locaio will affec he price of he ui. Over ime, he dwellig ui depreciaes; uless here is oe hoss shay depreciaio, he uiliy geeraed by a paricular dwellig for he occupyig household will ed o declie over ime due o he effecs of he agig of he srucure. O he oher had, he effecs of depreciaio ca be offse by reovaio expediures, which icrease he uiliy of he dwellig ui For some purposes, i is impora o decompose he price of a propery io lad ad srucures compoes. To model he fac ha housig is a composie good, ( 29 ) For descripios of how o cosruc user coss by he age of he asse for each of hese depreciaio models, see Diewer ad Lawrece (2) or Diewer (25; 56-52). ( 3 ) I he housig coex where each house ca be regarded as a uique asse, i is ecessary o make some addiioal assumpios i order o ideify he form of depreciaio. The exra assumpios are of he followig ype: i is assumed ha all housig uis i a cerai class of srucures have a similar paer of depreciaio. Usig his ype of assumpio, empirical evidece suggess ha oe hoss shay depreciaio is ulikely i he housig marke sice reers are geerally willig o pay a re premium for a ew ui over a older ui of he same ype. For empirical evidece of his age premium, see Malpezzi, Ozae ad Thibodeau (987; 378) ad Hoffma ad Kurz (22; 9). Hadbook o Resideial Propery Prices Idices (RPPIs) 3

34 3 Elemes for a Cocepual Framework cosider a paricular ewly cosruced dwellig ui ha is purchased a he begiig of period. Suppose ha he purchase price is V. This value ca be regarded as he sum of he cos of producig he srucure, P S Q S, where Q S is he umber of square meers of floor space i he srucure ad P S is he begiig of period price of cosrucio per square meer, ad he cos of he lad, P L Q L, where Q L is he umber of square meers of he lad ha he srucure sis o ad he associaed yard ad P L is he begiig of period price of he lad per square meer. ( 3 ) Thus a he begiig of period, he value of he dwellig ui is V defied as follows: V = P S Q S + P L Q L (3.A) 3.56 Suppose ha he aicipaed price of a ui of a a ew srucure a he begiig of period is P S ad ha he aicipaed price of a ui of lad a he begiig of a period is P L. Defie he period aicipaed iflaio raes for ew srucures ad lad, i S ad i L respecively, as follows: a + i S P S /P S (3.A) a + i L P L /P L (3.A2) Le d be he period depreciaio rae for he srucure. The aicipaed begiig of period value for he srucure ad he associaed lad is he equal o V a a = P S ( - d a )Q S + P L Q L (3.A3) So he aicipaed value of he dwellig ui a he ed of period, V a, equals he aicipaed price (per ui of ew a srucure of he same qualiy) a he ed of he period, P S, imes oe mius he period depreciaio rae, ( - δ ), imes he quaiy of srucure purchased a he begiig of period, Q S, ( 32 ) plus he aicipaed price of lad a a he ed of period, P L, imes he quaiy of lad ha he srucure associaed wih he srucure, Q L Now calculae he cos (icludig he impued opporuiy cos of capial r ) ( 33 ) of buyig he dwellig ui a he begiig of period ad (hypoheically) sellig i a he ed of period. The followig ed of period user cos or impued real cos R for he dwellig ui is obaied usig (3.A)-(3.A3): R V ( + r ) - V a (3.A4) = [P S Q S + P L Q L ]( + r a ) - [P S ( - d a )Q S + P L Q L ] ( 3 ) If he dwellig ui is par of a muliple ui srucure, he he lad associaed wih i will be he appropriae share of he oal lad area. This share could be divided by he umber of uis o he plo or he floor space of he ui divided by he oal floor space of he eire srucure. Eiher share allocaio could be jusified. ( 32 ) Thus he period depreciaio rae d is a ed of period aicipaed cross secioal depreciaio rae; i.e., d is defied by he equaio (-d ) = V S a /(P S a Q S ), where V S a is he aicipaed marke value of he (depreciaed) srucure a he ed of period ad P S a Q S is he aicipaed ed of period value of a ewly cosruced srucure wih floor space area Q S. ( 33 ) More elaborae discussios o how o choose he appropriae opporuiy cos of capial whe he ower of a dwellig ui has a morgage o he ui ca be foud i Diewer ad Nakamura (29), Diewer, Nakamura ad Nakamura (29) ad Garer ad Verbrugge (29b; 76). = [P S Q S + P L Q L ]( + r ) - [P S ( + i S )( - d )Q S + P L ( + i L )Q L ] = p S Q S + p L Q L where separae period user coss of srucures ad lad, p S ad p L, are defied as follows: p S = [( + r ) - ( + i S )( - d )]P S = [r - i S + d ( + i S )]P S (3.A5) p L = [( + r ) - ( + i L )]P L = [r - i L ]P L (3.A6) Noe ha he above algebra idicaes some of he mos impora deermias of marke res for real properies. ( 34 ) The user cos formulae defied by (3.A5) ad (3.A6) ca be furher simplified if he approximaios ha were made i he previous secio are made here as well (recall equaio (3.A9) above); i.e., assume ha he erms r - i S ad r - i L ca be approximaed by a real ieres rae r * ad eglec he small erm d imes i S i (3.A5). The he user coss defied by (3.A5) ad (3.A6) simplify o p S = (r * + d )P S (3.A7) p L = r * P L (3.A8) 3.58 The above exposiio has egleced wo oher sources of period cos associaed wih owig a dwellig ui: Various maieace ad isurace coss ha are associaed wih he owership of a dwellig ui ad Propery axes ha may be payable by he ower o local or sae govermes. Assume ha period maieace ad isurace coss, M S, are maily associaed wih he srucure raher ha he lad uder he srucure. Suppose ha hese coss are paid a he ed of period. These coss ca be covered io a per ui srucure charge m S as follows: m S M S /(P S Q S ) (3.A9) Suppose he propery axes ha fall o he srucure, T S, ad he propery axes ha fall o he lad uder he srucure, T L, are paid a he ed of period. The he period srucure ad lad propery ax raes, S ad L, ca be defied as follows: S T S /(P S Q S ) ad L T L /(P L Q L ) (3.A2) These addiioal maieace ad propery ax coss eed o be added o he impued real cos for usig he dwellig ui R. Thus (3.A4) ow becomes: R V ( + r ) - V a + M S + T S + T L = p S Q S + p L Q L (3.A2) ( 34 ) Lookig a (3.A6), i ca be see ha he lad user cos could be egaive if he aicipaed rae of lad price appreciaio, i L, is greaer ha he begiig of he period opporuiy cos of capial, r. Possible soluios o his complicaio will be discussed below. 32 Hadbook o Resideial Propery Prices Idices (RPPIs)

35 Elemes for a Cocepual Framework 3 where he ew separae period user coss of srucures ad lad, p S ad p L, are defied as follows: p S = [r - i S + d ( + i S ) + m S + S ]P S p L = [r - i L + L ]P L (3.A22) (3.A23) The impued re for a dwellig ui usig he user cos approach o he valuaio of housig services is hus made up of six mai coss: The real opporuiy cos of he fiacial capial ied up i he srucure, (r - i S )P S Q S ; The real opporuiy cos of he fiacial capial ied up i he lad, (r - i L )P L Q L ; The depreciaio cos of he srucure, d ( + i S )P S Q S ; The maieace ad isurace coss associaed wih he srucure, m S P S Q S ; The propery axes associaed wih he srucure, S P S Q S, ad The propery axes associaed wih he lad udereah ad surroudig he srucure, L P L Q L The above user cos approach o pricig he services of a dwellig ui i period ca be applied o various housig sraa, e.g., o deached dwelligs, row houses or duplexes or ow houses ad aparme blocks. For he las wo ypes of dwellig uis, he lad compoe for each idividual dwellig ui eeds o be cosruced. For example, if here are 2 dwellig uis i a aparme block, he he lad share of each idividual dwellig ui could be se o /2 h of he oal lad area ha he aparme block occupies. ( 35 ) Dwellig uis ca also be grouped accordig o heir cosrucio ype, which could be primarily wood, brick, cocree or radiioal. 3.6 If a saisical agecy produces aioal balace shee esimaes, he daa o he oal value of resideial lad ad resideial srucures should be available. However, daa o he quaiy of resideial lad may o be kow. Esimaes of he coury s oal real sock of resideial srucures ca be obaied by deflaig he balace shee esimae of he value of resideial housig by he coury s correspodig ivesme price deflaor for resideial housig. 3.6 There are a leas wo uses for he above user cos approach o pricig he services of housig: The user coss ca be compared o marke res for dwellig uis ha are acually reed durig he period uder cosideraio, ad ( 35 ) I is o compleely sraighforward o allocae he commo lad shared by he dwellig uis io idividual shares; i.e., isead of a equal divisio of he lad, we could use he relaive floor spaces of each aparme as he allocaor. There are also problems associaed wih he relaive heigh of he idividual aparme uis; i.e., a aparme o a higher floor will ypically re for more ha a aparme o a lower floor. The user coss ca be used o value he services of ower occupied housig. As will be see laer i his secio, i urs ou ha user coss do approximae marke res (for lower cos housig i he US a leas), provided expecaios of fuure iflaio i house prices are formed i a cerai way As meioed before, wo mai mehods for valuig he services of ower occupied housig have bee suggesed for aioal accous purposes: he user cos approach jus explaied ad he real equivalece approach. The real equivalece approach is sraighforward; for ower occupied houses i a cerai sraum, we look for similar reed dwellig uis ad impue he marke real o he correspodig ower occupied house. I may couries, he real equivalece approach works well, bu i does o work well if real markes are hi or if here are price corols o res If user coss are used o value he services of ower occupied dwellig uis i a coury, he he maieace ad isurace rae erm m S i he user cos of srucures formula (3.A22) should be dropped from he formula, sice maieace ad isurace expediures for ower occupied houses will geerally be capured elsewhere i he household expediure accous The simplified approach o he user cos of housig explaied above i equaios (3.A7) ad (3.A8) ca be eve furher simplified by assumig ha he raio of he quaiy of lad o srucures is fixed ad so he aggregae user cos of housig is equal o [r * + δ + µ + τ]p H, where P H is a qualiy adjused price idex ha is applicable o he coury s eire housig sock (icludig boh srucures ad he uderlyig lad) for he period uder cosideraio ad δ, µ ad τ are respecively a depreciaio rae, a maieace ad isurace rae ad a propery ax rae ha applies o he composie of srucures ad lad. Uder his simplified approach o value he services of ower occupied housig, as was see i he las paragraph above, he erm µ should be dropped from he simplified user cos. The resulig simplified approach is applied i Icelad; see Gudaso (24) ad Gudaso ad Jósdóir (29) ( 36 ) ad i some Europea couries; see he deailed exposiio of he mehod by Kaz (29). ( 37 ) A varia of his approach is used by he US Bureau of Ecoomic Aalysis: Lebow ad Rudd (23; 68) oe ha he US aioal accous impuaio for he services of ower occupied housig is obaied by applyig re o value raios for ( 36 ) The real ieres rae ha is used is approximaely 4% per year ad he combied depreciaio rae for lad ad srucures is assumed o equal.25% per year. The depreciaio rae for srucures aloe is esimaed o be.5% per year. Propery axes are accoued for separaely i he Iceladic CPI. Housig price iformaio is provided by he Sae Evaluaio Board based o propery sales daa of boh ew ad old housig. The SEB also esimaes he value of he housig sock ad lad i Icelad, usig a hedoic regressio model based o propery sales daa. The value of each household s dwellig is colleced i he Household Budge Survey. ( 37 ) Kaz (29) ad Garer ad Verbrugge (29b; 76) give furher refereces o he lieraure o he simplified user cos mehod. Hadbook o Resideial Propery Prices Idices (RPPIs) 33

36 3 Elemes for a Cocepual Framework ea occupied housig o he sock of ower occupied housig wih he same characerisics as he reed propery. ( 38 ) The re o value raio ca be see as a esimae of he applicable real ieres rae plus he depreciaio rae plus a maieace ad isurace rae plus he propery ax rae, r * + δ + µ + τ. ( 39 ) 3.65 How exacly should he real ieres rae, r *, be esimaed? Oe possible mehod is o jus make a reasoable guess: ( 4 ) The remaiig quesio was wha value of he real rae of reur is appropriae? Evidece was preseed o he ask force ha suggesed ha, a leas i Weser Europea couries, he appropriae real rae of reur for oweroccupied dwelligs was lower ha ha for oher durables, perhaps i he 2.5 o 3. perce rage. I was he cosesus of he ask force ha give he acual siuaio i he CCs [Cadidae Couries from Easer Europe], real raes of reur o boh dwelligs ad lad should be assumed o be 2.5 perce. Arold J. Kaz (29; 46) A secod mehod is o use morgage ieres raes as esimaes for he omial opporuiy cos of fiacial capial ied up i housig ad o use ecoomeric forecasig echiques o esimae prediced house price iflaio raes (ad he he real ieres rae ca be se equal o he omial ieres rae less he prediced house price iflaio rae). Several varias of his secod approach were ried by Verbrugge (28) ad Garer ad Verbrugge (29a) (29b) usig US daa. However, as hese auhors show, his approach was o successful i ha he resulig user cos esimaes were exremely volaile (ad frequely egaive) ad o a all close o correspodig marke res A hird approach o he deermiaio of a appropriae real ieres rae o be used i a user cos formula for housig services was carried ou by Garer ad Verbrugge (29b) usig US daa. They used applicable morgage ieres raes as esimaes for he omial opporuiy cos of fiacial capial ad used curre period esimaes of cosumer price idex iflaio as heir esimae of expeced house price appreciaio. Much o heir surprise, hey foud ha he resulig user coss racked marke res raher well. ( 4 ) The coclusio is ha eiher makig a reasoable guess for he real ieres rae or usig ( 38 ) See also Croe, Nakamura ad Voih (29) ad Garer ad Shor (29; 237) for a descripio of his capializaio mehod for deermiig real prices for housig uis from esimaes of he correspodig asse values. I ca be see ha his mehod is acually a mehod for implemeig he real equivalece approach o valuig he services of ower occupied dwellig uis. ( 39 ) If a owed dwellig ui has he value V ad a reed dwellig ui wih he same characerisics has he re o value raio g = r * + δ + µ + τ, he he impued re for he owed dwellig ui is se equal o (g - µ)v = (r * + δ + τ)v, sice isurace ad maieace expediures o he owed dwellig will be recorded elsewhere i he Sysem of Naioal Accous. ( 4 ) The Ausralia Bureau of Saisics assumes a cosa real ieres rae equal o 4% per year whe cosrucig is esimaes of capial services. ( 4 ) Usig his approach, Garer ad Verbrugge (29b; 79) also foud ha here were o egaive esimaed user coss i heir US daa se. CPI iflaio as a proxy for expeced house price iflaio gives rise o reasoable user coss ha are likely o be fairly similar o marke res, a leas for relaively iexpesive housig uis I is evide ha he mai drivers for he user coss of srucures ad lad are price idices for ew dwellig cosrucio, P S, ad for resideial lad, P L. Mos saisical agecies have a cosa qualiy price idex for ew resideial srucures, because his idex is required i he aioal accous i order o deflae ivesme expediures o resideial srucures. This idex could be used as a approximaio o P S. ( 42 ) 3.69 This complees he overview of he user cos approach o pricig resideial housig services. I he followig secio, aoher approach o pricig he services of ower occupied housig will be reviewed: he opporuiy cos approach. The Opporuiy Cos Approach o he Valuaio of Ower Occupied Housig Services 3.7 Recall he wo mai mehods for valuig he services of ower occupied housig (OOH): he real equivalece approach ad he user cos approach. I he real equivalece approach, a ower of a dwellig ui who chooses o live i i (or a leas o re i ou o someoe else) values he services of he dwellig by he marke re which is foregoe. This is a very direc opporuiy cos of usig he dwellig. O he oher had, he user cos approach o valuig dwellig services is basically a fiacial opporuiy cos of usig he services of he dwellig ui durig he period uder cosideraio. I has bee suggesed ha he rue opporuiy cos of usig he services of a owed dwellig ui is he maximum of he re foregoe ad he user cos: We coclude his secio wih he followig (coroversial) observaio: perhaps 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 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. W. Erwi Diewer (29b; 3). Diewer ad Nakamura (29) ad Diewer, Nakamura ad Nakamura (29) pursued his opporuiy cos approach o he valuaio of ower occupied housig services i more deail bu i ca be see ha his approach seems o be a valid oe. Moreover, i has he advaage ( 42 ) This idex may oly be a approximaio sice i covers he cosrucio of real properies as well as ower occupied dwelligs. 34 Hadbook o Resideial Propery Prices Idices (RPPIs)

37 Elemes for a Cocepual Framework 3 of elimiaig he problem wih he user cos approach: amely, ha he user cos approach ca geerae egaive user coss if ex pos or forecased housig iflaio raes are used i he user cos formula. 3.7 I pracice, he opporuiy cos approach o pricig OOH services may lead o similar resuls as he real equivalece approach provided ha expeced iflaio i he user cos formula is se equal o CPI iflaio, sice Garer ad Verbrugge (29b) show ha for mos low ed real properies, he real equivalece ad user cos approaches give much he same aswer, a leas i he US. However, here is evidece ha user coss may be cosiderably higher ha he correspodig marke reals for high ed properies. Table 3. is ake from Heso ad Nakamura (29a; 3) (29b; 277) ad shows average aual marke re o marke value of real properies i a umber of regios; i.e., i shows capializaio raios as a fucio of he value of he real propery. Table 3. is based o a survey of US federal goverme employees coduced as par of a Safe Harbor process regardig he Cos of Livig Allowace (COLA) program admiisered by he Uied Saes Office of Persoel Maageme. This program bega i 948 ad pays a allowace above he federal salary schedule i hree geographic areas (Alaska, he Caribbea ad he Pacific) based o prices i hese COLA areas relaive o he Washigo D.C. housig area. ( 43 ) Two facs emerge from he Table 3.: Capializaio raios differ subsaially across regios ( 44 ), ad As oe moves from iexpesive properies o more expesive properies he capializaio raio for he high ed properies is abou oe half he raio for low ed properies for all regios. The secod poi lised above also emerges from he much more exesive US daa o aual res for he years as a fucio of he correspodig home values foud i Figure i Garer ad Verbrugge (29b; 78). For a $ home, he correspodig average aual re was abou $ while for a $9 home he correspodig average aual re was abou $3. Thus he capializaio raio fell from abou % o abou 3.3 % as he home value icreased from $ o $9. ( 43 ) This program is direced a comparig he coss of livig for federal employees i he o-coieal Uied Saes o Washigo D.C. area. Housig is oe of he mos impora ad mos difficul of he comparisos required uder his program. The COLA areas iclude Alaska, Guam, Hawaii, Puero Rico, ad he U.S. Virgi Islads: a very diverse rage of climaes ad housig eeds. ( 44 ) The relaively high capializaio raios for Alaska may be due o he iclusio of heaig services i he re. Table 3.. Esimaed Re o Value Raios as Perceages (Capializaio Raios) Reer Alaska Wash D.C. Carib Hawaii-Pacific Value($) () (2) (3) (4) Source: Heso ad Nakamura (29a) 3.72 Wha facors could explai his dramaic drop i he capializaio raio as we move from iexpesive properies o more expesive properies? As was idicaed previously, he re o value raio ca be regarded as a esimae of he applicable real ieres rae plus he depreciaio rae plus he propery ax rae, r * + δ + µ + τ, ad hese raes should o be all ha differe for properies of differig value. There are a leas hree possible explaaios: High value properies may have a much higher proporio of lad, hece he depreciaio rae δ, regarded as a declie i value of he propery due o agig of he srucure, will be smaller as he lad o srucure raio icreases. ( 45 ) A subsaial fracio of a ladlord s moiorig, accouig ad billig expeses may be i he aure of a fixed cos ad hece hese coss will drop as a fracio of he re as he value of he propery icreases. ( 45 ) This explaaio was suggesed by Diewer (29a; 486) ad Garer ad Verbrugge (29b; 82). Hadbook o Resideial Propery Prices Idices (RPPIs) 35

38 3 Elemes for a Cocepual Framework Reals of high value resideial properies are o made o a commercial basis; i.e., hey may be made o a emporary basis, wih he reers servig as house siers who pay somewha subsidized res as compared o he ower s fiacial opporuiy cos. I seems ulikely ha he imperfec deermiaio of he depreciaio rae ca explai he big declie i capializaio raios as he value of he propery icreases; esimaes of housig depreciaio raes are geerally i he o 2 % per year rage, ( 46 ) ad hese raes are oo low o fully ( 46 ) Garer ad Verbrugge (29b; 76) ad Garer ad Shor (29; 244) assume aual depreciaio raes (as fracios of he value of he propery icludig boh srucures ad lad) of % per year. explai he declies i he capializaio raios. Similarly, he coss of maiaiig ad isurig a real propery ha are colleced i he erm µ are likely o be relaively small ad hus are ulikely o fully explai he pheomeo. Thus i may be ha he hird explaaio is a impora explaaory facor. If his is ideed he case, he he opporuiy cos approach o he valuaio of OOH services would give a much higher valuaio o OOH services ha he real equivalece approach. ( 47 ) ( 47 ) Thus he discrepacy bewee he real equivalece approach o he valuaio of OOH services ad he opporuiy cos approach may o be very impora i he ime series coex because boh measures may move i adem. Bu i he coex of makig ieraioal comparisos, his argume will o be applicable due o he fac ha he perceage of ower occupied dwellig uis differs subsaially across couries. 36 Hadbook o Resideial Propery Prices Idices (RPPIs)

39 Sraificaio or Mix Adjusme Mehods 4

40 4 Sraificaio or Mix Adjusme Mehods Simple Mea or Media Idices 4. The simples measures of house price chage are based o some measure of ceral edecy from he disribuio of house prices sold i a period, i paricular he mea or he media. Sice house price disribuios are geerally posiively skewed (predomialy reflecig he heerogeeous aure of housig, he posiive skew i icome disribuios ad he zero lower boud o rasacio prices), he media is ypically used raher ha he mea. As o daa o housig characerisics are required o calculae he media, a price idex ha racks chages i he price of he media house sold from oe period o he ex ca be easily cosruced. Aoher aracio of media idices is ha hey are easy o udersad. 4.2 A impora drawback of simple media idices is ha hey will provide oisy esimaes of price chage. The se of houses acually raded i a period, or a sample hereof, is ypically small ad o ecessarily represeaive of he oal sock of housig. Chages i he mix of properies sold will herefore affec he sample media price much more ha he media price of he housig sock. For example, hik of a ciy wih wo regios, A ad B, ad ha regio A has more expesive houses ha regio B. Suppose ha he media house sold i 26 ad 28 comes from regio A, while he media house i 27 comes from regio B. I follows ha he media idex could record a large rise from 26 o 27 ad he a large fall from 27 o 28. Such a idex would be a very poor idicaor of wha is acually happeig i he housig marke. Thus, a media (or mea) idex will be a very iaccurae guide o price chage whe here is subsaial chage i he composiio of houses sold bewee periods. If here is a correlaio bewee urig pois i house price cycles ad composiioal chage, he a media could be especially misleadig i periods whe he premium o accuracy is highes. 4.3 A perhaps bigger problem ha shor-erm oise is sysemaic error, or bias. A simple media idex will be subjec o bias whe he qualiy of he housig sock chages over ime. The media idex will be upward biased if he average qualiy improves over he years. Bias ca also arise if cerai ypes of houses are sold more frequely ha oher ypes of houses ad a he same ime exhibi differe price chages. For example, whe higher qualiy houses sell more frequely ad also rise i price faser ha lower qualiy houses, a dowward bias may resul if he umber of sales per ype of house does o properly reflec he umber of houses i sock. This is someimes referred o as a sample selecio problem. The fac ha houses raded are usually a small ad o ecessarily represeaive par of he oal housig sock ca bias oher propery price idex mehods as well, icludig hedoic ad repea sales mehods (o be discussed i Chapers 5 ad 6). Sraificaio 4.4 Pos-sraificaio of a sample is a geeral echique for reducig sample selecio bias. I he case of resideial propery price idices, sraificaio is he simples ool for corollig for chages i he composiio or qualiy mix of he properies sold. The mehod is herefore also kow as mix adjusme. Sraificaio is also eeded if users desire price idices for differe housig marke segmes. 4.5 Sraificaio is ohig else ha separaig he oal sample of houses io a umber of sub-samples or sraa. Afer cosrucig a measure of he chage i he ceral edecy for each sraum, such as a mea or media price idex, he aggregae mix-adjused RPPI is ypically calculaed as a weighed average of idices for each sraum. Wih M differe sraa, he mix-adjused idex, as calculaed i pracice i various couries, ca be wrie i mahemaical form as follows: P = M m= w P m m (4.) where P m is he idex for sraum m which compares he mea (media) price i he curre or compariso period wih he mea (media) price i a earlier or base period, ad where w m deoes he weigh of sraum m. The weighs are value shares peraiig o he sraa. They refer o he base period, which is usually a year (whereas he compariso periods may be mohs or quarers). For pracical reasos, he weighs are ofe kep fixed for several years, bu keepig weighs fixed for a log ime is geerally o good pracice. More deails o aggregaio ad weighig issues i his coex are provided below. 4.6 Which ype of value weighs is used, depeds o he arge idex ha he RPPI is supposed o esimae. If he purpose is o rack he price chage of he housig sock he obviously sock-weighs he sock value shares of he sraa should be used. If, o he oher had, he arge is a sales or acquisiios RPPI, he sales (expediure) weighs should be applied. ( ) 4.7 The effeciveess of sraificaio will deped upo he sraificaio variables used because a mix-adjused measure oly corols for composiioal chage across he various groups. For example, if house sales are separaed solely accordig o heir locaio, a mix-adjused idex will corol for chages i he mix of propery ypes across he defied locaios. Bu he mix-adjused measure will o ( ) The house price idices compiled i he EU as par of a Eurosa pilo sudy are examples of such acquisiios idices (see Makaroidis ad Hayes, 26 or Eurosa, 2). 38 Hadbook o Resideial Propery Prices Idices (RPPIs)

41 Sraificaio or Mix Adjusme Mehods 4 accou for ay chages i he mix of propery ypes sold ha are urelaed o locaio. Also, a mix-adjused idex does o accou for chages i he mix of properies sold wihi each subgroup, i his case chages i he mix of properies sold wihi he boudaries of each locaio. 4.8 Very deailed sraificaio accordig o housig characerisics such as size of he srucure, plo size, ype of dwellig, locaio ad ameiies will icrease homogeeiy ad hus reduce he qualiy-mix problem, alhough some qualiy mix chages will mos likely remai. There is, however, a radeoff o be cosidered. Icreasig he umber of sraa reduces he average umber of observaios per sraum, ad a very deailed sraificaio migh raise he sadard error of he overall RPPI. Needless o say, a deailed sraificaio scheme ca be cosruced oly if he sraa-defiig characerisics are available for all sample daa. Aoher poeial pracical problem is ha i migh be difficul o obai accurae daa o he (sock) weighs for small subgroups. 4.9 Whe usig oly physical ad locaioal sraificaio variables, like hose meioed above, he he sraificaio mehod does o corol for qualiy chages of he idividual properies. By qualiy chages we mea he effec of reovaios ad remodelig doe o he properies i combiaio wih depreciaio of he srucures. This ca also be called e depreciaio. Depreciaio obviously depeds o he age of he srucure, alhough depreciaio raes may differ across differe ypes of dwelligs or eve across differe locaios. This is why age of he srucure was lised i Chaper 3 as oe of he mos impora price deermiig qualiy aribues. Cosequely, sraifyig accordig o age class may help reduce he problem of qualiy chage. 4. Iroducig age class as aoher sraificaio variable will furher reduce he average umber of observaios per sraum ad may give rise o ureliable esimaes of price chages. Uder hese circumsaces, hedoic regressio echiques which are discussed i Chaper 4 will geerally work beer ha sraificaio. As meioed earlier, some sor of hedoic regressio mehod will also be eeded o decompose he overall RPPI io lad ad srucures compoes if his is required for ay of he purposes discussed i Chaper 2. Such a decomposiio cao be provided by sraificaio mehods. 4. Mix-adjused RPPIs have bee compiled by umerous saisical offices ad oher goverme agecies, icludig he UK Deparme of he Evirome (982) ad he Ausralia Bureau of Saisics (ABS, 26). While mix adjusme has received relaively lile aeio i he academic lieraure, ( 2 ) here is a growig body of work ( 2 ) However, sraified media house price idices have bee used by several researchers, mosly for compariso purposes; see e.g. Mark ad Goldberg (984), Croe ad Voih (992), Gazlaff ad Lig (994), ad Wag ad Zor (997). o marke segmeaio usig saisical echiques like cluser aalysis ad facor aalysis; see e.g. Dale-Johso (982), Goodma ad Thibodeau (23), ad Thibodeau (23). These echiques could i priciple be used o defie housig sub-markes, which could subsequely be used as sraa for he cosrucio of a mix-adjused RPPI. The Ausralia Bureau of Saisics experimeed wih his approach (ABS, 25). 4.2 Prasad ad Richards (26) (28) proposed a ovel sraificaio mehod ad esed i o a Ausralia daa se. They grouped ogeher suburbs accordig o he log-erm average price level of dwelligs i hose regios, raher ha jus cluserig smaller geographic regios io larger regios. Their mehod of sraificaio was specifically desiged o corol for wha may be he mos impora form of composiioal chage, amely chages i he proporio of houses sold i higher- ad lower-priced regios i ay period. ( 3 ) Noe ha hey used media price idices a he sraum level. McDoald ad Smih (29) followed-up o his sudy ad cosruced a similar sraified media house price measure for New Zealad. Aggregaio ad Weighig Issues Firs-sage aggregaio 4.3 Sraificaio ivolves a wo-sage procedure: price idices are compiled a he sraum level, which are he aggregaed across he various sraa. As was meioed above, media sraa idices have ypically bee used, i paricular because hey will ofe be more sable ha he correspodig mea idices. Ye, we will focus o meas raher ha medias. Coveioal idex umber heory deals wih aggregaio issues, i his case aggregaio of house price observaios wihi sraa. Ulike he media, meas are aggregaor fucios, which lik up wih idex umber heory. The quesio he arises: wha kid of mea should be ake? 4.4 The CPI Maual (24) makes recommedaios abou how o cosruc price idices a he firs sage of aggregaio if iformaio o quaiies is uavailable ad he a he secod sage of aggregaio whe boh price ad value (or quaiy) iformaio is available. A he firs sage of aggregaio, Chaper 2 i he CPI Maual geerally recommeds usig he uweighed geomeric mea or ( 3 ) A geeral rule is ha sraificaio accordig o he variable of ieres should o be used sice ha ca lead o biased resuls. The sudy variable used by Prasad ad Richards (26) (28) is (log-erm) house price chage, o house price level, so heir sraificaio mehod could perhaps be defeded. However, lile is kow abou he saisical properies of his ype of sraificaio idex ad i would be advisable o ivesigae he issue of poeial bias before producig such a idex. Hadbook o Resideial Propery Prices Idices (RPPIs) 39

42 4 Sraificaio or Mix Adjusme Mehods Jevos idex o aggregae idividual price quoaios io a idex. However, his geeral advice is o applicable i he prese coex. 4.5 If he aim is o cosruc a price idex for he sales of resideial properies, he appropriae cocep of (elemeary) price i some ime period for a homogeeous sraum or cell i he sraificaio scheme is a ui value. Because each sale of a resideial propery comes wih is ow quaiy, which is equal o oe, he correspodig quaiy for ha cell is he simple sum of he properies rasaced i period. We ca formally Noe ha equaio (4.4) ca be rewrie i he form of (4.) if s = wih cell price idices P m = Pm / Pm ad M value shares wm = Pm Qm / m = Pm Q m. The Paasche price idex goig from period s o, P, is defied as follows: s P M P Q m m s s m= ( P, P, Q ) P M (4.5) s P Q m m m= s The Fisher price idex for period relaive o period s, P, F ca be defied as he geomeric mea of (4.4) ad (4.5): describe his as follows. Suppose ha i period here s s s s s s s s / 2 P F ( P, P, Q, Q ) [ PL ( P, P, Q ) PP ( P, P, Q )] are N (, m) propery sales observed i a paricular s s cell s s s s s s / 2 P F ( P, P, Q, Q ) [ PL ( P, P, Q ) PP ( P, P, Q )] m, wih he sellig price (value) of propery equal o (4.6) V for =,...,N(,m). The he appropriae price ad Recall ha all he quaiies occurrig i hese hree formulas are umbers of rasacios; ha is, umbers of ob- quaiy for cell m i period are: N (, m) P V / N(, m) served prices. Thus, for calculaig a Laspeyres, Paasche, or m (4.2) = Fisher price idex oe eeds he same iformaio. Q m N(, m) (4.3) This arrowly defied ui value cocep is acually recommeded i he CPI Maual (24; 356). If he sraificaio scheme leads o cells ha are o sufficiely arrow defied, he of course some ui value bias may arise, which is equivale o sayig ha some qualiy mix bias may remai. ( 4 ) P 4.8 The Laspeyres, Paasche ad Fisher price idices defied by equaios (4.4), (4.5) ad 4.6) are fixed base idices. For example, if here are 3 periods of sales daa, icludig he base period, he he Fisher formula (4.6) would geerae he followig idex umber series for hose 3 periods: ; P ( P, P, Q, Q ); P ( P, P, Q, Q ) F F (4.7) Secod-sage aggregaio 4.6 The ex issue o be resolved is: wha idex umber formula should be used o aggregae he elemeary prices ad quaiies io oe overall RPPI? The CPI Maual discusses his choice of formula issue a grea legh. A umber of idex umber formulae are recommeded bu a good overall choice appears o be he Fisher ideal idex sice his idex ca be jusified from several differe perspecives. ( 5 ) The Fisher idex is he geomeric mea of he Laspeyres ad Paasche idices. 4.7 To illusrae his poi, le P [ P,..., PM ] ad Q [ Q,..., QM ] deoe he period vecors of cell prices s ad quaiies. The Laspeyres price idex, P, goig from L (he base) period s o (he compariso) period ca be defied as follows: M s m m s s s m= ( P, P, Q ) L M (4.4) s s Pm Qm m= P P Q ( 4 ) I pracice, crude sraificaio accordig o regio ad ype of dwellig is ofe used. The sraificaio mehod accordig o price bads proposed by Prasad ad Richards (28), could be useful o miliae agais ui value bias. See Balk (998) (28; 72-74), Silver (29a) (29b) (2), ad Diewer ad vo der Lippe (2) for more geeral discussios of ui value bias. ( 5 ) See CPI Maual (24; Chapers 5-8) for aleraive jusificaios for he use of he Fisher formula. Chaiig 4.9 A aleraive o he fixed base mehod is he use of chaiig. The chai mehod uses he daa of he las wo periods o calculae a period o period chai lik idex which is used o updae he idex level from he previous period. Chaiig would, for example, geerae he followig Fisher idex umber series for he 3 periods: ; P F ( P, P, Q, Q ); P F ( P, P, Q, Q ) P 2 F ( P, P 2 2, Q, Q ) (4.8) 4.2 The ex issue o be discussed is wheher RPPIs should be cosruced by usig fixed base or chai idices. Boh he Sysem of Naioal Accous ad he CPI Maual recommed he use of chai idices provided ha he uderlyig price daa have reasoably smooh reds. ( 6 ) O he oher had, if here is a grea deal of variabiliy i he daa, paricularly whe prices bouce erraically aroud a red, he use of fixed base idices is recommeded. Propery price chages ed o be fairly smooh, ( 7 ) so i is likely ha chaied idices will work well i may cases. However, more experimeaio wih acual daa is ( 6 ) See SNA (28) ad CPI Maual (24; 349). ( 7 ) Alhough prices do o bouce aroud erraically i he real esae coex, quaiies do exhibi cosiderable variabiliy, paricularly if here are a large umber of cells i he sraificaio seup wih a limied umber of observaios i each cell. There is also a cosiderable amou of seasoal variaio i quaiies; i.e., sales of resideial properies fall off dramaically durig he wier mohs of he year. 4 Hadbook o Resideial Propery Prices Idices (RPPIs)

43 Sraificaio or Mix Adjusme Mehods 4 required i order o give defiiive advice o his issue. There may also be seasoal variaio i house prices as he example for he Duch ow of A, preseed below, suggess. I such cases oo, oe should be careful wih usig chai idices. Sock RPPIs 4.2 The above discussio was o he cosrucio of a price idex for he sales of resideial properies whe usig a sraificaio mehod. Bu how should a RPPI be cosruced for he sock of resideial properies? Assumig ha, for each cell m, he properies sold are radom (or represeaive ) selecios from he sock of dwellig uis defied by cell m, he period ui value prices P m defied by (4.2) ca sill be used as (esimaes of he) cell prices for a sock RPPI. The quaiies Q m defied by (4.3) are, however, o loger appropriae; hey eed o be replaced by (esimaes of) he umber of dwellig uis of he ype defied by cell m ha are i he referece sock a ime, * say Q m, for m =,..., M. Wih hese populaio quaiy weighs, he res of he deails of he idex cosrucio are he same as was he case for he sales RPPI To compile sock weighs, i will be ecessary o have a periodic cesus of he housig sock wih eough deails o he properies so ha i ca be decomposed io he appropriae cells i he sraificaio scheme for a base period. If iformaio o ew house cosrucio ad o demoliios is available i a imely maer, he he cesus iformaio ca be updaed ad esimaes for he housig * sock by cell (he Q m ) ca be made i a imely maer. The sock RPPI ca be cosruced usig a (chaied) Fisher idex as was he case for he sales RPPI. O he oher had, if imely daa o ew cosrucio ad demoliios is lackig, i will oly be possible o cosruc a fixed base Laspeyres idex usig quaiy daa from he las available * * * housig cesus (i say period ), Q = [ Q,..., Q M ], uil iformaio from a ew housig cesus is made available (i say period T). The Laspeyres sock RPPI hus is M P Q * m m * m= L ( P, P, Q ) M (4.9) * Pm Qm m= P =,...,T 4.23 I Chaper 3 i was meioed ha for some purposes i is useful o have a sock RPPI for Ower Occupied Housig, i.e. excludig reed homes. The cosrucio of such a idex proceeds i he same way as for he cosrucio of a RPPI for he eire housig sock excep ha he cells i he sraificaio scheme are ow resriced o ower occupied dwelligs. This will be possible if he periodic housig cesus collecs iformaio o wheher each dwellig ui is owed or reed I should be oed ha he cosrucio of a sraified (sock or sales) RPPI becomes more complex whe some of he cells i he sraificaio scheme are empy for some periods. A he ed of his chaper, where a empirical example usig daa o housig sales for he Duch ow of A is preseed, a mached-model approach will be oulied ha ca be used i case some cells are empy. Mai Advaages ad Disadvaages 4.25 We will summarize he mai advaages ad disadvaages of he sraified media or mea approach. The mai advaages are: Depedig o he choice of sraificaio variables, he mehod adjuss for composiioal chage of he dwelligs. The mehod is reproducible, codiioal o a agreed lis of sraificaio variables. Price idices ca be cosruced for differe ypes ad locaios of housig. The mehod is relaively easy o explai o users The mai disadvaages of he sraified media or mea mehod are: The mehod cao deal adequaely wih depreciaio of he dwellig uis uless age of he srucure is a sraificaio variable. The mehod cao deal adequaely wih uis ha have udergoe major repairs or reovaios (uless reovaios are a sraificaio variable). The mehod requires iformaio o housig characerisics so ha sales rasacios ca be allocaed o he correc sraa. If he classificaio scheme is very coarse, composiioal chages will affec he idices, i.e., here may be some ui value bias i he idices. If he classificaio scheme is very fie, he cell idices may be subjec o a cosiderable amou of samplig variabiliy due o small sample sizes or some cells may be empy for some periods causig idex umber difficulies A overall evaluaio of he sraificaio mehod is ha i ca be saisfacory if: a appropriae level of deail is chose; age of he srucure is oe of he sraificaio variables, ad a decomposiio of he idex io srucure ad lad compoes is o required. Hadbook o Resideial Propery Prices Idices (RPPIs) 4

44 4 Sraificaio or Mix Adjusme Mehods Sraificaio ca be ierpreed as a special case of regressio. ( 8 ) Chaper 5 discusses his more geeral echique, kow as hedoic regressio whe applied o price idex cosrucio ad qualiy adjusme. A Example Usig Duch Daa for he Tow of A 4.28 This chaper will be cocluded by a worked example for he cosrucio of a sraified idex usig daa o sales of deached houses for a small ow (he populaio is aroud 6 ) i he Neherlads, ow A, for 4 quarers, sarig i he firs quarer of 25 ad edig i he secod quarer of 28. The same daa se will be exploied i Chapers 5, 6, 7 ad 8 o illusrae he oher mehods for cosrucig house price idices ad he umerical differeces ha ca arise i pracice. ( 9 ) 4.29 A dwellig ui has a umber of impora price deermiig characerisics: The lad area of he propery; The floor space area of he srucure; i.e., he size of he srucure ha sis o he lad udereah ad surroudig he srucure; The age of he srucure; his deermies (o average) how much physical deerioraio or depreciaio he srucure has experieced; The amou of reovaios ha have bee uderake for he srucure; The locaio of he srucure; i.e., is disace from ameiies such as shoppig ceers, schools, resauras ad work place locaios; The ype of srucure; i.e., sigle deached dwellig ui, row house, low rise aparme or high rise aparme or codomiium; The ype of cosrucio used o build he srucure; Oher special price deermiig characerisics ha are differe from average dwellig uis i he same geeral locaio such as swimmig pools, air codiioig, elaborae ladscapig, he heigh of he srucure or views of oceas or rivers. The variables used i his sudy ca be described as follows: V is he sellig price of propery i quarer i Euros; L is he area of he plo for he sale of propery i quarer i meers squared; ( 8 ) See Diewer (23a) who showed ha sraificaio echiques or he use of dummy variables ca be viewed as a oparameric regressio echique. I he saisics lieraure, hese pariioig or sraificaio echiques are kow as aalysis of variace models; see Scheffé (959). ( 9 ) This maerial is draw from Diewer (2). S is he livig space area of he srucure for he sale of propery i quarer i meers squared; A is he approximae age (i decades) of he srucure o propery i quarer. 4.3 I ca be see ha o all of he price deermiig characerisics lised above were used i he prese sudy. I paricular, he las five ses of characerisics of he propery were egleced. There is a implici assumpio ha quarer o quarer chages i he amou of reovaios ha have bee uderake for he srucures, he locaio of he house, he ype of srucure, he ype of cosrucio ad ay oher price deermiig characerisics of he properies sold i he quarer did o chage eough o be a sigifica deermia of he average price for he properies sold oce chages i lad size, srucure size ad he age of he srucures were ake io accou. ( ) 4.3 The deermiaio of he values for he age variable A eeds some explaaio. The origial daa were coded as follows: if he srucure was buil i 96-97, he he observaio was assiged he decade idicaor variable BP = 5; 97-98, BP=6; 98-99, BP=7; 99-2, BP=8; 2-28, BP=9. The age variable i his sudy was se equal o 9 - BP. For a recely buil srucure i quarer, A =. Thus, he age variable gives he (approximae) age of he srucure i decades Houses which were older ha 5 years a he ime of sale were deleed from he daa se. Two observaios which had uusually low sellig prices (36 ad 4 Euros) were deleed as were 28 observaios which had lad areas greaer ha 2 m 2. No oher ouliers were deleed from he sample. Afer his cleaig of he daa, we were lef wih 2289 observaios over he 4 quarers i he sample, or a average of 63.5 sales of deached dwellig uis per quarer. The overall sample mea sellig price was 9 3 Euros, whereas he media price was 67 5 Euros. The average plo size was m 2 ad he average size of he srucure (livig space area) was 27.2 m 2. The average age of he properies sold was approximaely 8.5 years The sraificaio approach o cosrucig a house price idex is cocepually very simple: for each of he impora price explaiig characerisic, divide up he sales io relaively homogeeous groups. Thus i he prese case, sales were classified io 45 groups or cells, cosisig of 3 groupigs for he lad area L, 3 groupigs ( ) To suppor his assumpio, i should be oed ha he hedoic regressio models discussed i laer chapers cosisely explaied 8-9% of he variaio i he price daa usig jus he hree mai explaaory variables: L, S ad A. The R 2 bewee he acual ad prediced sellig prices raged from.83 o.89. The fac ha i was o ecessary o iroduce more price deermiig characerisics for his paricular daa se ca perhaps be explaied by he aure of he locaio of he ow of A o a fla, feaureless plai ad he relaively small size of he ow; i.e., locaio was o a big price deermiig facor sice all locaios have more or less he same access o ameiies. 42 Hadbook o Resideial Propery Prices Idices (RPPIs)

45 Sraificaio or Mix Adjusme Mehods 4 for he srucure area S ad 5 groups for he age A (i decades) of he srucure (3 3 5 = 45 separae cells). Oce quarerly sales were classified io he 45 groupigs of sales, he sales wihi each cell i each quarer were summed ad he divided by he umber of uis sold i ha cell i order o obai ui value prices, he cell prices P m. These ui values were he combied wih he umber of uis sold i each cell, he Q m, o form he usual p s ad q s ha ca be isered io a bilaeral idex umber formula, like he Laspeyres, Paasche ad Fisher ideal formulae defied by (4.4)-(4.6) above, ( ) yieldig a sraified idex of house prices of each of hese ypes. However, sice here are oly 63 or so observaios for each quarer ad 45 cells o fill, each cell had oly a average of 3 or so observaios i each quarer, ad some cells were empy for some quarers. This problem will be addressed subsequely How should he size limis for he L ad S groupigs be chose? Oe approach would be o divide he rage of L ad S by hree ad creae hree equal size cells. However, his approach leads o a large umber of observaios i he middle cells. I he prese sudy, size limis were herefore chose such ha roughly 5 % of he observaios would fall io he middle sized caegories ad roughly 25 % would fall io he small ad large caegories. For he lad size variable L, he cuoff pois chose were 6 m 2 ad 3 m 2, while for he srucure size variable S, he cuoff pois chose were m 2 ad 4 m 2. Thus if L < 6 m 2, he he observaio fell io he small lad size cell; if 6 m 2 L < 3 m 2, he he observaio fell io he medium lad size cell ad if 3 m 2 L, he he observaio fell io he large lad size cell. The resulig sample probabiliies for fallig io hese hree L cells over ( ) The ieraioal mauals o price measureme recommed his ui value approach o he cosrucio of price idices a he firs sage of aggregaio; see CPI Maual (24), PPI Maual (24), ad XMPI Maual (29). However, he ui value aggregaio should ake place over homogeeous iems ad his assumpio may o be fulfilled i he prese coex, sice here is a fair amou of variabiliy i L, S ad A wihi each cell. Bu sice here are oly a small umber of observaios i each cell for he daa se uder cosideraio, i would be difficul o iroduce more cells o improve homogeeiy sice his would lead o a icreased umber of empy cells ad a lack of machig for he cells. he 4 quarers were.24,.5 ad.25 respecively. Similarly, if S < m 2, he observaio fell io he small srucure size cell; if m 2 S < 4 m 2, he he observaio fell io he medium srucure size cell ad if 4 m 2 S, he he observaio fell io he large srucure size cell. The resulig sample probabiliies for fallig io hese hree S cells over he 4 quarers were.2,.52 ad.27 respecively As meioed earlier, he daa ha were used did o have a exac age for he srucure; oly he decade whe he srucure was buil was recorded. So here was o possibiliy of choosig exac cuoff pois for he age of he srucure. A = correspods o houses ha were buil durig he years 2-28; A = for houses buil i 99-2; A = 2 for houses buil i 98-99, A = 3 for houses buil i 97-98; ad A = 4 for houses buil i The resulig sample probabiliies for fallig io hese five cells over he 4 quarers were.5,.32,.2,.2 ad.3 respecively. See Table 4. for he sample joi probabiliies of a house sale belogig o each of he 45 cells There are several pois of ieres o oe abou Table 4.: There were o observaios for houses buil durig he 96s ( A = 4 ) which had a small lo (L = small) ad a large srucure (S = large), so his cell is eirely empy; There are may cells which are almos empy; i paricular he probabiliy of a sale of a large plo wih a small house is very low as is he probabiliy of a sale of a small plo wih a large house; ( 2 ) The mos represeaive model sold over he sample period correspods o a medium sized lo, a medium sized srucure ad a house ha was buil i he 99s ( A = ). The sample probabiliy of a house sale fallig io his highes probabiliy cell is ( 2 ) Thus lo size ad srucure size are posiively correlaed wih a correlaio coefficie of Boh L ad S are fairly highly correlaed wih he sellig price variable P: he correlaio bewee P ad L is.8234 ad bewee P ad S is.8. These high correlaios lead o mulicollieariy problems i he hedoic regressio models o be cosidered laer. Table 4.. Sample Probabiliy of a Sale i Each Cell L S A = A = A = 2 A = 3 A = 4 small small medium small large small small medium medium medium large medium small large medium large large large Source: Auhors calculaios based o daa from he Duch Lad Regisry Hadbook o Resideial Propery Prices Idices (RPPIs) 43

46 4 Sraificaio or Mix Adjusme Mehods 4.37 The average sellig price of he represeaive house, fallig io he medium L, medium S ad A = caegory, is graphed i Figure 4. alog wih he overall sample mea ad media price i each quarer. These average prices have bee covered io idices which sar a for quarer, which is he firs quarer of 25. I should be oed ha hese hree house price idices are raher variable Some addiioal idices are ploed i Figure 4., icludig a fixed base mached model Fisher idex ad a chaied mached model Fisher price idex. I is ecessary o explai wha a mached model idex i his coex meas. If a leas oe house was sold i each quarer for each of he 45 cells, he ordiary Laspeyres, Paasche ad Fisher price idices comparig he prices of quarer o hose of quarer s would be defied by equaios (4.4)-(4.6) respecively, where M = 45. This algebra is applicable o he siuaio where here are rasacios i all cells for he wo quarers beig compared. Bu for he prese daa se, o average oly abou 3 ou of he 45 caegories ca be mached across ay wo quarer, ad he formulae (4.4)-(4.6) eed o be modified i order o deal wih his lack of machig problem. Thus, whe cosiderig how o form a idex umber compariso bewee quarers s ad, defie he se of cells m ha have a leas oe rasacio i each of quarers s ad as he s s se S ( s, ). The he mached model couerpars, P, P ML MP s ad P MF, o he regular Laspeyres, Paasche ad Fisher idices bewee quarers s ad give by (4.4), (4.5) ad (4.6) are defied as follows: ( 3 ) s P Q m m s m S (, ) P s (4.) ML s s P Q m m S ( s, ) ( 3 ) A jusificaio for his approach o dealig wih a lack of machig i he coex of bilaeral idex umber heory ca be foud i he discussio by Diewer (98; 498-5) o he relaed problem of dealig wih ew ad disappearig goods. Oher approaches are also possible. For approaches based o maximum machig over all pairs of periods; see Ivacic, Diewer ad Fox (2) ad de Haa ad va der Grie (2) for approaches based o impuaio mehods; see Alerma, Diewer ad Feesra (999). A useful impuaio approach could be o esimae impued prices for he empy cells usig hedoic regressios. The discussio is lef uil various hedoic regressio mehods have bee discussed. m P s MP (4.) s s P [ P P ] (4.2) MF S ( s, P Q m m ) s Pm m S ( s, ) s / 2 ML MP I Figure 4., he Fixed Base Fisher idex is he mached model Fisher price idex defied by (4.2), where he base, period s is kep fixed a quarer ; i.e., he idices P MF,,2,4 P MF,, P MF are calculaed ad labeled as he Fixed Base Fisher Idex, PFFB. The idex ha is labeled he mached model Chaied Fisher Idex, PFCH, is he price idex,,,2,,2 2,3,,2 3,4,4 P, MF P MF P MF, P MF P MF P MF,, P MF P MF P MF P MF. Noice ha he Fixed Base ad Chaied (mached model) Fisher idices are quie close o each oher ad are much smooher ha he correspodig Mea, Media ad Represeaive Model idices. ( 4 ) The daa for hese 5 series ploed i Figure 4. are lised i Table The mached model Fisher idices mus be regarded as beig more accurae ha he oher idices which use oly a limied amou of he available price ad quaiy iformaio. As he red of he Fisher idices is fairly smooh, he chaied Fisher idex should be preferred over he fixed base Fisher idex, followig he advice give i Hill (988) (993) ad i he CPI Maual (24). Recall also ha here is o eed o use Laspeyres or Paasche idices i his siuaio sice daa o sales of houses coais boh value ad quaiy iformaio. Uder hese codiios, Fisher idices are preferred over he Laspeyres ad Paasche idices (which do o use all of he available price ad quaiy iformaio for he wo periods beig compared). ( 4 ) The meas (ad sadard deviaios) of he 5 series meioed hus far are as follows: P FCH =.737 (.375), P FFB =.737 (.37), P Mea =.785 (.454), P Media =.785 (.5), ad P Represe =.586 (.366). Thus he represeaive model price idex has a smaller variace ha he wo mached model Fisher idices bu i has a subsaial bias relaive o he wo mached model Fisher idices: he represeaive model price idex is well below he Fisher idices for mos of he sample period. Q m m 44 Hadbook o Resideial Propery Prices Idices (RPPIs)

47 Sraificaio or Mix Adjusme Mehods 4 Figure 4.. Mached Model Fisher Chaied ad Fixed Base Price Idices, Mea, Media ad Represeaive Model Price Idices Source: Auhors calculaios based o daa from he Duch Lad Regisry P FCH P FFB P MEAN P MEDIAN P REP Table 4.2. Mached Model Fisher Chaied ad Fixed Base Price Idices, Mea, Media ad Represeaive Model Price Idices Quarer P FCH P FFB P Mea P Media P Represe Source: Auhors calculaios based o daa from he Duch Lad Regisry Hadbook o Resideial Propery Prices Idices (RPPIs) 45

48 4 Sraificaio or Mix Adjusme Mehods 4.4 Sice here is a cosiderable amou of heerogeeiy i each cell of he sraificaio scheme, here is he srog possibiliy of some ui value bias i he mached model Fisher idices. However, if a fier sraificaio were used, he amou of machig would drop dramaically. Already, wih he prese sraificaio, oly abou 2/3 of he cells could be mached across ay wo quarers. There is a rade-off bewee havig oo few cells wih he possibiliy of ui value bias ad havig a more deailed sraificaio scheme bu wih a much smaller degree of machig of he daa wihi cells across he wo ime periods beig compared. 4.4 Lookig a Table 4.2 ad Figure 4., i ca be see ha he chaied Fisher idex shows a drop i house prices durig he fourh quarers of 25, 26 ad 27. There is a possibiliy ha house prices drop for seasoal reasos i he fourh quarer of a year. I order o deal wih his possibiliy, i he ex secio a rollig year mached model Fisher idex will be cosruced. The Treame of Seasoaliy for he Duch Example 4.42 Assumig ha each commodiy i each seaso of he year is a separae aual commodiy is he simples ad heoreically mos saisfacory mehod for dealig wih seasoal goods whe he goal is o cosruc aual price ad quaiy idices. This idea ca be raced back o Mudge i he cosumer price coex ad o Soe i he producer price coex: The basic idex is a yearly idex ad as a price or quaiy idex is of he same sor as hose abou which books ad pamphles have bee wrie i quaiy over he years. Bruce D. Mudge (955; 97). The exisece of a regular seasoal paer i prices which more or less repeas iself year afer year suggess very srogly ha he varieies of a commodiy available a differe seasos cao be rasformed io oe aoher wihou cos ad ha, accordigly, i all cases where seasoal variaios i price are sigifica, he varieies available a differe imes of he year should be reaed, i priciple, as separae commodiies. Richard Soe (956; 74-75). Diewer (983) geeralized he Mudge-Soe aual framework o allow for rollig year comparisos for 2 cosecuive mohs of daa wih a base year of 2 mohs of daa or for comparisos of 4 cosecuive quarers of daa wih a base year of 4 cosecuive quarers of daa; i.e., he basic idea is o compare he curre rollig year of price ad quaiy daa o he correspodig daa of a base year where he daa peraiig o each seaso is compared. ( 5 ) I he prese coex, we have i priciple, ( 6 ) price ad quaiy daa for 45 classes of housig commodiies i each quarer. If he sale of a house i each seaso is reaed as a separae good, he here are 8 aual commodiies For he firs idex umber value, he four quarers of price ad quaiy daa o sales of deached dwelligs i he ow of A (8 series) are compared wih he same daa usig he Fisher ideal formula. Naurally, he resulig idex is equal o. For he ex idex umber value, he daa for he firs quarer of 25 are dropped ad he daa peraiig o he firs quarer of 26 are appeded o he daa for quarers 2-4 of 25. The resulig Fisher idex is he secod ery i he Rollig Year (RY) Mached Model series ha is illusraed i Figure 4.2. However, as was he case wih he chaied ad fixed base Fisher idices ha appeared i Figure 4., o all cells could be mached usig he rollig year mehodology; i.e., some cells were empy i he firs quarer of 26 which correspoded o cells i he firs quarer of 25 which were o empy ad vice versa. So whe cosrucig he rollig year idex P RY ploed i Figure 4.2, he compariso bewee he rollig year ad he daa peraiig o 25 was resriced o he se of cells which were o empy i boh years; i.e., he Fisher rollig year idices ploed i Figure 4.2 are mached model idices. Umached models are omied from he idex umber compariso. ( 7 ) 4.44 The resuls are show i Figure 4.2. Noe ha here is a defiie dowur a he ed of he sample period bu ha he dowurs which showed up i Figure 4. for quarers 4 ad 8 ca be ierpreed as seasoal dowurs; i.e., he rollig year idices i Figure 4.2 did o ur dow uil he ed of he sample period. Noe furher ha he idex value for observaio 5 compares he daa for caledar year 26 o he correspodig daa for caledar year 25 ad he idex value for observaio 9 compares he daa for caledar year 27 o he correspodig daa for caledar year 25; i.e., hese idex values correspod o Mudge-Soe aual idices. ( 5 ) For addiioal heory ad examples of his rollig year approach, see he chapers o seasoaliy i he CPI Maual (24) ad he PPI Maual (24), Diewer (998), ad Balk (28; 5-69). To jusify he rollig year idices from he viewpoi of he ecoomic approach o idex umber heory, some resricios o prefereces are required; deails ca be foud i Diewer (999; 56-6). I should be oed ha weaher ad he lack of fixiy of Easer ca cause seasos o vary ad a breakdow i he approach; see Diewer, Fikel ad Arsev (29). However, wih quarerly daa, hese limiaios of he rollig year idex are less impora. ( 6 ) I pracice, as we have see i he previous secio, may of he cells are empy i each period. ( 7 ) There are rollig year comparisos ha ca be made wih he daa for 4 quarers ha are available. The umbers of umached or empy cells for rollig years 2, 3,..., are as follows: 5, 52, 55, 59, 6, 6, 65, 65, 66, 67. The relaively low umber of umached or empy cells for rollig years 2, 3 ad 4 is due o he fac ha for rollig year 2, ¾ of he daa are mached, for rollig year 3, ½ of he daa are mached ad for rollig year 4, ¼ of he daa are mached. 46 Hadbook o Resideial Propery Prices Idices (RPPIs)

49 Sraificaio or Mix Adjusme Mehods I is a fairly labour iesive job o cosruc he rollig year mached model Fisher idices because he cells ha are mached over ay wo periods vary wih he periods. A shor-cu mehod (which is less accurae) for seasoally adjusig a series, such as he mached model chaied Fisher idex P FCH ad he fixed base Fisher idex P FFB lised i Table 4.2, is o simply ake a 4 quarer movig average of hese series. The resulig rollig year series, P FCHMA ad P FFBMA, ca be compared wih he rollig year Mudge-Soe-Diewer series P RY ; see Figure 4.2. The daa ha correspods o Figure 4.2 are lised i Table 4.3. Figure 4.2. Rollig Year Fixed Base Fisher, Fisher Chaied Movig Average ad Fisher Fixed Base Movig Average Price Idices Source: Auhors calculaios based o daa from he Duch Lad Regisry P FFBRY P FCHMA P FFBMA Table 4.3. Rollig Year Fixed Base Fisher, Fisher Chaied Movig Average ad Fisher Fixed Base Movig Average Price Idices Rollig Year P FFBRY P FCHMA P FFBMA Source: Auhors calculaios based o daa from he Duch Lad Regisry Hadbook o Resideial Propery Prices Idices (RPPIs) 47

50 4 Sraificaio or Mix Adjusme Mehods 4.46 I ca be see ha a movig average of he chaied ad fixed base Fisher quarer o quarer idices, P FCH ad P FFB, lised i Table 4.2, approximaes he heoreically preferred rollig year fixed base Fisher idex P FFBRY fairly well. There are differeces of up o % bewee he preferred rollig year idex ad he movig average idex, however. Recall ha he fixed base Fisher idex compared he daa of quarers o 4 wih he correspodig daa of quarer. Thus he observaios for, say, quarers 2 ad, 3 ad, ad 4 ad are o as likely o be as comparable as he rollig year idices where daa i ay oe quarer is always lied up wih he daa i he correspodig quarer of he base year. A similar argume applies o he movig average idex P FCHMA ; he comparisos ha go io he liks i his idex are from quarer o quarer ad hey are ulikely o be as accurae as comparisos across he years for he same quarer. ( 8 ) ( 8 ) The sroger is he seasoaliy, he sroger will be his argume i favour of he accuracy of he rollig year idex. The sregh of his argume ca be see if all house price sales for each cell ur ou o be srogly seasoal; i.e., he sales for ay give cell occur i oly oe quarer i each year. Quarer o quarer comparisos are obviously impossible i his siuaio bu rollig year idices will be perfecly well defied. 48 Hadbook o Resideial Propery Prices Idices (RPPIs)

51 Hedoic Regressio Mehods 5

52 5 Hedoic Regressio Mehods Hedoic Modelig ad Esimaio 5. The hedoic regressio mehod recogizes ha heerogeeous goods ca be described by heir aribues or characerisics. Tha is, a good is esseially a budle of (performace) characerisics. ( ) I he housig coex, his budle may coai aribues of boh he srucure ad he locaio of he properies. There is o marke for characerisics, sice hey cao be sold separaely, so he prices of he characerisics are o idepedely observed. The demad ad supply for he properies implicily deermie he characerisics margial coribuios o he prices of he properies. Regressio echiques ca be used o esimae hose margial coribuios or shadow prices. Oe purpose of he hedoic mehod migh be o obai esimaes of he willigess o pay for, or margial cos of producig, he differe characerisics. Here we focus o he secod mai purpose, he cosrucio of qualiy-adjused price idices. Hedoic Modelig 5.2 The sarig poi is he assumpio ha he price p of propery i period is a fucio of a fixed umber, say K, characerisics measured by quaiies z. k Wih T+ ime periods, goig from he base period o period T, we have p = f ( z,..., zk, ε ) (5.) =,..., T where ε is a radom error erm (whie oise). I order o be able o esimae he margial coribuios of he characerisics usig sadard regressio echiques, equaio (5.) has o be specified as a parameric model. The wo bes-kow hedoic specificaios are he fully liear model K p = β + z β + ε (5.2) k k k= ad he logarihmic-liear model K l p = β + βk zk + ε (5.3) k= where β ad β k are he iercep erm ad he characerisics parameers o be esimaed. I boh specificaios he characerisics may be rasformaios, like logarihms, of coiuous variables. I pracice, may explaaory variables will be caegorical raher ha coiuous ad represeed by a se of dummy variables which ake he value of if a propery belogs o he caegory i quesio ad he value of oherwise. ( ) The hedoic regressio approach daes back a leas o Cour (939) ad Griliches (96). Lacaser (966) ad Rose (974) laid dow he cocepual foudaios of he approach. Colwell ad Dilmore (999) argue ha he firs published hedoic sudy was a 922 Uiversiy of Miesoa maser s hesis o agriculural lad values. 5.3 For producs such as high-ech goods, he logliear model (5.3) is usually preferred, amog oher higs because i mos likely reduces he problem of heeroskedasiciy (o-cosa variace of he errors) as prices ed o be log-ormally disribued (Diewer, 23b). I he housig coex, o he oher had, he liear model has much o recommed. I Chaper 3, he size of he srucure ad he size of he lad i is buil o were meioed as wo impora price deermiig variables. Sice he value of a propery is geerally equal o he sum of he price of he srucure ad he price of lad, i ca be argued ha lad ad srucures should be icluded i he model i a liear fashio, provided ha he daa are available. Chaper 8 will discuss his issue i more deail, icludig a decomposiio of he hedoic price idex io lad ad srucures compoes. Uforuaely, o all daa sources will coai iformaio o lo ad srucure size. Lo size i paricular may be lackig. Whe lo (or srucure) size is o icluded as a explaaory variable, may empirical sudies have foud log-liear models o perform reasoably well. 5.4 The characerisics parameers β k i (5.2) ad (5.3) are allowed o chage over ime. This is i lie wih he idea ha housig marke codiios deermie he margial coribuios of he characerisics: whe demad ad supply codiios chage, here is o a priori reaso o expec ha hose coribuios are cosa (Pakes, 23). Ye, i seems mos likely ha marke codiios chage gradually. Therefore, he simplifyig assumpio ca cofidely be made, perhaps oly for he shor erm, ha he characerisics parameers (bu o he iercep erm) are cosa over ime. I he log-liear case his would give rise o he followig cosraied versio of (5.3): K l p = β + βk zk + ε (5.4) k= As will be see below, he ime depede iercep erms (he β ) ca be covered io a cosa qualiy price idex. 5.5 Suppose we have daa o sellig prices ad characerisics for he samples S ( ), S(),..., S( T ) of properies sold i periods =,..., T wih sizes N ( ), N(),..., N( T ). Uder he classic error assumpios, i paricular a zero mea ad cosa variace, he parameers of he hedoic models (5.2) ad (5.3) ca be esimaed by Ordiary Leas Squares (OLS) regressio o he sample daa of each ime period separaely. The cosraied versio (5.4) ca be esimaed o he pooled daa peraiig o all ime periods, provided ha dummy variables are icluded which idicae he ime periods (leavig ou oe dummy o preve perfec collieariy). The esimaig equaio for he cosraied log-liear model (5.4), which is geerally referred o as he ime dummy variable hedoic model, hus becomes T K τ τ l p = β + δ D + βk zk + ε (5.5) τ = k= 5 Hadbook o Resideial Propery Prices Idices (RPPIs)

53 Hedoic Regressio Mehods 5 where he ime dummy variable D has he value if he observaio comes from period ad oherwise; a ime dummy for he base period is lef ou. Alhough uusual, i is also possible o specify a ime dummy model wih he urasformed price as he depede variable. This specificaio will be cosidered i he empirical example give a he ed of his chaper. Some Pracical Issues 5.6 A impora issue is he choice of he se of explaaory variables icluded i he hedoic equaio. If some releva variables characerisics ha ca be expeced o affec he price of a propery (lised i Chaper 3) are excluded, he he esimaed parameers of he icluded characerisics will suffer from omied variables bias. The bias carries over o he prediced prices compued from he regressio coefficies ad o he hedoic idices. Each propery ca be viewed as a uique good, for a large par due o is locaio. Bu deailed iformaio o locaio ad eighbourhood ca be hard o obai (Case, Pollakowski, ad Wacher, 99). Oher characerisics may be uavailable also ad some could be difficul o measure direcly. So i is fair o say ha i pracice some omied variables bias will always be prese whe esimaig a hedoic model for housig. ( 2 ) The sig ad magiude of he bias, ad is impac o he price idex, are difficul o predic. The magiude depeds amog oher higs o he correlaio bewee he omied ad icluded variables. 5.7 The imporace of locaio has led researchers o make use of logiude ad laiude daa of idividual properies i hedoic regressios. This is usually achieved by cosrucig a marix of disaces bewee all properies i he daa se ad he usig appropriae (hough raher specialized) ecoomeric mehods o allow for spaial depedece i he esimaed equaio. Explicily accouig for spaial depedece ca ameliorae he omied locaioal variables problem. Spaial depedece ca be capured eiher i he regressors or he error erm. The firs approach, i.e., icludig locaio as a explaaory variable usig geospaial daa, is he mos sraighforward oe. This ca be doe paramerically or oparamerically, for example by makig use of splies, as demosraed by Hill, Melser ad Reid (2). For a elaborae discussio ad a review of he lieraure o spaial depedece, he use of geospaial daa ad also o oparameric esimaio, we refer he reader o Hill (2). ( 3 ) 5.8 Mulicollieariy is a well-kow problem i hedoic regressios. A high correlaio bewee some of he icluded variables icreases he sadard errors of he regressio coefficies; he coefficies become usable. Agai, i is difficul o say a priori how his will affec hedoic idices. For some purposes, mulicollieariy may o be oo problemaic. For example, if we are o so much ieresed i he values of he parameers bu merely i he prediced prices o be used i he esimaio of he overall qualiy-adjused house price idex, he he problem of mulicollieariy should o be exaggeraed. I his case i is beer o iclude a releva variable, eve if his would cause mulicollieariy, ha leavig i ou as he laer gives rise o omied variables bias. Bu whe he parameer values are of ieres as such, for example whe we are ryig o decompose he propery prices io lad ad srucures compoes, he mulicollieariy does pose problems. I Chaper 8 i will be show ha his is ideed a problem. 5.9 As wih oher mehods, some daa cleaig migh be ecessary. Obvious ery errors should be deleed. Ye a cauious approach is called for. Deleig ouliers from a regressio wih he aim of producig more sable coefficies (hece, more sable price idices) is ofe arbirary ad could lead o biased esimaes. The use of hedoics requires daa o all characerisics icluded i he model. Uforuaely, parial o-respose is prese i may daa ses. Tha is, he iformaio o oe or more characerisics may be missig for a par of he sample. Procedures have bee developed o impue he missig daa, bu agai i is impora o avoid arbirary choices ha ca have a impac o he resuls. 5. I he ex wo secios, he wo mai hedoic approaches, he ime dummy approach ad he impuaios approach, o cosrucig qualiy-adjused house price idices will be discussed. Wihou deyig poeial ecoomeric problems, our focus will be o he use of leas squares regressio o esimae he models. Time Dummy Variable Mehod 5. The ime dummy variable approach o cosrucig a hedoic house price idex has bee used frequely i academic sudies bu o so much by saisical agecies. ( 4 ) Oe advaage of his approach is is simpliciy; he price idex follows immediaely from he esimaed ( 2 ) A relaed poi is ha he characerisics of each house i he sample should be available i real ime. House characerisics ca chage over ime (which is acually he reaso why hey are give a superscrip for ime i he hedoic models above). Keepig he characerisics fixed implies ha he hedoic price idex would o be adjused for such qualiy chages. ( 3 ) Colwell (998) proposed a oparameric spaial ierpolaio mehod which seems well adaped o model lad prices as a fucio of he propery s geographical wodimesioal coordiaes. ( 4 ) This mehod was origially developed by Cour (939; 9-) as his hedoic suggesio umber wo. The ermiology adoped by us is o uiformly employed i he real esae lieraure. For example, Croe ad Voih (992) refer o he ime dummy mehod as he cosraied hedoic mehod, Gazlaff ad Lig (994) call i he explici ime-variable mehod, while Kigh, Dombrow ad Sirmas (995) ame i he varyig parameer mehod. Oher erms also appear i he lieraure so ha saemes abou he relaive meris of differe hedoic mehods require careful ierpreaio. Hadbook o Resideial Propery Prices Idices (RPPIs) 5

54 5 Hedoic Regressio Mehods pooled ime dummy regressio equaio (5.5). Ruig oe overall regressio o he pooled daa of he samples S ( ), S(),..., S( T ) relaig o periods =,..., T (wih sizes N ( ), N(),..., N( T ) ) yields coefficies ˆβ, dˆ ( =,..., T ) ad βˆ ( k =,..., K). The ime dummy parameer shifs he hedoic surface upwards or dowwards k ad measures he effec of ime o he logarihm of price. Expoeiaig he ime dummy coefficies hus corols for chages i he quaiies of he characerisics ad provides a measure of qualiy-adjused house price chage bewee he base period ad each compariso period. I oher words, he ime dummy idex goig from period o period is give by ( 5 ) exp( ˆ P = δ ) (5.6) TD 5.2 Poolig cross-secio daa preserves degrees of freedom. The regressio coefficies βˆ k will herefore geerally have lower sadard errors ha he coefficies βˆ ha would be obaied by esimaig model (5.9) k separaely o he daa of he samples S ( ), S(),..., S( T ). Alhough he icreased efficiecy ca be see as a advaage, i comes a a expese: he assumpio of fixed characerisics parameers is a disadvaage of he ime dummy hedoic mehod. 5.3 Whe usig OLS, he ime dummy hedoic idex ca be wrie as (see e.g. Diewer, Heravi ad Silver, 29; de Haa, 2a) P TD / N ( ) ( p ) K S ( ) = exp ˆ β ( z z ) / N () k k k p (5.7) ( ) k= S () s s where z k = z / ( ) S ( s) k N s is he sample mea of characerisic k i period s ( s =, ). Equaio (5.7) ells us ha he ime dummy idex is esseially he produc of wo facors. The firs facor is he raio of he geomeric mea prices i he periods ad. The secod facor, K exp[ ˆ = β k k ( zk z k )], adjuss his raio of raw sample meas for differeces i he average characerisics z k ad z k ; i serves as a qualiy-adjusme facor which accous for boh chages i he qualiy mix ad qualiy chages of he idividual properies (provided ha all releva qualiy-deermiig aribues are icluded i he hedoic model). Noice ha he ime dummy price idex simplifies o he raio of geomeric mea prices if z k = zk, i.e. if he average characerisics i period ad period happe o be equal. 5.4 Suppose for simpliciy ha he housig sock is cosa, i he sese ha here are o houses eerig or exiig, ad ha he qualiy of he idividual properies ( 5 ) The expeced value of he expoeial of he ime dummy coefficie is o exacly equal o he expoeial of he ime dummy parameer. The associaed bias is ofe referred o as small sample bias: i dimiishes whe he sample size grows. Uless he sample size is exraordiary small, he bias will be small compared o he sadard error ad ca usually be egleced i pracice. does o chage. Suppose furher ha S () ad S () are radom or represeaive selecios from he housig sock. I ha case he ime dummy mehod implicily aims a a raio of geomeric mea prices for he oal sock, which is equal o he geomeric mea of he idividual price raios. ( 6 ) Alhough i is rue ha he arge of measureme may be differe for differe purposes, i is difficul o see wha purposes a geomeric sock RPPI would mee. Arihmeic arge RPPIs, such as a idex ha racks he value of he fixed housig sock over ime, seem o be more appropriae (see also Chapers 4 ad 8). 5.5 The samples of houses raded, S () ad S (), may o be represeaive for he oal housig sock (or for he oal populaio of houses sold). A soluio could be o weigh he samples i order o make hem represeaive. Ruig a OLS regressio o he (pooled) weighed daa se is equivale o ruig a Weighed Leas Squares (WLS) regressio o he origial daa se. Uder he assumpio of a cosa variace of he errors, ecoomeric exbooks do o sugges he use of WLS sice his will iroduce heeroskedasiciy. Noe ha a WLS ime dummy mehod will sill geerae a geomeric idex, i his case a weighed oe. 5.6 A beer opio ha usig WLS regressios could be o sraify he samples, ru separae OLS regressios o he daa of he differe sraa, ad he explicily weigh he sraum-specific hedoic idices usig sock (or sales) weighs o cosruc a overall RPPI wih a arihmeic srucure a he upper level of aggregaio. This sraified hedoic approach has several oher advaages as well, as will be explaied laer. 5.7 A problem wih he ime dummy mehod is he revisio ha goes wih i. If he ime series is exeded o T + ad ew sample daa is added, he characerisics coefficies will chage. Cosequely, he ewly compued price idex umbers for he periods =,..., T will differ from hose previously compued. ( 7 ) Whe addiioal daa become available, he efficiecy due o he poolig of daa icreases ad beer esimaes ca be made. This ca acually be see as a sregh raher ha a weakess of he mehod. O he oher had, saisical agecies ad heir users will mos likely be reluca o accep coiuous revisios of previously published figures. 5.8 The muliperiod ime dummy mehod herefore appears o be of limied use for he producio of official house price idices alhough here are ways o deal wih he problem of revisios. Oe way would be o esimae ime dummy idices for adjace periods - ad ad he muliply hem o obai a ime series which is free of revisios. This high-frequecy chaiig has he addiioal advaage of relaxig he assumpio of fixed parameers. ( 6 ) I idex umber heory such a idex is referred o as a Jevos idex. ( 7 ) I he words of Hill (24), he ime dummy approach violaes ime fixiy. 52 Hadbook o Resideial Propery Prices Idices (RPPIs)

55 Hedoic Regressio Mehods 5 I is, however, o eirely wihou problems. Drif i he idex ca occur whe he daa exhibi sysemaic flucuaios such as seasoal flucuaios. ( 8 ) Characerisics Prices ad Impuaio Mehods 5.9 I he secod mai approach o compilig a hedoic price idex, separae regressios are ru for all ime periods ad he idex is cosruced by makig use of he prediced prices based o he regressio coefficies. Because he implici characerisics prices are allowed o vary over ime, his mehod is more flexible ha he ime dummy variable mehod. Two varias ca be disiguished: he characerisics prices approach ad he impuaios approach. I will be show ha, uder cerai circumsaces, boh approaches are equivale. We will firs discuss he characerisics prices approach. ( 9 ) Characerisics Prices Approach 5.2 To illusrae his approach, suppose as before ha sample daa are available o prices ad releva characerisics of houses sold i he base period ad each compariso period. We will firs assume ha he liear hedoic model (5.2) holds rue ad is esimaed o he daa of period ad period separaely. This yields regressio coefficies ˆβ s s ad βˆ k ( k =,..., K) for s =,. The prediced K prices for each idividual propery are pˆ = ˆ β + ˆ k = β z k k K ad pˆ = ˆ β + ˆ k = β z k k. I is also possible o compue prediced period ad period prices for a sadardized * propery wih fixed (quaiies of) characerisics z k. The resulig esimaed price relaive is 5.2 Suppose ha we were aimig a a sales-based RPPI. * There are wo aural choices for z k i (5.8): he sample average characerisics of he base period, z k, ad he sample averages of he compariso period ( =,..., T ), z k. The usual soluio i idex umber heory is o rea he resulig price idices which are equally valid i a symmeric * maer by akig he geomeric mea. Seig z k = z k i (5.8) geeraes a Laspeyres-ype characerisics prices (CP) idex: Seig z = * k z k ˆ β + K k= = CPL K ˆ β + k= P ˆ β z k k ˆ β z k k i (5.8) yields a Paasche-ype idex: ˆ β + K k= = CPP K ˆ β + k= P ˆ β z k k ˆ β z k k (5.9) (5.) By akig he geomeric mea of (5.9) ad (5.) he Fisher-ype characerisics prices idex is obaied: P [ ] / 2 CPF = PCPLPCPP (5.) 5.22 The characerisics prices mehod ca also applied i combiaio wih he log-liear model give by (5.3). Ruig separae regressios of his model o he sample daa for periods ad yields prediced prices (afer expoeiaig) ˆ K ˆ exp( )exp[ ˆ p = β ] k = β z k k ad ˆ K ˆ exp( )exp[ ˆ p = β ] k = β z k k. Similar o wha was doe i (5.8) for he liear model, prices ca be prediced for a sadardized house. Usig he sample averages of he characerisics i he base period o defie he sadardized house, he geomeric couerpar o he Laspeyres-ype characerisics prices idex (5.9) is foud: K K ˆ * exp( ˆ β )exp ˆ β z k k β + ˆ β z k k K pˆ k= k= P = = ˆ ˆ ˆ ˆ = (5.8) exp( β CPGL K β )exp ( β k β k ) zk K pˆ ˆ ˆ k= ˆ * exp( β )exp β + ˆ β k z β k zk k k= k= K Expressio (5.8) is a qualiy-adjused price idex exp( ˆ because β )exp ˆ β z k k K * k= he characerisics are kep fixed. Bu differe P = values of z = exp( ˆ β ˆ ˆ ˆ CPGL k K k k z β )exp ( β β ) k (5.2) will give rise o differe idex umbers. So wha ˆ ˆ k= exp( would β )expbe k z β k he preferred choice? k= The geomeric couerpar o he Paasche-ype hedoic idex (5.) is obaied by usig he sample averages of he characerisics i he compariso period: ( 8 ) A aleraive approach would be he use of a movig widow. For example, suppose we iiially esimaed a ime dummy idex o he daa of welve mohs. Nex, we delee he daa of he firs moh ad add he daa of he hireeh moh ad esimae a ime dummy idex o his daa se, ad so o. By muliplyig (chaiig) he las moh-o-moh chages a o-revised ime series is obaied. For a applicaio, see Shimizu, Nishimura ad Waaabe (2). I he example for he ow of A, give a he ed of his chaper, drif does o seem o be a major problem; he movig widow mehod gives much he same resuls as he muliperiod ime dummy regressio. ( 9 ) Agai, he ermiology differs bewee auhors. For example, Croe ad Voih (992) ad Kigh, Dombrow ad Sirmas (995) refer o his approach as he hedoic mehod (as opposed o he cosraied hedoic or varyig parameer mehod, wha we have called he ime dummy variable approach), while PCPGP Gazlaff ad Lig (994) refer o i as he sricly cross-secioal mehod. K exp( ˆ β )exp ˆ β z k k K k= P = = exp( ˆ β ˆ CPGP K β )exp ( ˆ β ˆ k β k ) z k= exp( ˆ β )exp ˆ β k zk K k= exp( ˆ β )exp ˆ β z k k K k= = = exp( ˆ β ˆ K β )exp ( ˆ β ˆ k β k ) zk (5.3) k= exp( ˆ β )exp ˆ β k zk k= k Hadbook o Resideial Propery Prices Idices (RPPIs) 53

56 5 Hedoic Regressio Mehods P CPGF K 5.25 The quesio arises how he characerisics pˆ () prices ˆ β + mehod described above relaes o he S () sadard (machedmodel) mehodology o cosruc price K S ( ) k P = = = HDIL pˆ idices. From a ˆ idex umber poi of view we ca S () β + look a he issue i he S ( ) k= Arihmeic Impuaio Idices Takig he geomeric mea of (5.2) ad (5.3) yields K P = [ ] = CPGF PHGLP / 2 HGP exp( ˆ β ˆ β )exp ( ˆ β ˆ k β k ) zk 5.26 The Laspeyres impuaio idex impues period k= K = [ P ] = prices for he properies belogig o he base period HGLP / 2 HGP exp( ˆ β ˆ β )exp ( ˆ β ˆ k β k ) zk (5.4) k= sample S (), evaluaed a base period characerisics o corol for qualiy chages. Usig he liear model (5.), where z ( K k = zk + zk ) / 2 i (5.4) deoes he mea of he he impued prices are pˆ () = ˆ β + ˆ k = βk z, ad he hedoic impuaio Laspeyres idex becomes k average characerisics i he base ad compariso period If he arge idex is a sock-based raher ha a K K ˆ ˆ () + ˆ ˆ + ˆ sales-based RPPI, he wo aural choices for he characerisics z k= p β βk zk β β z k k * S () S ( ) k= k i equaio (5.8) would be he average sock characerisics of he base period ad hose of he compariso p p p / N() P = = = HIL S () S () S () period. The firs choice would produce a Laspeyres-ype K K sock RPPI, he secod choice a Paasche-ype ˆ ˆ sock RPPI. () + ˆ ˆ + ˆ p β βk zk β β z k k Boh idices measure he qualiy-adjused value chage S () S ( ) of k= k= P = = = (5.5) he housig sock, bu he resuls HIL will pusually differ. No p p / N() oly does he average qualiy of he Shousig () sock chage S () S () over ime, he Laspeyres-ype idex igores ew properies Noice ha he quaiy associaed wih each price is ; basically, every house is uique ad cao be mached ex- ha eered he housig marke whereas he Paasche-ype idex does o ake io accou disappearig properies. cep hrough he use of a model Of course he assumpio of kow sock averages for all propery characerisics icluded i he hedoic model is urealisic. I mos siuaios we have o rely o esimaes, i.e. o he sample averages z k ad z k which are based o he same characerisics daa ha is used o esimae he hedoic equaios. This leads o formulae (5.9) ad (5.), or he geomeric mea (5.), which describe sales-based RPPIs. Oce agai we are remided ha sales RPPIs ca be see as esimaors of sock RPPIs, provided ha he samples are represeaive of he oal sock. The laer is raher doubful, however, ad he usual approach is o sraify he samples ad weigh he esimaed sraum idices usig sock weighs. Hedoic Impuaio Approach followig way. The period prices of properies sold i period cao be observed ad are missig because hose properies, or a leas he greaer par, will o be resold i period. Similarly, he period prices of he properies sold i period are uobservable. To apply sadard idex umber formulae hese missig prices mus be impued. ( ) Hedoic impuaio idices do his by usig prediced prices, evaluaed a fixed characerisics, based o he hedoic regressios for all ime periods. ( ) As oed earlier, he hedoic heory daes back a leas o Cour (939; 8). Impuaio was his hedoic suggesio umber oe. His suggesio was followed up by Griliches (97a; 59-6) (97b; 6) ad Triple ad McDoald (977; 44). More rece coribuios o he hedoic impuaios lieraure iclude Diewer (23b), de Haa (24) (29) (2a), Triple (24) ad Diewer, Heravi ad Silver (29). I a housig coex he hedoic impuaio mehod is discussed i deail by Hill ad Melser (28) ad Hill (2) The hedoic impuaio Laspeyres idex (5.5) is a example of a sigle impuaio idex i which he observed prices are lef uchaged. I ca be argued ha i would be beer o use a double impuaio approach, where he observed prices are replaced by he prediced values. This is because biases i he period ad period esimaes resulig from omied variables are likely o offse each oher, a leas o some degree; see e.g. Hill, 2. K Usig pˆ = ˆ β + ˆ k = β z, he hedoic double impuaio (DI) Laspeyres price idex k k is k P ˆ β z HDIL k k ˆ β z = S () pˆ () = pˆ S () K ˆ β + S ( ) k= K ˆ β + S ( ) k= ˆ β z k k ˆ β z k k ˆ β + = ˆ β + K k= K k= ˆ β z k k ˆ β z K ˆ ˆ β + β k zk k= = = P K CPL (5.6) ˆ ˆ k β + β k zk k= A compariso wih equaio (5.2) shows ha, usig he liear model, he double impuaio idex equals he Laspeyres-ype characerisics prices idex. This resul does o deped o he esimaio mehod. If we would use OLS regressio o esimae he liear model, he he sigle impuaio idex would be equal o he double impuaio idex ad also coicide wih he characerisics prices idex as i his case p = ( ) ˆ S p S (), due o he fac ha he hedoic model icludes a iercep erm so ha he OLS regressio residuals sum o zero The hedoic sigle impuaio Paasche idex impues base period prices for he properies belogig o he period sample S (), evaluaed a period characerisics. Usig agai he liear model (5.), hese impued prices k k = P CPL 54 Hadbook o Resideial Propery Prices Idices (RPPIs)

57 Hedoic Regressio Mehods 5 ˆ β + ˆ β + K k= K k= K are give by pˆ ( ) = ˆ β + ˆ k = β z. To save space we will k k oly show he double impuaio varia. Here, he observed (period ) prices are replaced by heir model-based K predicios pˆ = ˆ β + ˆ k = β z. Thus, he hedoic double impuaio Paasche price idex k k is P ˆ β z k HDIP k k ˆ β z k = pˆ = ) S ( ) pˆ ( S ( ) ˆ β + = ˆ β + K k= K k= ˆ β z k k ˆ β z k K ˆ β + S ( ) k= K ˆ β + S ( ) k= k = P CPP ˆ β z k k ˆ β z K ˆ + k= K ˆ P + HDIGL k= S ( ) PHDIGP ( pˆ ( S ( ) 5.29 The hedoic double impuaio Fisher idex is k k β = β he double impuaio uweighed geomeric idex, i which he base period prices are replaced by prediced values ˆ K ˆ exp( )exp[ ˆ p = β β z ], is ( pˆ () k = / N () K S () P ˆ ˆ HDIGL = = exp( β ˆ / N () β )exp ( k ( pˆ ) β ˆ z k= k k S () / N () ( = pˆ P () CPP K ˆ Sz () ˆ ˆ ˆ ˆ k = exp( N β )exp ( k k ) zk = P / () CPGL ( pˆ ) β β k k= S () β = β β (5.9) (5.7) k Similarly, he geomeric couerpar o he impuaio Paasche price idex (5.6) is obaied by impuig period prices for he properies belogig o he period sample S (), which are give by ˆ K ˆ ( ) exp( )exp[ ˆ p = β β z ] k k k, ad replacig he observed period prices by he predicios ˆ K ˆ = exp( )exp[ ˆ p β β z ]. So we have k = 5.3 Whe OLS is used o esimae he log-liear regressio equaios, he deomiaor of (5.9) ad he umeraor of (5.2) will equal he geomeric sample meas of he prices i period ad period, respecively, ad he double impuaio idices coicide wih sigle impuaio idices. Takig he geomeric mea of (5.9) ad (5.2) yields ˆ β k ) zk = P which coicides wih he Paasche-ype characerisics prices idex. If OLS regressio is used, he (5.7) is equal o k = k k he sigle impuaio Paasche idex because i his paricular case he umeraor equals ( / N ( ) pˆ ) K S ( ) P ˆ ˆ ˆ ˆ S ( p ). I will he = HDIGP = exp( β N β )exp ( k k ) zk = P / ( ) ( pˆ ( ) β β be uecessary o esimae he hedoic equaios for he k= compariso periods =,..., T ; esimaig he base period / N ( ) S ( ) ( pˆ ) K hedoic equaio o obai he base period impued values ˆ ˆ ˆ ˆ will suffice. = = exp( β N β )exp ( k k ) zk = P / ( ) CPGP ) β β (5.2) k= foud by akig he geomeric mea of (5.6) ad (5.7): P = P P / (5.8) HDIF [ ] 2 HDIL HDIP The above impuaio idices ca be give wo ierpreaios. They ca be viewed eiher as esimaors of he qualiy-adjused value chage of he eire housig sock, i.e., as sock-based RPPIs, or as esimaors of qualiy-adjused sales-based RPPIs. Uder he firs ierpreaio, o produce approximaely ubiased resuls, each sample should k= PHDIGF = HDIGL HDIGP k k k K be a radom or represeaive selecio from he housig 2 P [ ] HDIGF PHDIGLP / ˆ ˆ ˆ ˆ sock. Sample selecio bias problems could be less severe = = HDIGP exp( β β )exp ( β k β k ) zk = PCPGF (5.2) k= uder he secod ierpreaio, alhough his depeds o he samplig desig. ( ) Geomeric Impuaio Idices 5.3 The impuaio approach ca also be applied o geomeric price idex umber formulae. Le us sar wih wha migh be called he geomeric couerpar o he impuaio Laspeyres price idex (5.5). For reasos of cosisecy he impuaios will ow be compued usig he log-liear hedoic model (5.3) isead of he liear model. The impued period prices for he properies belogig o he base period sample S (), evaluaed a base period characerisics, are ˆ K ˆ () exp( )exp[ ˆ p = β β z ]. Hece, k = ( ) If all propery rasacios are observed, here is o samplig ivolved from a sales poi of view, ad sample selecio bias is o a issue. I may couries he Lad Regisry records all rasacios, a leas for resold houses. However, such daa ses usually have limied iformaio o characerisics; see e.g. Lim ad Pavlou (27) or Academerics (29). k k K 2 [ P P ] / ˆ ˆ )exp ( ˆ ˆ = exp( β β β β ) z = P where z ( k = zk + zk ) / 2 deoes he mea of he average characerisics i periods ad, as before The symmeric impuaio idex equaio (5.2) ca be rewrie i a way ha is surprisigly similar o equaio (5.7) for he ime dummy idex whe OLS is used o esimae he hedoic equaios (see Diewer, Heravi ad Silver, 29, ad de Haa, 2a): P HDIGF / N ( ) ( p ) K S ( ) = exp ˆ β N k ( zk z / () k ) p (5.22) ( ) k= S () where ˆ ˆ ( ˆ β k = β k + β k ) / 2 deoes he average value of he k-h coefficie i periods ad. Equaio (5.22) adjuss he raio of observed geomeric mea prices for ay differeces i he average sample characerisics. Triple (26) refers o his as hedoic qualiy adjusme. A compariso wih equaio (5.7) shows ha if he sample averages of CPGL CPGP CPGF Hadbook o Resideial Propery Prices Idices (RPPIs) 55

58 5 Hedoic Regressio Mehods all characerisics say he same ( z k = zk ), he he symmeric hedoic impuaio idex ad he ime dummy idex coicide ad equal he raio of observed geomeric mea prices, bu his will obviously, rarely happe. Boh ypes of hedoic idices also coicide if, for each characerisic, he average coefficie ˆβ k from he wo separae regressios would be equal o he coefficie βˆ k from he ime dummy regressio. This is rare as well, bu i suggess ha boh approaches geerae similar resuls if he characerisics parameers are approximaely cosa over ime If he characerisics parameers ca be assumed cosa over ime, he average coefficies ˆβ k i equaio (5.22) ca be replaced by he base period coefficies ˆ β k. I ha case here would be o eed o ru a regressio i each ime period, ad we would i fac be usig he o-symmeric impuaio price idex give by equaio (5.3).( 2 ) The base period regressio could be ru o a bigger daa se o icrease he sabiliy of he coefficies. I is advisable o regularly check if he coefficies have sigificaly chaged ad o updae hem whe ecessary As meioed earlier, geomeric price idices are less suiable as esimaors of qualiy-adjused RPPIs. This is o o say ha hey should ever be used. I cojucio wih sraificaio, he use of (5.2) could produce saisfacory resuls sice his would combie qualiy adjusme (usig a log-liear hedoic regressio model) ad a symmeric idex umber formula wihi he differe sraa wih mix adjusme across sraa. The sraified hedoic approach will be discussed i he ex secio. Sraified Hedoic Idices 5.35 Chaper 4 deal wih sraificaio or mix adjusme. Sraificaio is a simple ad powerful ool o adjus for chages i he qualiy mix of he properies sold. However, some qualiy mix chages wihi he sraa are likely o remai, as esseially every propery is a uique good, ad some ui value bias could herefore occur. A more deailed sraificaio scheme may be () ufeasible, pˆ S () M especially whe he umber of observaios m= S P = is relaively m () = HIL M small. Provided ha he ecessary daa o characerisics p S p () are available, i could be worhwhile o work wih a less m= S m () fie sraificaio scheme ad use hedoic regressio a he sraum level o adjus for qualiy mix chages. This wosage approach combies hedoics a he lower (sraum) level ad explici weighig a he upper level o form a overall RPPI Two advaages of sraificaio have bee meioed earlier. Firs, sraificaio eables he saisical ( 2 ) I Europe his ype of hedoic qualiy adjusme is called hedoic re-pricig, especially i case he sample size is fixed (Desais, 29). agecy o publish differe RPPIs for differe marke segmes. Users will beefi from his because i is well kow ha differe ypes of houses, differe regios, ec. ca exhibi quie differe price reds. Secod, sraificaio ca be helpful for reducig sample selecio bias, icludig bias due o o-respose, i paricular for a sock-based RPPI Whe usig hedoic regressio echiques o adjus for qualiy (mix) chages, sraificaio is highly recommeded. I is very ulikely ha a sigle hedoic model holds rue for all marke segmes, hece separae regressios should be ru for differe ypes of properies, differe locaios, ec. There are i fac wo issues ivolved. Perhaps he bigges issue is ha differe ses of propery characerisics will be eeded for differe marke segmes. For example, he characerisics ha are releva for deached dwellig uis differ from hose ha are releva for high rise aparmes, if oly because he floor of he aparme seems a impora price deermiig variable. The secod, hough probably less impora, issue is ha he parameer values for he same characerisics ca differ across housig marke segmes. Saisical ess for differeces i parameer values bewee sub-samples ca be foud i ay ecoomerics exbook The sraified hedoic approach ca be illusraed mos easily wih referece o he impuaio mehod, especially i combiaio wih he Laspeyres idex formula. Recall he hird expressio o he righ-had side of he hedoic sigle impuaio Laspeyres price idex (5.5), where he period prices for he houses i he base period sample S () are missig ad impued (usig he esimaed hedoic regressio model for period ) by p ˆ (). Suppose, as i Chaper 4, ha he oal sample is (pos) sraified io M sub-samples S ( m ). Equaio (5.5) ca he be rewrie as M M pˆ () pˆ () p pˆ () S () m= S m S S m () m ) m () P = = = HIL M M p p p pˆ () = S () M p M m= S m () m= S m () m= S m ( ) S m () S m () pˆ () where = ˆ HIL, m p () / ) p m= S m () = ( S m () p = S m ( S m () M m= s P m HIL, m (5.23) P p deoes he hedoic (sigle) impuaio Laspeyres price idex bewee he base period ad period for cell m; s m = p / S m ( ) p S () is he correspodig sales value share, which serves as he weigh for P HIL, m. Noe ha he las expressio of (5.23) has a similar srucure as he mix-adjused idex give by equaio (4.), bu i he prese case he cell idices are hedoic impuaio idices raher ha ui value idices. p = 56 Hadbook o Resideial Propery Prices Idices (RPPIs)

59 Hedoic Regressio Mehods Equaio (5.23) shows ha if he impued prices p ˆ () for all houses i he sample S () are based o oe overall hedoic regressio, he he aggregae hedoic impuaio Laspeyres idex ca be wrie i he form of a sraified idex. Bu his is jus aoher way of wriig higs, o wha is mea by a sraified hedoic approach. Also, as argued above, he use of a commo model is very urealisic. So isead of ruig oe big hedoic regressio, separae regressios should be performed o he daa of he sub-samples i each ime period o obai impued (period ) prices ad impuaio cell idices. Tha would lead o a sraified Laspeyres-ype hedoic impuaio idex. 5.4 I would be preferable o esimae a sraified Fisher hedoic idex raher ha a Laspeyres oe. This is perfecly feasible for a sales RPPI bu may o be feasible for a sock RPPI, as was already meioed i Chaper 3, sice up-o-dae cesus daa o he umber of properies is ofe lackig. Mai Advaages ad Disadvaages 5.4 This secio summarizes he advaages ad disadvaages of hedoic regressio mehods o cosruc a RPPI. The mai advaages are: If he lis of available propery characerisics is sufficiely deailed, hedoic mehods ca i priciple adjus for boh sample mix chages ad qualiy chages of he idividual properies. Price idices ca be cosruced for differe ypes of dwelligs ad locaios hrough a proper sraificaio of he sample. Sraificaio has a umber of oher advaages as well. The hedoic mehod is probably he mos efficie mehod for makig use of he available daa. The impuaio varia of he hedoic regressio mehod is aalogous o he mached model mehodology ha is widely used i order o cosruc price idices The mai disadvaages of hedoic regressio are: I may be difficul o corol sufficiely for locaio if propery prices ad price reds differ across deailed regios. However, a sraified approach o hedoic regressios will help overcome his problem o some exe. The mehod is daa iesive sice i requires daa o all releva propery characerisics, so i is relaively expesive o impleme. ( 3 ) ( 3 ) However, as will be see from he Duch example give below, jus havig iformaio o locaio, ype of propery, is age, is floor space area ad he plo area may explai mos of he variaio i he sellig price. While he mehod is esseially reproducible, differe choices ca be made regardig he se of characerisics icluded i he model, he fucioal form, possible rasformaios of he depede variable ( 4 ), he sochasic specificaio, ec., which could lead o varyig esimaes of overall price chage. Thus, a lo of meadaa may be required. The geeral idea of he hedoic mehod is easily udersood bu some of he echicaliies may o be easy o explai o users The overall evaluaio of he hedoic regressio mehod is ha i is probably he bes mehod ha could be used i order o cosruc cosa qualiy RPPIs for various ypes of propery. ( 5 ) We are i favor of he (double) impuaio varia because his is he mos flexible hedoic approach ad because his approach is aalogous o he sadard mached-model mehodology o cosruc price idices I he ex hree secios, he various hedoic regressio mehods will be illusraed usig he daa for he ow of A ha was described a he ed of Chaper 4. The followig wo secios show he resuls of ime dummy hedoic regressios, usig he log of he sellig price as he depede variable ad usig he urasformed sellig price, respecively. The las secio illusraes he hedoic impuaio mehod. All of he resulig price idices are for he sales of deached houses; some resuls usig he daa for he ow of A for idices of he sock of houses will be pospoed uil Chaper 8. Time Dummy Models Usig he Logarihm of Price as he Depede Variable The Log Liear Time Dummy Model 5.45 Recall he descripio of he daa for he Duch ow of A o sales of deached houses. I quarer, here were N() sales of deached houses i A where p is he sellig price of house sold durig quarer. There is iformaio o hree characerisics of house sold i period : L is he area of he plo i square meers (m 2 ); S is he floor space area of he srucure i m 2 ad A is he age i decades of house i period. Usig hese variables, he ( 4 ) For example, he depede variable could be he sales price of he propery or is logarihm or he sales price divided by he area of he srucure ad so o. ( 5 ) This evaluaio agrees wih ha of Hoffma ad Lorez (26; 5): As far as qualiy adjusme is cocered, he fuure will ceraily belog o hedoic mehods. Gouriéroux ad Laferrère (29) have show ha i is possible o cosruc a official aiowide credible hedoic regressio model for real esae properies. Hadbook o Resideial Propery Prices Idices (RPPIs) 57

60 5 Hedoic Regressio Mehods sadard log liear ime dummy hedoic regressio model is defied by he followig sysem of regressio equaios: ( 6 ) l p = ε (5.24) α + βl + γs + δa + τ + =,...,4; =,...,N(); where is a parameer which shifs he hedoic surface i quarer upwards or dowwards as compared o he surface i quarer. ( 7 ) 5.46 I is easy o cosruc a price idex usig he log liear ime dummy hedoic model (5.24). Expoeiaig boh sides of equaio (5.24), ad eglecig he error erm, yields β γ δ p = exp( α)[exp( L )] [exp( S )] [exp( A )] exp( τ ). If we could observe a propery wih he same characerisics i he base period ad i some compariso period (> ), he he correspodig price relaive (agai eglecig error erms) would simply be equal o exp( ). For wo cosecuive periods ad +, he price relaive (agai e- glecig error erms) would equal exp( + ) / exp( ), ad his ca serve as he chai lik i a price idex. Figure 5. shows he resulig idex, labeled as P H (hedoic idex 2 o. ), ad Table 5. liss he idex umbers. The R for his model was.842, which is quie saisfacory for a hedoic regressio model wih oly hree explaaory variables. ( 8 ) For laer compariso purposes, oe ha he log likelihood was A problem wih his model is ha he uderlyig price formaio model seems implausible: S ad L ierac muliplicaively i order o deermie he overall house price whereas i seems mos likely ha lo size L ad house size S ierac i a approximaely addiive fashio o deermie he overall house price Aoher problem wih he regressio model (5.24) is ha age is eered i a addiive fashio. The problem is ha we would expec age o ierac direcly wih he srucures variable S as a (e) depreciaio variable ad o ierac direcly wih he lad variable L, because lad does o depreciae. I he followig model, his direc ieracio of age wih srucures will be made. The Log Liear Time Dummy Model wih Qualiy Adjusme of Srucures 5.49 If age A ieracs wih he quaiy of srucures S i a muliplicaive maer, a appropriae explaaory variable for he sellig price of a house would be g ( d ) A S (i.e., geomeric depreciaio where δ is he decade geomeric depreciaio rae) or g ( da) S (sraigh lie depreciaio where δ is he decade sraigh lie depreciaio rae) isead of he addiive specificaio g S + da. I wha follows, he sraigh lie varia of his class of models will be esimaed ( 9 ). Thus, he log liear ime dummy hedoic regressio model wih qualiy adjused srucures becomes l p = ) ε (5.25) α + βl + A S γ ( δ + τ + =,...,4; =,...,N(); 5.5 Regressio model (5.25) was ru usig he 4 quarers of sales daa for he ow of A. Noe ha a sigle commo sraigh lie depreciaio rae δ is esimaed. The esimaed decade (e) depreciaio rae ( 2 ) was ˆ δ =.94% (or aroud.2 % per year), which is very reasoable. As was he case wih model (5.24), if a house wih he same characerisics i wo cosecuive periods ad + could be observed, he correspodig price relaive (eglecig error erms) exp( + ) / exp( ) ca serve as he chai lik i a price idex; see Figure 5. ad Table 5. for he resulig idex, labeled P 2 H 2. The R for his model was.8345, a bi lower ha he previous model ad he log likelihood was 354.9, which is quie a drop from he previous log likelihood of ( 2 ) 5.5 I appears ha he imposiio of more heory wih respec o he reame of he age of he house has led o a drop i he empirical fi of he model. However, i is likely ha his model ad he previous oe are misspecified ( 22 ): hey boh muliply ogeher lad area imes srucure area o deermie he price of he house while i is likely ha a addiive ieracio bewee L ad S is more appropriae ha a muliplicaive oe. ( 6 ) The esimaig equaio for he pooled daa se will iclude ime dummy variables o idicae he quarers. For all he models esimaed for he ow of A, i is assumed ha he error erms e are idepedely disribued ormal variables wih mea ad cosa variace. Maximum likelihood esimaio is used i order o esimae he ukow parameers i each regressio model. The oliear opio i Shazam was used for he acual esimaio. ( 7 ) The 5 parameers a,,..., 4 correspod o variables ha are exacly colliear i he regressio (5.24) ad hus he resricio = is imposed i order o ideify he remaiig parameers. ( 8 ) Laer o i his chaper ad i Chaper 8, some hedoic regressios will be ru ha use p as he depede variables raher ha he logs of he prices. To faciliae prices comparisos of goodess of fi across models, we will rasform he prediced values for he log price models io prediced price levels by expoeiaig he prediced prices ad he calculaig he correlaio coefficie bewee hese prediced price levels ad he acual prices. Squarig his correlaio coefficie gives us a levels ype measure of goodess of fi for he log price models which is deoed by R paricular model, R =.86. *2 *2. For his ( 9 ) This regressio is esseially liear i he ukow parameers ad hece i is very easy o esimae. ( 2 ) I is a e depreciaio rae because we have o iformaio o reovaio expediures, i.e., δ is equal o gross wear ad ear depreciaio of he house less average expediures o reovaios ad repairs. ( 2 2 *2 ) The levels ype R for his model was R =.7647, which agai is quie a drop from 2 R for he previous log price model. he correspodig levels ( 22 ) If he variaio i he idepede variables is relaively small, he differece i idexes geeraed by he various hedoic regressio models cosidered i his secio ad he followig wo secios is likely o be small sice virually all of he models cosidered ca offer roughly a liear approximaio o he ruh. Bu whe he variaio i he idepede variables is large, as i is i he prese housig coex, he choice of fucioal form ca have a subsaial effec. Thus a priori reasoig should be applied o boh he choice of idepede variables i he regressio as well as o he choice of fucioal form. For addiioal discussio o fucioal form issues, see Diewer (23a). 58 Hadbook o Resideial Propery Prices Idices (RPPIs)

61 Hedoic Regressio Mehods Noe ha, give he depreciaio rae δ, qualiy adjused srucures (adjused for he agig of he srucure) for each house i each quarer ca be defied as follows: S ( da ) S (5.26) * =,...,4; =,...,N() The Log Log Time Dummy Model wih Qualiy Adjusme of Srucures for Age 5.53 I he remaider of his secio, qualiy adjused (for age) srucures, ( da) S, will be used as a explaaory variable, raher ha he uadjused srucures area, S. The log log model is similar o he previous log liear model, excep ha ow, isead of usig L ad ( da) S as explaaory variables i he regressio model, he logarihms of he lad ad qualiy adjused srucures areas are used as idepede variables. Thus he log log ime dummy hedoic regressio model wih qualiy adjused srucures is he followig: ( 23 ) l p = ] ε (5.27) α + β l L + γ l[( δa ) S + τ + =,...,4; =,...,N(); ( 23 ) This hedoic regressio model urs ou o be a varia of McMille s (23) cosumer orieed approach o hedoic housig models. His heoreical framework draws o he earlier work of Muh (97) ad is oulied i Diewer, de Haa ad Hedriks (2). See also McDoald (98) Usig he daa for he Duch ow of A, he esimaed decade (e) depreciaio rae was ˆ d =. 5 (sadard error.374). If boh sides of (5.27) were expoeiaed ad he error erms were egleced, he β * γ house price p would equal exp( α)[ L ] [ S ] exp( ) τ, * where S deoes qualiy adjused srucures as defied by (5.26). So if we could observe a house wih he same characerisics i wo cosecuive periods ad +, he correspodig price relaive (eglecig error erms) would be equal o exp( + ) / exp( ) ad his agai ca serve as he chai lik i a price idex; see Figure 5. ad 2 Table 5. for he resulig idex, labeled P H 3. The R for his model was.8599 (he levels measure of fi was *2 R =.888), which is a icrease over models (5.25) ad (5.26); he log likelihood was 545.4, a big icrease over he log likelihoods for he oher wo models (47.6 ad 354.9) The house price series geeraed by he hree log-liear ime dummy regressios described i his secio, P H, P H 2 ad P H 3, are ploed i Figure 5. alog wih he chaied sraified sample mea Fisher idex, P FCH. These four house price series are lised i Table 5.. All four idices capure he same red bu here ca be differeces of over 2 perce bewee hem i some quarers. Noice ha all of he idices move i he same direcio from quarer o quarer wih decreases i quarers 4, 8, 2 ad 3 excep ha P H 3 he idex ha correspods o he log log ime dummy model icreases i quarer 2. Figure 5.. Log-Liear Time Dummy Price Idices ad he Chaied Sraified Sample Mea Fisher Price Idex Source: Auhors calculaios based o daa from he Duch Lad Regisry P H P H2 P H3 P FCH Hadbook o Resideial Propery Prices Idices (RPPIs) 59

62 5 Hedoic Regressio Mehods Table 5.. Log-Liear Time Dummy Price Idices ad he Chaied Sraified Sample Mea Fisher Price Idex Quarer P H P H2 P H3 P FCH Source: Auhors calculaios based o daa from he Duch Lad Regisry 5.56 Alhough model (5.27) performs he bes of he simple hedoic regressio models cosidered hus far, i has he usaisfacory feaure ha he quaiies of lad ad of qualiy adjused srucures deermie he price of a propery i a muliplicaive maer. I is more likely ha house prices are deermied by a weighed sum of heir lad ad qualiy adjused srucures amous. I he followig secio, a addiive ime dummy model will herefore be esimaed. The expecaio is ha his model will fi he daa beer. Time Dummy Hedoic Regressio Models usig Price as he Depede Variable The Liear Time Dummy Hedoic Regressio Model 5.57 There are reasos o believe ha he sellig price of a propery is liearly relaed o he plo area of he propery plus he area of he srucure due o he compeiive aure of he house buildig idusry. ( 24 ) If he age of he srucure is reaed as aoher characerisic ha has a ( 24 ) See Clapp (98), Fracke ad Vos (24), Gyourko ad Saiz (24), Bosic, Loghofer ad Redfear (27), Davis ad Heahcoe (27), Fracke (28), Diewer (29b), Koev ad Saos Silva (28), Saisics Porugal (29), Diewer, de Haa ad Hedriks (2), Diewer (2) ad Chaper 8 below. imporace i deermiig he price of he propery, he he followig liear ime dummy hedoic regressio model migh be a appropriae oe: p = a + βl + gs + da + + ε (5.28) =,...,4; =,...,N(); 5.58 The above liear regressio model was ru usig 2 he daa for he ow of A. The R for his model was.8687, much higher ha hose obaied i he previous regressios ( 25 ); he log likelihood was (which cao easily be compared o he previous log likelihoods sice he depede variable has chaged from he logarihm of price o jus price ( 26 ) Usig he liear model defied by equaios (5.28) o form a overall house price idex is a bi more difficul ha usig he previous log-liear or log log ime dummy regressio models. I he previous secio, holdig characerisics cosa ad eglecig error erms, he relaive price for he same house over ay wo periods urs ou o be cosa, leadig o a uambiguous overall idex. I he prese siuaio, holdig characerisics cosa ad eglecig error erms, he differece i price for he same house urs ou o be cosa, bu he relaive prices for differe houses will o i geeral be cosa. Therefore, a overall idex will be cosruced which uses he prices geeraed by he esimaed parameers for model (5.28) ( 25 ) However, recall ha he levels adjused measure of fi for he log log model described by (5.27) was.888, which is higher ha ( 26 ) Marc Fracke has poied ou ha i is possible o compare log likelihoods across wo models where he depede variable has bee rasformed by a kow fucio i he secod model; see Davidso ad McKio (993; 49) where a Jacobia adjusme makes i possible o compare log likelihoods across he wo models. 6 Hadbook o Resideial Propery Prices Idices (RPPIs)

63 Hedoic Regressio Mehods 5 ad evaluaed a he sample average amous of L, S ad he sample average age of a house A. ( 27 ) The resulig quarerly prices for his average house were covered io a idex, P, which is lised i Table 5.2 ad chared i Figure 5.2. H The hedoic regressio model defied by (5.28) is perhaps he simples possible oe bu i is a bi oo simple sice i eglecs he fac ha he ieracio of age wih he sellig price of he propery akes place via a muliplicaive ieracio wih he srucures variable ad o via a geeral addiive facor. I wha follows, model (5.28) is reesimaed usig qualiy adjused srucures as a explaaory variable raher ha jus eerig age A as a separae sad aloe characerisic. The Liear Time Dummy Model wih Qualiy Adjused Srucures 5.6 The liear ime dummy hedoic regressio model wih qualiy adjused srucures is described by p = ( ) ε (5.29) a + βl + g da S + + =,...,4; =,...,N(); This is he mos plausible hedoic regressio model so far. I works wih qualiy adjused (for age) srucures S * equal ( 27 ) The sample average amous of L ad S were m 2 ad 27.2 m 2 respecively ad he average age of he deached dwelligs sold over he sample period was.85 decades. o ( da) S isead of havig A ad S as compleely idepede variables ha eer io he regressio i a liear fashio The resuls for his model were a clear improveme over he resuls of model (5.28). The log likelihood icreased by 92 o ad he R 2 icreased o.8789 from he previous The esimaed decade depreciaio rae was ˆ d =. 9 (.48), which is reasoable as usual. This liear regressio model has he same propery as he model (5.28): house price differeces are cosa over ime for all cosa characerisic models bu house price raios are o cosa. So agai a overall idex will be cosruced which uses he prices geeraed by he esimaed parameers i (5.29) ad evaluaed a he sample average amous of L, S ad he average age of a house A. The resulig quarerly house prices for his average model were covered io a idex, P H 5, which is lised i Table 5.2 ad chared i Figure 5.2. For compariso purposes, P H 3 (he ime dummy Log Log model idex) ad P FCH (he chaied sraified sample mea Fisher idex) will be chared alog wih P H 4 ad P H 5. The preferred idices hus far are P FCH ad P H I ca be see ha agai, all four idices capure he same red bu here ca be differeces of over 2 perce bewee he various idices for some quarers. Noe ha all of he idices move i he same direcio from quarer o quarer wih decreases i quarers 4, 8, 2 ad 3, excep ha P H 3 icreases i quarer 2. Figure 5.2. Liear Time Dummy Price Idices, he Log Log Time Dummy Price Idex ad he Chaied Sraified Sample Mea Fisher Price Idex Source: Auhors calculaios based o daa from he Duch Lad Regisry P H4 P H5 P H3 P FCH Hadbook o Resideial Propery Prices Idices (RPPIs) 6

64 5 Hedoic Regressio Mehods Table 5.2. Liear Time Dummy Price Idices, he Log Log Time Dummy Price Idex ad he Chaied Sraified Sample Mea Fisher Price Idex Quarer P H4 P H5 P H3 P FCH Source: Auhors calculaios based o daa from he Duch Lad Regisry 5.64 A problem wih he hedoic ime dummy regressio models cosidered hus far is ha he prices of lad ad qualiy adjused srucures are o allowed o chage i a uresriced maer from period o period. The class of hedoic regressio models o be cosidered i he followig secio does o suffer from his problem. Hedoic Impuaio Regressio Models 5.65 The heory of hedoic impuaio idices explaied earlier is applied o he prese siuaio as follows. For each period, ru a liear regressio of he followig form: p = a + β L + g ( d A ) S + ε (5.3) =,...,4; =,...,N() Usig he daa for he ow of A, here are oly four parameers o be esimaed for each quarer: a, β, g ad d for =,...,4. Noe ha (5.3) is similar i form o he model defied by equaios (5.29), bu wih some sigifica differeces: Oly oe depreciaio parameer is esimaed i he model defied by (5.29) whereas i he prese model, here are 4 depreciaio parameers; oe for each quarer. Similarly, i model (5.29), here was oly oe a, β ad g parameer whereas i (5.3), here are 4 a, 4 β ad 4 g parameers o be esimaed. O he oher had, model (5.29) had a addiioal 3 ime shifig parameers (he ) ha required esimaio. Thus he hedoic impuaio model ivolves he esimaio of 56 parameers, he ime dummy model oly 7, so i is likely ha he hedoic impuaio model will fi he daa much beer I he housig coex, precisely mached models across periods do o exis; here are always depreciaio ad reovaio aciviies ha make a house i he exac same locaio o quie comparable over ime. This lack of machig, say bewee quarers ad +, ca be overcome i he followig way: ake he parameers esimaed usig he quarer + hedoic regressio ad price ou all of he housig models (i.e., sales) ha appeared i quarer. This geeraes prediced quarer + prices for he quarer models, pˆ + ( ), as follows: + + p ˆ + + ˆ ( ) ˆ L ˆ ( ˆ + a + β + g d A ) S (5.3) =,...,3; =,...,N() where â, βˆ, gˆ ad dˆ are he parameer esimaes for model (5.3) for =,...,4. Now we have a se of pseudo mached quarer + prices for he models ha appeared i quarer ad he followig Laspeyres ype hedoic impuaio (or pseudo mached model) idex, goig from quarer o +, ca be formed: ( 28 ) N ( ) + pˆ ( ), + = P HIL N ( ) (5.32) p = =,...,3 ( 28 ) Due o he fac ha he regressios defied by (5.3) have a cosa erm ad are esseially liear i he explaaory variables, he sample residuals i each of he regressios will sum o zero. Hece he sum of he prediced prices will equal he sum of he acual prices for each period. Thus he sum of he acual prices i he deomiaor of (5.32) will equal he sum of he correspodig prediced prices ad similarly, he sum of he acual prices i he umeraor of (5.34) will equal he correspodig sum of he prediced prices. 62 Hadbook o Resideial Propery Prices Idices (RPPIs)

65 Hedoic Regressio Mehods 5 As meioed earlier, he quaiy ha is associaed wih each price is as each housig ui is basically uique ad ca oly be mached hrough he use of a model The same mehod ca be applied goig backwards from he housig sales ha ook place i quarer +; ake he parameers for he quarer hedoic regressio ad price ou all of he housig models ha appeared i quarer + ad geerae prediced prices, pˆ ( + ), for hese + models: ˆ + ˆ + + pˆ ( + ) ˆ + + ˆ a β L g ( d A ) S (5.33) =,...,3; =,...,N(+) Now we have a se of mached quarer prices for he models ha appeared i period + ad we ca form he followig Paasche ype hedoic impuaio (or pseudo mached model) idex, goig from quarer o +: N ( + ) + p P (5.34) ( + ), + = HIP N ( + ) pˆ = =,..., Oce he above Laspeyres ad Paasche impuaio price idices have bee calculaed, he correspodig Fisher ype hedoic impuaio idex goig from period o + ca be formed by akig he geomeric average of he wo idices defied by (5.32) ad (5.34):, +, [ P P ] / 2, + + P HIF HIL HIP (5.35) =,..., The resulig chaied Laspeyres, Paasche ad Fisher impuaio price idices, P HIL, P HIP ad P HIF, based o he daa for he ow of A, are ploed below i Figure 5.3 ad are lised i Table 5.3. The hree impuaio idices are amazigly close. The Fisher impuaio idex is our preferred hedoic price idex hus far; i is beer ha he ime dummy idices because impuaio allows he price of lad ad of qualiy adjused srucures o chage idepedely over ime, whereas he ime dummy idices shif he hedoic surface i a parallel fashio. The empirical resuls idicae ha, a leas for he prese daa se for he ow of A, he Laspeyres impuaio idex provides a close approximaio o he preferred Fisher impuaio idex. Figure 5.3. Chaied Laspeyres, Paasche ad Fisher Hedoic Impuaio Price Idices Source: Auhors calculaios based o daa from he Duch Lad Regisry P HIL P HIP P HIF Hadbook o Resideial Propery Prices Idices (RPPIs) 63

66 5 Hedoic Regressio Mehods Table 5.3. Chaied Laspeyres, Paasche ad Fisher Hedoic Impuaio Price Idices Quarer P HIL P HIP P HIF Source: Auhors calculaios based o daa from he Duch Lad Regisry Figure 5.4. The Fisher Impuaio Price Idex, he Chaied Sraified Sample Mea Fisher Price Idex, he Liear Time Dummy Price Idex ad he Log Log Time Dummy Price Idex Source: Auhors calculaios based o daa from he Duch Lad Regisry P HIF P H5 P H3 P FCH 5.7 To coclude: our wo bes idices are he Fisher impuaio idex P HIF ad he sraified chaied Fisher idex P FCH. Overall, he impuaio idex P HIF should probably be preferred o P FCH sice he sraified sample idices will have a cerai amou of ui value bias which will mos likely be greaer ha ay fucioal form bias i P HIF. These wo bes idices are ploed i Figure 5.4 alog wih he log-log ime dummy idex P H 3 ad he liear ime dummy idex wih qualiy adjused srucures P H 5. All of he price idices excep P H 3 show dowward movemes i quarers, 4, 8, 2 ad 3 ad upward movemes i he oher quarers; P H 3 moves up i quarer 2 isead of fallig like he oher idices. 64 Hadbook o Resideial Propery Prices Idices (RPPIs)

67 Repea Sales Mehods 6

68 6 Repea Sales Mehods The Basic Repea Sales Model 6. The repea sales mehod was iiially proposed by Bailey, Muh ad Nourse (963). They saw heir procedure as a geeralizaio of he chaied mached model mehodology applied by he pioeers i he cosrucio of real esae price idices like Wygarde (927) ad Wezlick (952). The bes-kow repea sales idices are he Sadard ad Poor s/case-shiller Home Price Idices i he US, which are compued for 2 ciies (Sadard ad Poor s, 29). The Federal Housig Fiace Agecy (FHFA) also compues a repea sales idex for he US, ( ) usig a slighly differe approach. Residex ad he UK Lad Regisry compue repea sales idices for Ausralia ciies ad for he UK, respecively. ( 2 ) 6.4 The followig sochasic model explaiig he logarihm of he value (price) p for propery i period ca be foud i he lieraure: l p = P + H + ε (6.) where P is a commo erm for all properies (he log of price level i some regio or ciy), H is a Gaussia radom walk ha represes he drif i idividual housig value over ime, ad ε is a radom error erm or whie oise. Model (6.) is ofe ake as he sarig poi for derivig he esimaig repea sales equaio. 6.5 Aoher poi of deparure could be he cosraied log-liear hedoic model (5.4), where he parameers β k of he price-deermiig characerisics are cosraied o be fixed over ime. As ideical properies are compared, here is a secod resricio ivolved: he (amous of he) characerisics of a idividual propery are also assumed fixed over ime. Deoig he k h characerisic for propery by z k, he cosraied log-liear model ow becomes K l p = β + βk zk + ε (6.2) k= 6.6 A model for he logarihm of he chage i value of propery bewee wo periods, say s ad ( s < T ), is foud by subracig (6.2) for hose periods. I follows ha 6.2 As he ame idicaes, he mehod uilizes iformaio o properies which have bee sold more ha oce. Because i is a mached-properies ype of mehod, corollig for period-o-period differeces i he sample of properies is o required. However, because of he low icidece of resale uis a imes, i would o be very useful o compue a repea sales RPPI usig he sadard mached model mehodology ad coveioal idex umber formulae. Therefore, a sochasic model is posulaed which explais he price chages of houses ha l p l p = l( p / p ) = ( β β s s s s s s ) + ( ε ε ) = l P + ( ε ε ) have bee sold repeaedly. This (dummy s variable) s regressio model is he esimaed o he pooled daa (i.e., o s s s s l p l p = l( p / p ) = ( β β ) + ( ε ε ) = l P + ( ε ε ) (6.3) he pooled price chages) across he sample period. Model (6.3) is esseially sayig ha, eglecig he error s erm ε ε, he logarihm of he price chage is he same s for all properies, deoed by P. 6.3 The oly iformaio required o esimae a sadard repea sales regressio equaio is price, sales dae ad address of he properies; herefore his mehod is much less daa iesive ha hedoic mehods. Also, he repea sales mehod corols by defaul for locaio a he fies level of deail (he address), somehig which hedoic regressio mehods are ofe uable o do wih grea precisio. ( 3 ) Oe problem wih he repea sales mehod however is ha a dwellig ui ha is sold a wo differe pois i ime is o ecessarily ideical due o such facors as depreciaio ad reovaios. Cosequely, he loger he spa of ime bewee sales, he more quesioable he cosa-qualiy assumpio uderlyig he repea sales approach becomes. ( ) The FHFA was esablished i 28 as a combiaio of he former US Office of Federal Housig Eerprise Oversigh (OFHEO), who published he repea sales idex uil he, ad he Federal Housig Fiace Board (FHFB). ( 2 ) The Duch Lad Regisry compued a repea sales idex for he Neherlads uil 27 whe hey chaged over o a SPAR idex, which is published joily wih Saisics Neherlads. For he SPAR mehod, see Chaper 7. ( 3 ) However, he use of geospaial daa o allow for spaial depedece i he hedoic equaio could remedy he omied locaioal variables problem; see Chaper 5 ad Hill (2) for more deails. 6.7 Now suppose we have a sample of houses ha have bee sold more ha oce over he sample period =,...,T for which we have daa o rasacio prices, hece o heir price chages. The (holdig) period bewee subseque sales will differ amog hose properies. However, give ha i model (6.3) all idividual propery prices are expeced o chage a he same rae (excludig radom disurbaces), he repea sales daa ca be pooled ad he model esimaed wih he sadard repea sales equaio T s l( p / p ) = g D + m (6.4) = where D is a dummy variable wih he value i he period ha he resale occurs, - i he period ha he previous sale occurs, ad oherwise; m i is agai a error erm. ( 4 ) Uder he so-called classical assumpios, i paricular ( 4 ) Muliple resales are reaed as idepede observaios. As oed by Shiller (99), his should o be overly problemaic because here is o overlap bewee he holdig periods of muliple resales. 66 Hadbook o Resideial Propery Prices Idices (RPPIs)

69 Repea Sales Mehods 6 ha he errors have a zero mea ad cosa variace, equaio (6.4) ca be esimaed by OLS regressio. Some mulicollieariy may be prese i he daa, bu soluios o remedy his issue are limied if his is he case. 6.8 The repea sales idex goig from period o period is obaied by expoeiaig he correspodig regressio coefficies gˆ : P = exp( ˆ γ ) (6.5) RS The simpliciy ad araciveess of he sadard repea sales model resides o he fac ha i oly requires dummy variables; o characerisics daa oher ha he locaio (address) are eeded. ( 5 ) This, coupled wih he sraighforward way o compue he repea sales price idex, migh explai par of he populariy of he mehod i he real esae ad housig lieraure. 6.9 Wag ad Zor (997) derived a aalyical expressio for he repea sales idex. I appears o have a raher complex geomeric srucure. Thus, despie he fac ha he idea of machig is easily udersood, he mehod may be difficul o explai i deail. Moreover, as meioed earlier, a geomeric propery price idex may be udesirable as a arge, especially for a sock RPPI. A soluio could be he use of a arihmeic versio of he repea sales mehod, which was suggesed by Shiller (99). Sadard ad Poor s (Case-Shiller) Home Price Idices are based o he arihmeic repea sales mehod (see Sadard ad Poor s, 29). Issues ad Improvemes o he Basic Model 6. I his secio we will discuss a umber of issues relaed o he repea sales mehod ad give a brief overview of exesios ad improvemes o he basic model ha have bee proposed i he lieraure. Daa Cleaig 6. I pracical applicaios, properies ha were resold very rapidly as well as hose ha were o resold for log periods, have someimes bee excluded from he repea sales regressios as such rasacios migh be aypical ad herefore bias he resulig price idex. Clapp ad Giacoo (998) ad Seele ad Goy (997) suggesed elimiaig very shor holds from he daase as hese could be ( 5 ) I some couries, such as he UK ad he Neherlads, he Lad Regisry collecs all rasacio price daa bu oly a very limied umber of characerisics, like ype of dwellig ad of course address. I is herefore o surprisig o see ha i hose couries repea sales idices have bee compued from Lad Regisry daa. Noe ha he FHFE s repea sales idex i he US is based o daa obaied from Faie Mae ad Freddie Mac for morgages. disressed sales arisig from, for example, divorce or job loss, or speculaive rasacios. Jase e al. (28), usig daa from he Duch Lad Regisry, foud ha houses resold wihi 2 mohs showed relaively srog price icreases. 6.2 Reproducibiliy is oe of he sreghs of he repea sales mehod. Bu if he procedure for excludig aypical observaios differs from ime o ime, he reproducibiliy migh be compromised. Heeroskedasiciy 6.3 Case ad Shiller (987, 989) argued ha chages i house prices iclude compoes whose variace icreases wih he ierval of sales, so ha he assumpio of a cosa variace of he errors is violaed. They proposed a Weighed Leas Squares (WLS) approach o correc for his ype of heeroskedasiciy. The weighs are derived by regressig he squared residuals from he sadard (OLS) repea sales regressio o a iercep ad he ime ierval bewee sales. A modified versio of heir weighed repea sales approach is used by he US Federal Housig Fiace Agecy o cosruc quarerly price idices for siglefamily homes. I ca be argued ha he error variace will be o-liear i ime iervals (Calhou, 996), hece he squared OLS residuals are regressed o a iercep erm, he ime ierval ad he square of he ime ierval. 6.4 Some sudies foud ambiguous resuls for heeroskedasiciy adjusme. Leishma, Wakis ad Fraser (22), usig Scoish daa, ad Jase e al. (28), usig Duch daa, applied he sadard (OLS) repea sales mehod ad various weighed mehods. Boh sudies cocluded ha he sadard mehod was o iferior. Sample Selecio Bias 6.5 A impora problem wih repea sales idices is he possibiliy of sample selecio bias. The problem is ha some ypes of houses may rade more frequely o he marke ha oher ypes so ha hey will be over-represeed i he repea sales sample (wih respec o he sock of houses or he sales durig some period). Whe hese ypes of houses exhibi differe price chages, he he repea sales idex eds o be biased. For example, if low qualiy houses sell more frequely ha high qualiy houses bu high qualiy houses rise i price a a slower rae, a repea sales idex will ed o have a upward bias. 6.6 There are various reasos why he holdig duraio of properies ca be uevely disribued. Life-cycle heories o propery holdig periods sugges ha less expesive houses are raded more frequely; whe people move up he propery ladder hey will ed o move home less ofe. Lower rasacio coss for less expesive properies, for isace due o lower samp duies, may also Hadbook o Resideial Propery Prices Idices (RPPIs) 67

70 6 Repea Sales Mehods resul i a higher urover rae of less expesive homes. I addiio, he Buy-o-Le marke i some couries is more acive i lower rages of he price segmes. 6.7 Quie a few sudies addressed he issue of holdig duraio ad sample selecio bias i repea sales price idices; see for example Case, Pollakowski ad Wacher (99) (997), Cho (996), Clapp, Giacoo ad Tiriroglu (99), Gazlaff ad Hauri (997), Hwag ad Quigley (24), ad Seele ad Goy (997). No all of hese sudies foud srog evidece of sample selecio bias. Clapp, Giacoo ad Tiriroglu (99) did o fid ay sysemaic differeces bewee he repea sales sample ad he full sample of rasacios over he log ru. They argued ha arbirage ypically forces prices for he repea sample o grow a he same rae as he prices for he full sample. Wallace ad Meese (997) cocluded ha heir repea sales sample was sufficiely represeaive of all sales durig he sample period i quesio. However, he sample of all housig sales hemselves may o be represeaive of he oal housig sock. 6.8 Poeial sample selecio problems are ihere o he repea sales mehod. To some exe hey ca be correced for by sraifyig he repea sales sample. A problem i his coex is ha he sub-samples may become very small ad produce volaile idices. Thus here may be a argume for smoohig he idex umbers. Moreover, i ca be argued ha sellig prices do o always exacly represe he marke values of he properies, which ca be viewed as a lae variable. There may be rasacio oise ivolved ha causes volailiy of he measured price idices. Fracke (2) proposed a smoohig procedure ha akes io accou he fac ha sellig prices of repeaedly sold properies deped o he ime ierval bewee subseque sales. Iefficiecy ad Revisio 6.9 The repea sales mehod is ofe criicized for beig iefficie sice, by is aure, i is waseful of daa. This is rue compared wih he muli-period ime dummy hedoic mehod: sice oly housig uis ha have sold more ha oce are used wih he repea sales mehod, he resulig daa se is usually much smaller ha he sample of rasacios over a give period. O he oher had, he loger he sample period, he more daa will be used by he repea sales mehod (as more ad more houses will have bee resold). Thus, whe he sample period grows ad more daa are added, he efficiecy of he repea sales mehod will icrease faser ha ha of he hedoic approach. Besides, he repea sales mehod is efficie i he sese ha i does o use ay oher housig characerisics ha he ui s address. 6.2 I is possible o augme a repea sales daase by usig assessme daa (also referred o as appraisals) as approximaios for pas or curre values of houses ha have o bee resold durig he sample period. Some of he daa o which he repea sales idex would he be based would be pseudo raher ha geuie repea daa. Mos empirical sudies o his issue are based o appraisals of dwelligs ha are abou o be re-fiaced. I has bee suggesed ha appraisals ed o over-esimae he acual sellig price of he propery. Bu he magiude of he bias could deped o he purpose for which assessme iformaio is colleced. De Vries e al. (29) ivesigaed he reliabiliy of he Duch appraisal daa, which are colleced o he goverme s behalf for icome ad local ax purposes, ad cocluded ha he qualiy was quie saisfacory ad eve improvig over ime. For more o he use of assessme iformaio i a repea sales idex ad he removal of appraisal bias, see for example Geler (996), Edelsei ad Qua (26), ad Leveis (26). 6.2 Similar o he muli-period ime dummy mehod, he repea sales mehod suffers from revisio of previously compued idices: whe addiioal repea sales iformaio becomes available, re-esimaio will resul i chages o he esimaed coefficies ad hus i he price idices iferred. There have bee few empirical sudies o his issue o dae, e.g. Clapp ad Giaccoo (999), Buler, Chag ad Crews Cus (25), ad Clapham e al. (26). The las auhors foud evidece o sugges ha repea-sales idices are relaively less sable ha ime dummy hedoic idices. Noe ha revisios may be relaed o sample selecio bias; whe he sample period is exeded ad he coefficies re-esimaed, sample selecio bias migh decrease as he umber of observed repea sales icreases. Qualiy Chage 6.22 Repea sales idices are esimaed o he premise ha he qualiy of he idividual properies (as measured by heir characerisics) is uchagig over ime. I is someimes argued ha i he aggregae, he value of reovaios is approximaely equal o he value of depreciaio. For idividual dwellig uis, however, his cao be rue because over ime, may uis are demolished. Oe way o avoid his issue is o limi he sample of repeaed sales observaios o hose uis for which heir qualiy is hough o be relaively cosa from oe sale period o he ex. Case ad Shiller (989), for example, exraced [. ] daa o houses sold wice for which here was o appare qualiy chage. The problem is ha he price chages iferred may o be idicaive of he price chages for he full sample of repeaed sales ad may exacerbae he sample selecio bias problem. ( 6 ) ( 6 ) Meese ad Wallace (997) repor ha repea sales uis wih chaged characerisics ed o be larger ad i worse codiio ha he average of uis wih sigle rasacios. 68 Hadbook o Resideial Propery Prices Idices (RPPIs)

71 Repea Sales Mehods If iformaio o maieace ad reovaio expediures was available a he micro level, his could be used i he coex of esimaig a repea sales (or hedoic) regressio model for housig. I pracice his kid of iformaio is ofe lackig. Abraham ad Schauma (99) suggesed adjusig he repea sales idex from aggregae daa o reovaio expediures ad make a adjusme for depreciaio of he srucures; see also Palmquis (98) (982). This approach o measurig e depreciaio seems oo crude ad arbirary o be suiable for he compilaio of official saisics, however Shimizu, Nishimura ad Waaabe (2) recely developed a repea sales mehod ha akes e depreciaio io accou. Their mehod relies o a ukow ase parameer for which a guessimae has o be made. While makig a adjusme seems o be beer ha compleely igorig he (e) depreciaio problem, makig guesses migh o be a aracive opio for saisical agecies Shiller (993a) developed a repea sales mehod ha accous for possible chages i housig characerisics bewee firs ad secod sales. The mehod ivolves icludig characerisics i a radiioal repea sales model. Clapp ad Giaccoo (998) advocaed he use of assessed values a ime of firs ad secod sales as a parsimoious corol for qualiy chages of he properies. Goezma ad Spiegel (997) suggesed icludig a cosa erm i he repea-sales regressio o capure average qualiy chage across all characerisics over he average holdig period Case ad Quigley (99) were he firs o advocae hybrid models. Hybrid models exploi all sales daa by combiig repea sales ad hedoic regressios ad address o oly he qualiy chage problem bu also sample selecio bias ad iefficiecy problems. Case ad Quigley (99) ad Quigley (995) used samples of sigle-sale ad repea-sale properies o joily esimae price idices usig geeralized leas squares regressio. Hill, Kigh ad Sirmas (997) uderook a similar hough more geeral exercise. Their model sacks wo equaios, a ime dummy hedoic model (icludig age of he dwellig) ad a repea sales model, which are joily esimaed usig maximum likelihood. They used a characerisics prices mehod o derive he price idices; see Chaper 5, equaio (5.9). ( 7 ) 6.27 The raioale for hybrid mehods is o ry ad combie he bes feaures of he repea sales ad hedoic approaches. By combiig boh approaches, o daa are discarded while repea sales are sill allowed o play a promie role i he idex cosrucio mehodology. However, we agree wih Hill (2) who has difficuly accepig ha a repea-sales price relaive should be preferred o a (say double) impuaio hedoic price relaive. He oes ha: If repea-sales price relaives are o deemed more reliable ha double impuaio price relaives, here is o reaso o prefer hybrid mehods o hedoic mehods. I he ed, he complexiy of hybrid models mos likely makes hem usuiable for implemeaio by saisical agecies. Mai Advaages ad Disadvaages 6.28 Below, he mai advaages ad disadvaages of he repea sales mehod are lised. The mai advaages are: The repea sales mehod i is basic form eeds o characerisics oher ha address of he properies ha are rasaced more ha oce over he sample period. Source daa may be available from admiisraive records such as hose from he Lad Regisry. Sadard repea sales regressios are easy o ru ad he price idices easy o cosruc. The repea sales mehod is a mached-model ype of mehod wihou ay impuaios. By cosrucio, locaio is auomaically corolled for. The resuls are esseially reproducible provided ha he reame of ouliers ad possible correcios for heeroskedasiciy (as well as he choice bewee a geomeric or arihmeic mehod) are clearly described The mai disadvaages of he repea sales mehod are: The mehod is iefficie i he sese ha i does o use all of he available rasacio prices; i uses oly iformaio o uis ha have sold more ha oce durig he sample period. The basic versio of he mehod igores (e) depreciaio of he dwellig ui. ( 8 ) There may be a sample selecio bias problem i repea sales daa. The mehod cao provide separae price idices for lad ad for srucures. The mehod cao be used if idices are required for very fie classificaios of he ype of propery sold. I paricular, if mohly propery price idices are required, he mehod may fail due o a lack of marke sales for smaller caegories of propery. I priciple, esimaes for pas price chage obaied by he repea sales mehod should be updaed as ew rasacio iformaio becomes available. Thus he repea ( 7 ) Oher papers o he use of hybrid models iclude Clapp ad Giaccoo (992), Kigh, Dombrow ad Sirmas (995), Eglud, Quigley ad Redfear (998), ad Hwag ad Quigley (24). ( 8 ) As meioed previously, here are ways o deal wih his problem bu hey all appear o be oo crude or oo complex o be used for he compilaio of official saisics. Hadbook o Resideial Propery Prices Idices (RPPIs) 69

72 6 Repea Sales Mehods sales propery price idex could be subjec o perpeual revisio. ( 9 ) 6.3 Hauri ad Hedersho (99) summarize he disadvaages of he repea sales mehod as follows: The mehod is subjec o may criicisms: () i does o separae house price chage from depreciaio, (2) reovaio bewee sales is igored, (3) he sample is o represeaive of he sock of housig, (4) aribue prices may chage over ime, ad (5) a large umber of sales are required before a reasoable repea-sales sample is obaied. Doald R. Hauri ad Paric H. Hedersho (99; 26) The fifh criicism i his quoaio he large umber of sales required o obai a reasoable daa se wih repea sales was o meioed hus far. I he ex secio a basic OLS repea sales idex will be cosruced usig he daa for he ow of A ha was used earlier i ( 9 ) I pracice, his is o ecessarily a big problem. A similar problem occurs whe mohly scaer daa are used i a CPI; a movig widow of observaios ca be used o cosruc a mohly CPI compoe where oly he icremeal iflaio rae for he las moh is used o updae he idex; see Ivacic, Diewer ad Fox (2) ad de Haa ad va der Grie (2). Chapers 4 ad 5 o show he effec of havig a very small repea sales daa se. A Example Usig Daa for he Tow of A 6.3 Recall ha, afer deleig houses which were older ha 5 years a he ime of sale ad also deleig observaios which had lad areas greaer ha 2 m, we were 2 lef wih 2289 sales i he 4 quarer sample period, sarig i he firs quarer of 25 ad edig i he secod quarer of 28. Tha is, we had a average of 63.5 sigle sales of deached dwellig uis per quarer for he Duch ow of A. A few houses were sold wice durig he same quarer, ad we deleed hose shor holds for he esimaio of he repea sales idex (as hey could be disressed sales). We eded up wih oly 85 repea sales over he 4 quarer period. The OLS repea sales idex compued usig his small daa se, labeled as P RS, is ploed i Figure 6. alog wih he chaied sraified sample mea Fisher idex, P FCH, described i Chaper 4 ad he hedoic impuaio Fisher idex, P HIF, described i Chaper 5. These hree price series are lised i Table 6.. Figure 6.. Repea Sales Price Idex, Chaied Sraified Sample Fisher Price Idex ad Hedoic Impuaio Fisher Price Idex Source: Auhors calculaios based o daa from he Duch Lad Regisry P RS P HIF P FCH 7 Hadbook o Resideial Propery Prices Idices (RPPIs)

73 Repea Sales Mehods 6 Table 6.. Repea Sales Price Idex, Chaied Sraified Sample Mea Fisher Price Idex ad Hedoic Impuaio Fisher Price Idex Quarer P RS P FCH P HIF Source: Auhors calculaios based o daa from he Duch Lad Regisry 6.32 Compared o he oher wo price idices, he repea sales idex urs ou o be highly erraic durig he secod half of he sample period. I quarer 4, he repea sales idex shows a price decrease whereas he hedoic impuaio ad sraified sample meas idices measure a price icrease. Of course we cao draw ay defiiive coclusios from his simple example, bu i does cofirm ha repea sales mehods require a large umber of observaios o esimae price idices wih accepable precisio. Hadbook o Resideial Propery Prices Idices (RPPIs) 7

74

75 Appraisal-Based Mehods 7

76 7 Appraisal-Based Mehods Iroducio 7. As was meioed i previous chapers, he mached model mehodology o cosruc price idices, where prices of ideical iems are compared over ime, cao be applied i he housig coex. Oe of he reasos is he low icidece of re-sales ad he resulig chage i he composiio of he properies sold. The repea sales mehod, which was discussed i Chaper 6, aemps o deal wih he qualiy mix problem by lookig a properies ha were sold more ha oce over he sample period. However, usig oly repea-sales daa could be very iefficie sice all sigle sales observaios are hrow ou ad could also lead o sample selecio bias. 7.2 I several couries iformaio o assessed values or appraisals of properies is available, which migh be useful as proxies for sellig prices or, more geerally, marke values. I couries where hey have bee colleced for ax purposes, appraisals will ypically be available for all properies a a paricular referece period. I a umber of sudies assessed values were used i addiio o sale prices i a repea sales framework o reduce he problem of iefficiecy ad he poeial problem of sample selecio bias. For example, Gazlaff ad Lig (994) used sale prices as he firs measure ad appraisals as he secod measure i a repea sales regressio. Clapp ad Giaccoo (998) did he reverse ad used appraisals as he firs ad sellig prices as he secod measure. Boh sudies foud ha hese mehods produced price idices similar o a sadard repea sales idex. 7.3 The above assessed-values repea sales mehods are based o pseudo price relaives i which he appraised values may be derived from differe periods. Bu whe assessed values for all properies are available ha do relae o a sigle valuaio period or referece dae, he i will be possible o use he sadard mached model mehodology. For each propery sold i some compariso period for which we have a sale price, a base period price he assessed value is ow available also. Price relaives wih a commo base period he valuaio period ca he be cosruced, ad hese sale price appraisal raios ca be aggregaed usig a sadard idex umber formula, hough some re-scalig may be required. 7.4 The use of a coveioal mached model idex umber formula simplifies he compuaio of he idex because here is o eed o use ecoomeric echiques o esimae he idex or o adjus for composiioal chage, as is he case wih hedoic ad repea sales mehods; see Chapers 5 ad 6. Aoher feaure of he sale price appraisal raio mehod (SPAR) mehod discussed i he prese chaper is ha i is free from revisios because here is o modelig ad poolig of daa ivolved. Thus, i coras o he repea sales mehod ad he muliperiod ime dummy hedoic mehod, previously compued price idices are o re-esimaed whe ew sales daa become available. 7.5 The SPAR mehod has bee used i New Zealad sice he early 96s ad is currely also used i several Europea couries, oably i Demark, he Neherlads ad Swede. Give ha a few couries aroud he world are acually usig he SPAR mehod, i is o surprisig ha here is oly a small hough expadig lieraure available. I would appear ha Bourassa, Hoesli ad Su (26) were he firs o publish a paper o his mehod. Accordig o hem, he advaages ad he relaively limied drawbacks of he SPAR mehod make i a ideal cadidae for use by goverme agecies i developig house price idices. Rossii ad Kershaw (26) foud ha he SPAR mehod ouperformed several oher mehods i erms of reduced volailiy of weekly idex umbers. De Vries e al. (29) repored a higher precisio of mohly SPAR idices for he Neherlads compared wih mohly repea sales idices. Shi, Youg ad Hargreaves (29) compared SPAR ad repea sales idices for New Zealad ad foud a raher low correlaio o a mohly basis. 7.6 Whe he properies are reassessed ad ew appraisal daa become available, he SPAR idex ca, ad probably should be, rebased. A log-erm idex series is obaied by splicig he exisig ad ew series. Properies i he Neherlads are currely beig re-valued each year, which makes i possible o cosruc a aually chaied RPPI, where he valuaio period (which is Jauary) serves as he lik moh. Shi, Youg ad Hargreaves (29) argued ha bias could arise from freque reassessmes. De Vries e al. (29) did o fid ay chai-lik bias bu observed ha he sadard error of he chaied SPAR idex icreases each ime ew appraisals are iroduced because a addiioal source of samplig error is added. The SPAR Mehod i Deail 7.7 Suppose ha we have samples of properies sold a our disposal for he sarig or base period ad for compariso periods ( =,..., T ). As i earlier chapers, he samples will be deoed by S () ad S (). I each period we kow he sale prices of all sampled properies; he price of propery i period is represeed by p. As meioed before, houses ha were sold i period were geerally o sold i period, so here is a lack of machig. However, suppose ha assessed values or appraisals are available for all properies i he housig sock, ad ha hey relae o a sigle valuaio period. The valuaio period will serve as he base period, ad he appraisal for propery will be deoed by a. Thus, for each propery belogig o he period sample S () we kow boh he period sellig price p ad he base period assessed value a. I oher words, for all S() we ca esablish a price relaive a sale price appraisal raio p / a, which ca be used i a mached model framework o compue a RPPI. 74 Hadbook o Resideial Propery Prices Idices (RPPIs)

77 Appraisal-Based Mehods Alhough i would be possible o cosruc geomeric appraisal-based idices, we will focus here o arihmeic idices as hese seem o be more appropriae i he housig coex. The arihmeic appraisal-based idex ca be defied as S ( ) p p P = = ( ) AP w (7.) a S ( ) a S ( ) Expressio (7.) describes a Paasche-ype idex because we are usig he compariso period sample S () i boh he umeraor ad he deomiaor. The quaiies are equal o as every propery is basically a uique good. The cosrucio of a Laspeyres-ype price idex would be problemaic or eve impossible: period price iformaio for dwellig uis belogig o he base period sample S () is oly available for hose few uis, if ay, ha were resold i period. This meas ha he cosrucio of a Fisherype idex will o be feasible eiher. As show by he secod expressio, (7.) ca be wrie as a value-weighed average of he sale price appraisal raios p / a, where he weighs w ( ) = a / a S ( ) reflec he base period assessed value shares wih respec o he sample S (). 7.9 The appraisal-based Paasche-ype idex, AP, give by (7.) is obviously a mached model idex. Accordigly, here is o composiioal chage o accou for whe comparig period direcly wih period. However, as here is geerally o overlap, he samples S () i periods =,...,T will be compleely differe ad composiioal chage will be prese from oe period o he ex. Those period o period sample mix chages cao be adjused for, which suggess ha shor-erm volailiy will mos likely occur. This feaure is o uique o he appraisal-based idex; we would expec o observe more or less he same for he Paasche-ype hedoic impuaio idices discussed i Chaper 5. The similariy wih he impuaio Paasche idex will be addressed i he ex secio. 7. The appraisal-based price idex (7.) does o make use of he observed sellig prices i he base period. As a resul, he idex will differ from i he base period, which is problemaic. However, his problem ca easily be resolved by ormalizig he idices by dividig hem by he base period value. We he obai he followig arihmeic SPAR idex: p p p / N( ) a / S ( ) S () S ( ) S () P = = SPAR a a p / N() a / S ( ) S () S () S ( ) p p p / N( ) a / N() S ( ) S () S ( ) S () P = = SPAR (7.2) a a p / N() a / N( ) S ( ) S () S () S ( ) P where N () ad N () deoe he umber of properies sold i periods ad (he respecive sample sizes). 7. The secod expressio o he righ-had side of (7.2) wries he SPAR idex as he produc of he raio of sample meas ad a brackeed facor. Sice he SPAR mehod is a mached model mehod (wih respec o periods ad ), he brackeed facor adjuss he raio of sample meas for composiioal chages occurrig bewee each period ad he base period. So, while shor-erm volailiy is likely o be prese due o period o period mix chages, he SPAR mehod is expeced o exhibi much less volailiy ha he raio of sample meas. 7.2 The arihmeic SPAR idex ca be ierpreed as a proxy for a sales based Paasche RPPI. ( ) Bu may couries, icludig EU member saes, are ypically aimig a a Laspeyres idex raher ha a Paasche idex. Sraificaio could be used as a meas o approximae his arge idex while usig he SPAR mehod. The SPAR (Paasche) idices a he sraum level will he be aggregaed usig base period expediure share weighs o obai he overall Laspeyres-ype idex. The RPPI i he Neherlads is a example of such a sraified SPAR approach, where regio ad ype of house are used as sraificaio variables. The idex is compiled mohly ad published joily wih he Duch Lad Regisry Office. Sraificaio migh also help o accou for ay sysemaic differeces bewee appraisals ad marke values across regios or differe ypes of houses (de Vries e al., 29; de Haa, va der Wal ad de Vries, 29). 7.3 The SPAR idex ca aleraively be ierpreed as a sample esimaor of a sock RPPI. If i each period he properies sold are viewed as radom samples from he base period housig sock, he he SPAR idex is a esimaor of he Laspeyres sock RPPI. Properies sold ha were added o he sock afer he base period should i his case be excluded. ( 2 ) As meioed i earlier chapers, he sample of houses sold may o be represeaive of he oal sock so ha sample selecio bias could arise. Sraificaio will agai be a helpful ool o miigae his problem. ( ) Admiisraive daa ses, paricularly hose from he lad regisry, ypically coai all sales (excludig ewly-buil properies) i each period. From a sales poi of view here N() is o samplig ivolved. I his ierpreaio, he SPAR idex has o samplig error, bu i does have error due o he use of appraisals, which are esimaes of he rue marke values. N( 2 )( I ) may seem ha properies which are ew o he sock cao eve be used because he ecessary appraisals are lackig. However, his depeds o he appraisal sysem. If former real houses have bee sold ad are hus added o he sock of ower occupied housig, he hey will have a base period appraisal value if real houses are also assessed. Moreover, if propery axes are uiformly based o period valuaios for a umber of years, he he auhoriies would eed hose values for ewly buil houses as well. The difficuly is of course ha he auhoriies would have o ive a assessed value for a ew house i period, eve if i did o exis i ha period. Such assessmes migh be problemaic ad hece should probably be excluded from he compuaio of he idex. Hadbook o Resideial Propery Prices Idices (RPPIs) 75

78 7 Appraisal-Based Mehods Mehodological ad Pracical Issues Qualiy Chage 7.4 Sice he appraisals relae o he base period, i geeral he properies will have bee valued a heir base period characerisics. Bu for he SPAR idex (7.) o be a cosa qualiy price idex, he appraisals should be evaluaed a characerisics of he compariso period. Thus, if housig characerisics chage over ime, he SPAR mehod will o adjus for hose chages, similar o he repea sales mehod. This is a impora drawback. 7.5 Ye i pracice here could be some implici adjusme for qualiy chages. I he case of he New Zealad SPAR idex, Bourassa, Hoesli ad Su (26) oe: he base appraisal is adjused for subseque improvemes o he propery ha require a buildig permi. If his is doe i real ime, adjusmes for major qualiy improvemes will ideed be made. However, apar from he fac ha o all propery improvemes require a buildig permi, i is ulikely ha hese adjusmes adequaely deal wih he e effec of improvemes ad depreciaio of he srucures. 7.6 I he Neherlads here may also be some implici qualiy adjusme i he SPAR idex. The assessmes are ypically carried ou some ime afer he appraisal referece moh ad may ake io accou major improvemes o he properies. Furhermore, as meioed above, he assessmes are owadays performed every year. Aual chaiig by iself could alleviae he problem of qualiy chage if he updaed appraisals properly accou for chages i he characerisics. Of course his will deped o he exac way he properies are valued, which may o be kow o he idex compilers. Qualiy of he Assessme Iformaio 7.7 Absracig ow from qualiy adjusme issues, he SPAR mehod is obviously depede o he qualiy of he assessme iformaio. There are hree broad ways i which assessmes of (o-raded) properies ca be carried ou: by usig hedoic regressio, by comparig hem o similar raded properies, ad by exper judgme. The mehods used differ amog couries ad someimes eve wihi a paricular coury. I various couries, privae compaies are egaged i mass appraisal. Alhough he deails of he mehods used are ofe o publicly available, some of hose compaies appear o combie hedoic regressio wih local marke iformaio or exper judgme. 7.8 Bourassa, Hoesli ad Su (26) oed ha he appraisals i New Zealad are derived from hedoic regressios, bu uforuaely hey did o prese he exac mehod. I Chaper 5 i was explaied ha here are differe hedoic approaches ad ha he prediced prices i his case he appraisals deped o he ype of daa used ad he umber of observaios, he specified fucioal form, he variables icluded ad oher choices made. Thus, eve hough hedoic regressio is he leas arbirary of he hree assessme mehods meioed above, here ca sill be a lo of uceraiy ad error ivolved, which has a ukow impac o he sale price appraisal raios ad he resulig SPAR idex. 7.9 The use of comparable properies seems o be widespread. Chiloy, Cho ad Megbolugbe (997) compared a sample of U.S. privae secor appraisals o sellig prices. They suspeced ha he reliace o a relaively small umber of comparable houses leads o more volailiy ha ca be observed i marke-wide sellig prices. More imporaly perhaps, hey foud ha appraisals exceeded sale prices i approximaely 6 perce of he cases, leadig o a average upward bias of wo perce. 7.2 I couries where official assessmes are desiged for propery axaio purposes, like i he Neherlads, he assessed values may o o be oo far off he mark sice he goverme has a iceive o make he assessmes as large as possible i order o maximize ax reveue while axpayers have he opposie iceive o have he assessmes as small as possible. I he Neherlads he muicipaliies are resposible for makig he assessmes. The mehods used differ across he muicipaliies. Some of hem, for example he capial ciy of Amserdam, use he comparable house mehod whereas ohers apparely use some kid of hedoic regressio mehod. De Vries e al. (29) argued ha Duch auhoriies may i fac have a iceive o make he assessmes o oo high o avoid cour procedures because households who feel he appraised value is oo high ca lodge a appeal. Oher Issues 7.2 The advaage of he SPAR mehod as compared o hedoic regressio mehods is ha iformaio o oly a few propery characerisics is eeded: assessed values (relaig o a commo referece period), possibly some sraificaio variables, ad addresses o merge he daa files if he sellig prices ad appraisals come from differe sources. I he Neherlads, for example, rasacio prices ad a limied umber of sraificaio variables are recorded by he Lad Regisry whereas he appraisals are from a secod admiisraive daa source. I is well kow ha mergig daa files by address ca be difficul, alhough i he Neherlads his does o seem o be a major issue. 76 Hadbook o Resideial Propery Prices Idices (RPPIs)

79 Appraisal-Based Mehods Daa cleaig is aoher impora pracical issue. The SPAR mehod is depede o he qualiy of he appraisals. Some of he sale price appraisal raios migh be foud implausible, perhaps because he appraisals are deemed wrog, ad deleed from he daa se. ( 3 ) Deleig erroeous observaios, such as obvious ery errors, is good pracice. A cauious approach is called for, however, as deleig price relaives ca lead o biased resuls. A leas a rule for deleig ouliers should be explicily formulaed o iform users. P IP ˆ β if he appraisal sysem works well. (4 ) Equaio (7.5) will be used below o predic he missig prices i he deomiaor of he impuaio Paasche idex (7.3). P IP 7.26 For coveiece we firs rewrie (7.3) as = S ( ) p S () p / N( ) / N() S () S ( ) p / () N = pˆ ( ) / N( ) S ( ) p S () p / N( ) / N() S () pˆ S ( ) p / ( ) / () / ( ) ˆ / () N p N p N p N S ( ) S () S ( ) S () = = (7.6) p / N() pˆ ( ) / N( ) p / N() pˆ ( ) / N( ) S () S ( ) A Regressio-Based Impuaio Ierpreaio 7.23 I his secio we will show ha he SPAR mehod is esseially a impuaios approach i which he missig base period prices are esimaed from a liear regressio of sellig prices o appraisals. Recall firs ha he base period prices of he properies belogig o he period sample S () cao be observed direcly sice hose properies were geerally o raded i period. We ca ry o esimae he missig prices o obai he impuaio Paasche price idex S ( ) p P IP = pˆ ( ) (7.3) S ( ) ˆ 7.24 The impued value p ( ) i (7.3) should predic he period price for propery, evaluaed a is period characerisics. Keepig he (quaiies of he) characerisics fixed is ecessary o adjus for qualiy chage. The use of hedoic impuaio was discussed i Chaper 5. Hedoic regressio models explai he sellig price of a propery i erms of a se of price-deermiig characerisics ha relae o he srucure ad he locaio. This secio addresses a differe ype of regressio-based impuaio Cosider he followig wo-variable regressio model for he base period: p = β + βa + ε (7.4) Equaio (7.4) is a simple descripive model where sellig prices are regressed o appraisals. We assume ha his model is esimaed by Ordiary Leas Squares (OLS) o he daa of he base period sample S (). The prediced prices for S() are pˆ ˆ ˆ = β + βa (7.5) where ˆβ is he esimaed iercep erm ad ˆβ he esimaed slope coefficie. We expec o fid ˆ β ad ( 3 ) The example for he ow of A a he ed of his chaper shows ha he removal of a relaively low umber of ouliers ca have a subsaial effec o he SPAR idex. S () S ( ) I he secod sep of (7.6) we have used p / () = () ˆ / () S N p S () N, which holds rue because he OLS regressio residuals sum o zero. The firs problem we face is ha he housig characerisics should be kep fixed whe predicig he base period prices pˆ ( ) for S(). This is obviously o possible usig equaio (7.5). Thus, he firs assumpio is ha of o qualiy chage, ad we accordigly replace ˆ p ( ) i (7.6) by p ˆ () ˆ = p. Usig (7.5) for boh S() ad S(), equaio (7.6) becomes P IP = S ( ) S () p ˆ + ˆ / N( ) β β p / () ˆ + ˆ N β β S () S ( ) a / N() a / N( ) / N() pˆ ( ) / N( ) (7.7) Noice ha if ˆ β =, ha is, if he regressio lie passes hrough he origi, (7.7) simplifies o he SPAR idex (7.2), irrespecive of he slope coefficie ˆβ. So, if he aim is o esimae a impuaio Paasche idex, he secod assumpio uderlyig he SPAR mehod seems o be ha he iercep erm ˆβ is egligible The hird assumpio is ha equaio (7.5) holds for S() : he liear relaioship bewee base period sellig prices ad appraisals posulaed ad esimaed for he properies acually sold durig he valuaio or base period (for S() ) is assumed o hold also for properies ha were o sold. Bu his is a very resricive assumpio. While he liear relaio ca be esed for S(),( 5 ) i would be difficul if o impossible o es i for S() as he sellig prices are missig. The presece of appraisal bias, i he sese ha he appraisals over- or uderesimae he ukow marke values (he prices a which he properies would have bee sold), ca bias he SPAR idex. Bias i he SPAR idex will paricularly arise ( 4 ) If he sellig prices would be used as official valuaios, he of course he values ad would exacly hold ad we would fid a perfec fi of (7.4) o he period daa. ( 5 ) Va der Wal, er Seege ad Kroese (26) ad de Vries e al. (29) compared Duch goverme appraisals o sellig prices. I he laer sudy he liear relaioship (7.4) was explicily esed (for he properies raded i he valuaio moh) for various valuaio mohs. I ured ou ha he cosa erm was ideed very small ad ha he slope coefficie did o sigificaly differ from. Hadbook o Resideial Propery Prices Idices (RPPIs) 77

80 7 Appraisal-Based Mehods if he rue value of β for S() would be very differe from β for S() I his secio we focused o he SPAR idex as a sales RPPI. A relaed approach, where he appraisals serve as auxiliary iformaio i a geeralized regressio (GREG) framework i order o esimae a sock based RPPI, was described by de Haa (2b). The GREG mehod uses populaio iformaio o he appraisals isead of sample iformaio. He showed ha he SPAR idex is a sraighforward esimaor of he GREG sock based idex which, whe applied o Duch daa, ured ou o be almos as efficie. Mai Advaages ad Disadvaages 7.29 The meris of he SPAR mehod are lised below. The mai advaages are: The SPAR mehod is esseially based o he sadard mached model mehodology ad liks up wih radiioal idex umber heory. The mehod is compuaioally simple. Iformaio o housig characerisics is o required i order o impleme his mehod; he oly iformaio required is daa o sale prices ad appraisals. I some couries he daa is available from admiisraive sources such as he lad regisry, ad usually covers all rasacios (for resold properies). This mehod uses much more daa ha he repea sales mehod ad hece here are fewer problems due o sparse daa. I paricular, sample selecio bias is likely o be smaller. Also, he SPAR mehod does o suffer from revisio of previously calculaed figures whe ew daa becomes available. Codiioal o he daa cleaig rules, he SPAR mehod is reproducible. 7.3 The mai disadvaages of he SPAR mehod are: The mehod cao deal adequaely wih qualiy chages (major repairs or reovaios ad depreciaio) of he dwellig uis. ( 6 ) The SPAR mehod is depede o he qualiy of he base period assessme iformaio. The exac way he valuaios are carried ou may o always be clear ad has a ukow impac o he resuls. The mehod cao decompose he overall propery price idex io lad ad srucures compoes. ( 7 ) ( 6 ) I couries where he assessmes provide separae iformaio o he value of he srucures ad he value of he lad, he SPAR idex could i priciple be adjused by usig exogeous iformaio o he e depreciaio of houses of he ype beig cosidered. ( 7 ) If fresh propery assessme iformaio appeared every moh or quarer, his iformaio could be used o form separae price idices for boh lad ad srucures, A Example o Daa for he Tow of A 7.3 Usig he daa se for he ow of A, which was described i Chaper 4, a SPAR idex was compued. Recall ha his daa se coaied sales of deached houses for 4 quarers, sarig i he firs quarer of 25 ad edig i he secod quarer of 28. Afer some daa cleaig i paricular deleig houses ha were older ha 5 years a he ime of sale were a oal of 2289 sales remaied To compue SPAR idex umbers we also eed assessed values for he properies sold. Our appraisal daa relae o he firs quarer (i.e., Jauary) of 25. Machig he sales daa se ad he appraisal daa se was quie successful; 99.3 % of he sellig prices could be mached wih he correspodig appraisals; i.e. for oly 5 observaios we could o fid a appraisal, so hese were deleed. The resulig SPAR idex, P SPAR, is ploed i Figure 7. ad lised i Table 7., alog wih he hedoic impuaio Fisher idex, P HIF, described i Chaper 5, ad he repea sales idex, P RS, esimaed i Chaper 6. The red of P SPAR is very similar o ha of P HIF, bu P SPAR is slighly more volaile A poeial drawback of he SPAR mehod is ha is eirely depede o he accuracy of he appraisal daa. A ispecio of he disribuio of he sale price appraisal raios idicaed a umber of big ouliers. Specifically, here were several observaios wih very high sale price appraisal raios (up o.5), i mos isaces as a resul of uusually low appraised values. I is mos likely ha a sigifica proporio of hese ouliers were recordig errors. Hece, we decided o delee he bigges ouliers. Followig Saisics Neherlads daa cleaig mehods a he ime, based o he disribuio of he aural logarihm of he sale price appraisal raios, 26 observaios were removed for which he log of price raio differed more ha 5 sadard deviaios from he mea. ( 8 ) We eded up wih 2248 observaios The improved SPAR idex, labeled P SPAR*, compued o he cleaed daa se is also show i Figure 7. ad Table 7.. As ca be see, cleaig of he daa had a subsaial impac o he resul: P SPAR* is much less volaile ha he idex P SPAR ha was compued o he iiial daa se. The red was also affeced: P SPAR* is geerally lower ha P SPAR due o he fac ha mos of he deleed observaios had uusually high sale price appraisal raios. provided ha he assessmes decomposed he oal assessed value of he propery io lad ad srucures compoes. Uforuaely, official assessmes geerally are made oly oce a year or oce every few years. This low frequecy iformaio could however be used o check he lad ad srucures price idices geeraed by hedoic regressio mehods. ( 8 ) As a firs sep i he daa cleaig procedure, Saisics Neherlads removed all properies wih sellig prices or appraisals below or above 5 Euros. I our daa se, however, here were o such properies. Noe ha Saisics Neherlads recely chaged he oulier deecio ad removal procedures. 78 Hadbook o Resideial Propery Prices Idices (RPPIs)

81 Appraisal-Based Mehods 7 Figure 7. cofirms ha usig a relaively small daa se which covers a shor ime period he SPAR mehod geeraes more credible resuls ha he sadard repea sales mehod, especially afer cleaig he daa A compariso of P SPAR* wih he hedoic impuaio Fisher idex P HIF reveals ha i several periods, for example i he las four quarers, he price chages accordig o he wo mehods are i opposie direcios. Also, P SPAR* is geerally lower ha P HIF ; a he ed of he sample period, i quarer 4, he differece amous o.26 idex pois. A firs sigh his seems o sugges ha P SPAR* has a dowward bias. However, a differece of he same magiude (.27 pois) is already foud i quarer 2. So if we had ormalized boh series o equal i quarer 2, he wo mehods would have produced approximaely he same idex value i quarer 4. This is a illusraio of a geeral sarig problem ecouered whe comparig volaile ime series: he choice of sarig or base period affecs he average differece durig he sample period. Figure 7.. SPAR Idex, Hedoic Impuaio Fisher Price Idex ad Repea Sales Idex Source: Auhors calculaios based o daa from he Duch Lad Regisry P SPAR P HIF P RS P SPAR Table 7.. SPAR Idex, Hedoic Impuaio Fisher Price Idex ad Repea Sales Idex Quarer P SPAR P HIF P RS P SPAR Source: Auhors calculaios based o daa from he Duch Lad Regisry Hadbook o Resideial Propery Prices Idices (RPPIs) 79

82

83 Decomposig a RPPI io Lad ad Srucures Compoes 8

84 8 Decomposig a RPPI io Lad ad Srucures Compoes Iroducio 8. I Chaper 3 i was meioed ha for aioal accous ad CPI purposes, i will be useful or ecessary o have a decomposiio of he resideial propery price idex (RPPI) io wo compoes: a qualiy adjused price idex for srucures ad a price idex for he lad o which he house is buil. The prese chaper oulies how hedoic regressio ca be uilized o derive such a decomposiio. Hedoic regressio mehods were discussed i Chaper Some ecoomic reasoig will be helpful o derive a appropriae hedoic regressio model. Thik of a propery developer who is plaig o build a srucure o a paricular propery. He or she will likely deermie he sellig price of he propery afer he srucure is compleed by firs calculaig he oal expeced cos. This cos will be equal o he floor space area of he srucure, say S square meers, imes he buildig cos per square meer, g say, plus he cos of he lad, which will be equal o he cos per square meer, β say, imes he area of he lad sie, L. We follow a cos of producio approach o modelig he propery price. Tha is, he fucioal form for he hedoic price fucio is assumed o be deermied by he supply side of he marke, i.e., by idepede coracors. ( ) 8.3 Now cosider a sample of properies of he same geeral ype, which have srucure areas S ad lad areas L i period for =,..., N( ) ; he prices p are equal o coss of he above ypes plus error erms ε which are assumed o have meas. This gives rise o he followig hedoic regressio model for period where β ad γ are he parameers o be esimaed: ( 2 ) p = ε (8.) β L + g S + =,...,T ; =,..., N( ) The quaiy of lad L ad he quaiy of srucures S associaed wih he sale of propery i period are he oly wo propery characerisics icluded i his very simple model; he correspodig prices i period are he price of a square meer of lad β ad he price of a square meer of srucure floor space g. Separae liear regressios of he form (8.) ca be performed for each ime period i he sample. 8.4 The builder s model (8.) esseially relaes o ewly-buil dwelligs. To make i applicable o exisig ( ) McMille (23) discusses a Cobb Douglas demad side model. O ideificaio issues i hedoic regressio models, see Rose (974). ( 2 ) Followig Muh (97), Thorses (997; ) has a relaed cos of producio model. He assumed ha he value of he propery uder cosideraio i period, ρ, is equal o he price of housig oupu i period, ρ, imes he quaiy of housig oupu H(L,K) where he producio fucio H is a CES fucio. Thus Thorses assumed ha p = ρ H(L,K) = ρ [αl σ + βk σ ] /σ where ρ, σ, α ad β are parameers, L is he lo size of he propery ad K is he amou of srucures capial (i cosa qualiy uis). Our problem wih his model is ha here is oly oe idepede ime parameer ρ whereas our model has wo, β ad γ for each, which allow he price of lad ad srucures o vary freely bewee periods. or resold houses we should accou for he fac ha older srucures will be worh less ha ewer srucures due o depreciaio of he srucures. Iformaio o he age of he srucure will herefore be eeded. The ex secio shows how depreciaio ca be icorporaed io he model, similar o wha was doe i he examples for he ow of A preseed i Chaper 5. I will also be show how addiioal lad ad srucures characerisics ca be icluded as explaaory variables. Accouig for Depreciaio ad Addiioal Characerisics Depreciaio 8.5 Suppose ha i addiio o iformaio o he sellig price of propery a ime period, p, he lad area of he propery, L, ad he srucure area, S, iformaio o he age of he srucure a ime, say A, is available. If sraigh lie depreciaio is assumed, he followig model is a sraighforward exesio of (8.) o iclude exisig houses: p = β L + g ( da ) S + ε (8.2) =,...,T ; =,..., N( ) where he parameer d reflecs he (sraigh lie) depreciaio rae as he srucure ages oe addiioal period. If srucure age is measured i years, d will probably be bewee.5 % ad 2 %. This will be a uderesimae of rue depreciaio because i will o accou for major reovaios or addiios o he srucure. The esimaed sraigh lie depreciaio rae i (8.2) should herefore be ierpreed as a e depreciaio rae; i.e., a gross depreciaio rae less he rae of reovaios ad addiios o he srucure. Model (8.2) will o work for very old srucures sice, if hey are sill i use, hey will likely have bee exesively reovaed. ( 3 ) 8.6 Noice ha (8.2) is a oliear regressio model whereas (8.) is a liear regressio model. ( 4 ) Because he depreciaio parameer d is regarded as fixed over ime, (8.2) would have o be esimaed as oe oliear regressio over all ime periods i he sample, whereas model (8.) ca be ru as a period by period liear regressio. The period price of lad i model (8.2) will be he esimae for he parameer β ad he price of a ui of a ewly buil srucure for period will be he esimae for ( 3 ) See for example Meese ad Wallace (99; 32) who foud ha he age variable i heir hedoic regressio model had he wrog sig. ( 4 ) The model defied by (8.2) ca be covered io a liear regressio model. 82 Hadbook o Resideial Propery Prices Idices (RPPIs)

85 Decomposig a RPPI io Lad ad Srucures Compoes 8 γ. The period quaiy of lad for propery is L ad he period quaiy of srucures for propery, expressed i equivale uis of a ew srucure, is ( da ) S, where S is he floor space area of propery i period. 8.7 Expesive properies probably have relaively large absolue errors compared o iexpesive properies, so i migh be beer o assume muliplicaive raher ha addiive errors. However, we prefer a addiive model specificaio as he purpose is o decompose he aggregae value of housig io he sum of srucures ad lad compoes; he use of addiive errors faciliaes his decomposiio. Whe here is evidece of heeroskedasiciy, weighed regressios ca be cosidered. Several researchers suggesed hedoic regressio models ha lead o addiive decomposiios of a propery price io lad ad srucures compoes. ( 5 ) 8.8 There is a poeial problem wih he above builder s model, amely mulicollieariy. Large srucures are geerally buil o large plos of lad, so ha S ad L could be highly colliear (i.e., he lad-srucure raios L / S could be ceered aroud a cosa). This could give rise o usable esimaes of he qualiy adjused prices β ad g for lad ad srucures. As will be see i he example usig daa for he Duch ow of A, he problems of mulicollieariy ad isabiliy do ideed occur. I geeral, mulicollieariy is o a major problem if he goal is o produce a overall house price idex, bu i is problemaic if he goal is o produce separae price idices for lad ad srucures compoes. Some possible mehods for overcomig he mulicollieariy problem will be suggesed i laer o. 8.9 The hedoic regressio model (8.2) has he implicaio ha he parameers would have o be re-esimaed wheever he daa for a ew period became available. To overcome his problem, a rollig widow approach could be applied. A suiable widow legh T would be chose, ( 6 ) he model defied by (8.2) or (8.3) would be esimaed usig he daa for he las T periods, ad he exisig series for price of lad ad for price of srucures would be updaed T T T T usig he chai lik facors β / β ad g / g. This approach will be illusraed below. Addig More Characerisics 8. The above basic oliear hedoic regressio 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 rasaced i period a lis of K characerisics ( 5 ) See Clapp (98), Fracke ad Vos (24), Gyourko ad Saiz (24), Bosic, Loghofer ad Redfear (27), Diewer (27), Fracke (28), Koev ad Saos Silva (28), Saisics Porugal (29), Diewer, de Haa ad Hedriks (2) (2) ad Diewer (2). ( 6 ) The model becomes a modified adjace period hedoic regressio model for T = 2. X,..., for he lad o which he srucure was buil ad a similar lis of M characerisics Y, Y,..., Y ha are price deermiig characerisics for he ype of srucure. The follow- 2 M ig equaios geeralize (8.2) o he prese seup: ( 7 ) p, X X ha are price deermiig characerisics 2 K β + + Y λ S ε m m + =,...,T ; =,..., N( ) (8.3) K M = X η L γ δa k k + ( ) k= m= where he parameers o be esimaed are ow he K qualiy of lad parameers, η,...,η K he M qualiy of srucures, parameers, λ,...,λm, he period qualiy adjused price for lad β ad he period qualiy adjused price for srucures g. The qualiy adjused amou of lad, L *, ad he * correspodig qualiy adjused amou of srucures, S, for propery i period are defied as follows: L S * * K + X η L k k (8.4) k= M + Y λ S m m m= =,...,T ; =,..., N( ) 8. To illusrae how X ad Y variables ca be formed, cosider he lis of explaaory variables i he hedoic housig regressio model repored by Li, Prud homme ad Yu (26; 23). The followig variables i heir lis of explaaory variables ca be viewed as variables ha affec srucures qualiy; i.e., hey are Y ype variables: umber of bedrooms, umber of bahrooms, umber of garages, umber of fireplaces, age of he ui, age squared of he ui, exerior fiish is brick or o, dummy variable for ew uis, ui has hardwood floors or o, heaig fuel is aural gas or o, ui has a paio or o, ui has a ceral buil i vacuum cleaig sysem or o, ui has a idoor or oudoor swimmig pool or o, ui has a ho ub ui or o, ui has a saua or o, ad ui has air codiioig or o. The followig variables ca be assumed o affec he qualiy of he lad; i.e., hey are X ype locaio variables: ui is a he iersecio of wo srees or o (corer lo or o), ui is a a cul-de-sac or o, shoppig ceer is earby or o, ad various suburb locaio dummy variables. 8.2 Equaios (8.3) ad (8.4) show how he qualiy adjused amous of lad ad srucures would be calculaed if he goal is o cosruc price idices for he sales of properies of he ype ha are icluded i he hedoic regressio model. If he goal is o cosruc price idices for he sock of properies of he ype icluded i he regressio, he he cosrucio of appropriae weighs becomes more complex. These weighig problems will be discussed i he ex secio. ( 7 ) This geeralizaio was suggesed by Diewer (27). Hadbook o Resideial Propery Prices Idices (RPPIs) 83

86 8 Decomposig a RPPI io Lad ad Srucures Compoes Aggregaio ad Weighig Issues: Idices for Sales versus Socks of Housig 8.3 As was explaied i Chaper 5, he cosrucio of a RPPI for he sales of propery usig sadard hedoic regressio echiques is fairly sraighforward. Typically, a separae hedoic regressio of he ype defied by (8.3) will be ru for each localiy or regio i a coury. ( 8 ) Recall ha oce a paricular regressio has bee ru, period qualiy adjused prices for lad, P L, ad for srucures, P S, for he regio uder cosideraio ca be defied i erms of he esimaed parameers for he model as follows: PL PS β (8.5) =,...,T g (8.6) =,...,T The correspodig qualiy adjused quaiies of lad ad srucures for he regio, say Q L ad Q S ca also be defied i erms of he esimaed parameers usig defiiios (8.4) above as follows: N ( ) N ( ) K * = + QL L X η k k L (8.7) = = k= =,...,T N ( ) N ( ) M * = + QS S Y λ m m S (8.8) = = m= =,...,T 8.4 If hedoic regressios, for say R regios, of he ype defied by (8.3) have bee ru for he T periods of daa, he he algebra associaed wih (8.5)-(8.8) ca be repeaed for each regio r. Deoe he resulig prices ad quaiies for regio r ha are he couerpars o (8.5)-(8.8) by P Lr, P Sr, Q Lr ad Q Sr for r =,..., R ad =,...,T. Now Fisher (sales) RPPIs for lad ca be cosruced usig he regioal price ad quaiy daa for lad, PL [ PL,..., PLR ] ad QL [ QL,..., QLR ], for each ime period ( =,..., T ). Similarly, Fisher (sales) RPPIs for srucures ca be cosruced usig he price ad quaiy daa for srucures i each period, PS [ PS,..., PSR ] ad Q [ Q,..., Q ], for =,..., T.( 9 ) S S SR ( 8 ) Separae hedoic regressios may also be ru for differe ypes of propery as well as for differe locaios. However, cos cosideraios may mea ha a comprehesive sysem of regressios coverig all properies i he coury cao be implemeed so ha here will oly be a sample of represeaive hedoic regressios. The aggregaio issues i he samplig case are oo complex o be cosidered here; he exac deails for cosrucig a aioal idex would deped o he aure of he samplig desig. ( 9 ) As was he case for sraificaio mehods, fixed base or chaied idices could be cosruced. Rollig widow hedoic regressios could also be ru. The rollig widow approach will be explaied laer. 8.5 As was he case wih sraificaio mehods, i is ow ecessary o cosider how o cosruc a RPPI for he sock of resideial properies whe hedoic regressio mehods are used. The period hedoic cell prices P Lr ad P Sr defied by he regio r couerpars o (8.5) ad (8.6) ca sill be used as cell prices o cosruc sock price idices for lad ad srucures, bu he couerpar quaiies Q Lr ad Q Sr defied by (8.7) ad (8.8) are o loger appropriae; hese quaiies eed o be replaced by esimaes ha apply o he oal sock of dwellig uis i he regio (or some oher referece populaio) for regressio r a * * ime, say Q Lr ad Q Sr, for r =,..., R. Thus, he couerpar summaios i (8.7) ad (8.8) are ow ake over he eire sock of dwelligs i regio r i period isead of jus he dwellig uis ha were sold i period. Period iformaio o he quaiy of lad L r for every ui i he regio ha is i scope for he hedoic regressio model m is ow required, alog wih he accompayig characerisics iformaio X rk for every lad characerisic k, as well as daa o he quaiy of he srucures S r, alog wih he accompayig characerisics iformaio Y rm for every srucures characerisic m. Wih hese ew populaio quaiy weighs, he res of he deails of he idex cosrucio are he same as was he case for he sales RPPI. 8.6 I order o cosruc appropriae period populaio sock weighs, i will be ecessary for he coury o have cesus iformaio o he housig sock wih eough deails o each dwellig ui i he sock so ha he required iformaio o he quaiy of lad ad srucures ad he accompayig characerisics ca be calculaed. If iformaio o ew house cosrucio (plus he required characerisics daa) ad o demoliios is available i a imely maer, he cesus iformaio ca be updaed ad period esimaes for he cosa qualiy amous * * of lad ad srucures, he Q Lr ad Q Sr, ca be approximaed i a imely maer. Hece, sock RPPIs for lad ad srucures ca be cosruced usig Fisher idices, as was he case for he sales RPPI. If imely daa o ew cosrucio ad demoliios is uavailable, i may oly be possible o cosruc fixed base Laspeyres ype price idices usig he quaiy weighs from he las available housig cesus. 8.7 If cesus iformaio is o available a all (or if daa o he characerisics of he dwellig uis is missig), i sill may be possible o approximae RPPIs for lad ad srucures usig hedoic regressio echiques. If characerisics daa o he resideial properies ha are sold i each period is sored over a large period of ime, a approximae disribuio of dwellig uis by ype ca be cosruced. This iformaio may he be used o approximae a sock based RPPI i he maer explaied above. 84 Hadbook o Resideial Propery Prices Idices (RPPIs)

87 Decomposig a RPPI io Lad ad Srucures Compoes 8 Mai Advaages ad Disadvaages 8.8 This secio summarizes he mai advaages ad disadvaages of usig hedoic regressio mehods o cosruc a RPPI for lad ad srucure compoes. The mai advaages are: If he lis of available propery characerisics is sufficiely deailed, he mehod adjuss for boh sample mix chages ad qualiy chages of he idividual houses. Price idices ca be cosruced for differe ypes of dwelligs ad locaios hrough a proper sraificaio of he sample. Sraificaio has a umber of addiioal advaages. The mehod is probably he mos efficie mehod for makig use of he available daa. The mehod is virually he oly mehod ha ca be used o decompose he overall price idex io lad ad srucures compoes. 8.9 The mai disadvaages of he hedoic regressio approach are: The mehod is daa iesive sice i requires daa o all releva propery characerisics (i paricular, he age, he ype ad he locaio of he properies i he sample as well as iformaio o he srucure ad lo size) so i is relaively expesive o impleme. The mehod may o lead o reasoable resuls due o mulicollieariy problems. While he mehod is esseially reproducible, differe choices ca be made regardig he se of characerisics eered io he regressio, he fucioal form for he model, he sochasic specificaio, possible rasformaios of he depede variable, ec., which could lead o varyig esimaes of overall price chage. The geeral idea of he hedoic mehod is easily udersood bu some of he echicaliies may o be easy o explai o users. Applicaio o Daa for he Tow of A : Prelimiary Approaches 8.2 The geeral echiques explaied i his chaper will ow be illusraed usig he daa se for he Duch ow of A, which was described a he ed of Chaper 4. We have daa o sales of deached dwelligs for 4 quarers, sarig i he firs quarer of 25. Recall he oaio used above ad i Chapers 4 ad 5: here were N () sales of deached houses i quarer, where p is he sellig price of house. There is iformaio available o hree characerisics: area of he plo i square meers, L ; floor space area of he srucure i square meers, S ; ad age i decades of house i period, A. The Simple Case 8.2 The simple hedoic regressio model defied by (8.2) will be esimaed o his daa se ad is repeaed here for coveiece: p = β L + g ( da ) S + ε (8.9) =,...,4; =,..., N( ) The parameers o be esimaed are β (i.e., he price of lad i quarer ), g (he price of cosa qualiy srucures i quarer ) ad δ (he commo depreciaio rae for all quarers). Model (8.9) has 4 ukow β parameers, 4 ukow g parameers ad oe ukow δ or 29 ukow parameers i all. ( ) 8.22 The R 2 for his model was equal o.8847, which is he highes ye for regressios usig he daa se for he ow of A. The log likelihood was -642., which is cosiderably higher ha he log likelihoods for he wo ime dummy regressios ha used prices as he depede variable; recall he regressio resuls associaed wih he cosrucio of idices P H 4 ad P H 5 defied i Chaper 5 where he log likelihoods were ad The esimaed decade sraigh lie e depreciaio rae was.68 (.284) The esimaed lad price series ˆ β,..., ˆ β (rescaled o equal i quarer ), labeled P L, ad qualiy adjused price series for srucures ˆ γ,..., ˆ4 γ (rescaled also), labeled P S, are ploed i Figure 8. ad lised i Table 8.. Usig hese price series ad he correspodig quaiy daa for each quarer, i.e., he amou of lad rasaced, N ( ) L = L, ad he quaiy of cosa qualiy srucures, = * N ( ) ( ˆ S d A ) S, a overall propery price idex has bee cosruced usig he Fisher formula. This overall idex, labeled P, is also ploed i Figure 8. ad lised i Table 8.. For compariso purposes, he Fisher hedoic impuaio idex from Chaper 5, P HIF, is also preseed. ( ) Model (8.9) is similar i srucure o he hedoic impuaio model described earlier excep ha he prese model is more parsimoious; here is oly oe depreciaio rae, as opposed o 4 depreciaio raes i he impuaio model defied by equaios (5.25), ad here is o cosa erm. The impora facor i boh models is ha he prices of lad ad qualiy adjused srucures are allowed o vary idepedely across ime periods. Hadbook o Resideial Propery Prices Idices (RPPIs) 85

88 8 Decomposig a RPPI io Lad ad Srucures Compoes Figure 8.. The Price of Lad (P L ), he Price of Qualiy Adjused Srucures (P S ), he Overall Cos of Producio House Price Idex (P ) ad he Fisher Hedoic Impuaio House Price Idex Source: Auhors calculaios based o daa from he Duch Lad Regisry P L P S P P HIF Table 8.. The Price of Lad (P L ), he Price of Qualiy Adjused Srucures (P S ), he Overall Cos of Producio House Price Idex (P ) ad he Fisher Hedoic Impuaio House Price Idex Quarer P L P S P P HIF Source: Auhors calculaios based o daa from he Duch Lad Regisry 8.24 I ca be see ha he ew overall hedoic price idex based o a cos of producio approach o he hedoic fucioal form, P, is very close o he Fisher hedoic impuaio idex P HIF. However, he price series for lad, P L, ad he price series for qualiy adjused srucures, P S, are o credible a all: here are large radom flucuaios i boh series. Noice ha whe he price of lad spikes upwards, here is a correspodig dip i he price of srucures. This is a clear sig of mulicollieariy bewee he lad ad qualiy adjused srucures variables, which leads o highly usable esimaes for he prices of lad ad srucures. The Use of Liear Splies 8.25 There is a edecy for he price of lad per meer squared o decrease for large los. I order o accou for his, a liear splie model for he price of lad 86 Hadbook o Resideial Propery Prices Idices (RPPIs)

89 Decomposig a RPPI io Lad ad Srucures Compoes 8 will be used. ( ) For los ha are less ha 6 m 2, i is assumed ha he cos of lad per meer squared is β S i quarer. For properies ha have lo sizes bewee 6 m 2 ad 3 m 2, i is assumed ha he cos of lad chages o a price of β M per addiioal square meer i quarer. Fially, for plos above 3 m 2, he margial price of a addiioal ui of lad is se equal o β L per square meer i quarer. Le he ses of sales of small, medium ad large plos be deoed by S S (), S M () ad S L (), respecively, for =,..., 4. For sales of properies ha fall io he small lad size group durig quarer, he hedoic regressio model is give by (8.); for he medium group by (8.) ad for he large lad size group by (8.2): p p p = ( ) ε (8.) β S L + g da S + β S 6] + β M [ L 6] + g ( da S + =,...,4; S () = [ ) ε (8.) =,...,4; S () = [ ) ε, β 6] + β [4] + β [ L 3] + g ( da S + S M L S S =,...,4; S () (8.2) 8.26 Esimaig he model defied by (8.)-(8.2) o he daa for he ow of A, he esimaed decade depreciaio rae was ˆ d =. 4 (.49). The R 2 for his model was.8875, which is a icrease over he previous o-splies model where he R 2 was The log likelihood was (a icrease of 28 from he previous model s log likelihood.) The firs period parameer values for he hree margial prices for lad were ˆ β = 28. S 4 (55.9), ˆ β M = (48.5) ad ˆ β L = (27.5). I oher words, i quarer, he margial cos per m 2 of small los is esimaed o be 28.4 Euros per m 2, for medium sized los, he esimaed margial cos is 38.4 Euros/m 2, ad for large los, he esimaed margial cos is 88.9 Euros/m 2. The firs period parameer value for qualiy adjused srucures is ˆ g = 978. Euros/m 2 wih a sadard error of The lowes saisic for all of he 57 parameers was 3.3, so all of he esimaed coefficies i his model are sigificaly differe from zero Oce he parameers for he model have bee esimaed, he i each quarer, he prediced value of lad for small, medium ad large lo sales, V LS, V LM ad V LL, respecively, ca be calculaed alog wih he associaed quaiies of lad, L, L ad L, as follows: LS LM LL ( ) This approach follows ha of Diewer, de Haa ad Hedriks (2) (2). The use of liear splies o model olieariies i he price of lad as a fucio of lo size is due o Fracke (28). S V LL V LM S L ( ) S M ( ) ˆ V β L LS S (8.3) S S ( ) =,...,4 ˆ + ˆ { β [6] β [ L 6]} (8.4) S M =,...,4 ˆ + ˆ [6] [4] + ˆ { β β β [ L 3]} (8.5) S M S S ( ) L =,...,4 L L (8.6) LS S M ( ) =,...,4 L L (8.7) LM =,...,4 L L (8.8) LL S L ( ) =,...,4 The correspodig average quarerly prices, P LS, P LM ad P LL, for he hree ypes of lo are defied as he above values divided by he above quaiies: P LS VLS / LLS ; P LM VLM / LLM ; P LL VLL / LLL (8.9) =,..., The average lad prices for small, medium ad large los defied by equaio (8.9) ad he correspodig quaiies of lad defied by (8.6)-(8.8) ca be used o cosruc a chaied Fisher lad price idex, which is deoed by P L2. This idex is ploed i Figure 8.2 ad lised i Table 8.2. As before, he esimaed quarer price per meer squared of qualiy adjused srucures is gˆ ad he quaiy of cosa qualiy srucures is give by * N ( ) = ( ˆ S d A ) S. The srucures price ad quaiy * series gˆ ad S were combied wih he hree lad price ad quaiy series o form a chaied overall Fisher house price idex P 2, which is also graphed i Figure 8.2 ad lised i Table 8.2. The cosa qualiy srucures price idex P 4 S 2 (which is a ormalizaio of he series ˆ γ,..., ˆ γ ) is preseed as well The overall house price idex resulig from he splie model, P 2, is fairly close o he Fisher hedoic impuaio idex P HIF. However, he splie model does o geerae sesible series for he price of lad, P L2, ad he price of srucures, P S 2 : boh series are exremely volaile bu i opposie direcios. As was he case wih he previous cos of producio model, he prese model suffers from a mulicollieariy problem. Hadbook o Resideial Propery Prices Idices (RPPIs) 87

90 8 Decomposig a RPPI io Lad ad Srucures Compoes 8.3 Comparig Figures 8. ad 8.2, i ca be see ha i Figure 8. he price idex for lad is above he overall price idex for he mos par ad he price idex for srucures is below he overall idex while i Figure 8.2, his paer reverses. This isabiliy is agai a idicaio of mulicollieariy. I he followig secio a aemp o cure his problem will be made by imposig moooiciy resricios o he prices of he cosa qualiy srucures. Figure 8.2. The Price of Lad (P L2 ), he Price of Srucures (P S2 ), he Overall Price Idex Usig Splies o Lad (P 2 ) ad he Fisher Hedoic Impuaio Price Idex Source: Auhors calculaios based o daa from he Duch Lad Regisry P L2 P S2 P 2 P HIF Table 8.2. The Price of Lad (P L2 ), he Price of Srucures (P S2 ), he Overall Price Idex Usig Splies o Lad (P 2 ) ad he Fisher Hedoic Impuaio Price Idex Quarer P L2 P S2 P 2 P HIF Source: Auhors calculaios based o daa from he Duch Lad Regisry 88 Hadbook o Resideial Propery Prices Idices (RPPIs)

91 Decomposig a RPPI io Lad ad Srucures Compoes 8 A Approach Based o Moooiciy Resricios 8.3 I is likely ha Duch cosrucio coss did o fall sigificaly durig he sample period. ( 2 ) If his is ideed he case, moooiciy resricios o he quarerly prices of qualiy adjused srucures, γ, γ, γ,..., γ, ca be imposed o he hedoic regressio model (8.)-(8.2) by replacig he cosa qualiy quarer srucures price parameers by he followig sequece of parameers for he 4 quarers: g, g + (φ ), g + ( φ ) + ( φ ),..., γ + ( φ ) + ( φ ) ( φ ), where φ, φ,..., φ are scalar parameers. ( 3 ) For each quarer sarig a quarer 2, he price of a square meer of cosa qualiy srucures g is hus equal o he previous period s price γ plus he square of a parameer φ, ( φ ) 2. Now replace his reparameerizaio of he srucures price parameers g i (8.)-(8.2) i order o obai a liear splie model for he price of lad wih moooiciy resricios o he price of cosa qualiy srucures Implemeig his ew model usig he daa for he Duch ow of A, he esimaed decade depreciaio rae was ˆ d =. 3 (.386). The R 2 for his model was.8859, a drop from he previous uresriced splie model where he R 2 was The log likelihood was -63.5, ( 2 ) Some direc evidece o his asserio will be preseed i he followig secio. ( 3 ) This mehod for imposig moooiciy resricios was used by Diewer, de Haa ad Hedriks (2) wih he differece ha hey imposed moooiciy o boh srucures ad lad prices, whereas here, moooiciy resricios are imposed o srucures prices oly. a decrease of 6.3 over he previous uresriced model. Eigh of he 3 ew parameers φ are zero i his moooiciy resriced hedoic regressio. The firs period parameer ˆ values for he hree margial lad prices are β = S (37.2), ˆ β M = (4.) ad ˆ β L = 88. ; hese values are almos ideical o he correspodig esimaes i he previous uresriced model. The firs period parameer esimae for qualiy adjused srucures is ˆ g = 98.5 (49.9) Euros/m 2., which is lile chaged from he previous uresriced esimae of 978. Euros/m Oce he parameers for he model have bee esimaed, cover he esimaed φ parameers io esimaed parameers usig he followig recursive equaios: ˆ ˆ + g g + ˆ ( φ ) 2 (8.9) = 2,...,4 Now use equaios (8.3)-(8.9) i he previous secio i order o cosruc a chaied Fisher idex of lad prices, which is deoed by P L3. This idex is ploed i Figure 8.3 ad lised i Table 8.3. As i he previous wo models, he esimaed period price for a squared meer of qualiy adjused srucures is gˆ ad he correspodig quaiy * N ( ) of cosa qualiy srucures is = ( ˆ S d A ) S. * The price ad quaiy series gˆ ad S were combied wih he hree lad price ad quaiy series o cosruc a chaied overall Fisher house price idex P 3 which is also graphed i Figure 8.3 ad lised i Table 8.3. The cosa qualiy srucures price idex P S 3 (a ormalizaio of he series ˆ γ,..., ˆ4 γ ) may be foud i Figure 8.3 ad Table 8.3 as well. Figure 8.3. The Price of Lad (P L3 ), he Price of Qualiy Adjused Srucures (P S3 ), he Overall House Price Idex wih Moooiciy Resricios o Srucures (P 3 ) ad he Overall House Price Idex Usig Splies o Lad (P 2 ) Source: Auhors calculaios based o daa from he Duch Lad Regisry P L3 P S3 P 2 P 3 Hadbook o Resideial Propery Prices Idices (RPPIs) 89

92 8 Decomposig a RPPI io Lad ad Srucures Compoes Table 8.3. The Price of Lad (P L3 ), he Price of Qualiy Adjused Srucures (P S3 ), he Overall House Price Idex wih Moooiciy Resricios o Srucures (P 3 ) ad he Overall House Price Idex Usig Splies o Lad (P 2 ) Quarer P L3 P S3 P 3 P Source: Auhors calculaios based o daa from he Duch Lad Regisry 8.34 The ew overall house price idex P 3 ha imposed moooiciy o he qualiy adjused price of srucures i Figure 8.3 ca hardly be disiguished from he previous overall house price idex P 2, which was based o a similar hedoic regressio model excep ha he movemes i he price of srucures were o resriced. The flucuaios i he price of lad ad qualiy adjused srucures are o loger viole While he above resuls seem reasoable, he early rapid rise i he price of srucures ad he slow growh i srucures prices from quarer 6 o 4 are o very likely. I he followig secio, oe more mehod for exracig separae srucures ad lad compoes ou of real esae sales daa will herefore be ried. A Approach Based o Exogeous Iformaio o he Price of Srucures 8.36 May couries have ew cosrucio price idices available o a quarerly basis. This is he case for he Neherlads. ( 4 ) If oe is willig o make he assumpio ha cosrucio coss for houses have he same rae ( 4 ) From he Saisics Neherlads (2) olie source, Salie, he followig series was dowloaded for he New Dwelligs Oupu Price Idex for he 4 quarers i our sample of house sales: 98.8, 98.,.3, 2.7, 99.5,.5,.,.3, 2.2, 3.2, 5.6, 7.9,.,.. This series was ormalized o i he firs quarer by dividig each ery by The resulig series is deoed by μ (=), μ 2,...,μ 4. of growh over he sudy period across all ciies i he Neherlads, he iformaio o cosrucio coss ca be used o elimiae he mulicollieariy problem ecouered i he previous secios Recall equaios (8.)-(8.2) above. These are he esimaig equaios for he uresriced hedoic regressio model based o coss of producio. I he prese secio, he cosa qualiy price parameers for he srucures, he g for = 2,..., 4 i (8.)-(8.2), are replaced by he followig umbers, which ivolve oly he sigle ukow parameer g : ( 5 ) γ = γ µ (8.2) = 2,...,4 where m is he saisical agecy s cosrucio cos price idex for he locaio ad he ype of house uder cosideraio, ormalized o equal i quarer. The ew hedoic regressio model is agai defied by equaios (8.)-(8.2) excep ha he 4 ukow g parameers are ow defied by (8.2), so ha oly g eeds o be esimaed. The umber of parameers o be esimaed i his ew resriced model is 44 whereas he old umber was Usig he daa for he ow of A, he esimaed decade depreciaio rae was ˆ d =. 28 (.433). The R 2 for his model was.8849, a small drop from he previous resriced splie model, where he R 2 was.8859, ad a larger drop from he uresriced splie model R 2 i secio 8.5, which was The log likelihood was -64., ( 5 ) The echique suggesed here for decomposig propery prices io lad ad srucures compoes ca be viewed as a varia of a echique used by Davis ad Heahcoe (27) ad Davis ad Palumbo (28). 9 Hadbook o Resideial Propery Prices Idices (RPPIs)

93 Decomposig a RPPI io Lad ad Srucures Compoes 8 a decrease of over he moooiciy resriced model. The firs period parameer esimaes for he 3 margial prices for lad are ow ˆ β S = (3.), ˆ β M = (46.7) ad ˆ β L = (28.4). They differ slighly from he previous figures. The firs period parameer esimae for he qualiy adjused srucures is ˆ g = (22.9) Euros/m 2, which is sigificaly higher ha he uresriced esimae of 98.5 Euros/m 2. So he imposiio of a (aiowide) growh rae o he chage i he price of qualiy adjused srucures has had some effec o he esimaes for he levels of lad ad srucures prices As usual, equaios (8.3)-(8.9) were used i order o cosruc a chaied Fisher idex of lad prices, which is deoed by P L4. This idex is ploed i Figure 8.4 ad lised i Table 8.4. As for he previous hree models, he esimaed price i quarer for a square meer of qualiy adjused srucures is gˆ (which ow equals ˆ g m ) ad * N ( ) he correspodig quaiy is = ( ˆ S d A ) S. These srucures price ad quaiy series were agai combied wih he hree lad price ad quaiy series o form a chaied overall Fisher house price idex P 4, which is graphed i Figure 8.4 ad lised i Table 8.4. The cosa qualiy srucures price idex P S 4 (a ormalizaio of he series ˆ γ,..., ˆ4 γ ) is also preseed. 8.4 A compariso of Figures 8.3 ad 8.4 shows ha he imposiio of he aioal growh raes for ew dwellig cosrucio coss has chaged he aure of he lad ad srucures price idices: i Figure 8.3, he price series for lad lies below he overall house price series for mos of he sample period while i Figure 8.4, he paer is reversed: he price series for lad lies above he overall house price series for mos of he sample period (ad vice versa for he price of srucures). Bu which model is bes? Alhough he previous model ca be preferred o saisical grouds because he log likelihood is somewha higher, we would everheless prefer he prese model ha uses of exogeous iformaio o srucures prices because i yields a more plausible paer of price chages for lad ad srucures. Figure 8.4. The Price of Lad (P L4 ), he Price of Qualiy Adjused Srucures (P S4 ) ad he Overall House Price Idex usig Exogeous Iformaio o he Price of Srucures (P 4 ) Source: Auhors calculaios based o daa from he Duch Lad Regisry P L4 P S4 P 4 Hadbook o Resideial Propery Prices Idices (RPPIs) 9

94 8 Decomposig a RPPI io Lad ad Srucures Compoes Table 8.4. The Price of Lad (P L4 ), he Price of Qualiy Adjused Srucures (P S4 ) ad he Overall House Price Idex usig Exogeous Iformaio o he Price of Srucures (P 4 ) Quarer P L4 P S4 P Source: Auhors calculaios based o daa from he Duch Lad Regisry Choosig he Bes Overall Idex 8.4 This secio is cocluded by lisig ad charig our four bes overall idices: he chaied sraified sample Fisher idex P FCH cosruced i Chaper 4, he chaied hedoic impuaio Fisher idex P HIF sudied i Chaper 5, he idex P 3 ha resuled from he cos based hedoic regressio model wih moooiciy resricios cosruced earlier, ad he idex P 4 ha resuled from he cos based hedoic regressio model usig exogeous iformaio o he price of srucures sudied i he prese secio. As ca be see from Figure 8.5, all four idices pai much he same picure. Noe ha P 3 ad P 4 are virually ideical All higs cosidered, he hedoic impuaio idex P HIF is our preferred idex sice i has fewer resricios ha he oher idices ad seems closes o a mached model idex i spiri, followed by he wo cos of producio hedoic idices P 4 ad P 3, followed by he sraified sample idex P FCH. The laer likely suffers from some ui value bias. Hedoic idices ca be biased oo (if impora explaaory variables are omied or if a icorrec fucioal form is chose), bu i geeral we would prefer hedoic regressio mehods over sraificaio mehods. If separae lad ad srucures idices are required, we are i favour of he cos based hedoic regressio model ha uses exogeous iformaio o he price of srucures. 92 Hadbook o Resideial Propery Prices Idices (RPPIs)

95 Decomposig a RPPI io Lad ad Srucures Compoes 8 Figure 8.5. House Price Idices Usig Exogeous Iformaio (P 4 ) ad Usig Moooiciy Resricios (P 3 ), he Chaied Fisher Hedoic Impuaio Idex ad he Chaied Fisher Sraified Sample Idex Source: Auhors calculaios based o daa from he Duch Lad Regisry P 4 P 3 P HIF P FCH Table 8.5. House Price Idices Usig Exogeous Iformaio (P 4 ) ad Usig Moooiciy Resricios (P 3 ), he Chaied Fisher Hedoic Impuaio Idex ad he Chaied Fisher Sraified Sample Idex Quarer P 4 P 3 P HIF P FCH Source: Auhors calculaios based o daa from he Duch Lad Regisry Hadbook o Resideial Propery Prices Idices (RPPIs) 93

96 8 Decomposig a RPPI io Lad ad Srucures Compoes Rollig Widow Hedoic Regressios 8.43 A problem wih he hedoic regressio model discussed i he previous secio (ad all oher hedoic models discussed i his Hadbook excep hedoic impuaio models) was meioed i Chaper 5: whe more daa are added, he idices geeraed by he model chage. This feaure of hese regressio based mehods makes hese models usaisfacory for saisical agecy use, where users expec he official umbers o remai uchaged as ime passes. Users may olerae a few revisios o rece daa bu ypically, hey would o like all he umbers o be revised back io he idefiie pas as ew daa become available. A simple soluio o his problem is available, however. he so-called rollig widow approach. This approach will be oulied i more deail ad applied o he cos based hedoic regressio model ha uses exogeous iformaio o he price of srucures Firs, oe chooses a suiable umber of ime periods (equal o or greaer ha wo) where i is hough ha he hedoic model yields reasoable resuls; his will be he widow legh (say M periods) for he sequece of regressio models which will be esimaed. Secodly, a iiial regressio model is esimaed ad he appropriae idices are calculaed usig daa peraiig o he firs M periods i he daa se. Nex, a secod regressio model is esimaed where he daa cosis of he iiial daa less he daa for period bu addig he daa for period M+. Appropriae price idices are calculaed for his ew regressio model bu oly he rae of icrease of he idex goig from period M o M+ is used o updae he previous sequece of M idex values. This procedure is coiued wih each successive regressio droppig he daa of he previous earlies period ad addig he daa for he ex period, wih oe ew updae facor beig added wih each regressio. If he widow legh is a year, he his procedure is called a rollig year hedoic regressio model; for a geeral widow legh, i is called a rollig widow hedoic regressio model. ( 6 ) 8.45 Usig he daa for he ow of A, he rollig widow procedure was applied wih a widow legh of 9 quarers. The hedoic regressio model defied by equaios (8.)-(8.2) ad (8.2) was iiially esimaed for he firs 9 quarers. The resulig price idices for lad ad for cosa qualiy srucures ad he overall idex are deoed by P RWL4, P RWS 4 ad P RW 4 ad are lised i he firs 9 rows of Table 8.6. ( 7 ) Nex, a regressio coverig quarers 2- was ru ad he resulig lad, srucures ad overall price idices were used o updae he iiial idices; i.e., he price of lad i quarer of Table 8.6 is equal o he price of lad i quarer 9 imes he price relaive for lad (quarer lad idex divided by he quarer 9 lad idex) obaied from he regressio coverig quarers 2-, ec. Similar updaig was doe for he ex 4 quarers usig regressios coverig quarers 3-, 4-2, 5-3 ad The rollig widow idices ca be compared o he correspodig idices based o he daa peraiig o all 4 quarers cosruced i he previous secio by lookig a Table 8.6. Recall ha he esimaed depreciaio rae ad he esimaed quarer price of qualiy adjused srucures for he las model were ˆ d =. 28 ad ˆ g = 85. 9, respecively. If by chace he 6 rollig widow hedoic regressios geeraed he exac same esimaes for d ad g, he he idices resulig from he rollig widow regressios would coicide wih he idices P L4, P S 4 ad P 4. The esimaes for d geeraed by he 6 rollig widow regressios are.24,.85,.6,.3,.857 ad.592. The esimaes for g geeraed by he 6 rollig widow regressios are 89.6, 3.9, 88.,., 23.5 ad.9. While hese esimaes are o ideical o he correspodig esimaes of.28 ad 85.9 for P 4, hey are fairly close. So we ca expec he rollig widow idices o be close o heir couerpars for he las model i he previous secio. The R 2 values for he 6 rollig widow regressios were.883,.883,.8825,.8852,.88 ad The rollig widow series for he price of qualiy adjused srucures, P RWS, is o lised i Table 8.6 sice i is ideical o he series P S 4. ( 8 ) The rollig widow price series for lad, P RWL, is exremely close o is couerpar P L4, ad he overall rollig widow price series for deached dwelligs i he ow of A, P RW, is also close o is couerpar P 4. The correspodig series i Table 8.6 are so close o each oher ha we decided o o provide a char. ( 6 ) This procedure was recely used by Shimizu, Nishimura ad Waaabe (2) ad Shimizu, Takasuji, Oo ad Nishimura (2) i heir hedoic regressio models for Tokyo house prices. A aalogous procedure has also bee recely applied by Ivacic, Diewer ad Fox (2) ad de Haa ad va der Grie (2) i heir adapaio of he GEKS mehod for makig ieraioal comparisos o he scaer daa coex. ( 7 ) We imposed he resricios (33) o he rollig widow regressios ad so he rollig widow cosa qualiy price idex for srucures, P RWS, is equal o he cosa qualiy price idex for srucures lised i Table 8.4, P S4. ( 8 ) By cosrucio, P S4 ad P RWS are boh equal o he official Saisics Neherlads cosrucio price idex for ew dwelligs, μ /μ for =,...,4. 94 Hadbook o Resideial Propery Prices Idices (RPPIs)

97 Decomposig a RPPI io Lad ad Srucures Compoes 8 Table 8.6. The Price of Lad (P L4 ), he Price of Qualiy Adjused Srucures (P S4 ), he Overall House Price Idex usig Exogeous Iformaio o he Price of Srucures (P 4 ) ad heir Rollig Widow Couerpars (P RWL ) ad (P RW ) Quarer P RWL P L4 P RW P 4 P S Source: Auhors calculaios based o daa from he Duch Lad Regisry 8.48 Usig he daa for he ow of A, rollig widow hedoic regressios gave much he same resuls as a hedoic regressio ha covers he whole sample period. This suppors our view ha he rollig widow approach ca be used by saisical agecies o compile a RPPI based o hedoic regressios, icludig a decomposiio io lad ad srucures compoes. The Cosrucio of Price Idices for he Sock of Dwellig Uis 8.49 This secio shows how hedoic regressio models ca be used o form a approximae RPPI for he sock of dwellig uis. We will firs look a he hedoic impuaio model discussed i Chaper 5 ad compare he resulig idex wih a approximae sock based idex usig he sraificaio approach. The Hedoic Impuaio Model 8.5 Recall ha he hedoic impuaio model was defied by equaios (5.25), where L, S ad A deoed, respecively, he lad area, srucure area, ad age (i decades) of propery sold i period. To form a price idex for he sock of deached houses i he ow of A, i would i priciple be ecessary o kow L, S ad A for all deached houses i A durig some base period. This iformaio is o available o us, bu we ca rea he oal umber of deached houses sold over he sample period as a approximaio o he sock of his ype. ( 9 ) I our daa se here were N ( ) + N(2) N(4) = 2289 of such rasacios. ( 2 ) 8.5 The esimaed parameers for lad size, srucure size ad depreciaio i quarer are deoed by βˆ, gˆ ad dˆ ; â deoes he cosa erm. Our approximaio o he oal value of he housig sock for quarer, V, is defied as V N ( s) 4 s= = + ˆ s [ ˆ + ˆ ( ˆ s s α β L γ δ A ) S ] (8.2) =,...,4 Tha is, V is (approximaed by) he impued value of all houses raded durig he 4 quarers i our sample, where he regressio coefficies from he quarer hedoic impuaio model give by (5.25) serve as weighs for he characerisics of each house. Dividig he V series by he value for quarer, V, is our firs esimaed sock price idex, P Sock, for he ow of A. ( 2 ) This is a form of a Lowe idex; see he CPI Maual (24) for he properies ( 9 ) This approximaio would probably be a adequae oe if he sample period were a decade or so. Obviously, our sample period of 4 quarers is oo shor o be accurae ad here are also sample seleciviy problems, i.e., ewer houses will be over represeed. However, he mehod we are suggesig here ca be illusraed usig his rough approximaio. ( 2 ) We did o delee he observaios for houses ha were rasaced muliple imes over he 4 quarers sice a paricular house rasaced durig wo or more of he quarers is o acually he same house due o depreciaio ad reovaios. ( 2 ) Sice V is a value, i does o appear o be a price series a firs glace. Bu i each quarer, he quaiy vecor which uderlies his value is a vecor of oes of dimesio 2289, which is cosa over he 4 quarers. Hece V ca also be ierpreed as a price series, which is ormalized o equal oe i quarer. Hadbook o Resideial Propery Prices Idices (RPPIs) 95

98 8 Decomposig a RPPI io Lad ad Srucures Compoes of Lowe idices. I Table 8.7 ad Figure 8.6 his price idex for he sock of houses is compared wih he correspodig sales based Fisher hedoic impuaio price idex, P A addiioal approximae sock price idex based o sraificaio, P Sock 2 is also graphed i Figure 8.6 ad lised i Table 8.7. This idex uses he ui value prices for he oempy cells i he sraificaio scheme i each quarer, as explaied i Chaper 4, ad uses he impued prices based o he hedoic impuaio regressios from Chaper 5 for he empy cells i each quarer. The quaiy vecor used for P Sock 2 is he (sample) oal quaiy vecor by cell, which makes P Sock 2 a aleraive Lowe price idex. I ca be see ha while P Sock 2 has he same geeral red as P Sock ad P HIF, i differs subsaially from hese HIF hedoic impuaio idices durig several quarers. These differeces are due o he exisece of some ui value bias i he sraificaio idices. Thus, alhough sraificaio idices ca be cosruced for he sock of dwellig uis of a cerai ype ad locaio (wih he help of hedoic impuaio for empy cells), i appears ha he resulig sock idices will o be as accurae as idices ha are eirely based o he use of hedoic regressios. ( 22 ) ( 22 ) If he impued prices are used for every oe of he 45 cell prices for each period (isead of jus for he zero rasacio cells as was he case for he cosrucio of P Scock2 ) ad he same oal sample quaiy vecor is used as he approximae sock quaiy vecor, he he resulig Lowe idex urs ou o be exacly equal o P Sock. Thus hese wo differe ways for cosrucig a sock idex ur ou o be equivale. The fac ha P Sock is o equal o P Sock2 is clear evidece ha here is ui value bias i he cells of he sraificaio scheme: he cells are simply o defied arrowly eough. Figure 8.6. Approximae Sock Price Idices ad Based o Hedoic Impuaio (P Sock ) ad Sraificaio (P Sock2 ) ad he Fisher Hedoic Impuaio Sales Price Idex Source: Auhors calculaios based o daa from he Duch Lad Regisry P Sock P Sock2 P HIF 96 Hadbook o Resideial Propery Prices Idices (RPPIs)

99 Decomposig a RPPI io Lad ad Srucures Compoes 8 Table 8.7. Approximae Sock Price Idices ad Based o Hedoic Impuaio (P Sock ) ad Sraificaio (P Sock2 ) ad he Fisher Hedoic Impuaio Sales Price Idex Quarer P Sock P Sock2 P HIF Source: Auhors calculaios based o daa from he Duch Lad Regisry The Use of Exogeous Iformaio o he Price of Srucures 8.53 The same kid of cosrucio of a approximae sock price idex ca be applied o he oher hedoic regressio models discussed i his chaper. Here we will show how his works for he cos based model ha used exogeous iformaio o he price of srucures. This model was defied by equaios (8.)-(8.2) ad (8.2). Recall ha he ses of period sales of small, medium ad large lo houses were deoed by S S (), S M () ad S L (), respecively; he oal umber of sales i period was deoed by N () for =,..., 4. The esimaed model parameers are dˆ, gˆ ad ˆ β S, ˆ β M ad ˆ β L for =,..., 4. The esimaed period values of all small, medium ad large lo houses raded over he 4 quarers, V, V LS LM ad V LL, respecively, are defied by (8.22)-(8.24): V LL V LM 4 s= S L ( s) 4 ˆ s V β L (8.22) LS 4 s= S M ( s) S s= S S ( s) =,...,4 ˆ + ˆ s { β [6] β [ L 6]} (8.23) S M =,...,4 ˆ + ˆ [6] [4] + ˆ s { β β β [ L 3]} (8.24) S M L =,...,4 The esimaed period value of qualiy adjused srucures, V, is defied by S N ( s) 4 ˆ ( ˆ s s V γ µ δa ) S (8.25) S s= = =,...,4 where all srucures raded durig he 4 quarers are icluded The quaiies ha correspod o he above period valuaios of he hree lad socks ad he sock of srucures are defied as follows: ( 23 ) 4 Q L (8.26) LS s s= S S ( s) 4 s s= S M ( s) =,...,4 Q L (8.27) LM 4 s s= S L ( s) =,...,4 Q L (8.28) LL N ( s) 4 s= = =,...,4 ( ˆ s s Q δ A ) S (8.29) S =,...,4 ( 23 ) The quaiies defied by (8.26)-(8.29), which are cosa over he 4 quarers, are equal o 77455, 25855, ad for small los, medium size los, large los ad srucures, respecively. Hadbook o Resideial Propery Prices Idices (RPPIs) 97

100 8 Decomposig a RPPI io Lad ad Srucures Compoes 8.55 Approximae sock prices, P LS, P LM, P ad P, LL S ha correspod o he values ad quaiies defied by (8.22)-(8.29), ca be compued i he usual way: P LS VLS / QLS (8.3) P V / Q LM LM LM P LL VLL / QLL P S VS / QS =,...,4 Usig he above prices ad quaiies, a approximae sock idex of lad prices, P LSock, is formed by aggregaig he hree ypes of lad ad a approximae cosa qualiy sock price idex for srucures, P SSock, is simply formed by ormalizig he series P. The approximae S overall sock idex, P Sock, is obaied by aggregaig he hree ypes of lad wih he cosa qualiy srucures (or, equivalely, by aggregaig P LSock ad P SSock ). Sice he quaiies are cosa over all 4 quarers, he Laspeyres, Paasche ad Fisher price idices are all equal. ( 24 ) The sock price idices P LSock, P SSock ad P Sock are chared i Figure 8.7 ad lised i Table 8.8. For compariso purposes, he correspodig price idices based o sales of properies for he model preseed previously, P L4, P S 4 ad P 4, are also lised i Table 8.8. As ca be see from Table 8.8, he approximae sock price idex for srucures P SSock coicides wih he sales based price idex for cosa qualiy srucures P S 4, so P S 4 is o chared i Figure 8.7. ( 24 ) Fixed base ad chaied Laspeyres, Paasche ad Fisher idices are also equal uder hese circumsaces. Figure 8.7. Approximae Price Idices for he Sock of Houses (P Sock ), he Sock of Lad (P LSock ), he Sock of Srucures (P SSock ) ad he Correspodig Sales Idices (P L4 ad P 4 ) Source: Auhors calculaios based o daa from he Duch Lad Regisry P Sock P 4 P LSock P L4 P SSock 98 Hadbook o Resideial Propery Prices Idices (RPPIs)

101 Decomposig a RPPI io Lad ad Srucures Compoes 8 Table 8.8. Approximae Price Idices for he Sock of Houses (P Sock ), he Sock of Lad (P LSock ), he Sock of Srucures (P SSock ) ad he Correspodig Sales Idices (P L4 ad P 4 ) Quarer P Sock P 4 P LSock P L4 P SSock P S Source: Auhors calculaios based o daa from he Duch Lad Regisry 8.56 The overall approximae price idex for he oal sock of deached houses i he ow of A ( P Sock ) ca hardly be disiguished from he correspodig overall sales price idex ( P 4 ) i Figure 8.7. Similarly, he approximae price idex for he sock of lad i A ( P LSock ) ca barely be disiguished i Figure 8.7 from he correspodig sales price idex for lad ( P L4 ). Neverheless, here are small differeces bewee he sock ad sales idices, as Table 8.8 shows Our coclusio is ha he hedoic regressio models for he sales of houses ca readily be adaped o compue Lowe ype price idices for he sock of houses. There do o appear o be major differeces bewee he wo idex ypes whe usig our daa se, bu his resul may o hold for oher daa ses. Hadbook o Resideial Propery Prices Idices (RPPIs) 99

102

103 Daa Sources 9

104 9 Daa Sources Iroducio 9. I pracice, because of he high cos of uderakig purpose-desiged surveys of house prices, he mehods adoped by saisical agecies ad ohers o cosruc resideial propery price idices have maily made use of admiisraive daa, he laer usually beig a fucio of he house price daa ses geeraed by a coury s legal ad admiisraive processes associaed wih buyig a house. The idices so cosruced ca vary accordig o he poi i he house purchasig process a which he price is measured. For example, he fial rasacio price or he earlier valuaio used for securig a loa could be used as he price of he propery. Furhermore, differe admiisraive daa ses will geerally collec iformaio o differe ses of characerisics associaed wih he sales of he properies. These differig iformaio ses will geerally affec idex compilaio mehods, ofe acig as a cosrai o he echiques available o qualiy adjus for houses of differe sizes, locaios, ec. Thus daa ses have hisorically aced as a cosrai o idex cosrucio. 9.2 This chaper examies he differe sources of daa used for cosrucig resideial propery prices idices. Alhough i focuses maily o price daa, he chaper also cosiders how he choice of weighig scheme ca be cosraied by he iformaio geeraed from he housepurchasig process. Differe weighig schemes, oably wheher a idex is sock or sales weighed, produce price idices which measure differe coceps. I hese circumsaces i is impora ha here is a clear udersadig of wha he arge measure is so ha he idices compiled ca be evaluaed agais he arge measure o deermie fiess-for-purpose. Prices The Process of Buyig ad Sellig a House 9.3 The process of buyig ad sellig a propery ormally akes place over a period of several mohs or more. The paricular sage i his process a which he price is eered io a idex will deped o he source of he daa ad his has cosequeces for wha is beig measured ad for he comparabiliy of differe idices. Price daa for a resideial propery price idex may be ake a he followig sages: As soo as he propery is o he marke (adverised or askig price). Typical daa sources: ewspapers, real esae ages. Morgage applicaios. Typical daa source: morgage leders. Morgage approved. Typical daa source: morgage leders. Sigig of bidig corac. Typical daa source: lawyers, oaries. Trasacio compleed. Typical daa sources: lad regisries, ax auhoriies. 9.4 Each source of price daa has is advaages ad disadvaages. For example, a disadvaage of adverised prices ad prices o morgage applicaios ad approvals is ha o all of he adverised prices will ed i rasacios, ad he price may differ from he fial egoiaed rasacio price. These prices are likely o be available someime before he fial rasacio price. Idices ha measure he price earlier i he purchase process are able o deec price chages firs, bu hey will measure fial prices wih error because prices ca be reegoiaed exesively before he deal is fialized. 9.5 I should be oed ha he availabiliy of differe sources of price iformaio a differe pois i he buyig ad sellig process ca be a advaage. For isace, chages i he relaioship bewee askig price ad sellig price may provide a early idicaio of a chage i he housig marke. The diagram below illusraes he siuaio i he UK; see also he case sudy for he UK i Chaper. 9.6 Mos daa sources are suscepible o all he disadvaages of usig admiisraive sysems for saisics. The use of admiisraive daa i ecoomic saisics has bee associaed wih four challeges: defiiios, coverage, qualiy, ad imeliess wih expeced rade-offs agais compilaio coss. Defiiios ad coverage are someimes placed uder he oe headig of coverage : o embrace he ypes of uis covered ad he degree of coverage. For example, cash sales could be recorded bu properies bough wih a morgage may o be covered or some cash sales may o be recorded if, for example, hey are uder he hreshold for ax liabiliy. 9.7 The uderlyig problem arises from he fac ha he daa are primarily recorded as a sep i he admiisraive process ad o as a ipu io a saisical sysem. The daa are o uder he corol of he saisicia. The ihere weakesses i admiisraive daa eed o be ake io accou whe usig he daa ad i ierpreig he resuls, i paricular whe hey are used as a subsiue for saisical daa raher ha as a suppleme o or i cojucio wih purpose-desiged saisics. Some of he weakesses may be overcomed by a appropriae mehodology, such as combiig complemeary daa sources, ad possibly by usig some form of modelig. 2 Hadbook o Resideial Propery Prices Idices (RPPIs)

105 Daa Sources 9 Diagram: House purchase imelie ad house price idices House purchasig process House price idices. Begi search Righmove weeks 2. Verbal offer 4 weeks 3. Morgage approved Halifax, Naiowide, Homerack 4 weeks 4. Exchage of coracs week 5. Trasacio compleed ODPM idex 4-6 weeks 6. Trasacio regisered Lad Regisry Source: Bak of Eglad ad former Office of he Depuy Prime Miiser (ODPM) 9.8 A umber of basic characerisics come io play i cosiderig he suiabiliy of differe daa sources. Defiiio. This is closely associaed wih cocepual issues ad wha he arge measure of a idex is. Coverage. Issues relaig o coverage will be deermied by he operaioal boudaries of he agecy or busiess providig he housig daa. For example, he agecy could cover coury-wide propery sales or jus cover a paricular regio or he rasacios covered could relae oly o cash purchases or o properies purchased usig a morgage loa. For a goverme agecy, he operaioal boudaries will be dicaed by he regulaios ad legal processes ivolved wih he purchase of resideial propery. Ieviably, for public ad privae daa providers coverage will also be heavily depede o he resources a he disposal of he agecy or busiess ad is efficiecy i providig daa. All hese facors are ouside he corol of he idex compiler ad ca impac o daa qualiy ad o ay divergece bewee ieded coverage of he resideial propery price idex ad acual coverage. Qualiy. Whe cosiderig he issue of daa qualiy, i should be bore i mid ha he admiisraive auhoriy is likely o focus o validaig he iformaio which is perie o he sale ad o he execuio of is duies ad which reflec he laws ad regulaios which i is required o comply wih. There may be oher iformaio which is colleced which is of ieres o he saisical agecy, bu which is oly of limied relevace o he admiisraive auhoriy. For isace, his may be he case for some house characerisics which he saisical agecy may wish o use for qualiy adjusme. A he ed of he day, he reliabiliy of admiisraive daa will deped o he iceive for daa suppliers o give correc iformaio ad complee iformaio. There ca be muual advaage o boh paries from he saisical agecy helpig he admiisraive auhoriy o improve he qualiy of is daa. This ca be doe by givig feedback o he cosisecy of daa eries ad from advisig o more geeral weakesses. Some saisical agecies provide he admiisraive agecy wih a iceive o improve heir daa collecio by compilig cusomdesiged saisics for he daa supplier i reur for access o he raw daa. Timeliess. The imeliess of admiisraive daa will deped o who is resposible for reporig o he Hadbook o Resideial Propery Prices Idices (RPPIs) 3

106 9 Daa Sources admiisraive auhoriy ad o he iceive for imely reporig. For isace, here may be a big iceive for a buyer o obai approval from he morgage compay, for a house loa ad for he morgage compay, o quickly ge a accurae ad up-o-dae valuaio so ha he sale ca go hrough, wih all paries safeguarded, before aoher poeial purchaser akes a ieres i he propery. O he oher had, here may be less of a iceive o regiser he sale quickly wih he official lad regisry oce compleed. Oe of he keys o he successful use of admiisraive daa is o have a iimae ad deailed kowledge of he daa collecio processes ad associaed operaioal sysems. 9.9 Each source of price daa is cosidered separaely below. Where more ha oe daa source is available o he idex compiler, he opporuiy arises for cosisecy checks ad for daa from differe sources o be combied. For isace, i may be possible o use he propery valuaios carried ou for he approval of loas o predic he fial rasacio price recorded much laer o by he lad regisry. This depeds of course o he sabiliy of ay correlaio foud bewee he wo. Seller s Askig Price: Esae Ages, Newspapers, Eceera 9. Iformaio o he seller s askig price ca be colleced hrough surveys of real esae ages or from a examiaio of adverisemes i ewspapers, magazies or olie. Oe of he mai advaages of idices cosruced from such iformaio is heir imeliess. By akig askig prices, idices cosruced usig his iformaio ca provide a imelier esimae of house prices ha hose idices ha are based o subseque rasacios. They also have a advaage over house price idices based o iformaio from morgage leders, as he laer are limied o rasacios ivolvig morgages. However, idices based o iiial askig prices have a major drawback. Houses ca be wihdraw from marke ad he agreed sellig price may o equal he seller s askig price. These idices igore reducios i prices ha sellers subsequely make, for example whe he housig marke is o a dowur, or offer prices above he askig price whe he housig marke is buoya. Such idices ca herefore prese a over-opimisic oulook whe he housig marke becomes depressed ad a over-pessimisic oulook whe he housig marke is recoverig. The fac ha hey cao be relied upo o prese a accurae picure of he housig marke i he shor erm devalues heir usefuless o mos users, mos paricularly hose ieresed i he early deecio of urig pois i he housig marke or a advaced idicaor of he fuure direcio of house prices. I should be oed ha he differeces bewee iiial askig price compared o acual rasacio price also imply ha he calculaio of average house price esimaes ca someimes be misleadig. 9. Iformaio colleced o a seller s askig price cao always be easily verified ad, as well as depedig o a balaced ad represeaive sample, relies o he hoesy ad kowledge of hose beig surveyed ad whe draw from adverisemes, he accuracy of he iformaio, especially whe i is from a websie. For example, i has bee argued ha real esae ages are more likely o be opimisic abou prices ad have a vesed ieres i prices goig up raher ha dow ad ha his may ifluece survey resuls. O he oher had, a esae age migh sugges o a seller a urealisically low askig price i order o ge he propery off heir books quickly o ge he commissio. I has also bee argued ha websies will ed o be biased owards properies ha have a compeiive askig price o eice poeial sellers. All his is, of course, speculaio bu i does brig home some of he poeial difficulies associaed wih hese sources. 9.2 Surveys of real esae ages have some ihere advaages over surveys of adverisemes. Agecy surveys ca be based o a more scieifically seleced sample ad ca provide iformaio o a represeaive selecio of hose properies o he marke, icludig hose which ypically are o covered i adverisemes. Daa from real esae ages migh iclude exesive iformaio o he characerisics of he propery ad his iformaio is exremely impora for qualiy adjusme (usig eiher hedoic regressio mehods or sraificaio mehods as was see i previous chapers). Also he survey quesioaire could collec iformaio o issues such as: wha is he average sellig ime or wha has bee he rece differece bewee askig prices ad sellig prices (e.g. higher or lower ) or o he umber of poeial buyers regiserig ad he umber of properies lised wih he age. This iformaio ca help pu he price iformaio used i compilig he idex io coex ad ca be useful for ierpreaio of he fial resuls. Bu such surveys ypically do o record he askig price of a specific propery. Raher, he quesioaire would ormally ask he real esae age o give he average askig price for a selecio of represeaive properies. ( ) For example, his migh be for each of four sadard propery ypes (fla, erraced, semi-deached ad deached) i a umber of differe locaios. I is his iformaio which is used o creae a average propery price for each propery ype i each locaio, which is used i ur o compile he correspodig price idex. I coras, he ihere advaage of a survey of adverisemes is ha he laer will collec he acual askig price for each of he adverised properies. ( ) Some surveys also ask for achievable price ad use his o cosruc a house price idex. 4 Hadbook o Resideial Propery Prices Idices (RPPIs)

107 Daa Sources I summary, alhough a house price idex based o surveys of askig prices may be more imely, he difficulies i deermiig exacly how he survey iformaio was compiled ad he ucerai relaioship bewee askig price ad sellig price mea ha care should ake if such a idex is o be used as a baromeer of house prices. The Iiial Offer Price Acceped by Seller: Morgage Compaies 9.4 May couries ur o morgage leders as he mai daa source for heir house price idex. The iformaio is sored i he leder s compuer sysem ad serves he operaioal busiess eeds of he morgage leders. This daabase may iclude he iiial offer price made by he poeial purchaser, he valuaio price used for auhorisig a loa ad someimes also he fial rasacio price. Iformaio from morgage compaies ca suffer from all he disadvaages of usig daa draw from admiisraive sysems, as described above, bu hese daabases ca be a rich source of imely iformaio. 9.5 However, daa from morgage leders suffer from a major drawback: hey exclude o-fiaced home purchases. Research has idicaed ha cash buyers accou for abou a hird of he UK marke ad cash buyers ed o purchase eiher very cheap or very expesive properies. This would o be problemaic if i was o for he fac ha dwelligs purchased for cash ca experiece differe price developmes compared o hose fiaced by a morgage. This is likely o be paricularly he case a urig pois i he marke where differe eds of he housig marke may reac differely o he ecoomic circumsaces ad he premium for a cash-buyer icrease. For isace i a dow-ur, people a he op ed of he marke who were cosiderig sellig heir homes o release equiy may hold back from puig heir homes o he marke a a reduced price, so he supply of houses for sale falls ad is maily from owers who, for oe reaso or aoher, are very kee o sell. However, a he same ime he umber of acive poeial morgage-based buyers could drop sigificaly as people are reluca o ake ou larger morgages. Bu some people will eed o sell. I his siuaio a cash-buyer for a house a he upper ed of he marke will be i a relaively sroger posiio o egoiae a bargai price ha i a more sable marke. The Valuaio Price for a Loa: Morgage Compaies 9.6 Morgage compaies will obai a idepede valuaio of a propery before approvig a loa. The valuaio ha he morgage compay provides he cusomer wih a he ime of he morgage approval ca be some weeks afer he buyer ad seller have egoiaed a fial price ad he buyer has made he iiial applicaio for a loa. I pracice here is a egoiaio process bewee hese wo sages i which i is possible for he agreed purchase price of he dwellig o chage. This ca be he case whe he idepede valuaio differs from he price he purchaser ad buyer had agreed upo or where he purchaser has paid for a deailed survey of he propery which reveals ha subsaial repairs are ecessary. For isace, i is fairly commo for a buyer o ry o leverage a price reducio if he valuaio by he morgage compay urs ou o be sigificaly lower ha he previously agreed price, or if a survey of he codiio of he propery reveals he eed for ew roofig. Clearly, he differece bewee he iiial offer price ad he follow-up valuaio ad ay process of re-egoiaio which akes place subsequely ca resul i he measured rae of house price iflaio o differ from he rue rae as measured by he acual rasacio price. 9.7 The house price chage measured by idices based o valuaios by morgage compaies ( 2 ) ca differ from he price chage show by he offer price ad boh may differ from he price chage based o fial rasacio prices eve whe ake from he same sample of morgage leders. Thus, i is impora o udersad exacly wha a idex is measurig. The Fial Trasacio Price: Morgage Compaies 9.8 The ime lag bewee he morgage applicaio, morgage approval ad purchase compleio sages ad he differeces i he correspodig values of he house prices illusrae he rade-off bewee imeliess ad accuracy. The fial rasacio price is o always recorded by morgage leders ad is ofe exraced isead from legal records such as eries made i lad regisers, which addiioally also iclude sales ha did o require a morgage. Bu here ca be a log ime lag bewee he compleio of he rasacio ad he recordig of he sale i he lad regiser. Oe of he mai advaages of daa from morgage leders is is imeliess. Iiial offer prices ad valuaios provide a earlier idicaio of curre prices, as hese daa are available earlier, ad fial rasacio prices may be available sooer from he morgage leder ha from he lad regisry. I is for his reaso ha he exploiaio of iformaio from morgage leders o fial rasacio price may be a preferred opio. The fial rasacio price held by morgage leders ca be easily verified agais lad regisry records o alleviae ay cocers regardig accuracy ad credibiliy. ( 2 ) I has o be ake io accou ha prices from morgage valuaios, like prices based o ay valuaio, deped o he objeciviy of he evaluaio process. Thus, i has bee meioed ha he morgage valuaios ca someimes be iflueced by he credi policy of he bak, idicaig poeial difficulies associaed wih hese sources. Hadbook o Resideial Propery Prices Idices (RPPIs) 5

108 9 Daa Sources The Fial Trasacio Price: Admiisraive Daa from Propery Regisers ad Tax Offices 9.9 Ideally a house price idex would be based o acual rasacio prices a he ime whe he propery is sold ad he sale compleed. The sigig of he firs bidig corac bes fis his requireme because of is imeliess bu i pracice here ca be some ambiguiy abou he poi a which a corac is bidig, e.g. wheher his is a he poi where a offer is formally acceped (e.g. whe sealed bids are opeed), or whe a corac is siged or whe he corac is exchaged. Similarly, here ca be a differece bewee whe a corac is siged ad whe he rasfer of owership akes place ad whe i is recorded i he propery regisers or a he ax office. 9.2 I heory, iformaio from propery regisers or ax offices will cover all properies, icludig cash purchases as well as purchases via a morgage ad hus hese daabases should be he mos comprehesive of all he sources available o he idex compiler. Bu, i pracice, comprehesiveess cao be guaraeed, paricularly if here is a disiceive for he ower o regiser a propery. For example, whe he primary purpose of regisraio is for axaio purposes, properies may o ge regisered a all, or may be regisered wih some releva deail such as square meres of floor space missig or icorrecly recorded, i order o avoid ax or reduce he ax charges. ( 3 ) Valuaio Price for Taxaio ad Payme for Local Services: Tax Offices 9.2 I may couries, he ceral or a local goverme may impose a mohly or aual ax or service charge o resideial properies, for fudig he provisio of public services such as road maieace, police ad fire services or refuse collecio. I may cases, he ax bill faced by a idividual is proporioal o he assessed value of propery ad he laer is usually based o a valuaio uderake by professioal charered surveyors eiher uder corac or direcly employed by he axaio auhoriy. The valuaios should ake io accou characerisics of he propery, such as locaio ad size of plo. However, hey rely o accurae iformaio abou he properies ad also o he charered surveyors assessmes, which are difficul o verify. Also he updaig of he valuaios eds o be ifreque due o he field coss ivolved. Because of hese drawbacks, he iformaio colleced ca someimes be of limied use i he cosrucio of resideial propery price idices. ( 3 ) There is a relaed problem: he rasacio price may o be a marke price because he rasacio, while geuie, is bewee relaives or frieds. For example, pares may decide o pass o he family home o heir childre a a below marke price. Tha said, his source of official valuaio iformaio has bee exploied by saisical agecies; see he maerial o he SPAR mehod of idex cosrucio described i Chaper 7. Oher Exper Opiio Iformaio: Surveys of Esae Ages Orgaisaios, oher Professioal Bodies ad heir Members 9.22 I some couries, regular surveys are coduced of real esae ages, charered surveyors or heir correspodig professioal bodies, askig abou house prices ad housig sock. These opiio surveys are ypically resriced o askig respodes o give a view o wheher house prices are movig up, dow or fla. These surveys do o give a idicaio of how much houses are worh or by how much prices are fallig or risig bu hey ca provide a up-o-dae ad broad-based picure o he direcio of price chage i he housig marke o suppleme ad help o add credibiliy o he laes figures from a resideial propery price idex. For isace, a sigifica chage i he differece i he proporios of real esae ages who hik prices are goig up ad hose who hik prices are goig dow migh provide a early idicaio of a chage i he housig marke o ye deeced by he currely available saisics o morgage leder valuaios. Coexual iformaio of his kid adds value ad is regularly used by commeaors whe ierpreig official house price idices. Evaluaio of Daa Sources for Fiess-for-Purpose 9.23 The overall usefuless of he above sources of iformaio o resideial propery prices will very much deped o heir fiess-for-purpose for he paricular applicaios o which hey are beig used. To gauge fiessfor-purpose requires a evaluaio of he irisic advaages ad disadvaages of he idex agais a agreed se of crieria, i.e. a evaluaio agais user eeds Chaper 2 reviewed he may differe uses of house price idices: as a macro-ecoomic idicaor of iflaio; for moeary policy argeig; as a measureme of chage i wealh; as a fiacial sabiliy idicaor o measure risk exposure; as a deflaor for he aioal accous; as a ipu io a idividual ciize s decisio makig o wheher o ives i resideial propery; as a ipu io oher price idices, i paricular he Cosumer Price Idex (CPI), ad for use i wage bargaiig or idexaio. 6 Hadbook o Resideial Propery Prices Idices (RPPIs)

109 Daa Sources A effecive evaluaio of he differe sources of daa o house prices is depede o a sysemaic aalysis of user requiremes. User eeds have a sigifica impac o decisios relaig o he cocepual basis of a idex ad he associaed saisical requireme. This may ake he form of a series of quesios reflecig he differe reasos why users may wa iformaio o house prices. For isace, wheher a idex of house prices is o be used as oe of a suie of geeral macroecoomic idicaors, as a ipu io he measureme of cosumer price iflaio, as a eleme i he calculaio of household wealh or as a direc ipu io a aalysis of leders exposure. Such a aalysis ca he be rasformed io a saisical user requireme ad a associaed cocepual framework by expressig he eeds i saisical erms ad ideifyig he commo likages ad correspodig relaioships a a micro ad macro level. The differe daa sources ca he be evaluaed agais he saisical eed The followig lis of desirable properies for a resideial propery price idex cosiue a possible se of crieria for a evaluaio of aleraive daa sources for fiess-for-purpose for differe uses. ( 4 ) The lis builds upo he discussio a he begiig of his chaper. The relaive imporace of each of he crieria will deped o use ad i essece cosiues a saisical requireme. There will also be he usual rade-offs bewee fully meeig user eeds ad he coss of daa collecio. Defiiios ad Measureme Cocep 9.27 This also covers coherece wih oher saisical oupus. I represes he user requireme a he mos basic level. Cosider he eeds of govermes ad aalyss lookig a iflaioary pressures ad hose wih a direc ivesme i real esae. The primary focus of hese users may be he cyclical aure of prices ad he abiliy of real esae prices o lead o desabilisig booms ad slumps i he ecoomy as a whole. For his purpose, users will be lookig o a variey of idicaors, icludig idices of he volume ad price of real esae rasacios, as well as macro-ecoomic idicaors for modellig he ecoomic cycle ad predicig peaks ad roughs. Aalyss lookig a he iflaioary pressures of real esae price rises i compariso o oher price rises may be ieresed i icludig i a CPI he iflaioary coss of ower-occupier housig coss by meas of a house price idex based o he e acquisiio cos basis bu excludig lad For users waig a geeral macro-ecoomic idicaor, a idex based o all purchases boh cash ad hose wih a morgage is appropriae. Takig rasacio prices ( 4 ) See also Chaper 3 where a lisig of user eeds is preseed based o discussios bewee users of house price idices ad he Office for Naioal Saisics. I ha secio, i was poied ou ha here is a rade-off bewee he desires of users o have a family of more deailed idices (sraified by locaio ad ype of housig) ad he qualiy of he idices: more deail ieviably leads o less accurae idices. solely from daa supplied by morgage leders represes a serious deficiecy. Cocepually, lad regisry daa would represe a beer source as i should cover all rasacios. The challege is o fid a source of price daa which readily fis, or ca be maipulaed o mee, he requiremes of users ieresed i he iclusio of ower-occupier housig coss i a CPI o a e acquisiio cos basis, ha is, excludig he price of lad. ( 5 ) 9.29 I coras, users ieresed i a aalysis of he curre value of he real esae porfolio agais which ousadig morgages are secured, will require a idex of chages i he price of he properies for which morgages were issued, weighed by he amous loaed for each ype of propery a he ime a which hey were issued. For boh of hese measures, he value of he lad uderlyig he buildigs is as impora as he value of he buildigs hemselves ad i is he oal value of he lad ad buildigs which is of ieres. For hese users, daa from morgage providers o propery prices ad he size of ew morgages ad ousadig deb will fi he purpose. 9.3 Now cosider he eeds of employers ad rade uios whe egoiaig wage selemes. Their primary focus will be he effecs of price chages o he sadard of livig of workers. For his purpose users will be lookig o a CPI ha icludes he cos of keepig a roof over heir heads for ower-occupiers he cos of morgage ieres paymes ad he repairs coss. The measureme of his will require he calculaio of he morgage oulay a ime of purchase ad he subseque repayme hisory will eed a sales weighed house price idex. I a ideal world re-fiacig would be excluded. The repairs eleme may be measured by he calculaio of depreciaio. For his, a sock-weighed smoohed house price idex is mos appropriae. I addiio, here is he issue of lad where i is ofe argued ha i mos circumsaces lad is a ivesme which appreciaes ad ha is iclusio i a depreciaio calculaio is iappropriae. ( 6 ) Thus a idex excludig he price of lad may be required. 9.3 For he calculaio of morgage oulay, he user ca agai rely o iformaio supplied by morgage leders, bu o for he esimaio of depreciaio, where he value of lad may agai eed o be separaely ideified As a fial example, cosider he eeds of aioal accouas, who are seekig appropriae deflaors for aioal accous. Their eeds agai will be differe. Real esae appears i he Naioal Accous i several ways (for deails, see Chaper 3): ( 5 ) I mos couries for mos rasacios, lad ad buildig are purchased ogeher as a sigle package, so he wo compoes are ypically o separaed i he iformaio geeraed by records relaig o he rasfer of owership. As such separaig he prices would require a supplemeary exercise. I Chaper 8 i was oulied how hedoic regressio ca be used o decompose he overall price idex io lad ad srucures compoes. ( 6 ) There are oher more geeral issues, which are o addressed here, o do wih he measureme of depreciaio ad is iclusio i a cosumer price idex. Hadbook o Resideial Propery Prices Idices (RPPIs) 7

110 9 Daa Sources The impued real value received by ower occupiers for buildigs is par of household fial cosumpio. The capial formaio i buildigs, as opposed o lad, is par of gross fixed capial formaio, depreciaio, ad he measureme of he sock of fixed capial. Lad values, which are a impora par eleme of he aioal sock of wealh. I each case he derivaio of volumes from values requires price idices for respecively: he impued re of ower occupied dwellig uis weighed by he sock of differe ypes of ower occupied housig; ew house purchases weighed by he rasacios i ew houses bu excludig he lad compoe; ad of he whole housig sock icludig lad weighed by he housig sock 9.33 I ca be see ha user eeds will vary ad ha i some isaces more ha oe measure of house price or real esae iflaio may be required. I ca also be see ha coherece bewee differe measure ad wih oher ecoomic saisics is impora ad ha achievig his will be especially difficul as saisicias are ulikely o have a ideal se of price idicaors available o hem. Coverage 9.34 Coverage icludes o jus wheher all properies are covered irrespecive of wheher he propery is owed ourigh or beig fuded by a morgage bu also wheher coury-wide propery sales or valuaios are covered or jus hose i a paricular regio ad wheher all price rages are covered. I ca be oed ha eve where he primary eed is for a aioal idex, regioal idices ca be i demad for aalyical purposes. House price iformaio from ay idividual morgage leder is ulikely o be represeaive of he coury as a whole, o oly because of he exclusio of cash purchases bu also because leders ofe focus heir busiess o paricular regios. Qualiy 9.35 Qualiy relaes o he accuracy ad compleeess of he iformaio, i.e. here are o serious errors ad he iformaio is wha i purpors o be. Compared wih oher admiisraive daa, house price iformaio from a lad regisry is likely o score relaively highly i erms of accuracy due o he legal requiremes o record propery rasacios ad exchages of owership. However, he reliabiliy of daa from ay admiisraive source is difficul o validae. Timeliess 9.36 Idices ha measure prices earlier i he purchasig process are able sooer o deec price chages ad urig pois i house price iflaio. This is likely o be paricularly impora whe used, say, for macro-ecoomic policy ad moeary argeig bu less impora for a aioal accous deflaor. Daa from morgage leders may beer sui he eeds of hose egaged i macro-ecoomic policy ad moeary argeig, eve hough cash purchases are excluded, whils lad regisry daa may beer sui he eeds of, for example, hose calculaig deflaors. Deail for Qualiy Adjusme ad Mix-Adjusme 9.37 This relaes o wo (relaed) issues: he degree o which resideial propery price idices are able o adjus for chages i he mix of properies sold ad o elimiae he effec of qualiy chages of he idividual dwelligs. For his purpose, real ime iformaio is eeded o price deermiig aribues such as size of plo, size of house, ype of propery (fla, house, semi-deached or deached), locaio, he codiio of he propery, wheher i has ceral heaig, a fully-fied kiche ad bahroom, ec. Qualiy (or mix) adjusme is esseial i order o cosruc a accurae price idex for housig compoes. ( 7 ) I is ulikely ha ay of he sources of prices daa lised above will be ideal for all purposes. The amou of deailed ad releva characerisics daa will deped o he idividual daa se. ( 8 ) Frequecy 9.38 Frequecy esseially relaes o how frequely a idex ca be compued, e.g. oce a moh or oce a quarer. There is a radeoff bewee frequecy ad accuracy. For a paricular geographic area ad ype of housig, curre iformaio o he price of houses i a give sraa will come from sales of old ad ew houses i ha sraa durig he chose ime period. If he frequecy is chose o be a moh as opposed o a quarer, he mohly sample size will oly be approximaely oe hird of he quarerly sample size. Thus a mohly house price idex based o sales of properies i he give sraa will be subjec o icreased sample volailiy (ad hece will o be as accurae) as compared o he correspodig quarerly idex. Volailiy of a mohly idex may be reduced by makig he sraa bigger, ( 9 ) e.g., differe eighbourhoods could be combied wihi he same geeral locaio bu his leads o aoher radeoff bewee fieess ( 7 ) The various mehods available for cosrucig qualiy adjused house price idices were discussed i Chapers 4-8. ( 8 ) I cases where he real esae age daa base icludes he fial sellig price of he lised properies alog wih he mai characerisics of he properies, his iformaio base is probably he bes for mos purposes. However, he sample of lised properies eeds o be compared wih he properies lised i lad regisry offices o esure ha he coverage of lised properies is adequae for he purpose a had. Whe cosrucig price idices for he sock of housig, i will be ecessary o have cesus iformaio o housig socks alog wih pos cesus iformaio o demoliios ad he cosrucio of ew dwellig uis. ( 9 ) I is o cerai ha combiig sraa will reduce idex volailiy if house prices i he differe micro sraa have differe reds. 8 Hadbook o Resideial Propery Prices Idices (RPPIs)

111 Daa Sources 9 of he sraa (which may users may wa) ad accuracy of he idex (which all users wa) I may be possible o provide smoohed mohly house price idices ha are say a hree moh movig average of he raw mohly idices ( ) or he saisical agecy could provide boh mohly ad quarerly idices ad le users choose heir preferred idex. ( ) I is o possible o provide defiiive advice o how freque a house price idex coverig a cerai sraum should be published. The issue of frequecy mus be decided by he aioal saisical agecy, akig io accou user eeds ad daa availabiliy. Revisios 9.4 Revisios ca refer o eiher revisios resulig from subseque reurs (so ha he series iself is revised) or from oher sources of more releva daa subsequely comig o sream (so a early idicaive measure is eveually replaced by a precise measure of wha eeds o be measured). ( 2 ) For isace, a example of he former migh be revisios arisig from lae regisraio of propery sales. A example of he laer migh be where a iiial offer price recorded o he morgage applicaio form is used as a early idicaio of movemes i rasacio prices bu is subsequely discarded whe lad regisry daa o acual rasacio prices (which akes io accou ay price reegoiaio before he sale is fialised) eveually comes o sream a a much laer poi. 9.4 The exe o which figures are revised due o he receip of subseque reurs is parly deermied by he referece poi of he prices daa ad parly by he poi i ime whe he paricular daa se is received by he saisical agecy: he earlier is he daa referece period i he purchasig cycle ad he earlier he paricular daa se is received, he more he idex will be subjec o revisio. Thus, alhough iformaio from he regisraio of propery sales is appropriaely refereced ad provides a defiiive source of iformaio o propery prices, he ime delay ha ca someimes ake place i some couries for he legal regisraio of propery rasfers ca mea ha he regiser is o fial uil, say, welve mohs he sale of he propery. ( ) The Ausralia Bureau of Saisics makes freque use of his echique for a wide rage of is saisics. If he widow legh is 2 mohs, he he resulig smoohed idex ca be regarded as a seasoally adjused idex, ceered i he middle of he 2 moh period uder cosideraio. For a varia of his smoohig echique, see Chaper 4. ( ) There is a possibiliy ha some users may be cofused by havig more ha oe idex coverig esseially he same housig sraa. However, he Bureau of Labor Saisics ow has wo mohly published Cosumer Price Idices: heir headlie Lowe ype CPI which is o revised ad a secod idex which is a approximaio o a superlaive Törqvis idex (which is revised). Users i he U.S. seem o have acceped muliple idices i his coex. ( 2 ) A relaed issue is ha some of he mehods for cosrucig a RPPI, such as he muliperiod ime dummy hedoic mehod (see Chaper 5) ad he repea sales mehod (Chaper 6) suffer from revisio i he sese ha previously compued figure will chage whe ew daa is added o he sample. I some cases, revised idices are published while i oher cases, he rollig widow echique wih updaig due o Shimizu, Nishimura ad Waaabe (2) ad Shimizu, Takasuji, Oo ad Nishimura (2) is used. The rollig widow wih updaig echique does o revise he hisorical idex up o he curre period Valuaio prices kep by ax offices for axaio ad payme for local services ad he fial rasacio price recorded by morgage compaies are leas likely o be subjec o revisio, whils he fial rasacio price based o admiisraive daa held o propery regisers ad ax offices could be subjec o revisio over a log period depedig o he ime-lags ivolved i he legal processes of recordig chages i owership. Comparabiliy 9.43 Comparabiliy refers o he degree of ier-coury comparabiliy bewee house price idices. This is impora because comparig house prices from oharmoised aioal daa ca be problemaic as differeces i cocep, idex cosrucio, marke coverage, qualiy adjusme procedures, ec. ca make cross coury comparisos difficul. Differeces i frequecy, imeliess ad revisios policy ca also cause comparabiliy problems Problems ca arise a boh he aioal ad ieraioal levels: Users i idividual couries ca be cofroed eiher wih a lack of releva saisics or wih differe saisics for differe ime periods ad wih varyig ime-lags ad hese saisics ca be based o differe daa sources or compilaio mehods. For users seekig ieraioal comparisos he siuaio is complicaed by sigifica differeces amog couries wih regards o he availabiliy of daa ad he challege his represes for compilig like-for-like comparisos ad ierpreig relaive reds amog couries. The complicaio of aggregae price idices coverig groups of couries a requireme for co-ordiaed ecoomic policy ad moiorig across a ecoomic area such as he Eurozoe ( 3 ) is a furher challege. From Chaper i ca be see ha he mehods employed for he compilaio of resideial propery price idicaors vary cosiderably bewee couries, ad eve bewee aleraive sources wihi idividual couries. Weighs 9.45 The daa sources draw o for he weighs i a resideial propery price idex are a fucio boh of he daa eeds of he arge idex ad of he availabiliy of he required iformaio. Also he daa eeds deped o oly o he cocepual basis of he idex bu also o deailed aspecs of idex cosrucio, such as he mehod of qualiy adjusme ad ay subidices ha are required ( 3 ) Cosisig of he seveee member saes of he Europea Uio ha have adoped he Euro as of 22. Hadbook o Resideial Propery Prices Idices (RPPIs) 9

112 9 Daa Sources for aalyical ad oher purposes. For isace, he cosrucio of a mix adjused propery price idex based o rasacios requires ha eough iformaio is kow abou he sales i each period for hem o be classified io groups sufficiely homogeous so ha he ui values ca be reaed as prices. I he housig marke, he problems are compouded by he low volumes of sales for cerai house ypes i paricular geographical areas which could lead o may cells beig empy. ( 4 ) 9.46 Puig hese deailed issues of cosrucio o oe side, he cocepual basis of he idex is he mai facor deermiig he daa eeds relaig o weighs. Oe price idex cao mee he diverse eeds of users. For esimaig gross capial formaio, for isace, oly ew houses should be icluded while esimaig he effec of price chages o capial socks requires he idex o cover all rasacios The weighs ca be derived from a umber of sources, i paricular, from aioal accous daa, periodic aioal cesuses which collec iformaio o he housig sock, iformaio from baks o he loas ake ou for house purchase, cosrucio saisics, official regisers recordig owership, ec. There ca be a lack of coherece bewee hese differe daa sources resulig from he log ad quie ofe ivolved processes associaed wih buyig ad sellig a house ad he fac ha a valuaio or offer price associaed wih a applicaio for a morgage will o ecessarily lead o a sale ad chage of owership. Oher issues arise also, such as he disicio bewee wha is beig buil for sellig ad wha is beig buil for reig ou. This sor of iformaio is rarely readily available from oe saisical source. I is for his reaso ha he cosrucio of weighs may draw o a muliude of differe sources. Developig Couries, Tradiioal Dwelligs ad he Iformal Housig Marke 9.48 For may developig couries, a sigifica proporio of he housig sock cosiss of ewly cosruced buildigs o family owed lad or of old buildigs which have bee sigificaly upgraded sice hey were firs cosruced. There ca also be a sigifica eleme of owercosruced housig. Cosrucio may ake may years ad a ay poi i ime a subsaial proporio of he ( 4 ) The sraificaio or mix adjusme mehod was discussed i Chaper 4. I he example for he Duch ow of A, may cells were ideed empy. A mached-model approach was suggesed o cope wih his problem. houses could be cosidered icomplee. The use of formal morgage fiace is ofe very limied bu iformal fiace may be used. House cosrucio ca vary from shaies buil o compaced soil wih salvaged maerials o subsaial muli-room dwelligs buil o cocree foudaios wih cocree blocks. Ameiy levels ca vary from virually oe o he elaborae. Housig mobiliy, paricularly wih ower-cosruced dwelligs, is usually very low ad cosequely he markes for real or sale of owercosruced houses are limied ad here is very lile moveme bewee he wo. I priciple he compilaio of a house price idex is he same for ower-cosruced housig as for hird pary cosruced housig, bu he measureme problems are, a he leas, differe ad are geerally more difficul. ( 5 ) 9.49 The above complicaios mea ha formal records will rarely be kep of he cos of buildig he ew dwellig or of upgradig a old house, for example, by icorporaig ruig waer, a ieral WC or addiioal rooms. Formal rasfers of owership someimes do o ake place, formal valuaios are ofe o available ad mehods of fiacig ca be iformal hrough he family or may simply o be recorded or records o kep cerally. Thus i hese circumsaces i will o be possible o calculae morgage ieres paymes (icludig or excludig oioal ieres paymes o relaives), or o esimae e acquisiio coss. 9.5 The lack of such basic iformaio ofe meas ha he real equivalece or a impued re approach is he oly pracical opio for cosrucig a housig price idex. The price idicaor for impued res ca be derived eiher from a readily available price series for res, reweighed o reflec he curre composiio of he sock of ower-occupier housig, which ca he be applied o he real equivales i he base period, or from askig a exper o provide o a mohly basis he equivale res for a sample of houses which is represeaive of he oweroccupier housig sock. 9.5 I each case, sraificaio by ype of dwellig (house or fla), locaio (regio or area, urba or rural), plus oher characerisics which will ifluece re is impora so ha he res daa ca be combied o reflec he composiio of ower-occupied propery. Oher sraificaio variables may iclude such higs as he oal size of he plo, floor area ad umber of rooms, wheher here is mais waer, a ieral WC ad mais elecriciy, he maerial used i cosrucio ad wheher he buildig is of radiioal desig. The price saisicia should seek he advice of a exper acive i he field of reig domesic propery, such as a housig corporaio, ( 5 ) I paricular, he impora price deermiig characerisics of he srucure ca be quie differe for a developig coury ha for a developed coury. I a developed coury, here is perhaps less variaio i he ype of cosrucio ad he maerials used whereas he qualiy of shaies could differ more markedly. Also lad ile may be missig i may isaces i developig couries which agai ca creae problems for mix adjusme ad hedoic regressio echiques for adjusig housig qualiy. Hadbook o Resideial Propery Prices Idices (RPPIs)

113 Daa Sources 9 o ascerai he mos impora re-deermiig characerisics ad should bear i mid he eed o keep hese o a maageable umber. Weighs iformaio ca be derived from he laes Housig Cesus or Cesus of Populaio ad Housig. I pracice his iformaio may o be up-o-dae due o he chage i he ower-occupied housig sock which ca occur i he ime period bewee cesuses. Where his is he case special surveys may eed o be coduced or, paricularly i urba areas icludig owships, use made of plaig applicaios o updae he laes cesus Bu he measureme problems ca be sigifica. I summary, radiioal or iformal dwelligs are geerally buil by family members or oher upaid labour. The walls ca be made of less durable maerials such as dried clay, bamboo or laicework ad he roofs ca be made from reeds, sraw or palm frods or corrugaed iro. The dwelligs may or may o have elecriciy or piped waer i he dwellig, le aloe oher faciliies. Tradiioal dwelligs are geerally locaed i rural areas. Some associaed complicaios whe aempig o iclude he ower-occupier housig coss i a cosumer prices idex are: May such dwelligs are locaed i or very ear o large ciies, such as shay-ows. These dwelligs may be reed or ower-occupied ad i may be difficul o obai deails of owership. Coducig surveys ca be problemaic. There are may such dwelligs i rural areas ha may be buil wih family labour o family or uregisered lad or lad i commo owership. I hese circumsaces, he cocep of owership becomes a grey area. Thus he defiiio of ower-occupied housig ad wha a family acually ow is subjec o debae ad eve whe here is a agreed upo defiiio, eve basic records of he umber of such ower-occupied housig may o exis le aloe deails of he dwelligs Releva characerisics for he compuaio of a price idex, ha are ecouered i radiioal ad oher dwelligs i he iformal marke iclude: Elecriciy supply. This will ofe be elecriciy supplied by a geeraig or disribuio compay. However, elecriciy may also be geeraed by he household iself, e.g. from a diesel geeraor or wid power, or may be ake illegally from he disribuor. Ruig waer. This may be piped io he dwellig iself or he dwellig akes waer from a commual sadpipe or well. A privae or commual oile, which may be eiher a waer-flushig WC-ype or a chemical oile. I addiio here is, as wih ay home he issue of livig space, recorded i erms of umber of rooms, m 2, or boh. For his here eed o be releva defiiios. I paricular, defiiios of usable floor space (he floor area of he livig room, kiche, hall, bahroom ad all adjoiig rooms mius he wall hickess ad door ad widow recesses ad excludig e.g. sairs) ad of he umber of rooms (e.g. o wheher o iclude or exclude hall-ways) are required Fially, eve if iformaio o he characerisics of hese dwelligs is available here may o be a equivale real ui o value he services of a ower-occupied ui. Thus he idirec measureme of prices may o be possible. I his siuaio, saisicias ca pu a sysem i place o measure ipu prices (cosrucio coss) ad he use his iformaio o cosruc a user cos measure of he housig services as a proxy for he prices of he housig services cosumed. ( 6 ) For ow-accou cosumpio, he Sysem of Naioal Accous 993 (SNA 993) recogises ha i may oly be pracicable o measure ipu prices. The issues discussed above are cosidered i he case sudy o he compilaio of resideial propery price idices i Souh Africa, which ca be foud i Chaper. ( 6 ) See Blades (29) for addiioal maerial o cosrucig hese user coss for radiioal housig i developig couries. Hadbook o Resideial Propery Prices Idices (RPPIs)

114

115 Mehods Currely Used

116 Mehods Currely Used Iroducio. I pracice, he mehods used for cosrucig resideial propery price idices ca be cosraied i large par by he aure of he daa available. The daa required o cosruc he arge idex, oce defied, are o always available o a regular ad imely basis, if a all. Moreover, eve where suiable daa are available o cosruc a price idex o mee he eeds of oe se of users, more ofe ha o, he daa does o fi he requiremes of aoher se of users. For may couries seig up he required ifrasrucure ad procedures for he collecio of he daa ecessary for producig a propery price idex ca someimes be prohibiively cosly. Also, chages i mehodologies ad i he uderlyig daa sources ca frusrae he cosrucio of hisorical series, which are ofe required for ecoomeric modellig ad aalyses over more ha oe cycle of housig marke developmes o iform policy opios for he maageme of he ecoomy. Las bu o leas, he imeliess ad frequecy of he daa, whe available, may o be suiable for producig he kid of house price idex ha he users wa or eed..2 For users, his daa shorcomig for he cosrucio of house price idices ad relaed idicaors has someimes bee a source of frusraio. For example, he he Goveror of he Bak of Caada i a speech o he Coferece of Europea Saisicias (Dodge, 23) saed: Give ha he ivesme i housig represes a big chuk of household spedig, ad ha for mos people heir homes represe heir mos valuable asse, i is surprisig ha i may couries here are o comprehesive, qualiy-adjused daa o housig prices or res..3 I addiio, he daa sources ad he mehods are o always well documeed, ad surveys of mea-daa o resideial propery prices cofirm ha here is a lack of harmoisaio i he pracices. This represes a furher challege for users. I paricular, i compromises he possibiliy of makig meaigful ieraioal comparisos of reds i house prices ad makes ay comparaive ecoomic aalysis exremely difficul. This ca brig io quesio he credibiliy of he resuls..4 Daa availabiliy apar, he mehods used by couries o compile resideial propery price idices have also o cofro some ihere problems, mos paricularly, ha properies have uique characerisics, resulig i heerogeeiy i differe dimesios, may of which are difficul o measure objecively, ad ha rasacios of idividual properies are ifreque. Boh of hese issues make he compilaio of price idices especially challegig. I addiio, he fac ha askig prices are egoiable meas ha he rasacio price may differ from he iiial or fial askig price, he offer price ad a exper valuaio..5 The ideificaio of he echiques mos widely used i compilig idices of resideial propery prices also begs he quesio of wheher ieraioal bes pracice i he mehods for cosrucig such idices ca be ideified, or wheher he echiques adoped ieviably are govered ad depede o local codiios..6 Oher secios of his hadbook provide recommedaios o bes pracice. This chaper describes he rage of available idices by differe couries ad also preses some case sudies. I relies o mea-daa gahered by various orgaisaios, icludig he Bak for Ieraioal Selemes ad he Europea Ceral Bak ad more recely a fac-fidig exercise coduced by Eurosa i coecio wih he iclusio of ower occupied housig coss i he Europea Uio s Harmoised Idex of Cosumer Prices, which was exeded o cover some o-eu couries. Mea-daa o resideial propery price idices published by differe couries are available from he websie of he Bak for Ieraioal Selemes (BIS); see ( ) Idex Availabiliy.7 A a Europea level, Eurosa has sared releasig sice December 2 quarerly repors o experimeal house price idices i he EU ad euro area. ( 2 ) These repors coai, for hose EU saisical offices ha have give heir permissio for publicaio, experimeal daa o house price idices. The aexes o hese quarerly repors coai all currely available liks o Naioal Saisical Isiues web pages dealig wih house price idices, where deails cocerig he compilaio are give..8 I ca be see from he available mea-daa o he BIS websie ( 3 ) ha he mehods used o compile resideial propery price idices vary cosiderably, boh amog couries ad eve wihi idividual couries. The laer raises a key quesio for users wih regard o which series should be used o mee heir paricular eeds. Wih regards o he former, a key issue is raised for users abou he validiy of available ieraioal comparisos..9 The differeces bewee he available house price idices cover almos every aspec of price idex cosrucio. These have bee referred o i earlier chapers: he cocepual basis of idex (i.e., wha is he appropriae arge idex o suie each user eed); daa sources (propery regisraios, ax records, morgage applicaios ad ( ) The propery price saisics o he BIS websie iclude daa from hiry-seve couries ad are available a differe frequecies. The daa differ sigificaly from coury o coury, for isace i erms of sources of iformaio o prices, ype of propery, area covered, propery viage, priced ui, deailed compilaio mehods ad seasoal adjusme. This reflecs wo facs. Firs, ha he processes associaed wih buyig ad sellig a propery, ad hece he daa available, vary bewee couries ad, secod, ha here are currely o specific ieraioal sadards for propery price saisics. ( 2 ) See hp://epp.eurosa.ec.europa.eu/poral/page/poral/hicp/mehodology/ower_ occupied_housig_hpi/experimeal_house_price_idices ( 3 ) See hp://bis.org/saisics/pp.hm. 4 Hadbook o Resideial Propery Prices Idices (RPPIs)

117 Mehods Currely Used compleios, real esae ages, pri media such as ewspapers ad oher forms of adverisemes); marke coverage (geographical coverage, ype of propery, morgage/ cash rasacios); qualiy adjusme (hedoics, mixadjusme) ad weighig (sock or sales weighed). The problems caused by hese differe facors ca be exacerbaed by he fac ha housig markes ca be highly heerogeeous. Thus o oly do properies vary i price accordig o heir physical aribues such as floor area ad wheher hey are deached houses o heir ow plo of lad or a aparme i a high-rise complex. The prices ca also diverge widely depedig o, for example, he regio of he coury, he area of he ow or wheher he locaio is classified as rural or urba. Locaio affecs desirabiliy which leads o differe demad codiios, hus explaiig why a oherwise ideical house may have a differe price depedig o is locaio. For isace, a propery i a regio wih a high GDP per capia ad low uemployme ad i a localiy kow for he qualiy of is schools ad pleasa surroudigs will commad a higher price ha a oherwise ideical propery bu i a area plagued by high uemployme, low household icomes, poor qualiy schools, ad a high crime rae. ( 4 ). A overview of he curre siuaio is preseed below. I should be oed ha he posiio is chagig as more couries develop heir resideial propery price idices ad review he idices currely published. The reader should refer o he iformaio from he websies of he BIS, Eurosa ad he ECB for more facs abou he resideial propery price idices for a paricular coury. Resposibiliy for Compilaio. I he EU, saisical offices have bee cooperaig i developig ad compilig resideial propery price idices ha are based o broadly harmoised saisical approaches, hereby pioeerig he work owards ieraioally comparable house price idices. Also, several aioal ceral baks compile house price idicaors, icludig Belgium, Germay, Greece, Ialy, Cyprus, Luxembourg, Hugary, Mala, Ausria, Polad ad Slovakia. I Ausria, he aioal ceral bak works joily wih he Viea Uiversiy of Techology, while he price idex compiled by he Ceral Bak of Luxembourg is based o he daa from he coury s aioal saisical isiue. I Irelad, Frace, Spai, he UK ad he USA, resideial propery price idices are compiled by goverme deparmes oher ha he saisical office. I some isaces, such as i he UK, his reflecs i par he fac ha he saisical sysem is deceralised wih goverme saisicias locaed i goverme deparmes ad workig alogside heir policy ad service-delivery colleagues. I some cases, resposibiliy for he compilaio of he idex resides wih he deparme which has policy, operaioal or legal resposibiliy for he housig secor. The laer is he case wih he Federal Housig Fiace Agecy i he USA, for example, ad i he UK. The goverme deparme wih policy or operaioal or legal resposibiliies for he secor is ofe i a beer posiio o gai access o admiisraive iformaio for saisical purposes ad should also be well-iformed abou he secor ad may eve have access o addiioal useful backgroud iformaio. Daa Sources.2 I Caada, he USA ad several Europea couries ( 5 ), daa o resideial propery prices are colleced by he aioal saisical isiues or miisries. The source of official resideial propery price idices i Demark, Filad, Lihuaia, he Neherlads, Norway, Hog Kog, Sloveia, Swede ad he UK is daa gahered for regisraio or axaio purposes. I Germay, he Federal Saisical Office collecs prices from he local exper commiees for propery valuaio. The saisical isiues i Spai ad Frace calculae price idices from iformaio provided by oaries. I Belgium, Germay, Greece, Frace, Ialy, Porugal ad Slovakia, real esae agecies ad associaios, research isiues or propery cosulacies are he sources of price daa. Daa from ewspapers or websies are colleced for he compilaio of resideial propery price idices i, e.g., Mala, Hugary ( Origo ) ad Ausria ( Ausria Immobiliebörse ). The limied umber of cases of iegraio of differe daa sources o add value ad produce a beer idex is ieresig give he umber of couries ha repor muliple sources of iformaio o propery prices. I Germay, Irelad ad he UK, resideial propery price daa are, ier alia, provided by morgage leders. The price idex compiled by he UK s Deparme for Commuiies ad Local Goverme is based o a morgage survey coduced by he Coucil of Morgage Leders; he log ime-lag associaed wih he regisraio of propery owership rasfers udermies he use of he laer as a imely idicaor. I Germay, he Associaio of Germa Pfadbrief baks uses he daa of is member baks for compilig a resideial propery price idex..3 Comparabiliy bewee idices ca be very limied as a resul of he differe daa sources lised above morgage versus cash purchases; urba versus rural prices; he prices of old properies versus ew properies; valuaios versus adverised prices versus iiial offer prices versus fial rasacio prices. The e resul is ha published idices ca i pracice measure very differe aspecs of he price developme i he housig markes. The deployme of differe daa sources ad compilaio pracices, ad he use o which he idex is pu (i.e., he idex ( 4 ) See for example Chiodo, Heradez-Murillo ad Oryag (2). ( 5 ) Regardig he daa sources i EU couries, see also Eiglsperger (2). Hadbook o Resideial Propery Prices Idices (RPPIs) 5

118 Mehods Currely Used purpose) all explai he wide variaio boh i imeliess ad i revisios policy. Idex Mehodology.4 The ihere difficulies wih price measureme ad he varyig daa sources used, lead o a array of differe mehodological approaches beig adoped i he cosrucio of house price idices. Qualiy (Mix) Adjusme.5 Qualiy adjusme, o corol for composiioal chages (mix-adjusme) ad for chages i he qualiy of he idividual properies, is a esseial par of idex mehodology. I esures ha price comparisos are o a like wih like basis ad avoids he possibiliy of bias i he series whe, for isace, he qualiy of he housig sock is improvig as a resul of, amogs oher reasos, reovaios o he dwellig, which ca ake various forms, such as he moderisaio of kiches ad bahrooms, he iroducio of improved isulaio ad ceral heaig or air codiioig sysems. Qualiy adjusme echiques also play a impora role i he compilaio of house price idices because houses ha come oo marke will chage from period o period..6 Qualiy adjusme is applied i a umber of differe ways. For isace, a resideial propery price idex for Esoia is derived from ui values, i.e., he average rasacio price per square mere of floor space (i his paricular case, he sum of he value of all real esae rasacios divided by he sum of he square meres of floor space of all real esae sales, wih ouliers excluded). Bu ui value idices based o price per square meer of srucure floor space, whils adjusig for he size of he dwelligs i each period, does o adjus for differeces i he qualiy of cosrucio or he age of he srucure ad perhaps more imporaly, does o adjus for chages i he mix of plo sizes i he sample of properies sold i ay paricular period. Oher chages o he feaures of he house ca poeially occur which, ogeher wih geeral reds i he housig marke, are refleced i composiioal chages o he sample such as locaio, physical ad eviromeal ameiies, he geeral qualiy of housig, ec..7 The mai aleraive of mix-adjusme (discussed i Chaper 4) uilises a classificaio of dwelligs by wha are geerally recogised as impora price deermiig characerisics o calculae idividual price idices for each cell i he classificaio marix. The overall idex is he calculaed as he weighed average of hese sub-idices. Mix-adjusme is i essece a form of sraificaio. This mehod is adoped by, e.g., he Ausralia Bureau of Saisics o corol for composiioal chage o compile quarerly house price idices for each of he eigh capial ciies. Their approach sraifies houses accordig o wo characerisics: he log-erm level of prices for he suburb i which he house is locaed, ad he eighbourhood characerisics of he suburb, as represeed by he ABS Socio-Ecoomic Idexes for Areas (SEIFA) ( 6 ). I pracice, he umber of characerisics icluded i he classificaio is ofe limied by he umber of observaios ha ca regularly be foud for each cell, i.e. by he abiliy o populae he price-deermiig characerisics daabase from he available daa sources as well as by he availabiliy of iformaio o price-deermiig characerisics..8 The mos sophisicaed form of qualiy adjusme used by couries is he hedoic regressio approach (discussed i Chaper 5) which uses a regressio model o isolae he value of each of he chose characerisics ad corol for chages i he characerisics of he properies sold. Bu his mehod is usually more daa iesive. I is someimes used i cojucio wih sraificaio (by ype of srucure ad locaio). The use of hedoics i he compilaio of resideial propery price idices is, i large par, a fairly rece iovaio. Couries which publish idices ha have bee compiled usig hedoic regressio iclude Ausria, Germay, Irelad, Filad, Frace, Norway ad he UK. The hedoic model used i he compilaio of he Norwegia house price idex icludes oly a few explaaory variables ad does o adjus for housig sadards ad for he age of he buildig; ( 7 ) he idex adjuss oly for size ad locaio of he dwellig. The idex is likely o be biased (uless he age of he srucure ad ype of dwellig sold is sable over ime). This shorcomig is ackowledged by Saisics Norway..9 A addiioal mehod used i, for example, he USA ad Caada, is he repea sales mehod (described i Chaper 6); i.e., he Case-Shiller home price idex i he USA ad he Terae -Naioal Bak House Price Idex i Caada. This approach maches pairs of sales of he same dwelligs over ime. I requires a huge daabase of rasacios ad is o used by ay of he Europea idex compilers..2 I is ieresig o oe ha oe of he resideial propery price idices for Germay is based o daa ha is limied o good qualiy dwelligs, which migh imply ha he issue of qualiy adjusme is by-passed. I pracice, here could be a buil-i measureme problem, sice i is ulikely ha he marke defiiio of good qualiy is idepede of he geeral icrease i housig sadards over ime. For his reaso here is poeial for bias i he resulig idex i he loger erm. This is i addiio o ay cocers abou samplig ad, i paricular, he ( 6 ) See hp:// ( 7 ) As was see i previous chapers usig he daa for he ow of A, he age of he srucure is a impora price deermiig characerisic. 6 Hadbook o Resideial Propery Prices Idices (RPPIs)

119 Mehods Currely Used capabiliy of good qualiy housig o be able o represe he price red of all houses..2 I ca be see from he above paragraphs ha wo crucial quesios for all qualiy adjusme procedures are: () wheher he chose characerisics used for qualiy adjusme are he mai deermias of price differeces, ad (2) wheher he applicaio of differe echiques o he same daa se will produce he same resuls (i.e., he issue of saisical robusess). I realiy, while some of he price-deermiig characerisics such as he size of he livig area are easy o measure, oher impora facors such as locaio ( 8 ) ad he qualiy of cosrucio, ca be iherely difficul o capure ad measure. Also, i should be oed ha he applicaio of differe qualiy adjusme echiques o he same daa se will o ecessarily produce he same resuls. ( 9 ) The Value of Mea-Daa.22 A umber of orgaisaios have websies providig mea-daa o he resideial propery price idices published by differe couries. Mos paricularly, he Bak for Ieraioal Selemes provides such iformaio (see he earlier referece). This is i addiio o ay iformaio provided by idividual couries o, for isace, he websies of he aioal saisical isiue or ceral bak..23 As well as providig he user wih guidace o he sreghs ad weakesses of a paricular price idex ad is appropriae use, a sysemaic ad more deailed aalysis of he mea-daa o he currely available saisics ad daa sources ca help o ideify: major gaps i daa provisio; opios for fillig hese gaps cos effecively from readily available sources; daa coherece issues; he scope for furher daa iegraio ad he eed for ew daa sources..24 Such a aalysis of he basic mea-daa also provides evidece of he compromises made i relyig o readily available daa ad where oe all-purpose house price idex is used for a muliude of purposes. For example, he mai official house price idex published i he UK by he Deparme for Commuiies ad Local Goverme (DCLG) uses sales weighs ad is appropriae for iclusio i, for example, a Cosumer Price Idex used ( 8 ) The physical locaio of a propery ca be measured raher precisely bu he problem wih locaio is oe of groupig of properies. Sraificaio ad hedoic regressio mehods eed o group ogeher sales of properies i he same locaio bu how exacly should he boudaries of a locaio be deermied ( 9 ) This poi is illusraed by he differig idices ha resuled from he applicaio of differe mehods of qualiy adjusme described i Chapers 4-8 above usig he same daa se for he ow of A. However, all of he mehods did resul i roughly similar reds i prices. for idexaio of beefis bu does o fully sui he eeds of users who wa o calculae wealh, where sock raher ha expediure weighs are mos appropriae. The laer may be addressed eiher by a re-weighig of he official idex or by referece o oe of he may idices published by leders. However, he laer suffer from limied coverage. Thus re-weighig of he official idex may provide a cos effecive soluio o fillig his paricular daa gap..25 A more deailed gap aalysis may poi o soluios ivolvig syheic esimaes, based o he iegraio of daa from differe sources. For example, i ca be oed i he coex of he UK ha he DCLG house price idex referred o above has he advaages of beig imely ad o subjec o revisio bu has he drawback ha i excludes cash purchases..26 A sysemaic approach o he cosrucio of idices of resideial propery prices i he UK migh coclude ha i is possible o suppleme he official idex wih iformaio o cash purchases from he Lad Regisry. Alhough he laer is less up o dae due o he ime-lag i regiserig rasacios i he official regisry, ime series modellig may be able o address his misaligme. The Lad Regisry cosrucs a repea sales idex by rackig he average growh i house prices usig muliple rasacios associaed wih he same home i a aemp o hold qualiy cosa. I he ex secio a series of case sudies are preseed relaig o he resideial propery price idices published i a selecio of couries. Case Sudies Case Sudy: Caada.27 I Caada here are four house price idices ha are currely available. These are Saisics Caada s New House Price Idex, he Terae-Naioal Bak Composie House Price Idex, he Caadia Real Esae Associaio s measure of average house prices, ad he Royal LePage Survey of Caadia House Prices. Each oe will be explaied i ur. The New House Price Idex.28 The New Housig Price Idex (NHPI) is a mohly price idex ha measures chages over ime i he builders sellig prices of ew resideial houses. Prices ha are colleced are from a survey of builders from various areas of he coury. I is a cosa qualiy price idex iasmuch ha he feaures ad characerisics of he uis i he sample are ideical bewee successive mohs; i oher words, he NHPI is a mached-model idex. Separae Hadbook o Resideial Propery Prices Idices (RPPIs) 7

120 Mehods Currely Used esimaes provided by he builder abou he curre value (evaluaed a marke price) of he los are also a impora par of he survey. Cosequely, give his iformaio, Saisics Caada also publishes a idepede price idex series for lad excludig he srucure. The residual value (oal sellig price less lad value), provides a idicaor of he red i he cos of he srucure ad is also published as a idepede series. A he prese ime, he hree varias of he NHPI are published for 2 meropolia areas i Caada..29 Housig marke aalyss, academics, ad he public use he NHPI as a imely idicaor of pas ad curre housig marke codiios. The NHPI is also used as a ipu i he compilaio of oher ecoomic saisics. For isace, i is used for esimaig cerai sheler compoes of he Cosumer Price Idex. Moreover, he Caadia Sysem of Naioal Accous uses he NHPI i esimaig he cosa price value of ew resideial cosrucio. Due o he level of geographic deail provided ad he sesiiviy o chages i supply ad demad, he NHPI series are of paricular ieres o he real esae idusry for providig a proxy esimae of chages i he value of resale houses sold. The iformaio provided by he NHPI is also of ieres o buildig coracors, marke aalyss ieresed i housig policy, suppliers ad maufacurers of buildig producs, isurace compaies, federal goverme agecies such as Caada Morgage ad Housig Corporaio (CMHC), ad provicial ad muicipal orgaizaios ha are resposible for housig ad social policy..3 The prices colleced are askig prices by he builders ad exclude he Goods ad Services Tax ad oher ax relaed rebaes. Missig prices as a resul for example of he absece of a sale by a builder i a paricular moh, are impued usig he bes esimae he builder ca provide as if a house was o be sold. No all ypes of housig are icluded i he NHPI. Codomiiums are excluded from he sample, while sigle-family deached uis as well as row (errace) ad deached houses are icluded. Give ha builders do o repor he price of buildig los uiformly, he lad price idices may be less accurae ad precise ha he overall NHPI. The same cavea applies o he derived residual values ha are used for cosrucig he price idices for he srucure oly. Large builders as well as smaller idepede builders are represeed i he sample used for he NHPI..3 From is cocepual basis, he Caadia NHPI measures chages i he price of ew houses oly, so i is o represeaive of resale houses i Caada (or for mos ew houses buil i he core of he ciies surveyed). The houses surveyed for he idex are geerally foud i ew racs i suburbs of he survey ciies where he price of lad is sigificaly lower ha i he ciy core areas. The movemes over ime i lad prices i suburbs are geerally differe ha he movemes i he well esablished areas of Caadia ciies. While he cosrucio price idex par of he NHPI is likely o be accurae (he cos relaed o buildig he house srucure is approximaely he same regardless of he area), he lad compoe probably udersaes resideial lad price iflaio for he exisig housig sock by a sigifica amou i rece years. ( ) Terae Naioal Bak Composie House Price Idex ( ).32 The Terae-Naioal Bak House Price Idex (TNBHPI) is a idepede esimae of he rae of chage of home prices i six meropolia areas, amely Oawa, Toroo, Calgary, Vacouver, Moreal ad Halifax. The price idices for he six meropolia areas are he aggregaed io a composie aioal idex. The idices are esimaed o a mohly basis usig rasacio prices for codomiiums, row/ow houses, ad sigle-family deached homes wihi he six meropolia areas..33 The TNBHPI uses he repea sales mehodology. Esimaig he idices is herefore based o he premise ha houses ha are raded more ha oce i he sample periods are of a cosa qualiy. The TNBHPI aemps o adjus for qualiy chages of he idividual housig uis by miimizig or elimiaig he ifluece of ay chages i he physical characerisics (e.g., reovaios, addiios, ec.). Isofar as (e) depreciaio of he properies ha are resold is egleced, he idex is likely o exhibi a small dowward bias. ( 2 ) Properies ha are affeced by ( ) See Figure. for a compariso of he NHPI wih oher idices for Caada. This figure provides suppor for he likely dowward bias of he lad compoe of he NHPI. ( ) Terae ad Naioal Bak of Caada, all righs reserved. ( 2 ) This dowward bias does o seem o show up i Figure., sice he TNBHPI is more or less i bewee is wo compeior idices ha cover he resale marke, bu he laer idices also do o make adjusmes for e depreciaio. Some housig ecoomiss argue ha he repea sales mehod may have a upward bias due o a sample seleciviy problem; i may be ha dwellig uis ha are sold more frequely ha he average ui are beig more iesively reovaed ad upgraded ad hece he qualiy of a repea sales ui has acually icreased bewee he wo sale daes (raher ha decreased due o depreciaio). 8 Hadbook o Resideial Propery Prices Idices (RPPIs)

121 Mehods Currely Used edogeous facors are excluded from he calculaio of he repea sales idex. These facors may iclude: oarms-legh sale; chage of ype of propery (for example afer reovaios); daa error, ad high urover frequecy (biaual or higher). The MLS Average Resale House Price Idicaor.34 The Caadia Real Esae Associaio (CREA) racks, o a mohly basis, he umber ad prices of properies sold via he Muliple Lisig Service (MLS ) sysems of real esae boards i Caada. The saisics are available by paid subscripio o hose who wa o use hem. Alhough he coverage of he idicaor is limied o oly houses ha are sold hrough he MLS, he sysem is quie acive wih abou 7 % of all markeed resideial properies usig i. The daa are available for over 25 urba markes defied by CREA, as well for he provices ad wo erriories; a aioal aggregae is also published..35 The idicaors are simple arihmeic averages of all sales prices i he marke of ieres, regardless of housig ype. I addiio, o cosideraio is give o he issue of composiioal shifs i he sample over ime or for dispariies i qualiy i he sample of uis. So a chage i he price idicaor could reflec may facors oher ha he rue price developme. These facors rage from qualiy differeces ha exis i he sample from period o period o he ifluece of ouliers wih exremely high or low prices due o special circumsaces. I heir mohly repors, CREA saff have recely published a weighed versio of he aioal idex (available back o 26 oly), wih weighs correspodig o he share of owed dwellig uis by major markes derived from he 26 Cesus. However, he price for each major marke is sill calculaed as a simple average, ad o aemp is made o rack he poeially differe reds amog various housig ypes. The oe major advaage of he MLS price idices over oher idicaors is heir imeliess, sice daa are ypically released wo weeks afer he referece moh. Bak of Caada - Royal LePage Survey of Caadia House Prices.36 Prices i he Royal LePage survey reflec he opiios of Royal LePage wih regards o he fair marke value for seve ypes of properies i a large umber of geographical areas. The iformaio obaied is based o local daa ad marke kowledge provided by Royal LePage brokers. The geographical coverage is broad, jus like he MLS daa, ad he classificaio of housig is more refied. For example, he survey icludes prices o four ypes of sigles or deached houses (deached bugalow, execuive deached wo-sorey, sadard wo-sorey, seior execuive), wo ypes of codomiium aparme uis (sadard ad luxury), ad a owhouse. Royal LePage sadardizes each ype i erms of he square fooage, he umber of bedrooms, he umber of bahrooms, he ype of garage, lo characerisics, he saus of he baseme, ad oher crieria. I addiio, he properies i he survey are cosidered o lie wihi average commuig disace o he ciy cere ad are ypical of oher housig i he eighbourhood. As log as he broker fillig i he survey sicks o hese guidelies, his is oe way of esurig some degree of cosa qualiy. A comparaive disadvaage of he Royal LePage price daa is is log publicaio lag..37 This survey is a basis for oe of he house price idicaors used by he Bak of Caada for moiorig developmes i housig markes i Caada ( 3 ). Despie he wealh of price iformaio o may oher ypes of houses i he Royal LePage survey, he idicaor developed a he Bak relaes oly o a subse of sigles ha were regarded as represeaive of he marke whe i was creaed i 988. ( 4 ) For Caada ad local markes, he Bak s price idicaor is calculaed as a weighed sum of he price of deached bugalow (weigh of.75) ad he price of execuive deached wo-sorey (weigh of.25). The price of each ype of housig is i ur a weighed sum of sub-regios, wih weighs se o be he sub-regioal share of uis sold as of a fixed dae i he lae 98s. The uis daa were obaied from MLS. A Comparaive Aalysis.38 A comparaive aalysis of he four ypes of propery price idices available i Caada is give i Figure.. The period of aalysis covers February 999 o March 2. All four series show a upward red i resideial propery prices over his period. However, he growh raes differ amog he four series. The NHPI recorded he smalles icrease a 55 % over he eire period. By coras, he MLS showed a icrease of 22 %, more ha double ha of he NHPI. The Terae-Naioal Bak House Price Idex ad he Bak of Caada- Royal Lepage idicaor icreased by % ad 92 % respecively. ( 3 ) hp:// ( 4 ) The Bak of Caada idicaor is limied o deached bugalows ad execuive deached wo sorey houses. Hadbook o Resideial Propery Prices Idices (RPPIs) 9

122 Mehods Currely Used Figure.. Four Resideial Propery Price Idices for Caada (February 999 = ) Feb-999 Ju-999 Oc-999 Feb-2 Ju-2 Oc-2 Feb-2 Ju-2 Oc-2 Feb-22 Ju-22 Oc-22 Feb-23 Ju-23 Oc-23 Feb-24 Ju-24 Oc-24 Feb-25 Ju-25 Oc-25 Feb-26 Ju-26 Oc-26 Feb-27 Ju-27 Oc-27 Feb-28 Ju-28 Oc-28 Feb-29 Ju-29 Oc-29 Feb-2 MLS Terae -Naioal Bak NHPI Bak of Caada - Royal Lepage.39 The higher growh rae of he MLS price idicaor may be explaied, a leas parly, by he average price mehodology which is used for is calculaio. As is well kow, his approach does o corol for period-o-period composiioal shifs ad his ca resul i a higher rae of icrease i he idex if here is a shif owards he upper ed of he marke i he houses beig sold. The NHPI s slower rae of icrease is probably explaied by he fac ha he idex, alhough i corols for house ype over ime, does o corol for locaio. New houses are cosruced farher ad farher away from he ciy cere where markes behave differely compared o properies sold i or ear he ciy core..4 All four idices show he drop i house prices ha occurred durig he ecoomic dowur which bega lae i 28. Bu he MLS idex sars fallig slighly sooer ha he hree ohers ad is drop is deeper. Compared o he oher hree idices, he fall i he NHPI sars slighly laer ad is o as acue. All four idices sar o show a upswig early i 29 bu he MLS idex sars o ur earlier while he urig poi from he NHPI idex occurs las. ( 5 ) I erms of volailiy, he MLS is he more volaile aroud is red due o he composiioal shifs i he sample of houses sold each moh. The oher hree idices, which o some exe adjus for qualiy chages, show less erraic behaviour over ime. Case sudy: Germay.4 Quarerly resideial propery price idex series for Germay are available from 2. Prior o ha dae he siuaio i Germay could be characerised as a ( 5 ) For a illusraio of he impac o urig pois of he differe mehodologies, see Shimizu, Nishimura ad Waaabe (2). 2 Hadbook o Resideial Propery Prices Idices (RPPIs)

123 Mehods Currely Used ucoordiaed se of differe idicaors provided by several privae isiues. These idicaors mosly lacked a clear mehodological foudaio ad had a resriced coverage. Moreover hey gave o some exe coradicory sigals. ( 6 ).42 The Federal Saisical Office of Germay (Desais) ook acio o improve he siuaio buildig o available daa sources. Germay had well-esablished cosrucio price saisics ad saisics o purchasig values of buildig lad. I addiio, a he local level, he aiowide isiuio of Exper Commiees for Propery Valuaio, regulaed by federal law, provided access o comprehesive daabases which coaied rasacio prices of buildig lad ad dwelligs ad he correspodig propery characerisics. The mai barrier o he exploiaio cerally of he available daa had bee he differeces i he collecio sysems across he federal saes ad amog he idividual local commiees. The mehods followed by Germay provide a ieresig example of daa iegraio i.e. he drawig o muliple daa sources. Resideial Propery Price Idices.43 Differe daa sources ad compilaio mehods are used o cosruc price idices for differe marke segmes. These are he combied o compue a resideial propery price idex coverig all ypes of properies ad sub-idices relaig o exisig ad ew dwelligs respecively. The weighs used i he compilaio of a price idex for exisig dwelligs are he rasacio expediures i he base-year broke dow io houses ad flas ad by he federal sae. For ur-key dwelligs, he weighs are derived from official buildig aciviy saisics ad for self-builds cosrucio weighs are used. Idices are published wihi 9 days of he ed of he reporig. Newly buil urkey-ready dwelligs ad exisig dwelligs.44 Daa is ake from he iformaio gahered by he local Exper Commiees for Propery Valuaio. This daa, ha is colleced a he ime a corac is cocluded, covers all sales (cash ad morgage) ad cosiss of acual rasacio price (boh cash ad morgage) ad a umber of price-deermiig propery characerisics ype of dwellig (sigle-family house, wo-family ( 6 ) See Hoffma ad Lorez (26). house, freehold fla); ype of house (free-sadig, erraced, semi-deached); ype of cosrucio (coveioally buil, prefabricaed); year of cosrucio; size of plo of lad; size of livig area; furishig/luxury elemes (kiche, saua/swimmig-pool, aic sorey); car parkig faciliies; characerisics of locaio (sae, disric, muicipaliy; geeral raig of locaio: simple/medium/good); umber of rooms/floors. I addiio, a lad valuaio is provided..45 A combiaio of hedoic echiques ad sraificaio (oe sraum for sigle-family/wo-family houses ad oe for flas i aparme blocks) is used o adjus for he effecs of qualiy chages i he ype of properies beig sold. The hedoic regressio mehod ha has bee adoped is he double impuaio approach, which was described i Chaper 5, where prices are esimaed boh for he base period ad for he compariso period. Ouliers are excluded. Newly-buil sigle family resideial properies ( 7 ).46 The compilaio of a price idex for his paricular ype of ewly-buil properies draws o iformaio from official coury-wide cosrucio price idices. Cosrucio price idices are available for various ypes of srucure (e.g., resideial/o-resideial buildigs, roads, road bridges) as well as for maieace work. Prices are colleced quarerly for abou 9 cosrucio operaios (icludig maerials). I oal, abou 3 prices are repored by abou 5 eerprises a every collecio dae. The prices refer o he rasacio prices relaig o coracs cocluded i he quarer, excludig value added ax (VAT), i.e., profis ad chages i produciviy are ake io accou. For self-builds, he cosrucio price idex for coveioally buil sigle-family resideial buildigs is used. A mached model approach is followed for he cosrucio of he idex. Prefabricaed dwelligs.47 The price idex uses official producer price saisics for idusrial producs, i paricular he price idex for prefabricaed sigle-family houses wihou a baseme wih a specific se of characerisics. Agai a mached ( 7 ) These are someimes referred o as self-buil properies. The builders iclude boh fuure owers who do a major par of he buildig hemselves ad fuure owers who ivolve a buildig firm ha is resposible for he mai par of he buildig work (where he ower fializes he work). Hadbook o Resideial Propery Prices Idices (RPPIs) 2

124 Mehods Currely Used model approach is adoped for he compuaio of he idex. A specific feaure of prefabricaed dwelligs is ha he coracs usually provide for he purchase/sale of complee houses (e.g., sigle-family house wihou cellar), he characerisics of which do o chage sigificaly over he shor-erm. Buildig lad.48 The price idices for prefabricaed dwelligs ad self-builds exclude he cos of he lad. A price idex for buildig lad is compiled from official figures o he rasacio prices of buildig lad, recorded a he ime a corac is cocluded. Each daa se icorporaes he followig characerisics: locaio; characerisics of he muicipaliy; sale dae; size of plo; he deails of he oulie plaig permissio e.g. wheher for a house or for flas ad buildig size. Ulike Saisics Caada s NHPI, coverage is o resriced o developme racs he Germa idex aemps o cover all ewly-buil homes..49 The aggregae price idex for developed buildig lad is a weighed average, usig he oal sales value, of ui value idices for sub-aggregaes. These sub-aggregaes are formed o he basis of regioal differeiaio, maily a differeiaio by disrics, buildig area ypes ad muicipaliy size classes wihi federal saes. The federal saes are weighed by combiig daa o he oal of prices paid for developed buildig lad i resideial buildig areas ad i rural areas, urover achieved hrough buildig aciviy ad he umber of buildig permis for resideial buildigs wih oe or wo dwelligs. Case sudy: Japa Iformaio o Propery Prices.5 I Japa, official propery price idices oly relae o lad prices. Iformaio provided by he public secor icludes he Public Noice of Lad Prices (PNLP) coduced by he Miisry of Lad, Ifrasrucure, Traspor ad Tourism (MLIT), he Lad Price Survey of each prefecure, he Lad Value for Iheriace Tax of he Naioal Tax Agecy, ad he Lad Value for Fixed Asse Tax of each muicipal goverme. All of hese sources of iformaio represe appraisal values esimaed by licesed real esae appraisers..5 Iformaio o resideial propery price idices (icludig srucures) is colleced by he privae secor. The mos represeaive propery daa se is called REINS, which sads for he Real Esae Iformaio Nework Sysem. REINS is a daa ework ha was developed usig he muli-lisig service (MLS) of he US ad Caada as a model; he iformaio is obaied via real esae brokers. The REINS daa se coais boh he askig price whe he propery is pu o he marke ad he fial rasacio price a he ime of he sale corac. A secod, ad quie uique, housig price daa source is accumulaed hrough housig adveriseme vedors. Boh daa sources have bee used by he privae secor o compue ad publish housig price idices. However, all of hese idices have shorcomigs ad do o fully mee he eeds of users. MLIT has herefore begu a work programme which should lead o he cosrucio of a improved idex. This will be he firs resideial propery price idex o be published by he public secor. 22 Hadbook o Resideial Propery Prices Idices (RPPIs)

125 Mehods Currely Used Table.. Idices of Propery Prices Published i Japa Idex Sample Mehod Seasoally adjused? Ad (frequecy) Lad Price Cumulaive Chage Rae Idex(MLIT) Appraisal prices i Public Noice of Lad Prices by MLIT Precedig erm idex Avg. Volailiy No (Aual) Major Ciy Lad Trasacio Price Basic Saisic (MLIT) Sales prices Average value of ui price per square mere, media value, sadard deviaio, quarile, ec. No (Quarerly or aually) Urba Lad Price Idex (Japa Real Esae Isiue) Appraisal prices i Public Noice of Lad Prices by Japa Real Esae Isiue Precedig erm idex Avg. chage rae No (Semi-aual) Recrui Resideial Price Idex (Recrui Housig Isiue) Fial askig prices i Magazie or Olie prices i Magazie or Olie Overlappig Periods Hedoic Regressio Yes (Mohly) Resideial Marke Idex (Japa Real Esae Isiue, A Home Co., Ld., Ke Corporaio) Askig prices or sales prices Ui price per square mere (buildig age adjused by hedoic regressio) No (Semi-aual) Tokyo Area Codomiium Marke Price Idex (Japa Research Isiue, Limied Real Esae Iformaio Nework for Eas Japa) Sales prices regisered a he Real Esae Iformaio Nework for Eas Japa Hedoic regressio No (Mohly) Newly-Buil Codomiium Price Chage Idex (Tokyo Kaei Co., Ld.) Askig prices Movig average No (Quarerly) Source: Shimizu, Nishimura ad Waaabe Weighig mehod Sage of process No Appraisal value i Jauary s every year (published i he ed of March) No Survey afer sale regisraio (sales price) No Appraisal value i he ed of March ad Sepember every year Volume Offer made (fial askig price) No Offer made? (askig price or sales price) No Compleio of sales (sales price) No (askig price) Hadbook o Resideial Propery Prices Idices (RPPIs) 23

126 Mehods Currely Used A overview of all propery price idices i Japa is provided i Table.. This icludes idices based o lad appraisal values as well as idices relaig o propery sales. I is he laer ha geeraes he maerial for resideial propery price idices. Askig Prices ad Sellig Prices.52 I Japa, he seller of a house usually sells i hrough a real esae broker. Idividuals ha corac wih a broker have o sig oe of wo forms of a sales age corac: he exclusive agecy corac or he sole agecy corac. The oher opio is o selec a geeral agecy corac. These coracs are regulaed uder Aricle 34-2 of he Buildig Los ad Buildigs Trasacio Busiess Law..53 I he case of he exclusive agecy corac, he seller ca receive a repor a leas oce a week from he real esae broker, bu he seller loses he righ o ask aoher broker o fid a buyer ad o look for a buyer himself. I he case of he sole agecy corac, aoher broker cao be asked o fid a buyer, bu he seller ca look for a buyer o his ow ad he repor from he broker will be a leas bi-weekly. I he case of a geeral agecy corac, he seller ca look for a buyer o heir ow ad ask muliple brokers o fid a buyer. O he oher had, he seller does o receive repors from brokers..54 I he case of he exclusive agecy corac, he coraced broker mus regiser he lisig i REINS wihi five days of cocludig he lisig agreeme ad is required o widely look for buyers. I he case of he sole agecy corac, he broker mus regiser he lisig i REINS wihi seve days ad do he same. For regisraio i REINS, brokers are o oly required o record he askig price a he mome of regisraio bu also he fial rasacio price. Thus for some rasacios made via brokers, boh he askig price ad he fial rasacio price are regisered. Public Daa Gaherig Sysem of Trasacio Prices.55 MLIT has compiled ad published iformaio o propery rasacio prices sice 25. Propery rasacios are regisered by he Legal Affairs Bureau which he seds Chage i Regiser Iformaio o MLIT. Based o his iformaio, MLIT seds a quesioaire o he buyer o vaca los, lad wih buildigs, buildigs wih comparmealised owership (such as office, reail, ad aparmes) askig for he rasacio price. Nex, iformaio is added by real esae appraisers or heir couerpars. This iformaio icludes buildig use, lo codiios (lad form, ec.), road codiios (widh of froig road, ec.), disace o he eares railway saio ad oher iformaio relaed o coveiece, ad legal regulaios such as ciy plaig. The resulig Trasacio Case Daa colleced i his way is he made aoymous so ha he acual propery cao be ideified, ad is he published as rasacio price iformaio o MLIT s websie. ( 8 ) Sice eiher he supply of iformaio o rasacio prices or he supply of he iformaio requesed from real esae appraisers is madaory, o-respose ad imeliess are issues. The iformaio supplied, icludig he rasacio price, cao be idepedely verified. Time Lie for Buyig ad Sellig a House ad Price Accuracy.56 The choice of daa source is of imporace whe calculaig a housig price idex. There are various issues ivolved, such as he momes a which price daa is colleced, he chage i price (from he iiial askig price o he fial rasacio price), ad how imely he price daa is released. Figure.2, which is borrowed from Shimizu, Nishimura ad Waaabe (2), shows he real esae price iformaio which is currely available i Japa o a ime axis. O he righ, four sages are disiguished wih prices P o P4. The correspodig ime periods bewee hose momes are: he erm TM bewee he sar of he sellig process ad he mome a buyer is foud; he erm TM2 from whe a buyer is foud uil he sale corac is fialized; ad he erm TM3 bewee he fial sale corac ad he regisraio of he sellig price i he goverme s daabase. ( 8 ) See 24 Hadbook o Resideial Propery Prices Idices (RPPIs)

127 Mehods Currely Used Figure.2. Propery Iformaio Flow Timig of eves i real esae rasacio process Real esae price iformaio T.House placed o marke P.Askig price i Magazie or Olie ( weeks) TM T2.Offer made P2.Fial askig price i Magazie or Olie T3.Morgage approved (5.5 weeks) TM2 T4.Coracs exchaged T5.Compleio of sale wih Lad Regisry or REINS P3.Trasacio price i REINS T6.Trasacio regisered wih Lad Regisry (5.5 weeks) TM3 T7.Trasacio price survey based o Lad Regisry P4.Trasacio price i Goverme daabase Source: UK Office for Naioal Saisics.57 The average duraio of TM is 7 days. Tha is, o average a buyer is foud 7 days afer he seller eers io he sellig process; he maximum duraio was 3.72 years. The raio of P2 o P is.976 o average, meaig ha he price drops by 2.4 % from he iiial askig price o he las askig price. O average, TM2 is 39 days. The raio of P3 o P2 is.956 o average, i.e. o average he rasacio price is 4.4 % lower ha he fial askig price. TM3 is o average 9 days. This meas ha (for surveyed rasacio price daa) here is a ime lag of approximaely 3 mohs uil he sellig price is regisered i he goverme s daabase. The price differeials a differe pois i he sellig process ca, of course, vary over ime depedig o he sae of he ower-occupier housig marke. Hadbook o Resideial Propery Prices Idices (RPPIs) 25

128 Mehods Currely Used Figure.3. Four Resideial Price Idices for Japa (Jauary 999=) Ja-999 Jul-999 Ja-2 Jul-2 Ja-2 Jul-2 Ja-22 Jul-22 Ja-23 Jul-23 Ja-24 Jul-24 Ja-25 Jul-25 Ja-26 Jul-26 Ja-27 Jul-27 Ja-28 Jul-28 Ja-29 Jul-29 Ja-2 Jul-2 Source: Shimizu, Takasuji, Oo ad Nishimura (2) RRPI (Mohly) REINS (Mohly) PLPI (Yearly) ULPI (Half Yearly) Comparaive Aalysis of House Price Idices i Tokyo Meropolia Area.58 Figure.3 compares four propery price idices. The REINS daa are used by he Real Esae Iformaio Nework for Eas Japa ad he Japa Research Isiue who joily produce he Tokyo Used Codomiium Price Idex. This mohly idex has bee published sice 995 ad is cosruced usig a hedoic regressio mehod. The Recrui Resideial Price Idex (RRPI) is also a hedoic price idex ( 9 ), based o he fial offer price of properies i Recrui s magazie, ad relaes o re-sold sigle family homes ad codomiiums. This idex is also mohly ad has bee published sice Jauary 986 ( 2 ), alhough oly widely available i is curre form sice he begiig of 2. Two lad price idices, hus excludig buildigs, are show i Figure.3, he bi-aually ULPI ad he yearly PNLP. These are appraisal-based idices. ( 2 ) The propery price idices ha iclude he srucures clearly show a differe red ha he lad price idices. Also, he former bega o recover some years afer he fiacial crisis i 28 whereas he laer coiued o decrease. Noice ha he REINS idex is much lower ha he RRPI, i spie of he fac ha boh are hedoic idices. Case Sudy: Uied Kigdom.59 The UK probably has more house price idices published o a regular basis ha ay oher coury. The rage of resideial propery price idices ha are published i he UK maily sems from he ierrogaio ad exploiaio by differe orgaisaios of he differe daa ses which are geeraed a differe pois i he process of buyig ad sellig a house. The laer ofe akes place over a period of several mohs or more ad he paricular sage i his process a which he price is absraced ad eered io a idex ca impac o he measured rae of house price iflaio. I he UK he exploiaio of daa o propery prices occurs a he followig sages: As soo as he propery is o he marke. Askig price. Daa source: esae ages. ( 22 ) Publisher: esae ages, Fiacial Times ad propery websies. ( 9 ) The Recrui Resideial Price Idex uses he ime dummy mehod ad, i cosequece, is subjec o revisio (see Chaper 5). ( 2 ) See Shimizu, Takasuji, Oo ad Nishimura (2) for deails. ( 2 ) Shimizu ad Nishimura (26) (27) compare appraisal values ad sellig prices ad poi o he problems of valuaio errors ad smoohig i he appraisal-based idices. ( 22 ) Alhough o relaed o he issue of imig, a disadvaage of adverised prices ad morgage approvals is ha o all of he prices icluded ed i rasacios, ad i he former case, he price will ed o be higher ha he fial egoiaed rasacio price. 26 Hadbook o Resideial Propery Prices Idices (RPPIs)

129 Mehods Currely Used Morgage approved. Valuaio by morgage leder. Daa source: morgage leders. Publishers: various morgage leders. Morgage compleed. Morgage compleio price. Daa source: morgage leders. Publishers: The Deparme for Commuiies ad Local Goverme (DCLG) Trasacio regisered. Trasacio price. Daa source: Lad Regisry. The ime-lie for buyig ad sellig a house i he UK, icludig he differe pois a which iformaio is colleced ad used o produce a house price idex, is give i Figure.4..6 The UK currely has wo official house price idices. Oe is published mohly by he Deparme of Commuiies ad Local Goverme (DCLG) ad is based o iformaio provided by morgage leders, hrough he Coucil of Morgage Leders, o valuaio price a he poi whe he sale is compleed. I is published abou six weeks afer he referece dae for he house sale or, o average, abou four-five mohs afer a house is firs pu up for sale. I oly covers purchases ivolvig a morgage. The oher is published mohly by Lad Regisry based o sales of properies regisered wih hem. I is published a moh afer he referece dae; i.e., oe moh afer he regisraio of he sale bu suffers from a lack of imeliess due o delays from homebuyers or heir ages oifyig he Lad Regisry of rasfers of owership. Figure.4. House Purchase Time-lie SOLD DCLG, Lad Regisry, Regisers of Scolad, LSL/Acadamerics E UNDER OFFER Naiowide, Halifax M FOR Righmove I SALE RICS, Homerack T Source: UK Office for Naioal Saisics.6 Two morgage leders, Halifax ad Naiowide, publish idices based o heir valuaios of a propery a he ime ha hey gra a morgage. These idices are produced wihi a few weeks of he referece daa for graig he morgage ad abou hree o four mohs afer a propery is pu up for sale. They are a lile more imely ha he official DCLG idex bu have a much more resricive coverage wih o guaraee ha he properies ha hey have graed morgages o are represeaive of eiher all propery rasacios or all purchases ivolvig a morgage..62 Aoher idex is compiled by a orgaisaio amed Homerack, a busiess service compay which provides a rage of marke ielligece o he housig marke o orgaisaios across he resideial secor icludig Developers, Housig Associaios, Corporae Ivesors, Esae Ages, ad Local ad Ceral Goverme. Homerack coducs a mohly survey of esae ages who are asked o gives heir view o he achievable sellig price for each of four sadard propery ypes. I is he mos imely of all he published idices, beig published abou hree o four weeks afer he referece period wih i effec o oher ime-lags ivolved, bu i is a opiio survey of he likely sellig price of properies o he marke. A research based cosulacy firm, Acadamerics, also publishes a house price idex based o daa provided by he Lad Regisry. The LSL/Acadamerics idex is published a few weeks afer he ed of he referece period based o a idex of idices forecas mehod. The idex for each ime period is subsequely revised uil all rasacios have bee icluded. A idex based o askig prices adverised o he Righmove propery websie is also widely used i he UK. Hadbook o Resideial Propery Prices Idices (RPPIs) 27

130 Mehods Currely Used Table.2. Idices of Resideial Propery Prices Published i he UK DCLG ( ) Idex Sample Mehod Lad Regisry (mohly) Halifax Naiowide Homerack Righmove LSL/ Acadamerics Sample of Morgage Leders Sales Regisered i Eglad ad Wales wih a previous sale sice 995. Halifax loas approved for house purchase Naiowide loas approved for house purchase Survey of esae ages (valuaios) Askig prices posed o websie Sales Regisered i Eglad ad Wales Mix-adjusme ad hedoic regressio Seasoally adjused? Weighig mehod Sage of process Yes Expediure Morgage compleio (rasacio price o morgage docume) Repea Sales Regressio Yes Expediure Sale regisraio (rasacio price) Hedoic regressio (qualiy adjusme) Hedoic regressio (qualiy adjusme) Yes Volume Morgage approval (valuaio price) Yes Volume Morgage Approval (valuaio price) Mix-adjusme No? Expediure Achievable sellig price Mix-adjusme No Expediure (askig price) Forecasig model, icludes mix adjusme. Yes Volume Sale regisraio (rasacio price) ( ) Deparme of Commuiies ad Local Goverme. A review io house prices idices by he UK Naioal Saisicia ca be foud o web pages: hp:// uk/aioal-saisicia/s-guidace-ad-repors/aioal-saisicia-s-repors/idex.hml. Source: UK Office for Naioal Saisics.63 Table.2 summarises he scope ad defiiio plus he mai aspecs of compilaio mehod for he seve idices available i he UK show i he ime-lie i Figure.4. Give he differeces i defiiio, scope ad coverage i is o surprisig ha hese idices whe ake ogeher do o always show a cohere picure. Case Sudy: Idia.64 Moveme i prices of real esae, paricularly resideial housig, is of vial imporace o he macro ecoomy of Idia as well as o idividual households. I is o surprisig ha here is a user demad for a releva ad reliable idex for rackig house price movemes. Bu a lack of rasparecy i he resideial propery marke rasacios ad limied availabiliy of price iformaio pose impora challeges for keepig rack of real esae price dyamics..65 Regisraio of he propery price is a legal ecessiy for ay propery rasacio i Idia. So i priciple, he official auhoriy of propery regisraio has he deails of all rasacios durig a referece period. I heory he daa are available o a daily basis wih a moh lag from firs reporig a chage of owership. However, i is well kow ha he regisered prices of houses are grossly uderesimaed due o very high regisraio fees ad samp duy. The subseque obligaios for he payme of propery ax acs as a furher disiceive o idividual purchasers (excep corporae bodies) for revealig he exac sale price of a house. Furhermore, he regisraio procedure ad records maieace are o compuerized ad he records are maiaied i regioal laguages which ecessiaes furher work wih respec o brigig hem io commo forma..66 For hese reasos, he admiisraive daa relaig o he regisraio of chages of owership are o exploied ad a aleraive source of daa has had o be foud. This aleraive daa source relaes o marke daa based o rasacio prices colleced by he Naioal Coucil of Applied Ecoomic Research (NCAER), a aioal level research orgaisaio, from Reside Welfare Associaios (RWAs), real esae ages ad brokers. The valuaio daa of housig loas fiaced by Baks ad Housig Fiace Compaies (HFCs) are colleced o suppleme he acual rasacio price daa colleced hrough survey. These daa are he used o compile he Naioal Housig Bak s RESIDEX idex. The NHB RESIDEX Idex.67 NHB RESIDEX is a pioeerig aemp by he Naioal Housig Bak (NBH), a apex bak for he housig secor owed by he Ceral Bak of Idia, o measure resideial prices i Idia. As a pilo, five ciies Bagalore, Bhopal, Delhi, Kolkaa ad Mumbai were sudied. The process of daa collecio posed may challeges. There were also several mehodological issues relaig o he aalysis of daa. I he eve ad afer much work, he NHB lauched is firs RESIDEX for rackig prices of resideial properies i Idia, i July 27. The idex is based o acual rasacios usig he sale price 28 Hadbook o Resideial Propery Prices Idices (RPPIs)

131 Mehods Currely Used plus supplemeary daa o valuaios. Primary daa o housig prices is colleced from real esae ages by commissioig he services of a cosulacy/research orgaizaio of aioal repue, who obai rasacio prices. I addiio, daa o housig prices are also colleced from he housig fiace compaies ad commercial baks. The laer relaes o he valuaio prices associaed wih he housig loas coraced by hese isiuios..68 The salie feaures of NHB s RESIDEX are: I covers all ypes of resideial properies i fifee ciies. ( 23 ) Wih 27 as base, NHB RESIDEX idex is produced o a quarerly basis. ( 24 ) Aleraive series are compiled based o rasacio weighs ad sock weighs. I covers cash purchases ad purchases fiaced via a loa. I covers ew ad old cosrucios. The idex is cosruced usig weighed averages of price relaives. ( 25 ) ( 23 ) I due course, based o experiece ad depedig upo he availabiliy of daa, i may be expaded o cover commercial properies, as well. ( 24 ) 2 was ake as he base year for he pilo idex based o five ciies o be comparable wih he base year(s) of Wholesale Price Idex ad Cosumer Price Idex. Year o-yearprice movemes durig he period 2-25 were capured, ad subsequely updaed for wo more years i.e. up o 27. The idex was he expaded o cover e more ciies viz., Ahmedabad, Faridabad, Cheai, Kochi, Hyderabad, Jaipur, Paa, Luckow, Pue ad Sura, a which poi he base year shifed from 2 o 27. ( 25 ) I should be oed ha his is a weighed Carli idex ad as such is likely o have a upward bias; see CPI Maual (24), page 36. No qualiy adjusme is currely made i erms of locaio, size ec. I is revisable o ake accou of lae daa. Iformaio o he moveme i prices of resideial properies by locaio, zoe ad ciy, is also available, e.g., separae idices are available for each zoe i each of he fifee ows covered..69 For a coury he size of Idia he geographical dimesio is impora. For example, he ciy-wise price idices, show i Figure.5, help home buyers wih heir purchase decisios by eablig comparisos bewee localiies ad help builders ad developers i makig fuure ivesme decisios..7 Developme of he NHB RESIDEX o icrease is relevace o users coiues: The idex will be expaded i a phased maer o cover all 35 ciies i Idia havig a millio plus populaio as per he 2 Cesus. There is a proposal is o expad NHB RESIDEX o 63 ciies which are covered uder he Jawaharlal Nehru Naioal Urba Reewal Missio, he flagship aioal missio of he Goverme of Idia, o make i a Naioal Idex. I due course, based o experiece ad depedig upo he availabiliy of daa, i may be expaded o cover commercial properies. Figure.5. NHB RESIDEX Idices Idia Ciywise idex Delhi Begaluru Mumbai Kolkaa Bhopal Hyderabad Faridabad Paa Ahmedabad Cheai Jaipur Luckow Pue Sura Kochi Ja- Jue 28 Idex July- Dec 28 Idex Ja-Ju 29 Idex July-Dec 29 Idex Ja Mar 2 Idex Base Year (27) Idex Source: Naioal Housig Bak of Idia Hadbook o Resideial Propery Prices Idices (RPPIs) 29

132 Mehods Currely Used Case Sudy: Colombia.7 A house price idex for exisig houses, he IPVU, is compiled by he Baco de la República (Ceral Bak of Colombia). There are some oher idices ha relae o cosrucio coss ad he prices of ew housig uis, which are produced by DANE (he aioal saisics office of Colombia). No series is produced which amalgamaes he iformaio from he wo series o produce a idex coverig sales of all resideial propery i Colombia. ( 26 ) I he pas, cosideraio was give o he exploiaio of admiisraive daa bu his was foud o o be possible due o he complexiies ivolved. The IPVU.72 The projec o cosruc a price idex for exisig houses i Colombia, he IPVU, sared i 23. I he pas, he lack of access o basic iformaio had bee he pricipal barrier o he cosrucio of such idex. Afer cosulig wih several ledig baks abou he imporace of havig a measure of he value of exisig houses, he projec was lauched wih fiace from he Ceral Bak of Colombia (Baco de la República). The Saisics Secio of Baco de la República is i charge of he producio ad publicaio of he idex..73 The IPVU is resriced o he pricipal meropolia areas of Colombia, coverig he ciies of Bogoá, Medellí, Cali ad Soacha i Cudiamarca, ad Bello, Evigado ad Iaguí i Aioquia. The idex is calculaed usig iformaio from loa s appraisals repored by he morgage ledig baks Davivieda, BBVA, Av. Villas, Bacolombia, Colmea BCSC ad Colparia. I cosequece, he idex covers oly properies purchased usig a loa cash purchases are excluded. The baks provide he Baco de la República wih he commercial values ad addresses of all approved morgages. The prices which are eered io he idex are ake from idepede valuaios required by he morgage leder. The valuaio is close o he marke price whe he disburseme is made. The idex is published o he Bak s webpage, o a quarerly basis wih a lag of a quarer ad is revisable o a quarerly basis, reflecig he repea sales mehodology used (see below). I addiio a idex is published based o aual averages. Sub-idices are produced for he pricipal meropolia areas: Bogoa; Medelli; ad Cali..74 Houses are classified accordig o wheher hey receive subsidies or o. These relae o he VIS ad NOVIS idices, respecively. The receip of a subsidy depeds o he value ad locaio of he house. The erm Low-Icome Housig (LIH or VIS i Spaish) refers o resideces which are developed o guaraee he righ o a house for low-icome households. O each developme pla, he aioal goverme will esablish he maximum price ad ype of resideces mea for hese households. They will ake io accou, amogs oher aspecs, households access o credi markes, he amou of credi fudig available from he fiacial secor, ad available goverme fuds aimed o arge housig programs. ( 27 ).75 The mehodology applied is similar o he Case- Shiller repea sales mehodology. There is a lack of deailed iformaio o he characerisics of housig eeded o address he cosa mix requiremes of he Case- Shiller mehod hrough he use of sraificaio. However, progress is beig made wih he expecaio ha he iformaio provided by he morgage ledig baks will i he fuure iclude a wide array of daa o house specific characerisics. The curre lack of deailed characerisics is deal wih by daa ediig. If he propery shows a abormal price chage, i.e. if i is deemed o be a oulier, he price iformaio is discarded ad does o eer he idex. This is i order o preve re-modelled or egleced houses from eerig he idex. The idex is revisable, reflecig oe of he characerisics of he repea sales mehodology. A comparaive Aalysis.76 The deailed sub-idices which are available provide he opporuiy for a more-deailed aalysis of he marke i exisig homes. A idicaio of he rage of oupus available o he user is give by Figures.6-.. The idice omial uses he prices repored by he Baks, i.e., i is o deflaed; he idice real is he IPVU deflaed by he CPI average for he year. I he case of quarerly idices he IPVU is deflaed by he CPI quarerly average. ( 26 ) The iegraio of he wo idices would raise he issues of a lack of cosisecy ad icoherece. For example, he IPVU idex is based o idepede valuaios whe a morgage is applied for ad he DANE idex is based o askig price. ( 27 ) For more iformaio o his opic, see hp:// hm. 3 Hadbook o Resideial Propery Prices Idices (RPPIs)

133 Mehods Currely Used Figure.6. Quarerly Naioal House Price Idex for Exisig Uis Nomial ad Real (Base 99 = ) Idice Real Idice Nomial Q 989-Q 99-Q 99-Q 992-Q 993-Q 994-Q 995-Q 996-Q 997-Q 998-Q 999-Q 2-Q 2-Q 22-Q 23-Q 24-Q 25-Q 26-Q 27-Q 28-Q 29-Q 2-Q 2-Q 22-Q Source: Deparameo de Programació e Iflació Baco de la República, Colombia Real Nomial Figure.7. Quarerly Naioal Real House Price Idex for Exisig Uis Aual Perceage Chages Q 99-Q 99-Q 992-Q 993-Q 994-Q 995-Q 996-Q 997-Q 998-Q 999-Q 2-Q 2-Q 22-Q 23-Q 24-Q 25-Q 26-Q 27-Q 28-Q 29-Q 2-Q 2-Q 22-Q Real Source: Deparameo de Programació e Iflació Baco de la República, Colombia Hadbook o Resideial Propery Prices Idices (RPPIs) 3

134 Mehods Currely Used Figure.8. Aual Naioal House Price Idex for Exisig Uis ( ) (Base 99 = ) 2 2 Idice Real Idice Nomial Real Nomial ( ) The aual publicaio of he IPVU akes he average idex level over a period of welve mohs ad compares i wih he average for he previous welve mohs. Source: Deparameo de Programació e Iflació Baco de la República, Colombia Figure.9. Aual Real House Price Idex for Exisig Uis Pricipal meropolia areas (Base 99 = ) Source: Deparameo de Programació e Iflació Baco de la República, Colombia Cali Medelli Bogoá 32 Hadbook o Resideial Propery Prices Idices (RPPIs)

135 Mehods Currely Used Figure.. Aual Real House Price Idex for Exisig uis: Houses wih Subsidies (VIS) ad Houses wihou (NOVIS) (Base 99 = ) VIS NOVIS Source: Deparameo de Programació e Iflació Baco de la República, Colombia Case Sudy: Souh Africa.77 The followig case sudy from Souh Africa provides a illusraio of he obsacles o he compilaio of a resideial propery price idex whe a sigifica proporio of he housig sock relaes o iformal or radiioal dwelligs. Iroducio o he Souh Africa Housig Marke.78 Diverse dwellig ypes characerise he Souh Africa housig sock; i cosiss of formal, iformal, ribal, ad oher accommodaio i backyard or shared propery housig. Formal housig icludes sad-aloe houses (goverme subsidised ad privae houses), aached owhouses ad flas (aparmes), whereas iformal housig, ha is housig which does o have plaig cose ad will o be regisered by he auhoriies, icludes shacks (ypically buil ou of corrugaed seel plaes) ad radiioal dwelligs icludes rodavels ad hus made of radiioal meerials. Backyard housig cosiss of dwelligs ha are siuaed i a backyard of a propery wih a mai house, ad shared propery housig occurs whe more ha oe dwellig is cosruced o a sigle sad. The disribuio of he Souh Africa housig marke is as i Table.3. Accordig o he 2 Populaio Cesus, he umber of dwelligs i he formal marke has icreased by 37. % from 996 o 2; iformal housig by 26.4 % ad radiioal dwelligs by.6 %. I coras, backyard or shared propery has decreased by 4.5 %. Hadbook o Resideial Propery Prices Idices (RPPIs) 33

136 Mehods Currely Used Table.3. Teure Saus All Housig i Souh Africa (Accordig o Cesus 2) Housig ype Toal Ower-occupiers (%) Reers (%) Houses Subsidised housig (*) Flas Towhouses Iformal Tradiioal Backyard or shared propery Toal (*) Naioal Treasury esimae. Source: Saisics Souh Africa.79 I Souh Africa, builders ad/or propery developers cosruc all resideial propery, wih he excepio of ribal ad iformal housig. For he cosrucio of formal housig, a moeary rasacio akes place by fiacig he dwellig wih he moey of he buyer ad/ or a morgage bod. The dwelligs ad heir values are recorded a he local muicipaliy ad deeds office. For ribal ad iformal housig, very few moeary rasacios ake place. Where hey do ake place, he rasacios will be small cash expediures bu he dwellig will geerally o be recorded by a local muicipaliy. However, due o he demad for basic services, goverme has begu o record he umber of dwelligs i iformal selemes ad rural areas, bu he value of he dwellig is o recorded. The siuaio represes a excepioal challege for compilers of resideial propery price idices. Resideial Propery Price Idices i Souh Africa.8 There are various house idices published i Souh Africa, bu o by Saisics Souh Africa. Published house price idices iclude he Firs Naioal Bak (FNB) House Price Idex, he ABSA House Price Idex ad he Sadard Bak Media House Price Idex. ( 28 ).8 The FNB house price series is cosruced usig he average value of housig rasacios fiaced by FNB. To elimiae ouliers from he daa sample, rasacio values icluded i he sample mus be above 7 % of FNB Valuaios Divisio s valuaio of he propery bu below 3 %, while purchase prices recorded as above R- millio are excluded. I order o reduce he impac o he idex of rapid shor-erm chages i weighigs of differe propery segmes, due o relaive shifs i rasacio volumes, he weighigs of he differe marke segmes accordig o umber of rooms are kep cosa a heir 5-year average weighig. A saisical smoohig fucio ( 28 ) ABSA, FNB ad Sadard Bak have he majoriy of he bakig marke share i Souh Africa is applied o he daa ad he daa may be revised. The FNB idex is calculaed mohly..82 ABSA House Price Idex (HPI) measures he omial year o year house price movemes of houses purchased hrough approved morgage loas from ABSA. The ABSA HPI is based o he oal purchase price of houses i he 8m²- 4m² size caegory, priced a R3 millio or less (icludig improvemes). Prices were smoohed i a aemp o exclude he effec of seasoal facors ad ouliers i he daa. The idex is calculaed mohly..83 Sadard Bak s idex is based o he media house price of he full specrum of houses, usig a fivemoh movig average. Naioal daa from he Deeds Office are available oly wih a lag of up o ie mohs, so daa from Sadard Bak, which has a marke share of abou 27.7 % ad whose daa are geerally highly correlaed wih hose of he Deeds Office, are cosidered a good proxy for he aioal marke. The idex is cosruced o a mohly basis. Limiaios o he Cosrucio of a Resideial Propery Price Idex.84 I he cosrucio of he above house price idices oly formal housig (i.e., houses, owhouses ad flas) purchased by meas of a loa are icluded cash sales ad iformal housig are excluded. The difficuly i cosrucig a RPPI i Souh Africa is maily due o he lack of accepable esimaes o housig sock ad price iformaio o iformal ad radiioal dwelligs. These dwelligs make up 9.6 % of all srucures ad herefore cosiue a sigifica secor of he marke i Souh Africa..85 The secor also has is ow disic feaures. For example, wha defies a iformal dwellig? Resideial areas where a group of housig uis has bee cosruced o lad o which he occupas have o legal claim, or which hey occupy illegally; 34 Hadbook o Resideial Propery Prices Idices (RPPIs)

137 Mehods Currely Used Uplaed selemes ad areas where housig is o i compliace wih curre plaig ad buildig regulaios; Iformal dwelligs are ypically buil ou of corrugaed seel plaes for he walls ad roof (shack); The households hemselves mosly build hese dwelligs. Wha is a radiioal dwellig? This is a geeral erm, which icludes hus, rodavels ( 29 ), ec. Such dwelligs ca be foud as sigle uis or i clusers. The dwellig ca be made of clay, mud, reeds or oher locally available maerials. Primary Cocers i he Cosrucio of a Resideial Propery Price Idex.86 As saed elsewhere i his hadbook, wo mai problems i he cosrucio of a resideial propery price idex are he sporadic aure of rasacios ad a lack of machig due o he fac ha houses have uique price deermiig characerisics. I he case of formal housig, hese wo facors apply, bu for iformal housig, he secod facor is much less impora. Iformal dwelligs have, excepioally, sadard aribues sice mos of hem are made of corrugaed seel ad have oe o four rooms. Similarly heir locaio will ed o be i he same ypes of areas. I hese circumsaces he machig priciple may o be difficul o apply. I addiio, he fac ha he ower of he shack does o ow he lad ha he dwellig sads o, implies ha a decomposiio of he idex io lad ad srucures is o releva. The cesus 2 idicaed ha he disribuios of rooms are as i Table For radiioal dwelligs, he decomposiio io lad ad srucures is o releva eiher. I his case, he lad is allocaed o he perso or household by he chief of he ribal area, ad o cos or oly a small fee is levied. However, o esimae he price of he dwellig may prove problemaic if, ulike formal dwelligs, maily aural maerials are used i he cosrucio. ( 29 ) A circular ofe hached buildig wih a coical roof. Table.4. Disribuio of Number of Rooms i Iformal Dwelligs Number % of oal iformal dwelligs of rooms Source: Saisics Souh Africa Weighig of No-Formal Housig.88 Weighig of o-formal (iformal ad radiioal) housig will be complex i aure as he owers cosruc mos of he dwelligs hemselves ad moeary rasacios are limied. I addiio, maerials for he cosrucio of a iformal dwellig are mosly secod-had ad for radiioal dwelligs, aural maerials are used; cos esimaes for hese ypes of maerials are difficul o obai ad, ideed, hey may have bee gahered raher ha purchased..89 Alhough mos of he characerisics of he dwelligs are kow from he populaio cesus, he value of a iformal or radiioal dwellig is difficul o esimae because here are o orgaised markes ad he values are o regisered a a deeds or lad regisraio office. Also, he moveme of iformal dwelligs from oe seleme o aoher may pose a problem i he esimaio of he housig sock. The rae of ew cosrucios ad demoliios would be ukow, sice i is ucerai wheher all dwelligs ha were broke dow were ereced oce more i he ew area. Pricig of No-Formal Housig.9 No-formal house prices do o deped o ormal marke price deermias. The plo area, locaio, age ad reovaios ypically do o affec he price. The oly aspecs ha ifluece he cos of he dwellig are he maerials used ad his is of course iflueced by he size of he srucure; see Table.5. Hadbook o Resideial Propery Prices Idices (RPPIs) 35

138 Mehods Currely Used Table.5. Price Deermias Price deermias Tradiioal dwelligs Iformal dwelligs Formal dwelligs Area of srucure No No Yes Area of lad No No Yes Locaio No No Yes Age No No Yes Reovaios No No Yes Type of srucure No No Yes Maerials Yes Yes Yes Oher price deermiig characerisics No No Yes Source: Saisics Souh Africa Table.6. Perceage of Maerials Used i he Cosrucio of Iformal ad Tradiioal Dwelligs i Souh Africa Year Maerials used for roof Corrugaed iro/zic Orgaic maerials Asbesos Oher Toal Maerials used for walls Bricks Ceme block/cocree Corrugaed iro/zic Wood Mud ad ceme mix Wale ad daub Mud Oher Toal Source: Saisics Souh Africa.9 Price collecio for radiioal ad iformal dwelligs would be very difficul, sice he ower cosrucs he dwellig him/herself i mos cases ad moeary rasacio for he complee dwellig rarely akes place (he purchases of maerials are ormally i cash). The oly way o obai prices of ewly cosruced iformal ad radiioal dwellig is o coduc a survey of ewly cosruced dwelligs o a freque basis, sice mos of hese are o regisered a he deeds office, ad if regisered, he value of he dwellig is o recorded. A aleraive for hese ypes of dwellig, ye o be explored, is o compile a oioal cos of cosrucio idex based o he pricig of quaiy iformaio of he ype ha is show i Table.6. ( 3 ) ( 3 ) See Blades (29). Summary.92 I would be a very complex ask o calculae a comprehesive resideial propery price idex for Souh Africa, due o he diverse aure of housig i he coury. Differe mehods will be required for he collecio of prices for differe housig ypes. I addiio, weigh esimaio for each ype of housig will be difficul, as differe housig ypes have differe cos deermiig characerisics. Furhermore, he limied daa availabiliy for each housig ype exacerbaes he problem..93 The primary barriers o he cosrucio of a iclusive resideial propery price idex i Souh Africa are lised i Table.7 ad iclude: The absece of a orgaised marke for iformal ad radiioal housig; 36 Hadbook o Resideial Propery Prices Idices (RPPIs)

139 Mehods Currely Used The absece of reliable daa esimaes o he cos of iformal ad radiioal housig; The omadic life-syle. If a survey is coduced, movemes of iformal selemes from oe area o aoher pose a problem i erms of measurig he price developme of his ype of housig because prices are ormally colleced i specific areas; There is o regisraio of propery a he Deeds Office; Moeary rasacios do o always ake place o obai or build he dwellig; Prices do o deped o ypical price deermiig facors such as he price of lad, ad labour ad maerial coss. Table.7. Evaluaio of Barriers Possible problems Tradiioal dwelligs Iformal dwelligs Formal dwelligs Orgaised marke No No Yes Reliable price esimaes exis abou he cos of housig No No Yes Movemes of dwellig from oe seleme o aoher No Yes No Regisraio of propery a deeds office No No Yes Moeary rasacio a ledig isiuio No No Yes Trasfer of cash for buildig of srucure Someimes Someimes Yes Dwellig cosruced by propery developer or builder No No Yes Price depeds o ypical price deermiig facors No No Yes Source: Saisics Souh Africa Hadbook o Resideial Propery Prices Idices (RPPIs) 37

140

141 Empirical Examples

142 Empirical Examples Iroducio. The purpose of his chaper is o provide addiioal empirical examples dealig wih he cosrucio of house price idices based o he mehods ha were oulied i Chapers 5-9. These are broadly defied as follows: measures of ceral edecy (mea or media), hedoic regressio mehods, repea sales mehods, ad mehods based o appraisal daa. The followig hree secios of his chaper illusrae how he firs hree classes of mehods ca be implemeed o very small daa ses. Hopefully, workig hrough hese simple examples will eable readers o more readily follow he raher erse algebraic descripios of he various mehods ha were provided i Chapers The followig secio also illusraes various mehods ha ca be used o aggregae regioal house price idices io overall house price idices. This opic was o covered i ay deail i oher chapers of his Hadbook. ( 36K + 35K + 382K + 395K + 38K + 4K + 45K) / 7 = 388K Ceral Tedecy Mehods ad Sraificaio Mehods.3 Ceral price edecy esimaes, such as mea ad media prices, for cosrucig a RPPI are amog he leas daa iesive of all he mehods currely available o compilers. The basic mea or media mehods oly eed he sellig prices of he properies i a give locaio o build a price idex. Thus locaio iformaio will be required. I addiio, i is usual o sraify by he ype of dwellig ui ad if his is he case, he iformaio o he ype of dwellig ui will also be required..4 As a firs exercise, a idex is cosruced usig he mea price. I cosiss i calculaig he simple average of he observed prices for a sample of houses i a give period ad for a give geographical area. The idicaor, which ca be expressed i moeary erms or i idex form, is he measured simply as he chage (i per ce usually) of he average price of he sampled uis bewee wo periods. ( ).5 I is impora ha he sample of houses draw for calculaig he price idicaor be represeaive of he arge uiverse. Therefore some daa ediig may be required, he exe of which will deped o he isrucios ha he daa provider received from he compiler ad his willigess ad abiliy o deliver he daa accordig o he compiler s saed crieria. ( 2 ) For example, he sample of prices iiially colleced may iclude cerai propery ypes, such as agriculural lad, commercial properies, ad uis foud i muli-ui dwelligs, which are cosidered ouside he scope of he ieded idex. If his is he case, he hese observaios eed o be excluded from he sample whe measurig price reds for specific ypes of properies. Ouliers should also be ideified ad removed from he sample if i is believed ha hey may skew or disor i ay oher way he oucome..6 A simple umerical example usig 5 ad 7 price observaios respecively for periods ad 2 ( 3 ) will illusrae he approach used for measurig he progressio of he simple mea of house prices for a give geographical area, usually for a ciy or oher well-defied area. ( 4 ) Period house prices ad mea ( 35K + 352K + 378K + 366K + 42K) / 5 = 37K Period 2 house prices ad mea ( 36K + 35K + 382K + 395K + 38K + 4K + 45K) / 7 = 388K Oce he average prices for each period, e.g., a moh, a quarer or a year, are obaied, i is he sraighforward o calculae he period-o-period progressio (ypically i per ce) bewee $37K ad $388K. For isace, i his specific example, average house prices have icreased abou 5 % over boh periods..7 The presece of ouliers is miigaed whe he media price of properies i he sample is used isead of he mea price. For isace, if oe or more very expesive houses are sold i a give period, he resulig average price will likely o be ypical of houses ha o he marke a ha ime. As was discussed i Chaper 4, he media approach does o however compleely corol for period-operiod composiioal shifs i he sample of houses sold. I spie of his shorcomig he media is everheless a very popular resideial propery price idicaor maily because i is simple o compile ad is o very daa iesive, hus resulig i a imely idicaor. Moreover, is ierpreaio is sraighforward..8 Based o he same daa used for calculaig he mea, he media prices from he example samples for periods ad 2 are foud o be respecively $366K ad $382K. Cosequely, he media house price has icreased 4.4 % over hese wo periods..9 The above exercise is repeaed below bu wih a more exesive daase coaiig 5787 sampled price observaios for sigle-family houses draw from acual ( ) Regardless of he form used, expressed eiher i erms of values or idices, he per ce chage will be he same. ( 2 ) Of course he paricular circumsaces will dicae he exe of he daa cleaig. If he pricipal user is also maagig he collecio of iformaio, he he survey will be ailored o his or her eeds ad he exe of he cleaig will likely be less exesive. ( 3 ) Sice he umber of rasacios will likely vary from period o period, he umber of price observaios i he sample for each period will also vary. ( 4 ) Noe ha mos ceral edecy measures of house prices whe published do o ypically iclude idicaors of saisical qualiy such as he coefficie of variaio or sadard deviaio. 4 Hadbook o Resideial Propery Prices Idices (RPPIs)

143 Empirical Examples rasacios over may years for a small muicipaliy. ( 5 ) Some descripive saisics are preseed i Table.. Noe ha i his paricular case, he mea price of houses sold i ay year is always higher ha he correspodig media. For isace, i 22 he mea is $ agais 236 for he media; i 28 he mea is $ agais $34 6 for he media. Sice for ay give year he sample is characerized by he sale of some higher priced uis, his resul is o be expeced. I fac, he disribuio of prices is righ-skewed wih a skewess coefficie ragig from.44 o.87 over he various years. ( 6 ) Char. illusraes he disribuio of prices i 28 for he houses ( 5 ) Noe ha he required daa is obaied for calculaig eiher he media or mea prices; he seps ivolved are quie simple. Mos saisical sofware packages ca do he eire exercise quie rapidly wih lile ierveio from he compiler. ( 6 ) Skewess is a measure of he asymmery of a disribuio. Whe he degree of skewess is zero his meas ha he disribuio is symmeric aroud is mea. A posiive skew meas ha a relaively high umber of observaios from he sample is coceraed o he lef of he cere poi ad vice versa. ha were sold ha year. A similar graph cosruced for he remaiig years for his example yields similar price disribuios. ( 7 ). As for he aual per ce chages, hey vary accordig o he measure of ceral edecy ha is used here. ( 8 ) I some years, he differece i he resul bewee he media ad mea ca be quie small. For isace, i 22 he differece is oly oe eh of a perceage poi (8.2 % vs. 8. %) wih mea recordig a slighly higher icrease. I oher years, such as i 28, he differece is more proouced such as i 28 whe he aual chage measured usig he media price icreased by 6.8 % compared o a icrease i he mea price of 5.2 %. ( 7 ) Wih hese paricular daa, he mea was always greaer ha he correspodig media. This resul eed o always hold, paricularly wih very small samples. ( 8 ) Typically, he mea price will be higher ha he correspodig media price. However, whe mea ad media idices are formed, here is o presumpio ha he mea idex will icrease more rapidly ha he media idex. Table.. Meas, Medias, Perce Chages, Sadard Deviaios, ad Skewess Observaios Sadard deviaio Skewess Mea ($) Per ce chage 8.2% 7.6% 2.9% 5.4%.% 5.2% Media ($) Per ce chage 8.% 7.% 2.6% 4.3% 9.2% 6.8% Source: Auhors calculaios based o MLS daa for a Caadia ciy Char.: Disribuio of House Prices i Frequecy More Source: Auhors calculaios based o MLS daa for a Caadia ciy Prices Hadbook o Resideial Propery Prices Idices (RPPIs) 4

144 Empirical Examples. As is well kow, locaio plays a impora role i he deermiaio of o oly he level of house prices bu also i heir behaviour over ime. Therefore, o improve he reliabiliy of he idicaor, a sraified or mix-adjusme approach is rouiely recommeded, provided of course ha he iformaio for segmeig he marke (or sample of rasacios) is readily available. Geographical sraificaio has he advaage of reducig he effecs of period-o-period composiioal shifs i he housig uis ha characerize he simple mea ad media mehods. A popular approach o segmeig he housig marke is o group houses accordig o geographical area, hus esurig a cerai degree of homogeeiy of he uis foud wihi he sraa; oher locaioal effecs o house prices are also miimized by his mehod. Sraificaio ca also beefi users by providig hem wih addiioal house price idicaors for various sub-markes, such as by eighbourhood or ype of house. Goodma ad Thibodeau (23) add ha here is also a pracical reaso for groupig house by locaio i ha geographic variables are almos always icluded i daabases o housig rasacios. This iformaio should, whe available, be leveraged sice sraificaio makes efficie use of hese daa..2 Some couries, such as Ausralia (Braso 26), have ake advaage of he radiioally srog relaioship bewee price ad locaio ha ypifies resideial real esae by sraifyig he sample of properies accordig o geographical area or oher submarke srucures. This ca be a viable, albei imperfec, aleraive (or compromise soluio) for measurig cosa qualiy price chage i he absece of he resources ad he daa eeded o apply some of he more sophisicaed mehods for cosrucig a RPPI such as hedoic regressios. I fac, Prasad ad Richards (28) cosruc a measure of media house prices for six Ausralia capial ciies where he markes are sraified accordig o log-erm price movemes. Usig a daabase of over 3 millio observaios, he auhors fid ha heir approach o measurig chages i house prices, (i.e., usig he media approach bu sraified by zoe as defied by log erm price reds), will geerae resuls ha are comparable o hose usig more sophisicaed ad daa iesive mehods such as hedoics or repea sales..3 Sraifyig by geography hus likely esures ha he cluser of observaios wihi each group (or sraum) is more homogeeous ha observaios from he eire populaio. Sraificaio ca be exeded o iclude, i addiio o geography, oher price deermiig facors such as house ype ad/or umber of bedrooms. Groupig of houses by geography ad oher crieria will resul i a sample of eve more homogeeous properies, which is a desirable oucome for miigaig flucuaios i he idex ha are caused by composiioal shifs i he sample ha occur over ime. Oe poeial drawback however wih his approach is ha he compiler mus be aware ha a oo fiely defied sraum ca someimes geerae a hi sample of rasacios i ay give period, hus resulig i some samplig bias. The objecive is herefore o desig he idividual sraa i such a way ha he homogeeiy of price deermiig characerisics is balaced agais a sample size ha is sufficiely robus o yield a reliable ad represeaive measure of chages i house prices..4 As previously meioed, he cosrucio of submarke (or sraum) price idices ha are he aggregaed o he level of he marke of ieres will ofe use media prices i pracice. Cosrucig a mixed-adjused price idex cosiss i firs defiig he sraum. The secod sep is o calculae he media price for houses rasaced wihi he sraum for he period i quesio. Thirdly, he media prices for all sub-markes mus be weighed ogeher io a aggregae price measure for he marke uder sudy, which likely will be a ciy or eve he coury as a whole..5 The followig provides a simple example of he procedure ad seps ivolved wih calculaig a mixedadjusme price idex for resideial properies. ( 9 ) Sep : Defie he sraum. For he purpose of his exercise, he sraum is a geographical subdivisio of a ciy such as he wes-zoe or cere ow. There is o sric rule for delieaig he sraum i quesio bu geography appears o be a popular ad obvious choice which ca, if daa permiig, be combied wih oher housig feaures such as by house ype or accordig o umber of bedrooms i order o arrow he sraum. ( ) Sep 2: Calculae he media price for a sraum such as a eighbourhood for he releva period (moh or quarer). I is assumed ha he media will be he represeaive price of all sales i ha sraum. However, he mea price could aleraively be used. Repea his sep for fuure periods. Sep 3: Esimae he average price of houses sold for a give period by calculaig a sales weighed media of he eighbourhood or sraum prices. ( ).6 Suppose ha daa o house sales for wo periods ( ad ) ad hree geographical regios or eighbourhoods (A, B ad C) have bee colleced. Suppose prices are measured i housads of dollars ad ha for regio A i period, here were 4 sales wih prices 29, 45, 25 ad 3. Thus, he mea price for his period was 325, he media price was 3 (he arihmeic average of he wo middle prices 29 ad 3) ad he oal expediure was 3. For period, regio A had 5 sales of 3, 5, 25, 4 ad 275. Thus, he mea ad media price for his period was 345 ad 3 respecively ad he oal period expediure i regio A was 725. For regio B, here was oly oe sale i each period: ( 9 ) This example is loosely based o a example i McDoald ad Smih (29). ( ) This example uses he eighbourhood as he sub-sraum bu i realiy i ca be ay geographical area for which he compiler is cofide ha a sufficiely large eough sample of rasacios is available oday ad i he fuure o geerae a reliable represeaive price. ( ) This is assumig ha he compiler is usig sales as he basis for he weighig. 42 Hadbook o Resideial Propery Prices Idices (RPPIs)

145 Empirical Examples 5 i period ad 4 i period. Thus, he mea ad media price i period for regio B was 5, which was also equal o expediure i his period. The mea ad media price i period for regio B was 4, which was also equal o expediure i his period. For regio C, here were 3 sales i each period. For period, he sales were equal o 2, 3 ad 75 ad so he media price was 2, he mea price was 225 ad expediure was 675. For period, he sales i regio C were equal o 25, 35 ad 225 ad so he media price was 25, he mea price was 275 ad expediure was 825. These are he basic daa for he example..7 Suppose ha he media price i each regio correspods o houses of comparable qualiy over he wo periods beig compared. Sice i is desirable o have price imes volume equal o expediure i each period for each regio, oce a cosa qualiy price cocep has bee chose, he correspodig volume should equal expediures divided by price. Usig he media price i each regio as a cosa qualiy price for each ime period leads o he daa o expediures (he v ), prices (he p ) ad volumes or implied quaiies q = v / p ha are lised i Table.2 below. Table.2. Regioal Expediures, Prices ad Volumes (Implici Quaiies) Usig Media Prices as he Regioal Prices Period v A vb v C p A Source: Auhors calculaios based o MLS daa for a Caadia ciy p B p C q A q B q C Noe ha he regioal price idices for period are equal o p A / p A =., p B / p B =. 8, ad p / p =. 25 C C for regios A, B ad C respecively. Thus here are widely differig house price iflaio raes i he hree regios..8 A his poi, we ca apply ormal idex umber heory o he problem of aggregaig up he regioal price movemes io a overall house price iflaio rae. For example, Laspeyres ad Paasche overall price idices, P L ad P P, for period ca be cosruced. The formulae for hese idices are as follows: P L [ p Aq A + pbqb + pcqc ] [ p Aq A + pbqb + pcqc ] (.).2 Orgaizaios ha compile resideial propery price idices ed o use somewha differe formulas P P [ p Aq A + pbqb + pcqc ] [ p Aq A + pbqb + pcqc ] (.2) whe aggregaig over regios. A commo form of aggregaio is o use a weighed average of he regioal price.9 The CPI Maual (24) recommeds he cosrucio of superlaive idices if price ad quaiy daa idices o form a overall idex, usig he sales weighs are available for he periods uder cosideraio, as hey of period (or some average of sales weighs ha perai are i he prese siuaio. Two such superlaive idices o periods prior o period ). Deoe he share weighed are he Fisher ideal idex P F ad he Törqvis-Theil idex idex ha uses he sales weighs of period by P ad he P T, defied as follows for he period overall idices: share weighed idex ha uses he sales weighs of period by P P [ ] / 2. The period values ( 2 ) for he idices P, P ad F PL PP (.3) he arihmeic average of P ad P, deoed by P A, are defied as follows: P exp[.5( s + s )l( p / p ) +.5( s + s )l( p / p ) +.5( s + s )l( p / p )] T A A A A B B B B P s A ( p A / p A ) + s B ( pb / pb ) + sc ( pc / pc ) (.5) P exp[.5( s + s )l( p / p ) +.5( s + s )l( p / p ) +.5( s + s )l( / p )] T A A.5( s + s )l( p / p ) +.5( s + s )l( p / p )] (.4) B B B B C A C A C C B B B B geomeric average of he regioal price idices, p / A p, A p B / pb ad p C / pc, where he weighs are he arihmeic averages of he period expediure shares, s A, s B ad s C, ad he period expediure shares, s, s ad s..2 The resuls for he four idices defied by (.)- (.4) are lised i Table.3 below. I should be oed ha he wo superlaive idices, P F ad P T, are fairly close o each oher while he Laspeyres idex P L lies above hese superlaive idices ad he Paasche idex P P lies below hem. This is a ypical empirical resul. C C C C C C C C P s ( p / p ) + s ( p / p ) + s ( p / p ) (.6) A A A B B B C C C A B C where he period shares of sales i regios A, B ad C are give by s A v A /( v A + vb + vc ), s B vb /( v A + vb + vc ) ad s C vc /( v A + vb + vc ), respecively. Noe ha he Fisher (922) idex P F is equal o he geomeric average of he Laspeyres ad Paasche idices, P L ad P P ad ha he Törqvis-Theil idex P T is equal o a share weighed P A.5P + P (.7). 5 ( 2 ) The period values for all of he idices defied i his secio are se equal o. Hadbook o Resideial Propery Prices Idices (RPPIs) 43

146 Empirical Examples The above hree idices are also lised i Table.3. ( 3 ) I ca be see ha P is equal o P L ad is abou.26 perceage pois above he Fisher idex P i period, while F P is abou.77 perceage pois above P F. This resul is o uexpeced; he idices P ad P do o geerally closely approximae superlaive idices ad so heir use is o recommeded. ( 3 ) Fisher (922; 466) showed ha P defied by (.5) is equal o he Laspeyres idex P L defied by (.). Fisher also aribued he idex P defied by (.6) o Palgrave. Table.3. Overall House Price Idices usig Media Prices ad Aleraive Formulae o Aggregae over Regios A, B ad C Period PF PT PL P P P Source: Auhors calculaios based o MLS daa for a Caadia ciy PA PGL PGP.22 Two addiioal idices are lised i Table.3: he geomeric Laspeyres ad Paasche price idices, P GL ad P GP. The period values for hese idices are defied as follows: P exp[ s l( p / p ) + s l( p / p ) + s GL A A A B B B C l( p / p ) + s l( p / p ) + s l( p / p )] (.8) A B B B C C C P exp[ s l( p / p ) + s l( p / p ) + s GP A A A B B B C C l( p / p ) + s l( p / p ) + s l( p / p )] A B B B C C C (.9) C / p C / p Thus, he period values for each of hese wo idices are equal o share weighed geomeric averages of he regioal price idices, p A / p A, p B / pb ad p C / pc, where P GL uses he regioal share weighs peraiig o period, s A, s B ad s C, ad P GP uses he regioal share weighs peraiig o period, s A, s B ad s C. From Table.3 i ca be see ha he geomeric Laspeyres idex P GL is approximaely perceage poi below he superlaive idices P F ad P T while he geomeric Paasche idex P GP is approximaely perceage poi above he superlaive idices. ( 4 ) ( 4 ) I ca be verified ha he geomeric mea of P GL ad P GP is exacly equal o P T. Thus if P GL is below P T, he P GP will ecessarily be above P T. C )] )] Hece, he use of he geomeric Laspeyres or Paasche formulae cao be recommeded whe cosrucig aggregaes of regioal price idices; hese formulae are ulikely o closely approximae a superlaive idex, which ca readily be cosruced usig regioal daa o house price sales..23 The above mehods for aggregaig over regioal price idices assumed ha media prices i each regio correspod o houses of comparable qualiy over he wo periods beig compared. Now suppose ha isead of usig media prices i each regio o represe cosa qualiy house prices, i was decided o use mea prices i each regio. Agai, sice i is desirable o have price imes volume equal o expediure i each period for each regio, oce i is decided o use mea prices as he cosa qualiy a price cocep, he correspodig volume should equal expediures divided by price. Thus usig he mea price i each regio as a cosa qualiy price for each ime period leads o he daa o regioal expediures (he v ), prices (he p ) ad volumes (or implied quaiies q = v / p ) ha are lised i Table.4 below. Table.4. Regioal Expediures, Prices ad Volumes (Implici Quaiies) Usig Mea Prices as he Regioal Prices Period v A v B v C p A p B p C q A q B q C Source: Auhors calculaios based o MLS daa for a Caadia ciy 44 Hadbook o Resideial Propery Prices Idices (RPPIs)

147 Empirical Examples.24 Usig meas isead of medias as he cosa qualiy price i each regio chages he regioal price idices. The mea-based period regioal price idices are equal o p A / p A = 345 / 325 =. 654, p / p = 4 / 5 =.8 B B, ad p C / p C = 275/ 225 =. 2 for regios A, B ad C respecively. Agai, here are widely differig house price iflaio raes i he hree regios whe mea prices are used i place of media prices..25 Usig meas isead of medias, he various overall price idices defied by formulae (.) o (.9) ca be calculaed. The followig couerpar o Table.3 is obaied usig hese formulae applied o he daa i Table.4. Table.5. Overall House Price Idices usig Mea Prices ad Aleraive Formulae o Aggregae over Regios A, B ad C Period PF PT PL PP P P Source: Auhors calculaios based o MLS daa for a Caadia ciy PA PGL PGP I ca be see ha he use of mea prices isead of media prices for each regio has led o very differe idices; he superlaive idices P F ad P T are ow abou 3 perceage pois higher i period. However, he use of mea prices has led o Laspeyres ad Paasche idices, P L ad P P, ha are fairly close o heir superlaive couerpars. Sice he base period share weighed idex P is umerically equal o P L, P is also fairly close o P F ad P T. However, he oher wo shared weighed idices, P ad P A, are well above he superlaive idices. Fially, he Geomeric Laspeyres idex, P GL, is well below P T ad he Geomeric Paasche idex, P GP, is well above P T. I ay case, he use of mea prices i he housig coex is o recommeded sice he mea price of a house i a regio is ulikely o hold he qualiy of he houses cosa over ime. Hedoic Regressio Mehods.26 Chaper 5 discusses he use of hedoic echiques for calculaig house price idices. There are various ways of applyig his echique whe calculaig price idices i geeral ad resideial propery price idices i paricular. The hadbook preses hree varias of he hedoic approach. These are: he ime dummy variable mehod, he characerisics prices (or impuaio) mehod, ad he sraified hedoic mehod. Compared o he oher approaches, all hese hedoic mehods are ypically more daa iesive, ofe requirig more iformaio compared o he oher approaches for cosrucig cosa qualiy house price idices. This is because, i addiio o daa o prices, some perie characerisics (boh srucural ad eviromeal) for each observaio ha is used i he regressio are eeded wih hedoic mehods. I priciple, he more deailed he se of characerisics is ad he larger he sample of housig uis, he more reliable ad accurae will be he resulig price idex. ( 5 ).27 A hedoic model expresses he price of a good as a fucio of is price-deermiig characerisics (or aribues). Chaper 5 covered wo frequely used fucioal forms, which are he liear model ad he logarihmicliear (or semi-log) model, alhough oher opios (e.g., he Box-Cox echique) are ofe also reaed i he lieraure, hey are o covered here. The semi-log form is coveie because he ierpreaio of he regressio coefficies is sraighforward: oce muliplied by, he coefficies ca be ierpreed as he perce chage i he price of he house ha resuls from a ui chage i he explaaory variable..28 To illusrae as plaily as possible how he various hedoic house price idices are cosruced, he exesive versio of he daase used for calculaig he mea ad media prices above will also be cosuled for he followig examples. To simplify he preseaio, he umber of price-deermiig characerisics will be limied o four (coiuous) variables. These are: lo size (lad), umber of bedrooms (rooms), umber of bahrooms (bah), ad age (age). The iiial resuls for a regressio usig OLS wih a semi-log fucioal form for a sigle year (28) are summarised i Table.6. ( 5 ) Alhough mos hedoic regressios o house prices i he lieraure will ofe use may more explaaory variables, some sudies ad he examples i Chaper 5 show ha reliable hedoic price idices ca be obaied wih as few as four idepede variables. Hadbook o Resideial Propery Prices Idices (RPPIs) 45

148 Empirical Examples Table.6. Log-liear Regressio Resuls for a Simple Example Source SS df MS Number of obs = 796 F( 4, 79) = 56.2 Model Prob > F =. Residual R-squared =.44 Adj R-squared =.4382 Toal Roo MSE =.793 lprice Coef. Sd. Err. P> [95% Cof. Ierval] rooms bah age lad 9.39e-6.28e e-6.9 _cos Source: Auhors calculaios based o MLS daa for a Caadia ciy.29 From he regressio o a sample of 796 price observaios i is foud ha all four explaaory variables have he expeced sig ad are sigificaly differe from (usig a -es). The adjused R-squared (or coefficie of deermiaio) is 44 %, i.e., variaios i lo size, he umber of bedrooms, bahrooms, ad age accou for 44 % of house price variabiliy. By addig more explaaory variables o he regressio, he R-squared would icrease. I fac, by addig hree idepede variables (he presece of a fireplace, he presece of a garage, ad he age squared o accou for he o-lieariy associaed wih his variable) improved he adjused R-squared o 54 %..3 The regressio resuls ca be ierpreed as follows: A exra square foo of lo size will icrease he price of he house by.939%, ceeris paribus. Each addiioal bedroom adds.6% o he price of a house, ceeris paribus. A house wih a exra bahroom cos almos % more ha a house wihou he exra bahroom, ceeris paribus. By addig oe year o he house, is price declies (or he housig ui depreciaes) by.2%, ceeris paribus. The Lai locuio ceeris paribus meas all variables oher ha he oes beig sudied are assumed o be cosa. Turig o he variable umber of bedrooms as a example, i cao be cocluded ha houses wih more bedrooms will always cos more; oher facors are a play ha ca affec he price of he house such as is locaio ad age, ad overall qualiy of is cosrucio. Wha is mea by qualifyig he saeme by ceeris paribus is ha whe houses vary oly i erms of he umber of bedrooms for isace (i.e., hey are comparable i all oher respecs) he hose wih more bedrooms will cos more..3 Wha follows are simplified examples of he various mehods, as discussed i Chaper 5, for calculaig hedoic price idices. The ime dummy variable mehod is preseed firs. All examples use OLS regressios. The Time Dummy Variable Mehod.32 The ime dummy variable mehod is based o he esimaio of a logarihmic-liear hedoic regressio model where he daa are pooled across all periods. The model is give by equaio (6.5) ad is repeaed here for coveiece: T K τ τ = β δ + D + τ = k= l p β z + ε (.) k k where D is dummy variable which is equal o oe if he observaio comes from period ( =,..., T ) ad is zero oherwise. The ime dummy variable for he base period i.e., he sar period from which he subseque price chages will be compared is lef ou o avoid perfec collieariy of all dummies wih he iercep erm β, kow as he dummy rap. Wih he ime dummy variable approach he base period ad he subseque compariso periods, =,..., T, are he same uis of ime, i.e., a moh, a quarer, or a year, depedig o he paricular circumsaces such as he eeds of he users or daa availabiliy..33 The expoeial or ai-logarihm of he esimaed regressio coefficie dˆ measures he perce chage i cosa qualiy propery prices bewee he base period ad period. To udersad why exp( ˆ d ) is a measure of qualiy adjused, pure price chage, he followig seps have bee worked ou. The prediced logarihm of price i period for propery i, give is base period characerisics, z ( k =,..., K), is k 46 Hadbook o Resideial Propery Prices Idices (RPPIs)

149 Empirical Examples K l pˆ = ˆ β + ˆ β z (.) I period, he prediced logarihm of price mus be evaluaed a he propery s base period characerisics, because qualiy should be held cosa, hece k= k K * l pˆ = ˆ β + ˆ δ + ˆ β z (.2) Takig he differeces bewee he esimaes for boh periods yields * * ˆ l p ˆ l ˆ = l( ˆ / ˆ ) = δ p p p (.3) Expressio (.3) does o deped o. Tha is, he resul holds for all houses i he sample. As poied ou i Berd (99), he esimae of d ca be ierpreed as he chage i he logarihm of price due o he passage of ime, holdig all oher variables cosa. Takig he ai-log of d ˆ gives he esimaed price idex for period : P = exp( ˆ δ ) (.4) TD A similar exercise ca be doe for all oher periods. The ime dummy price idex goig from he base period o a compariso period ( < T ) herefore is exp( ˆ P = δ ) (.5) TD Obviously, he ime dummy hedoic idex for he base period is equal o. k= k k k depede variable. The righ-had side has he same explaaory variables (excep for he ime dummy variables) ha oe would fid i a oe period hedoic regressio. I his paricular case he explaaory variables are: lo size, umber of bedrooms, umber of bahrooms, ad age; he respecive parameers rage from β o β 4. Sice his is a pooled regressio, he esimaed parameers (or regressio coefficies) will be cosraied over he years for which daa are used i he regressio. The error erm ε idicaes if a observed value is above or below he regressio lie. Also o righ-had side of he equaio is he iercep erm, β..35 The regressio resuls usig he basic daa se are lised i Table.7. The coefficie of ieres is he oe 7 associaed wih year 27, ˆ δ. Is value is This coefficie is he rasformed o arrive a a esimae of he price idex (or he per ce chage i prices) for houses bewee years 26 ad 27. This rasformaio cosiss i akig he ai-logarihm of coefficie ˆ δ : 7 7 / 6 P TD = exp(.78548) =.829. Thus, he per ce chage i house prices bewee years 26 ad 27, holdig cosa all he characerisics of he house, is 8. %. Noe ha he mea ad he media yielded icreases of. % ad 9.2 %, respecively, for his same period..36 If a hird period (year 28) is added, he he hedoic regressio equaio becomes:.34 The followig example illusraes he procedure 2 for calculaig a ime dummy price idex. Suppose ha l p = Losize Bedroom Bahroom Age D β + β + β + β + β + δ δ deailed iformaio abou he houses ha were rasaced 2 2 over wo years ( = 26 o l= p27 = Losize Bedroom Bahroom Age D D β ) + β + β + β + β + δ + δ + is available. Usig ε (.7) he same iformaio as i he basic daa se above, he daa for all periods are combied io he followig pooled regressio equaio: l p = β + β Losize + β Bedroom + β Bahroom + β Age + e + β Bedroom + β Bahroom + β Age + δ D + ε (.6) The lef-had side of equaio (.6) has he logarihm of he price of house i i year (26 or 27) as he Table.8 coais he regressio oupu. The value of he ime dummy coefficie for year 28 is Takig is ai-logarihm geeraes a value of e =.4, showig δ Da icrease ε + i he cosa qualiy house price idex of 4 % bewee he base year, 26 ad he mos rece year, 28. By coras, he price progressio over he same period geeraed by he mea ad media was respecively 6 % ad 7 %. Hadbook o Resideial Propery Prices Idices (RPPIs) 47

150 Empirical Examples Table.7. Resuls from a Pooled Regressio for Years 26 ad 27 Source SS df MS Number of obs = 78 F( 5, 72) = Model Prob > F =. Residual R-squared =.457 Adj R-squared =.4555 Toal Roo MSE =.8386 lprice Coef. Sd. Err. P> [95% Cof. Ierval] rooms bah age lad e d cos Source: Auhors calculaios based o MLS daa for a Caadia ciy Table.8. Resuls from a Pooled Regressio for Years 26 o 28 Source SS df MS Number of obs = 254 F(6, 2497) = Model Prob > F =. Residual R-squared =.4684 Adj R-squared =.467 Toal Roo MSE =.8277 lprice Coef. Sd. Err. P> [95% Cof. Ierval] rooms bah age lad e d d _cos Source: Auhors calculaios based o MLS daa for a Caadia ciy.37 This echique ca be exeded o more ha hree periods as more periods become available. This cosiss i poolig more periods of daa ad addig addiioal ime dummy variables. However, muli-period pooled regressios are o ecessarily ideal for cosrucig a ime series sice addig ew periods of daa will likely modify he resuls from he previous periods. For isace, i he above example, whe year 28 is added o he previously pooled regressio, he coefficie for year 27 becomes.78257, which i his specific case is oly slighly differe compared o he esimae obaied wih he regressio of Table.7, where he correspodig coefficie was Moreover, he sabiliy of he coefficies i a pooled regressio ca become a issue as he umber of periods expads..38 A aleraive approach meioed i Chaper 5 is o use he adjace-period ime dummy variable echique. If he hedoic regressio is based o wo cosecuive periods ad +, he hedoic relaioship becomes: K τ + τ + β δ = + D + k= l p β z + ε (.8) k k I he coex of he hree periods of daa used i he above examples, a hedoic regressio is firs ru for periods ad, ad he a secod regressio is ru for periods ad 2 usig he four characerisics. The regressio oupu for he firs adjace period regressio is obviously he same as i Table.7, ad he resulig period-o-period price idex yields a esimae of 8.. Table.9 shows he regressio oupu for adjace years 27 ad Hadbook o Resideial Propery Prices Idices (RPPIs)

151 Empirical Examples Table.9. Resuls from a Pooled Regressio for Years 27 ad 28 Source SS df MS Number of obs = 67 F(5, 664) = 27.9 Model Prob > F =. Residual R-squared =.4497 Adj R-squared =.448 Toal Roo MSE =.8282 lprice Coef. Sd. Err. P> [95 % Cof. Ierval] rooms bah age lad e e-6.35 d _cos Source: Auhors calculaios based o MLS daa for a Caadia ciy.39 The cosa qualiy price idex is calculaed as he ailogarihm of he coefficie for year 28 (.55537), so ha he idex becomes exp(.55537) =. 57. Recall ha his is he price chage from period 27, o from he base period 26. From hese resuls, a ime series ca be cosruced by chaiig he wo period-o-period idices (sarig wih he value for he base period): idex, i a similar way as i a ypical price idex formula, bu where he regressio coefficies assume he role of he prices ad he quaiies are he quaiies are he umber of uis of characerisics. Thus, he hedoic equaio is esimaed for each ime period separaely. The liear hedoic models for he base period (26) ad for period (27) are 6 ; P 8 / TD, chai =.8.57 =. 43. This resul p = β + β Losize + β 2 Bedroom + β 3 Bahroom + β 4 Age + ε differs oly slighly from he full-period pooled regressio (see Table p.8) = β where + β Losize we esimaed + β 2 Bedroom a price chage + β 3 Bahroom of + β 4 Age + ε (.9) 4. % over he eire period. Now, wih chaiig adjace p = β + β Losize + β 2Bedroom + β 3 Bahroom + β 4 Age + ε period ime dummy idices, he esimaed price chage is 4.3 %. p = β + β Losize + β Bedroom + β Bahroom + β Age + ε (.2) 7 / 6 P TD =.8 Characerisics Prices or Impuaio Mehod.4 The ex hedoic regressio approach preseed i Chaper 5 is he characerisics prices or hedoic impuaio mehod, heceforh simply he characerisics mehod. Applyig his mehod o he same daa as previously used, a qualiy-adjused price idex is esimaed. For ease of preseaio ad ierpreaio, a liear model will be regressed o geerae he resuls. ( 6 ).4 The characerisics prices approach uses he implici prices of he characerisics of he model (he regressio coefficies) as he basis for cosrucig he price ( 6 ) There is ohig o preve however he use of a semi-log or log fucioal form. Boh ca be used wih his hedoic approach Esimaig hese equaios o he sample daa from 26 ad 27, respecively, usig OLS regressio, geeraes he resuls show i Tables. ad.. I his example, he implici price of a exra bedroom i 26 is $24329 while each addiioal bahroom will add $439 o he price of he house. The resuls for 27 i his highly simplified example are udersadably differe from hose for 26: a addiioal bedroom ow seems o icrease he price by $3547, while he price of a exra bahroom is ow esimaed o be $ ( 7 ) ( 7 ) Noe ha he coefficies for he umber of bedrooms are somewha volaile bewee boh years. This is o be expeced because hedoic regressios are ofe characerized by he presece of mulicollieariy bewee hese wo predicor variables. I should be sressed however ha mulicollieariy does o i iself affec he accuracy of he overall idex. This pheomeo is oly a issue if a accurae moeary value is eeded for he value of a addiioal bedroom ad/or for a addiioal bahroom, such as would be he case wih a propery assessme exercise. I should also be added ha for he purpose of his simplified exercise, he sample size is relaively small. This ca also explai why someimes he resuls are o quie as robus as is ofe he case wih larger samples. Hadbook o Resideial Propery Prices Idices (RPPIs) 49

152 Empirical Examples Table.. Resuls from a Regressio for 26 Source SS df MS Number of obs = 834 F(4, 829) = 4.49 Model 2.482e e+ Prob > F =. Residual 3.542e e+9 R-squared =.457 Adj R-squared =.429 Toal 5.96e e+9 Roo MSE = price Coef. Sd. Err. P> [95 % Cof. Ierval] rooms bah age lad _cos Source: Auhors calculaios based o MLS daa for a Caadia ciy Table.. Resuls from a Regressio for 27 Source SS df MS Number of obs = 874 F(4, 869) = Model e e+ Prob > F =. Residual 4.572e e+9 R-squared =.4385 Adj R-squared =.4359 Toal 8.397e e+9 Roo MSE = 7252 price Coef. Sd. Err. P> [95 % Cof. Ierval] rooms bah age lad _cos Source: Auhors calculaios based o MLS daa for a Caadia ciy.43 The ex sep is o compue a hedoic price idex from he regressio resuls. A price idex for 27 compared o period 26 ca, for example, be expressed as K characerisics are valued a heir implici prices i he base period ad i he curre period. Table.2 liss he average sample values for he characerisics i his example. Usig hese values ad he coefficies from Tables. ad., he Laspeyres-ype hedoic idex bewee he base year (26) ad 27 is compued as ˆ ˆ k zk + z + ˆ z + ˆ z + ˆ β β β β β β z4 k= P = = (.2) K ˆ β + ˆ β z + ˆ β z + ˆ β z + ˆ β z ˆ β z k k 7 / ( ) + ( ) + ( ) + (5 k= P = ( ) + ( ) + ( ) + (5 where z k is he sample mea value of he k-h characerisic i he base period; z =. Price idex compilers will recogize ha he idex described P = by (.2) is a Laspeyres-ype =.82 7 / ( ) + ( ) + ( ) + ( ) ( ) + ( ) + ( ) + ( ) price idex: he esimaed characerisics prices i period (26) ad period (27), ˆ β k ad ˆ β k, are weighed by The 8.2 % icrease i prices so obaied compares, i his he average base period quaiies of he characerisics. paricular case, quie closely wih he 8. % obaied usig Pu differely, he average base period quaiies for all he ime-dummy approach from Table.7. 5 Hadbook o Resideial Propery Prices Idices (RPPIs)

153 Empirical Examples Table.2. Mea Values of he Characerisics for he Base Period (26) Mea Sd. Err. [95 % Cof. Ierval] rooms bah age lad Source: Auhors calculaios based o MLS daa for a Caadia ciy.44 For subseque periods, he compiler has a decisio o make. He or she ca use he same base year quaiies o calculae he subseque idices usig he Laspeyres formula bu replacig he implici prices i he umeraor wih he releva oes. Aleraively, quaiies (mea characerisics) from he previous period could be used o geerae period-o-period price idices. These bilaeral idices would he be chaied o creae a coiuous ime series of liked idices. Oher opios are also available, ad hese are discussed i Chaper 5, bu he mechaics of cosrucig he idex remai esseially he same as preseed here. The Repea Sales Mehod.45 The mos sigifica problem wih usig (osraified) media or mea rasacio prices o measure reds i houses prices is ha he variaio i he composiio of he sample of properies sold from period o period is o always accuraely accoued for. This issue ca be parially circumveed by cosrucig a RPPI based o he repea sales mehod, which was discussed i Chaper 6. I fac, oe very popular house price idex ha is closely scruiized i he U.S., he Case-Shiller house price idex, is based o he repea sales mehodology..46 The sraegy for cosrucig a repea sales house price idex is quie sraighforward. I cosiss i comparig he chage i he price of ideical properies ha have sold a wo pois i ime. I oher words, i uses mached (or like-for-like) samplig as he basis for selecig he uis ha will be used i he calculaio of he idex. For he repea sales approach o be racable, oe mus have access o a large daabase of rasacios coverig a fairly log period. Oherwise he daa eeds are relaively modes: wih he basic repea sales mehod, oly iformaio o he dwelligs address (or aoher locaio ideifier) is required i order o ideify which uis have sold repeaedly, i addiio of course o he sellig price ad he sale dae. ( 8 ).47 A simple example ca illusrae he applicaio of he repea sales mehodology. ( 9 ) Assumig he objecive is o esimae a aual idex of price chage bewee 28 ad 2, Table.3 shows daa for a small umber of rasacios. Propery A sold i 28 for $ ad sold agai i 29 for $2 ; propery B is sold i 28 for $75 ad sold agai i 2 for $22 ; propery C sold i 29 for $8 ad sold agai i 2 a he same price. ( 8 ) Oe assumpio is ha he qualiy of he house has o chaged over he period bewee he wo sales. If iformaio abou he feaures of he propery is available o he compiler, he i is possible o exclude from he calculaio hose observaios ha have udergoe sigifica chages over ime ad ha are likely o affec he price ad hus disor he idex. Furhermore, give ha high urover is ofe a sig ha cerai udesirable feaures for ha paricular propery may be a play so ha hese observaios ca also be excluded from he calculaio. I should also be meioed ha repea-sales idices are o always sricly cosa qualiy price idices sice houses are ofe subjec o some loss i value over ime as a resul of depreciaio. Cosequely, repea-sales price idices ypically uderesimae rue house price iflaio, uless some correcive adjusme is made o he esimaes. If he purpose of he idex is o ac as a shor- o medium-erm idicaor of house prices, he he issue of depreciaio which he repea-sales approach does o hadle adequaely ca perhaps be se aside. ( 9 ) The example is parially draw from he Caadia Terae-Naioal Bak repea sales price idex documeaio: hp:// Table.3. Repea Sales Daa Propery A $ $2 No sale Propery B $75 No sale $22 Propery C No sale $8 $8 Average $37 5 $5 $2 Hadbook o Resideial Propery Prices Idices (RPPIs) 5

154 Empirical Examples As a firs sep, he price chage over he 28 o 2 period is esimaed usig he mea of prices approach. The aual average prices from 28 o 2 are respecively $37, $5 ad $2. The correspodig yearo-year chages i average prices are 9. % ad 33.3 % for he periods 29/28 ad 2/ These resuls are ow compared wih hose obaied if he repea sales echique is used. Le P be he price relaive of he house bewee he secod ad firs sale for each compleed rasacio ( 2 ) from 28 o 2. The logarihm of P will serve as he depede variable i a repea sales regressio. Three repeaed sales are ideified i Table.3 for he period 28 o 2. The firs repea sale, for propery A, has a P value of.2 (i.e., he price relaive bewee is sale prices i 29 ad 28); he secod repea sale, which occurs for propery B, has a P value of.257 (he price relaive bewee is sellig prices i 2 ad 28); propery C is he hird ( 2 ) Geler ad Pollakowski (26) use he erm roud rip. repea-sales rasacio which has a P value of because he price of his propery did o chage from 29 ad The idepede variables i a repea sales regressio are dummy variables, which ake he value - durig he year of he iiial sale, he ake he value + i he period of he secod sale, ad fially ake he value for all oher periods. The esimaed dummy variable coefficies from he regressio are used o calculae he repea sales price idex. Table.4 summarizes he values of he dummy variables for properies A o C. For example, sice propery A is sold for a secod ime i 29, he dummy variable D29 akes he value of bu D2 akes a value of sice his propery A is o sold afer 29. A similar reasoig applies o he oher properies ad he oher years. Noe ha o avoid perfec collieariy, he firs period (28) is disregarded from he explaaory variables ad he regressio. I oher words, if he firs sale occurs a he base year, he here is o dummy variable for ha period. Table.4. Dummy Variables for Repea Sales P D29 D2 Propery A.2 Propery B.257 Propery C. -.5 Give hese repea sales daa, he regressio equaio which has o iercep erm ca be expressed as (see also equaio (6.3): l P = γ D + γ D + ε (.22) where ε is a error erm ( whie oise ). The ai-logarihm of he esimaed parameers, i.e. exp( ˆ g 29 ) ad exp( ˆ g 2 ), will represe he price idices of he housig ui for each period whe compared o he base period 28. Usig Ordiary Leas Squares (OLS) o esimae equaio (.22) o he daa from Table.4, he resulig repea sales price idices are.29 ad.238 for 29 ad 2, respecively. The year-oyear growh raes of 2.9 % ad 23.8 % for his example are quie differe from hose foud wih he simple average approach, which were 9. % ad 33.3 %.( 2 ).5 The simple repea sales model ca be improved. Oe way of accomplishig his is by reducig he saisical oise i he idex series geeraed. As poied ou by ( 2 ) There are very few observaios so o meaigful coclusios should be draw from his simplified example. I should oly be used for illusraive purposes. Geler ad Pollakowski (26), he source of he esimaio error (or oise) i propery price idices is explaied by he fac ha he observed rasacio prices are radomly disribued aroud he rue bu uobservable marke values. The auhors add ha his oise is prese i ay house price idex, regardless of how he idex is cosruced. To miigae he effecs of he oise he sample of repeaed sales ca be expaded, daa availabiliy permiig..52 As previously poied ou, a OLS regressio ca be used o obai he se of price chages. The Bailey, Muh, ad Nourse (963) model is a classic example of he OLS repea sales mehodology usig he echique oulied above. However, subseque research has suggesed ha he basic OLS repea sales mehod may be improved by applyig a weighed leas squares (WLS) echique. I a ushell, he mehod cosiss i givig more weigh i he regressio o he observaios ha are deemed more accurae. I he coex of he repea sales mehod, givig less weigh o properies for which a log ime spa has elapsed bewee sales ad vice versa correcs for his ihere problem, beer kow as he heeroskedasiciy problem. 52 Hadbook o Resideial Propery Prices Idices (RPPIs)

155 Empirical Examples.53 Case ad Shiller (987) sugges he followig hree-sage approach:. Esimae model (.22) by OLS regressio ad reai he vecor of regressio residuals. 2. Ru a OLS regressio of he squared residuals o a cosa erm ad he ime ierval bewee sales. 3. Ru a OLS regressio of model (.22) bu where each observaio is divided hrough by he square roo of he fied value from he secod-sage regressio. The hird sage is a weighed leas squares regressio of model (.22) ha accous for he presumed heeroskedasiciy. Table.5. Uweighed Repea Sales Regressio Source SS df MS Number of obs = 86 F( 6, 8) = Model Prob > F =. Residual R-squared =.6586 Adj R-squared =.6569 Toal Roo MSE =.95 diflprice Coef. Sd. Err. P> [95 % Cof. Ierval] dy dy dy dy dy dy Source: Auhors calculaios based o MLS daa for a Caadia ciy Table.6. Weighed Repea Sales Regressio Source SS df MS Number of obs = 86 F( 6, 8) = Model Prob > F =. Residual R-squared =.6395 Adj R-squared =.6377 Toal Roo MSE =.2 difprice Coef. Sd. Err. P> [95% Cof. Ierval] dy dy dy dy dy dy Source: Auhors calculaios based o MLS daa for a Caadia ciy.54 Movig o he larger ad more realisic se of daa o sigle-family houses ha were previously used for mos of he previous examples of his chaper, wo versios of he repea sales mehod are illusraed. The resuls are firs compued for he uweighed repea sales regressio approach ad are preseed i Table.5. Table.6 preses he resuls for he weighed versio of he repea sales regressio. Noe ha for his paricular se of daa, all he coefficies are sigificaly differe from ad ha o iercep is used i he regressios for he repeas sales approach. Oe ofe cied drawback of he repea sales mehod is ha i is waseful of daa. The curre exercise cofirms his. Of he 5787 observaios ha were i he daabase a he sar, oly 86 (or abou 2 %) are foud o be uis ha sold more ha oce durig he 6 or so years..55 Similar o he ime dummy hedoic model preseed earlier, he correspodig price idices are obaied by akig he ailogarihm of he esimaed coefficie as Hadbook o Resideial Propery Prices Idices (RPPIs) 53

156 Empirical Examples he depede variable is he logarihm of he price. For example, he regressio for he uweighed repea sales approach yields a coefficie of for 27; akig he ailogarihm yields exp( ) =. 345 (or 3.5 oce rouded ad muliplied by ). The idices for he eire 22 o 28 period are show i Table.7. Noe ha he idices are quie similar, regardless wheher he uweighed or weighed repea sales versios are used. This is a feaure of his paricular daase ad may o ecessarily hold rue for house price idices esimaed from oher sources. Table.7. Repea Sales Price Idices (22 = ) Year Uweighed Per ce chage Weighed Per ce chage Source: Auhors calculaios based o MLS daa for a Caadia ciy.56 Table.8 summaries he idex resuls usig he various mehods preseed here usig he exeded daase for year 27. The simple mea shows he larges icrease of all he esimaed idices a. % wih he media beig slighly lower a 9.2 %. The hedoic idices icreased by 5.7 % ad 5.9 % for he adjace year pooled ad characerisics prices approaches, respecively (calculaio o show above). By corac, he repea sales weighed ad uweighed idices icreased by 8.5 % ad 8.6 %, respecively. Alhough he sample size is somewha small o make ay geeralisaio, oe impora observaio is oeworhy. The o-qualiy adjused idicaors, i.e., he mea ad media, geerae he highes growh raes, while he hedoic mehods geerae he smalles. The repea sales approaches, alhough hey corol for may poeial aspecs of qualiy, do o corol for age. Therefore, i is o so surprisig ha he price icreases obaied wih his approach are larger ha hose obaied wih he hedoic approaches. Table.8. Growh Raes i Perce for he Various House Price Idices (27) Characerisics Repea sales Repea sales Mea Media Pooled hedoics hedoics uweighed weighed Source: Auhors calculaios based o MLS daa for a Caadia ciy 54 Hadbook o Resideial Propery Prices Idices (RPPIs)

157 Recommedaios 2

158 2 Recommedaios 2. This hadbook provides deailed ad comprehesive iformaio o he compilaio of resideial propery price idices (RPPIs). I provides a overview of he cocepual ad heoreical issues ha arise, explais he differe user eeds for such idices ad gives advice o how o deal wih he pracical problems ha saisical offices are cofroed wih i he cosrucio of such idices. Earlier chapers cover all releva opics icludig: a descripio of he differe pracices currely i use; advice o he aleraive mehodologies available o he compiler; ad he advaages ad disadvaages of each aleraive. The purpose of his chaper is o draw ogeher all his iformaio ad make recommedaios o bes pracice for compilig resideial propery price idices, icludig how o improve ieraioal comparabiliy. The recommedaios ecessarily ake io accou he differe siuaios couries are cofroed wih i erms of daa availabiliy ad herefore cao be oo prescripive. 2.2 Users of RPPIs are also caered for. The hadbook provides iformaio o oly o he differe mehods ha are ad ca be deployed i compilig such idices, bu also o he saisical limiaios of wha is beig measured. Users will wa o bear he laer i mid so ha he resuls of a idex ca be ierpreed correcly. Ay se of recommedaios has o sar wih a udersadig of he basic cocep uderlyig he arge idex, i oher words wha a resideial propery price idex is ryig o measure. This will, of course, deped o user eeds ad he purpose of he idex. 2.3 The recommedaios give below follow he same order as Chapers 3 o 8. Chaper 3 describes he mai elemes of a cocepual framework for RPPIs, ad Chapers 4 o 8 describe he mai saisical mehods ha ca be used i cosrucig such idices. The differe mehods esseially relae o aleraive soluios o he problem of qualiy chage, ha is, how o adjus a RPPI for chages i he qualiy mix of he properies sold ad for qualiy chages (he e effec of reovaios, exesios ad depreciaio) of he idividual dwelligs. Cocepual Issues Targe ad Cocepual Basis 2.4 I priciple, he arge idex, i oher words he ype of idex o be compiled, will deped o is purpose. The Sysem of Naioal Accous 28 should be used as he cocepual framework for RPPIs. Weighig 2.5 A price idex which is required o measure he wealh associaed wih he owership of resideial propery should be sock-weighed. A sock-weighed idex is also appropriae for a fiacial sabiliy idicaor, i paricular for a idex which is beig used o ideify propery price bubbles. 2.6 A price idex which is required for measurig he real oupu of he resideial real esae cosrucio idusry should be sales-weighed. A sales-weighed idex is also appropriae for a cosumer price idex (CPI) ha follows a acquisiios approach. Idex Scope 2.7 A price idex which is required o measure he wealh associaed wih he owership of resideial propery should cover all resideial propery, ha is, boh exisig properies ad properies which have bee recely buil. ( ) This is also he case for a idex used as a fiacial sabiliy idicaor. 2.8 A price idex which is required for measurig real ivesme i he resideial real esae idusry should cover sales of ew propery. ( 2 ) The cosrucio par of ew housig produced is par of gross ivesme. The cos of he lad, apar from he value of ay improvemes made o his eleme, should be excluded for his purpose. However, as was explaied i Chaper 3, a price idex for he sales of boh ew ad exisig houses is required i order o cosruc real oupu measures for he aciviies of real esae ages i sellig ew ad exisig houses o purchasers. The scope of he idex for his applicaio should cover boh he srucure ad lad values of he resideial propery sales. 2.9 A price idex resriced o ew properies is also appropriae whe a resideial propery price idex is a ipu io a CPI for he measureme of ower-occupier housig coss o a e-acquisiio cos basis, ha is, where he CPI covers he cos of acquirig properies which are ew o he ower-occupier housig marke. This approach, oe of a umber of aleraives as was explaied i Chaper 3, reas he purchase of a dwellig exacly like he purchases of ay oher cosumpio good. ( 3 ) Cosa Qualiy 2. Regardless of he differe uses of he idex, he purpose of a resideial propery price idex is o compare ( ) This icludes coversios of exisig propery, for example where a warehouse has bee covered io flas or a exisig propery has bee sub-divided. ( 2 ) Reovaios o exisig dwellig uis are also par of resideial cosrucio ivesme. ( 3 ) The argume i favour of he e acquisiio approach is ha i is he closes o he acquisiio approach which has radiioally bee adoped for oher pars of a CPI ad is mos appropriae for a CPI beig used as a geeral idicaor of curre ecoomic codiios. Bu he mehod ca draw criicism from hose who require a CPI as a compesaio idex, as eiher he weigh or he price idicaor properly reflec he sheler coss of ower-occupiers. For isace, a rise i ieres raes would o be refleced i a e acquisiio idex. See CPI Maual (24) ad he Pracical Guide o Producig Cosumer Price Idices (Uied Naios, 29). 56 Hadbook o Resideial Propery Prices Idices (RPPIs)

159 Recommedaios 2 he values of he sales or of he sock of resideial propery bewee wo ime periods afer allowig for chages i he aribues of he properies. For his purpose i is ecessary o decompose price chages io hose associaed wih chages i aribues ad he residual which relaes o he uderlyig pure price chage. 2. A cosa qualiy price idex is appropriae for boh a sock ad sales-weighed price idex. There are a umber of pracical mehodologies which ca be used o cosruc such a idex. Recommedaios o which of he available mehods should be used i which circumsaces are provided below. Decomposiio bewee he Buildig ad Lad Compoes 2.2 A decomposiio of he RPPI i srucures ad lad compoes may be required, paricularly if a coury s balace shee esimaes of aioal wealh i he Naioal Accous make his disicio. Such decomposiio may also be ecessary whe a resideial propery price idex is a ipu io a CPI for he measureme of ower-occupier housig usig he e-acquisiio approach. Saisical Mehods for Compilig Cosa Qualiy Idices 2.3 The mehods adoped by saisical agecies o cosruc cosa-qualiy RPPIs vary amog couries ad are dicaed i large par by he availabiliy of daa geeraed by he processes ivolved i buyig ad sellig a propery. The challeges of compilig cosa-qualiy resideial price idices ca be summarized by he followig hree facors: Resideial properies are ooriously heerogeeous. No wo properies are ideical. Prices are ofe egoiaed. The (askig) price of a propery is o fixed ad ca chage hroughou he rasacio process uil he price is fialised. This meas ha a propery s marke value ca oly be kow wih ceraiy afer i has bee sold. ( 4 ) Propery sales are ifreque. I may couries, less ha e per ce of he housig sock chages hads every year, which meas ha a paricular house is likely o be resold approximaely oce every e years. ( 4 ) I some cases eve he sellig prices may o reflec he rue marke values, for example whe hey relae o disressed sales arisig from divorce ec. 2.4 The differe mehods of idex cosrucio used by a saisical agecy reflec he differig soluios used o mee he above challeges. Four mehods have bee sudied i deph i his hadbook: sraificaio or mixadjusme, hedoic regressio mehods, repea sales, ad appraisal-based mehods (i.e., he SPAR mehod). Below, recommedaios are made o each. Each mehod aemps o adjus for he chage i he qualiy mix of he houses whose prices are observed ad combied o cosruc he idex. Some mehods, however, are uable o adjus for qualiy chages of he idividual houses, i.e. for he e effec of depreciaio of he srucures ad reovaios ad exesios. Where daa from he admiisraive processes for buyig ad sellig a resideial propery are used i he cosrucio of he idex, he price will usually relae eiher o he offer price or o he sellig price hese ca differ from oe aoher. 2.5 The recommedaios do o address he challege of compuig a RPPI i couries where a sigifica proporio of he housig sock relaes o iformal or radiioal dwelligs. A example of compuig a RPPI uder he laer circumsaces is give i Chaper ad draws o he experiece of Souh Africa. I such circumsaces i is o possible o be very prescripive i erms of recommedaios sice he siuaio will vary cosiderably amog couries ad here is o ideal soluio ha will deliver a resideial propery price idex which is cocepually pure ad does o geerae pracical difficulies. Raher, he compiler will eed o draw o he bes available sources of iformaio ad will o doub have o make cocepual ad mehodological compromises i compuig a idex. I hese circumsaces i is paricularly impora ha saisical agecies provide evaluaios of he resulig price idices ad guide users o heir uses. Sraificaio or mix-adjusme 2.6 Sraificaio or mix-adjusme is he mos sraighforward way o corol for chages i he composiio or qualiy mix of he properies sold. I also addresses ay user eed for sub-idices relaig o differe housig marke segmes. The effeciveess of sraificaio will deped upo he sraificaio variables used because a mixadjused measure oly corols for composiioal chage across he various groups a mix-adjused idex does o accou for chages i he mix of properies sold wihi each subgroup or sraum. 2.7 I heory, he more deailed he sraificaio, he more he idex corols for chages i he characerisics of he properies covered by he idex. However, icreasig he umber of sraa reduces he average umber of price observaios per sraum ad i fac ca quickly lead o empy sraa. Sraa or cells which are empy he lead i ur o a lack of machig whe he average price ad Hadbook o Resideial Propery Prices Idices (RPPIs) 57

160 2 Recommedaios quaiy daa i each cell are compared across wo ime periods. A very deailed sraificaio migh also raise he sadard error of he overall idex. I addiio, i may be difficul o ideify he mos impora price-deermiig characerisics i he way ha a mehod usig hedoic regressio ca do (see ex secio). 2.8 The mai advaages of sraificaio/mixadjusme are: Depedig o he choice of sraificaio variables, he mehod adjuss for composiioal chage amogs he dwelligs. The mehod is reproducible, codiioal o a agreed lis of sraificaio variables. I is o subjec o revisio. Price idices ca be cosruced for differe ypes ad locaios of housig. The mehod is relaively easy o apply ad o explai o users. 2.9 The mai disadvaages of sraificaio/mixadjusme are: I cao deal adequaely wih depreciaio of he houses uless he age of he srucure is a sraificaio variable. The laer ca resul i problems associaed wih cells wih small umbers of price observaios. The mehod cao deal adequaely wih houses which have udergoe major repairs or reovaios (uless iformaio o reovaios is available). I requires iformaio o housig characerisics ha are icluded i he sraa so ha he sales ca be allocaed o he correc sraa. If he sraificaio scheme is very coarse, composiioal chages will affec he idices. If he sraificaio scheme is very fie, he cells ca be subjec o cosiderable samplig variabiliy due o small sample sizes or some cells may simply be empy for some periods causig idex umber difficulies. The value of lad cao be separaed ou usig his mehod. 2.2 Sraificaio/mix-adjusme is a appropriae mehod where a appropriae level of deail is chose for he cells ad ca be applied i pracice; he age group of he srucure is oe of he sraificaio variables; a decomposiio of he idex io srucure ad lad compoes is o required. 2.2 Sraificaio/mix-adjusme is recommeded where he volume of sales is large eough ad iformaio o housig characerisics deailed eough o suppor a deailed classificaio of properies. ( 5 ) ( 5 ) A coarse sraificaio by, say, major ciy ad house ype, where he laer is simply i erms of ewly-buil or exisig, is o recommeded. Hedoic regressio 2.22 The applicaio of hedoic echiques for qualiy adjusme ad for compuig price idices has made a sigifica coribuio o he mehodological developme of price idices i rece years ad is rapidly becomig a preferred mehod for compilig cosa-qualiy resideial propery price idices. ( 6 ) There is o uiformiy i he pracical applicaio of hedoic regressio, bu he idea uderlyig hedoics is raher simple. Hedoic regressio is a saisical echique ha measures he relaioship bewee he observable characerisics of a good or service ad is price or value. I he coex of resideial propery price idices, he bes form of he hedoic fucio may be liear raher ha log-liear o reflec he fac ha he value of a propery is geerally equal o he sum of he price of he srucure ad he price of he lad There are basically wo aleraive mehods of applicaio of hedoics o resideial propery: The ime dummy variables mehod. This mehod geerally uses a sigle regressio, wih ime dummies ad fixed characerisics coefficies, which covers all periods ad which is re-ru each ime he price idex is compiled. The (expoeials of he) ime dummy coefficies are ake o represe he period-o-period price chages excludig qualiy (mix) chages. This mehod has he beefi of simpliciy. Oe of he drawbacks is ha i raises he issue of revisabiliy of he idex because he ime dummy coefficies will be updaed each ime ew periods are added ad he regressio is ru. However, here is a varia of he ime dummy mehod, called he rollig widow ime dummy mehod, which ca work well i pracice ad solves he revisabiliy problem. A hedoic regressio is ru usig he daa for he las N periods ad he las ime dummy is used as a chai lik facor for updaig he idex for he previous period. For refereces o he lieraure o his mehod ad a example, see chaper 5. The hedoic impuaio mehod. A separae hedoic regressio is performed i each ime period ad he missig curre period prices for he properies sold i he base period are impued usig he prediced prices from he esimaed hedoic equaio. A symmeric approach is possible by also impuig he missig base period prices for he properies sold i he curre period ad he akig he geomeric mea of boh hedoic impuaio idices Boh hedoic regressio mehods ca poeially suffer from omied variable bias if some impora price deermiig characerisic is omied from he regressio ( 6 ) If we look a he harmoised house price idices produced by he Europea Naioal Saisical Isiues, as of 2 more ha half were usig hedoics for qualiy adjusme. For more deails, see Marola e al. (22). 58 Hadbook o Resideial Propery Prices Idices (RPPIs)

161 Recommedaios 2 equaio. Mulicollieariy ca be a pracical problem, paricularly whe a decomposiio of he idex io srucures ad lad compoes is required. The ime dummy variable mehod has bee frequely used by academics, i par due o is simpliciy, bu he hedoic impuaio mehod is more flexible i allows characerisics prices o chage idepedely over ime whereas he ime dummy mehod forces characerisics prices o move i a proporioal maer ad is esseially similar o he radiioal mached-model mehodology o compue price idices Hedoic regressio mehods ca be used i cojucio wih sraificaio o deal wih ay residual qualiy-mix chage ha remais wihi he sraa. This has he added advaage of dealig wih he fac ha differe model specificaios may be eeded for differe segmes of he housig marke or ha he value of some characerisics will vary across differe marke segmes The mai advaages of hedoics are: If he lis of propery characerisics is sufficiely deailed, he mehod adjuss for boh sample mix chages ad qualiy chages (depreciaio ad reovaio) of he idividual houses. Price idices ca be cosruced for differe ypes of dwelligs ad locaios hrough sraificaio ad he applicaio of hedoics o each idividual sraum. Sraified price idices based o hedoic regressios o corol for qualiy mix chages wihi sraa allow for relaive values of he sock of housig o be used o weigh he qualiy-mix adjused sraa idices (i a sock-weighed RPPI). The mehod maximizes he use of he available daa. I ca i priciple be used o decompose he overall price idex io lad ad srucures compoes, subjec o he availabiliy of daa The mai disadvaages of hedoic regressio are: The mehod is ofe regarded as beig daa iesive, especially i erms of he housig characerisics o be used as explaaory variables. ( 7 ) I may be difficul o corol sufficiely for locaio if propery prices ad price reds differ across deailed regios. The mehod ca be sesiive o he variables used i he regressio ad he fucioal form for he model. The mehod is o paricularly easy o explai o users ad from heir perspecive may lack rasparecy Subjec o daa beig available o salie housig characerisics, he hedoic regressio mehod is geerally he bes echique for cosrucig a cosa qualiy resideial propery price idex. The impuaios approach o ( 7 ) However, as was see i previous chapers, i some cases saisfacory resuls ca be obaied wih hedoic regressio mehods usig oly hree or four housig characerisics. hedoic qualiy (mix) adjusme has advaages over he ime dummy approach. Sraified hedoic idices are preferred over a sraighforward applicaio of hedoic regressio o he whole daa se. Repea Sales 2.29 The repea sales mehod observes he price developme of a specific house over a period of ime by referece o he sellig price each ime i is sold. The price chage of a selecio of houses durig overlappig ime periods ca he be observed o esimae, usig a dummy variable regressio model, he geeral red i resideial propery prices. Measurig he average price chages i repea sales o he same properies esures a like for like compariso (igorig he fac ha depreciaio ad reovaios o he srucure bewee he periods of sale ca chage he propery). 2.3 The mai advaages of he repea sales mehod are: I is basic form, i requires o iformaio o characerisics of he dwellig uis oher ha he addresses of he properies ha are raded. Source daa are ofe available from admiisraive records. I follows a mached-model mehodology, uder he assumpio ha depreciaio ad reovaios have o chaged he dwellig ui over he ime period bewee subseque sales. May locaioal ad oher price deermiig characerisics ha are difficul o measure are likely o be auomaically icluded. Sadard repea sales regressios are easy o ru ad he resulig price idices are easy o cosruc. No impuaios are ivolved. By cosrucio, locaio is auomaically corolled for. The resuls are, i priciple, reproducible. 2.3 The mai disadvaages of he repea sales mehod are: The mehod does o use all of he available sellig prices; i uses iformaio oly o hose properies ha have sold more ha oce durig he sample period. The sadard versio of he mehod igores (e) depreciaio of he dwellig ui. Sample selecio bias ca arise from he resricio o properies ha have bee sold more ha oce durig he sample period. The mehod cao geerae separae price idices for srucures ad for lad. The reliace o repea sales meas ha here may o be eough daa pois o compue mohly resideial propery price idices for smaller caegories of propery. The sample is updaed as ew rasacio iformaio becomes available. This meas ha he repea sales Hadbook o Resideial Propery Prices Idices (RPPIs) 59

162 2 Recommedaios propery price idex could be subjec o rerospecive revisios over a log ime period. ( 8 ) Sice a house mus be sold a leas wice i a repea sales idex, ewly buil dwellig uis are excluded from such a idex Alhough a aural sarig poi for cosrucig a idex, he repea sales mehod is o preferred over he (sraified) hedoic mehod for cosrucig a cosa qualiy resideial propery price idex. However, i ca offer a soluio where here is limied or o iformaio o housig characerisics ad here are a relaively large umber of repea rasacios o provide eough daa pois for he required ypes of resideces ad where sample selecio bias is o cosidered a problem. I is o recommeded whe a disicio eeds o be made bewee he price of he srucure ad he price of he lad. Appraisal-Based Mehods 2.33 Appraisal-based mehods use assessed values, such as valuaios for axaio purposes or valuaios from specially commissioed surveys usig esae ages, ofe doe by referece o similar properies ha have bee sold, o overcome he wo mai problems associaed wih he repea sales mehodology he relaively small umber of price observaios which are geeraed ad he suscepibiliy o sample selecio bias. Where he valuaios all refer o a sadard referece period, he mached model mehodology which uderlies appraisal-based mehods also has he advaage ha i ca be applied i a sraighforward way ad wih o ecessiy o use ecoomerics o adjus for composiioal chages. However, like he repea sales mehodology, appraisal-based mehods geerally cao deal adequaely wih qualiy chages o idividual houses. Also, hey geerally rely o exper judgme o how much a propery would sell for raher ha o a acual rasacio price. Thus, i ca be argued, a he exreme, ha appraisal-based mehods are iflueced by judgmes or opiios, albei auhoriaive ad objecive The Sale Price Appraisal Raio (or SPAR) mehod uses appraisals wih a commo referece period as base period prices i a sadard mached-model framework (hough he resuls are ormalized o obai a idex ha equals (or ) i he base period). The experieces of he few couries ha have compued a SPAR idex ( 9 ) are geerally posiive alhough some researchers have repored a bias arisig from freque re-assessmes ad reduced precisio over ime arisig from ew appraisals The mai advaages of he SPAR mehod are: Beig based o he sadard mached model mehodology, i is cosise wih radiioal idex umber heory. ( 8 ) I pracice, he lik facor for he las wo periods i he curre repea sales regressio ca be used o updae he ogoig idex. ( 9 ) I Europe, Demark, Swede ad he Neherlads are usig he SPAR mehod. I is sraighforward o compue. The mehod beefis from may more observaios ha he repea sales mehod ad is herefore less suscepible o problems arisig from havig a relaively small umber of price observaios. I is less suscepible o sample selecio bias ha he repea sales mehod. I does o suffer from revisios o previously compued figures. I is reproducible The mai disadvaages of he SPAR mehod are: I cao deal adequaely wih qualiy chages (depreciaio ad reovaios) of he dwellig uis. ( ) Daa o value assessmes a he address level mus be available for all properies. The mehod is depede o he qualiy of he assessmes. I cao be used o decompose he overall propery price idex io lad ad srucures compoes. ( ) 2.37 The SPAR mehodology addresses some of he weakesses of he repea sales mehodology ad is o be preferred o he laer mehodology if assessme daa of sufficie qualiy are available ad if seleciviy bias is cosidered o be a serious feaure of he applicaio of he repea sales mehodology. The SPAR mehodology does have is drawbacks bu is recommeded whe he use of hedoics is o possible. The resuls from he SPAR mehod are improved if i is used i cojucio wih sraificaio. Seasoal Adjusme 2.38 If he iiial house price series idicaes ha some seasoal flucuaios occur, he ormal seasoal adjusme echiques ca be used i order o seasoally adjus he iiial series. However, if he hedoic impuaio or he sraificaio mehod is used o cosruc he iiial idex, some more specific recommedaios are made below If he sraificaio mehod is used o cosruc he iiial idex ad i exhibis seasoaliy, he he rollig year mehod explaied i Chaper 5 ca be applied o seasoally adjus he series wihou relyig o ecoomeric mehods. 2.4 If he hedoic impuaio mehod is used o cosruc he iiial price idex ad i exhibis seasoaliy, he i order o obai a seasoally adjused series, i may be useful o cosruc year-over-year mohly or quarerly series as a iiial sep. These iiial series ca he be aggregaed usig he rollig year mehod io a smooheed seasoally adjused series. ( ) As wih he repea sales mehod, he price idex geeraed by he SPAR mehod ca i priciple be adjused by usig exogeous iformaio o he e depreciaio of properies of he ype beig cosidered. ( ) Where official decomposiios of he oal assessed value of he propery io lad ad srucures compoes are available, hese could be used o check he lad ad srucures price idices ha are geeraed by hedoic regressio mehods. 6 Hadbook o Resideial Propery Prices Idices (RPPIs)

163 Glossary Glossary Acquisiios approach A approach i which cosumpio is ideified wih he goods ad services acquired by a household i some period (as disic from hose wholly or parially used up for purposes of cosumpio). See also e acquisiios approach. Aggregae A se of rasacios (or heir oal value) such as he oal purchases made by households o resideial propery i a cerai period. Aggregaio Combiig, or addig, differe ses of rasacios o obai larger ses of rasacios. The larger se is described as havig a higher level of aggregaio ha he (sub-) ses of which i is composed. The erm aggregaio is also used o mea he process of addig he values of he lower-level aggregaes o obai higher-level aggregaes. I he case of price idices, i meas he process by which price idices for lower-level aggregaes are averaged o obai price idices for higher-level aggregaes. Askig price The price a which a propery is offered for sale. The askig price ca be adjused durig he process of buyig ad sellig a house uil he fial rasacio price is reached. Assessed value or appraisal Valuaio of he marke value of a propery. Valuaios may be eeded o obai a morgage loa. I some couries assessmes are performed o he goverme s behalf for (propery) ax purposes. Assessed propery values are also referred o as appraisals. See also Sale Price Appraisal Raio mehod. Axiomaic (es) approach The approach o idex umber heory ha deermies he choice of idex umber formula, o he basis of is mahemaical properies. A lis of ess is draw up, each es requirig a idex o possess a cerai propery or saisfy a cerai axiom. A idex umber may he be chose o he basis of he umber of ess saisfied. No all ess may be cosidered o be equally impora ad he failure o saisfy oe or wo key ess may be cosidered sufficie grouds for rejecig a idex. Base period The base period is usually udersood o mea he period wih which all he oher periods are compared. The erm may, however, have differe meaigs i differe coexs. Three ypes of base period may be disiguished: he price referece period he period ha provides he prices o which he prices i oher periods are compared. The prices of he price referece period appear i he deomiaors of he price relaives, or price raios, used o calculae he idex; he weigh referece period he period for which he expediures serve as weighs for he idex. If he expediures are hybrid (i.e., if he quaiies of oe period are valued a he prices of some oher period), he weigh referece period is he period o which he quaiies refer; he idex referece period he period for which he value of he idex is se equal o. I should be oed ha, i pracice, he duraio of he weigh referece period for a RPPI is ofe a year, whereas he RPPI is ypically calculaed mohly or quarerly, he duraio of he price referece period beig a moh or quarer. Thus, he weigh ad price referece period may o coicide i pracice, a leas whe a RPPI is firs calculaed, alhough he price ad idex referece periods frequely coicide. Bias A sysemaic edecy for he calculaed RPPI o diverge from some ideal or preferred idex, resulig from he mehod of daa collecio or processig or he idex formula used. See also sample selecio bias. Chai idex A idex umber series for a log sequece of periods ha is obaied by likig ogeher idex umbers spaig shorer sequeces of periods. A chai idex, compued accordig o some idex umber formula (such as he Fisher), is he produc of period-o-period idices which are compued wih he same formula. See also Likig. Characerisics The physical ad ecoomic aribues of a good or service ha serve o ideify i ad eable i o be classified. For resideial propery hese relae o boh he srucure (he buildig) ad he locaio/lad. Characerisics prices hedoic approach A hedoic regressio mehod where he chage i he esimaed values of he parameers for he characerisics of he (average) propery sold, i.e. he shadow prices of he characerisics, deermies he resideial propery Hadbook o Resideial Propery Prices Idices (RPPIs) 6

164 Glossary price idex. Uder cerai assumpios his approach is equivale o he hedoic impuaio approach. Compoe A se of he goods ad services ha make up some defied aggregae. Also used i he coex of decomposig he price propery price (idex) io lad ad srucures compoes. Cosisecy i aggregaio A idex is said o be cosise i aggregaio whe he idex for some aggregae has he same value wheher i is calculaed direcly i a sigle operaio, wihou disiguishig is compoes, or wheher i is calculaed i wo or more seps by firs calculaig separae idices, or sub-idices, for is compoes, or sub-compoes, ad he aggregaig hem, he same formula beig used a each sep. Cosumer price idex (CPI) A mohly or quarerly price idex compiled ad published by a official saisical agecy ha measures chages i he prices of cosumpio goods ad services acquired or used by households. Is exac defiiio, icludig he reame of ower-occupied housig, may vary from coury o coury. I Europe, he Harmoised Idex of Cosumer Prices (HICP) currely excludes ower-occupied housig. Coverage The se of properies of which he prices are acually icluded i a price idex. For pracical reasos, coverage may have o be less ha he ideal scope of he idex. Tha is, he ypes of propery acually priced may o cover all of he ypes ha are sold or belog o he housig sock. Curre period, or compariso period I priciple, he curre period refers o he mos rece period for which he idex has bee compiled or is beig compiled. The erm is widely used, however, o mea he compariso period; ha is, he period ha is compared wih he base period, usually he price referece or idex referece period. I is also used o mea he laer of he wo periods beig compared. The exac meaig is usually clear i he coex. Daa cleaig Procedures, ofe auomaed, used o delee ery errors i daa ses, observaios which are deemed implausible, or ouliers. Deflaig The divisio of he curre value of some aggregae by a price idex (i his coex referred o as a deflaor), i order o revalue is quaiies a he prices of he price referece period. Depreciaio The gradual ad permae decrease i he ecoomic value of a srucure or he housig sock hrough physical deerioraio or obsolescece over ime. Domai A aleraive erm for he scope of a idex. Drif A chai idex is said o drif if i does o reur o uiy whe prices i he curre period reur o heir levels i he base period. Chai idices are liable o drif whe prices flucuae over he periods hey cover. Durable cosumpio good A cosumpio good ha ca be used repeaedly or coiuously for purposes of cosumpio over a log period of ime, ypically several years. A house is a exreme form of a durable cosumpio good due o is very log expeced lifeime. This has led o differe approaches o he reame of ower-occupied housig i ecoomic saisics. Ecoomic approach The ecoomic approach o idex umber heory assumes ha he quaiies are fucios of he prices, he observed daa beig geeraed as soluios o various ecoomic opimizaio problems. While his approach is very releva for he CPI as a approximaio o a cosof-livig idex, i seems less releva for a resideial propery price idex. See also axiomaic or es approach. Ediig The process of scruiizig ad checkig he prices repored by price collecors. Some checks may be carried ou by compuers usig saisical programs wrie for he purpose. See also daa cleaig. Elemeary aggregae Usually defied as he lowes aggregae for which expediure daa are available ad used for idex cosrucio purposes. Elemeary aggregaes also serve as sraa for he samplig of iems o be priced. The values of he elemeary aggregaes are used o weigh he price idices for elemeary aggregaes o obai higher-level idices. I he coex of a sales-based resideial propery price idex, he erm elemeary aggregae is less appropriae. As every propery is basically uique, he quaiies are equal o, so ha weighs are available a he mos deailed level. Exisig dwelligs The erm exisig dwelligs is someimes used o disiguish hem from dwelligs ha are ewly buil (ad added o he housig sock). 62 Hadbook o Resideial Propery Prices Idices (RPPIs)

165 Glossary Fisher price idex The geomeric average of he Laspeyres price idex ad he Paasche price idex. The Fisher idex is symmeric ad superlaive. Sales based resideial propery price idices ca always be compued usig he Fisher formula because he quaiies are equal o (as each dwellig is esseially a uique good). Fixed weigh idices A abbreviaed descripio for a series of weighed arihmeic averages of price relaives of price idices where he weighs are kep fixed over ime. I a resideial propery price idex coex, he weighs ca be sales (expediure) weighs or sock weighs. Geomeric Laspeyres idex A weighed geomeric average of he price relaives usig he expediure shares of he price referece period as weighs. Goods Physical objecs for which a demad exiss, over which owership righs ca be esablished ad for which owership ca be rasferred bewee uis by egagig i rasacios o he marke. Hedoic regressio The esimaio of a hedoic model, usig regressio echiques, ha explais he price of he propery as a fucio of is characerisics (relaig o he srucures as well as he locaio). See also hedoic impuaio approach ad ime dummy variable hedoic approach. Hedoic impuaio approach A approach o esimaig a qualiy-adjused resideial propery price idex where missig prices are impued usig a hedoic regressio model. The model parameers are re-esimaed i each ime period, which makes his approach more flexible ha he ime dummy variable hedoic approach. Households Households may be eiher idividual persos livig aloe or groups of persos livig ogeher who make commo provisio for food or oher esseials for livig. Mos couries choose o exclude groups of persos livig i large isiuioal households (barracks, reireme homes, ec.) from he scope of heir CPIs. Housig sock The oal umber of resideial uis available for orasie occupacy. Depedig o he paricular defiiio used, he housig sock may or may o iclude mobile homes, ec. Hybrid (repea sales) models A regressio-based mehod o esimaig resideial propery price idices which combies repea-sales ad hedoic approaches. Ideiy es A es uder he axiomaic approach ha requires ha, if he price of each iem remais he same bewee he periods compared, he price idex mus equal uiy. Impued price The price assiged o a iem (e.g. a propery) for which he price is missig i a paricular period. This may be doe usig hedoic regressio mehods. See also hedoic impuaio approach. The erm impued price may also refer o he price assiged o a good or service iem ha is o sold o he marke, such as a good or service produced for ow cosumpio, icludig housig services produced by ower-occupiers measured by impued re. See also real equivalece. Idex referece period The period for which he value of he idex is se a (or, aleraively, ). Iformal housig marke Resideial areas where a group of housig uis has bee cosruced o lad o which he occupas have o legal claim, or which hey occupy illegally, or uplaed selemes ad areas where housig is o i compliace wih curre plaig ad buildig regulaios. Jevos price idex A elemeary price idex defied as he uweighed geomeric average of he sample price relaives. Laspeyres price idex A price idex i which he quaiies of he goods ad services refer o he earlier of he wo periods compared, he price referece period. The Laspeyres idex ca also be expressed as a weighed arihmeic average of he price relaives wih he expediure shares i he earlier period as weighs. The earlier period serves as boh he weigh referece period ad he price referece period. Likig Splicig ogeher wo cosecuive series of price observaios, or price idices, ha overlap i oe or more periods. If he wo sequeces overlap by a sigle period, he usual procedure is simply o rescale oe or oher sequece so ha he value i he overlap period is he same i boh sequeces ad he spliced sequeces form oe coiuous series. Hadbook o Resideial Propery Prices Idices (RPPIs) 63

166 Glossary Lowe price idex A price idex ha measures he chage bewee periods ad i he oal value of a se of goods ad services a fixed quaiies. The quaiies do o ecessarily have o cosis of he acual quaiies i some period. The class of idices covered by his defiiio is very broad ad icludes, by appropriae specificaio of he quaiy erms, he Laspeyres ad Paasche idices. Lower-level idex A sub-idex as disic from a aggregae idex. Mached models approach The pracice of pricig exacly he same produc, or model, i wo or more cosecuive periods. I is desiged o esure ha he observed price chages are o affeced by qualiy chage. The chage i price bewee wo perfecly mached producs is someimes described as a pure price chage. Marke value The value of a propery a a cerai poi of ime, or he price ha would resul if he propery would be sold i a free marke. Mea idex A price idex ha is calculaed as he raio of he sample meas (ui values) of he properies sold i wo periods. Media idex A price idex ha racks he chage of he media propery price over ime. The media is he middle of a (sample) disribuio: half he scores are above he media ad half are below he media. The media is less sesiive o exreme scores ha he mea ad is ofe preferred o he mea as a measure of ceral edecy i highly skewed disribuios. Mix adjusme A erm used o describe procedures which aemp o remove or reduce he effec of chages i he mix (composiio) of he sample of properies sold o he propery price idex. Moey oulays or paymes approach Oe of he hree mai approaches o icludig oweroccupied housig io a CPI. I he moey oulays approach, he ou of pocke expeses relaig o home owership are simply added up. Ne acquisiios approach Oe of he hree mai approaches o icludig Ower Occupied Housig io a Cosumer Price Idex. Dwelligs added o he ower occupied housig sock (i geeral maily ewly-buil dwelligs) are par of he coverage of he idex; exisig dwelligs are excluded. See also Acquisiios approach. Offer price The price a poeial buyer says he will be willig o pay for he propery. Oulier A erm ha is geerally used o describe ay exreme value i a se of survey daa. I a RPPI coex, i is used for a exremely high or low propery price or price relaive, which requires furher ivesigaio ad should be deleed whe deemed icorrec. Ower-occupied housig Dwelligs owed by he households ha live i hem. The dwelligs are fixed asses ha heir owers use o produce housig services for heir ow cosumpio, hese services beig usually icluded wihi he scope of a CPI. The res may be impued by he res payable o he marke for equivale accommodaio or by user coss. See also real equivalece ad User cos. Paasche price idex A price idex i which he quaiies of he goods ad services cosidered refers o he laer of he wo periods compared. The laer period serves as he weigh referece period ad he earlier period as he price referece period. The Paasche idex ca also be expressed as a weighed harmoic average of he price relaives ha uses he acual expediure shares i he laer period as weighs. Paymes approach See moey oulays approach. Price referece period The period of which he prices appear i he deomiaors of he price relaives. See also Base period. Price relaive The raio of he price of a idividual produc i oe period o he price of ha same produc i some oher period. Producs A geeric erm used o mea a good or a service. Idividual sampled producs seleced for pricig are ofe described as iems. Pure price chage The chage i he price of a propery of which he characerisics are uchaged or he chage i he propery price afer adjusig for ay chage i qualiy (due o reovaios, exesios ad depreciaio). Qualiy chage A chage i he (qualiy deermiig) characerisics of a good or service. I he case of a resideial propery his icludes boh depreciaio of he srucure ad reovaios, such as he moderisaio of kiches ad 64 Hadbook o Resideial Propery Prices Idices (RPPIs)

167 Glossary bahrooms, he iroducio of improved isulaio ad ceral heaig or air codiioig sysems. Qualiy adjusme A adjusme o he chage i he price of a propery of which he characerisics chage over ime ha is desiged o remove he coribuio of he chage i he characerisics o he observed price chage. I pracice, he required adjusme ca oly be esimaed. Differe mehods of esimaio, icludig hedoic mehods, may be used i differe circumsaces. These mehods ca also be used o corol for composiioal or qualiy mix chages over ime i he samples of properies sold. Real equivalece approach Oe of he hree mai approaches o icludig oweroccupied housig io a CPI Idex. The impued price for sheler coss should equal he price a which he dwellig could be reed. Repea sales mehod A mehod o compile a resideial propery price idex which compares properies ha were sold wice or more i he daa se a had. I is a regressio-based approach ha oly icludes ime dummy variables. Represeaive propery A propery, or caegory of properies, ha accous for a sigifica proporio of he oal expediures wihi some aggregae, ad/or for which he average price chage is expeced o be close o he average for all properies wihi he aggregae. Resideial propery Propery zoed for sigle-family homes, owhouses, mulifamily aparmes, codomiiums, ad coops. Reweighig Replacig he weighs used i a idex by a ew se of weighs. Rollig widow approach A approach where a widow of a fixed umber of ime periods is chose o compue he iiial (resideial propery) price idex. The ime series is subsequely updaed by movig he widow oe period forward i ime ad likig he las period-o-period idex chage o he exisig ime series. Sample A (radom or o-radom) selecio of elemes from a fiie populaio. I he housig coex, he properies sold i some ime period ca be viewed as a sample from he housig sock. This samplig view is paricularly releva for a sock based resideial propery price idex. Sample selecio bias Bias i a idex ha ca resul whe he sample is o represeaive of he populaio. I he housig coex, he sample of properies may eiher o be represeaive of all sales (which is paricularly releva for a sales based idex) or o be represeaive of he housig sock (which is releva for a sock based idex). I all sales are observed, here will be o sample selecio bias i a sales based propery price idex. Samplig frame A lis of he uis i he uiverse from which a sample of uis ca be seleced. The lis may coai iformaio abou he uis, which may be used for samplig purposes. Such liss may o cover all he uis i he desigaed uiverse ad may also iclude uis ha do o form par of ha uiverse. Scope The se of producs for which he idex is ieded o measure he price chages. The coverage of a idex deoes he acual se of producs icluded, as disic from he ieded scope of he idex. Seasoal goods Seasoal goods are goods ha eiher are o available o he marke durig cerai seasos or periods of he year, or are available hroughou he year bu wih regular flucuaios i heir quaiies ad prices ha are liked o he seaso or ime of he year. Sellig (or rasacio) price The fial rasacio price of a propery. Specificaio A descripio or lis of he characerisics ha ca be used o ideify a idividual dwellig ui o be priced. SPAR mehod A acroym for Sale Price Appraisal Raio mehod, a approach o cosrucig a resideial propery price idex which combies curre period sellig prices wih appraisals (assessed values) peraiig o some earlier base period. Sraificaio mehod Sraificaio ad re-weighig of a sample is a geeral echique for obaiig more sable resuls or miigaig ay bias due o sample selecio problems, icludig o-respose. I he coex of a resideial propery price idex, he sample of properies sold is subdivided io a umber of relaively homogeeous sraa or cells, accordig o a (limied) umber of price deermiig characerisics. Hadbook o Resideial Propery Prices Idices (RPPIs) 65

168 Glossary Average prices (ui values) or media prices ca he be used o compue price idices for each sraum. I he secod sage, hese sraum idices are aggregaed up usig sales weighs or sock weighs. This mehod has frequely bee used o adjus for composiioal chage of he samples, or chages i he qualiy mix of properies sold, ad is also kow as mix adjusme. Sraificaio ca also be used i cojucio wih oher mehods o corol for qualiy mix chages, for example wih hedoic regressio, repea sales or SPAR mehods. Superlaive idex Superlaive idices are geerally symmeric ad have good properies from a idex umber heoreic poi of view. Examples are he Fisher idex ad he Törqvis idex. Symmeric idex A idex ha reas boh periods symmerically by aachig equal imporace o he price ad expediure daa i boh periods. The price ad expediure daa for boh periods eer io he idex formula i a symmeric way. Sysem of Naioal Accous (SNA) A cohere, cosise ad iegraed se of macroecoomic accous, balace shees ad ables based o ieraioally agreed coceps, defiiios, classificaios ad accouig rules. Household icome ad cosumpio expediure accous form par of he SNA. Time dummy variable (hedoic) approach Oe of he mai hedoic regressio approaches o cosrucig a (resideial propery) price idex. I he sadard log-liear ime dummy variable model, he characerisics coefficies are cosraied o be fixed over ime, ad he price idex umbers ca be direcly compued from he ime dummy coefficies (hrough expoeiaio). Ui value or average value The ui value of a se of homogeeous producs is he oal value of he purchases/sales divided by he sum of he quaiies. I is herefore a quaiy-weighed average of he differe prices a which he produc is purchased/ sold. Ui values may chage over ime as a resul of a chage i he mix of he producs sold a differe prices, eve if he prices do o chage. User cos The cos icurred over a period of ime by he ower of a fixed asse or cosumer durable as a cosequece of usig i o provide a flow of capial or cosumpio services. User cos cosiss maily of he depreciaio of he asse or durable (measured a curre prices ad o a hisoric cos) plus he capial, or ieres, cos. Uses approach A approach o CPIs i which he cosumpio i some period is ideified wih he cosumpio goods ad services acually used up by a household o saisfy heir eeds ad was (as disic from he cosumpio goods ad services acquired). I his approach, he cosumpio of cosumer durables i a give period is measured by he values of he flows of services provided by he socks of durables owed by households. These values may be esimaed by he user coss. Value Price imes quaiy. The value of he expediures o a se of homogeeous producs ca be facored uiquely io is price, or ui value, ad quaiy compoes. Similarly, he chage over ime i he value of a se of homogeeous producs ca be decomposed uiquely io he chage i he ui value ad he chage i he oal quaiies. There are, however, may ways of facorig he chage over ime i he value of a se of heerogeeous producs io is price ad quaiy compoes. I a housig coex, value may also refer o a sigle propery. The price of a propery is acually a value as i is made up of he price of he srucures ad he price of he lad ha he srucure is buil o. Weigh referece period The period of which he expediure shares serve as he weighs or of which he quaiies make up he se of properies for a Lowe idex. There may be o weigh referece period whe he expediure shares for he wo periods are averaged, as i he Törqvis idex, or whe he quaiies are averaged, as i he Walsh idex. See also base period. Weighs A se of umbers summig o uiy ha are used o calculae averages. I a RPPI coex, he weighs are geerally expediure (sales) or sock value shares ha sum o uiy by defiiio. They are used o average price relaives for idividual properies 66 Hadbook o Resideial Propery Prices Idices (RPPIs)

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176 Bibliography McDoald, J.F. (98), Capial-Lad Subsiuio i Urba Housig: A Survey of Empirical Esimaes, Joural of Urba Ecoomics 9, 9-2. McDoald, C, ad M. Smih, (29), Developig sraified housig price measures for New Zealad, Discussio paper o. 29/7, Reserve Bak of New Zealad, Welligo. McMille, D.P. (23), The Reur of Ceralizaio o Chicago: Usig Repea Sales o Ideify Chages i House Price Disace Gradies, Regioal Sciece ad Urba Ecoomics 33, Meese, R. ad N. Wallace (99), Noparameric Esimaio of Dyamic Hedoic Price Models ad he Cosrucio of Resideial Housig Price Idices, America Real Esae ad Urba Ecoomics Associaio Joural 9, Mudge, B.D. (955), The Measureme of Seasoal Movemes i Price ad Quaiy Idexes, Joural of he America Saisical Associaio 5, Muellbauer, J. (974), Household Producio Theory, Qualiy ad he Hedoic Techique, America Ecoomic Review 64, Muh, R.F. (97), The Derived Demad for Urba Resideial Lad, Urba Sudies 8, Nabarro, R. ad T. Key (23), Performace measureme ad Real Esae Ledig Risk, paper preseed a he IMF/BIS Coferece o Real Esae Idicaors ad Fiacial Sabiliy, Ocober 23. Ohishi, T., T. Mizuo, C. Shimizu ad T. Waaabe (2), O he Evoluio of he House Price Disribuio, Discussio paper o.6, Research Ceer for Price Dyamics. Pakes, A. (23), A Recosideraio of Hedoic Price Idexes wih a Applicaio o PCs, America Ecoomic Review 93(5), Palmquis, R.B. (98), Aleraive Techiques for Developig Real Esae Price Idexes, Review of Ecoomics ad Saisics 62, Palmquis, R.B. (982), Measurig Eviromeal Effecs o Propery Values wihou Hedoic Regressios, Joural of Urba Ecoomics, Peigo-Cross, A. (25), Aggregaio Bias ad he Repea Sales Price Idex, pp i Real Esae Idicaors ad Fiacial Sabiliy, BIS Papers No 2, Bak for Ieraioal Selemes, Washigo DC: IMF. Phag, S.Y. (24), House Prices ad Aggregae Cosumpio: Do They Move Togeher? Evidece from Sigapore, Joural of Housig Ecoomics 3, 9. Plosser, C.I. (27), House Prices ad Moeary Policy, Speech for he Europea Ecoomics ad Fiacial Cere Disiguished Speakers Series, July, 27, Moograph, Federal Reserve Bak of Philadelphia. Prasad, N. ad A. Richards (26), Measurig House Price Growh Usig Sraificaio o Improve Media-based Measures, Research discussio paper o. 26-4, Reserve Bak of Ausralia. Prasad, N. L. ad A. Richards (28), Improvig Media Housig Price Idexes Through Sraificaio, Joural of Real Esae Research 3(), Quigley, J.M. (995), A Simple Hybrid Model for Esimaig Real Esae Price Idexes, Joural of Housig Ecoomics 4(), 2. Reihar, C.M. ad K.S. Rogoff (29), This Time is Differe; Eigh Ceuries of Fiacial Folly, Priceo ad Oxford: Priceo Uiversiy Press. Rose, S. (974), Hedoic Prices ad Implici Markes: Produc Differeiaio i Pure Compeiio, Joural of Poliical Ecoomy 82, Rossii, P. ad P. Kershaw (26), Developig a Weekly Resideial Price Idex Usig he Sales Price Appraisal Raio, paper preseed a he Twelfh Aual Pacific Rim Real Esae Sociey Coferece, Aucklad, Jauary. Saario M. (26), Housig Price Saisics a Saisics Filad, paper preseed a he OECD-IMF Workshop o Real Esae Price Idices, Paris, 6-7 November 26. Samuelso, Paul A. ad S. Swamy (974), Ivaria Ecoomic Idex Numbers ad Caoical Dualiy: Survey ad Syhesis, America Ecoomic Review 64, Hadbook o Resideial Propery Prices Idices (RPPIs)

177 Bibliography Scheffé, H. (959), The Aalysis of Variace, New York: Joh Wiley ad Sos. Shi, S., M. Youg ad B. Hargreaves (29), Issues i Measurig a Mohly House Price Idex i New Zealad, Joural of Housig Ecoomics 8(4), Shiller. R.J. (99), Arihmeic Repea Sales Price Esimaors, Joural of Housig Ecoomics (), 26. Shiller, R.J. (993a), Measurig Asse Values for Cash Seleme i Derivaive Markes: Hedoic Repeaed Measures Idices ad Perpeual Fuures, Joural of Fiace 48(3), Shiller, R.J. (993b), Macro Markes, Oxford: Oxford Uiversiy Press. Shiller, R.J. (25), Commes o Sessio Aggregaio Issues, pp i Real Esae Idicaors ad Fiacial Sabiliy, BIS Papers No 2, Bak for Ieraioal Selemes, Washigo DC: The Ieraioal Moeary Fud. Shimizu, C. ad K.G. Nishimura (26), Biases i Appraisal Lad Price Iformaio: The Case of Japa, Joural of Propery Ivesme & Fiace 24 (2), Shimizu, C. ad K.G. Nishimura (27), Pricig Srucure i Tokyo Meropolia Lad Markes ad Is Srucural Chages: Pre-bubble, Bubble, ad Pos-bubble Periods, Joural of Real Esae Fiace ad Ecoomics 35(4), Shimizu, C., K.G. Nishimura ad Y. Asami (24), Search ad Vacacy Coss i he Tokyo Housig Marke: Aemp o Measure Social Coss of Imperfec Iformaio, Regioal ad Urba Developme Sudies 6(3), Shimizu, C., K.G. Nishimura ad T. Waaabe (2), Housig Prices i Tokyo: A Compariso of Hedoic ad Repea Sales Measures, Joural of Ecoomics ad Saisics 23/6, Shimizu, C., H. Takasuji, H. Oo ad K.G. Nishimura (2), Srucural ad Temporal Chages i he Housig Marke ad Hedoic Housig Price Idices, Ieraioal Joural of Housig Markes ad Aalysis 3(4), Shimizu, C., K.G. Nishimura ad T. Waaabe (2), House Prices from Realors, Magazies, ad Goverme: A Saisical Compariso, Mimeo. Silver, M. (29a), Do Ui Value Expor, Impor, ad Terms of Trade Idices Represe or Misreprese Price Idices?, IMF Saff Papers 56, , IMF, Washigo DC. Silver, M. (29b), Ui Value Idices, Chaper 2 i XMPI Maual (29). Silver, M. (2), The Wrogs ad Righs of Ui Value Idices, Review of Icome ad Wealh, Series 56, Special Issue, S26-S223. Sadard ad Poor s (29), S&P/Case-Shiller Home Price Idices; Idex Mehodology, New York: Sadard ad Poor s. Saisics Porugal (Isiuo Nacioal de Esaisica) (29), Ower-Occupied Housig: Ecoomeric Sudy ad Model o Esimae Lad Prices, Fial Repor, paper preseed o he Eurosa Workig Group o he Harmoizaio of Cosumer Price Idices, March 26-27, Luxembourg: Eurosa. Seele, M. ad R. Goy (997), Shor Holds, he Disribuios of Firs ad Secod Sales, ad Bias i he Repea-Sales Price Idex, Joural of Real Esae Fiace ad Ecoomics 4(-2), Soe, R. (956), Quaiy ad Price Idices i Naioal Accous, Paris: OECD. Thibodeau, T.G. (992), Resideial Real Esae Prices: , The Blacksoe Compay, Mou Pleasa (MI). Thibodeau, T.G. (23), Markig Sigle-Family Propery Values o Marke, Real Esae Ecoomics 3(), 22. Thorses, P. (997), Cosise Esimaes of he Elasiciy of Subsiuio bewee Lad ad No-Lad Ipus i he Producio of Housig, Joural of Urba Ecoomics 42, Triple, J.E. (26), Hadbook o Hedoic Idexes ad Qualiy Adjusmes i Price Idexes; Special Applicaio o Iformaio ad Techology Producs, Direcorae for Sciece, Techology ad Idusry, Paris: OECD. Triple, J.E. ad R.J. McDoald (977), Assessig he Qualiy Error i Oupu Measures: The Case of Refrigeraors, The Review of Icome ad Wealh 23(2), Tse, R.Y.C. (22), Esimaig Neighbourhood Effecs i House Prices: Towards a New Hedoic Model Approach, Urba Sudies 39(7), Turvey, R., (989), Cosumer Price Idices: A ILO Maual, Geeva: Ieraioal Labour Office. Hadbook o Resideial Propery Prices Idices (RPPIs) 75

178 Bibliography UK Deparme of he Evirome (982), A New Idex of Average House Prices, Ecoomic Treds 348, Uied Naios (29), Pracical Guide o Producig Cosumer Price Idices, New York ad Geeva: Uied Naios. va der Wal, E., D. er Seege ad B. Kroese (26), Two Ways o Cosruc a House Price Idex for he Neherlads: The Repea Sale ad he Sale Price Appraisal Raio, paper preseed a he OECD-IMF Workshop o Real Esae Price Idices, Paris, November 6-7, 26. Verbrugge, R. (28), The Puzzlig Divergece of Aggregae Res ad User Coss, 98-24, The Review of Icome ad Wealh 54, de Vries, P., J. de Haa, E. va der Wal ad G. Marië (29), A House Price Idex Based o he SPAR Mehod, Joural of Housig Ecoomics 8(3), Wag, T. ad P.M. Zor (997), Esimaig House Price Growh wih Repea Sales Daa: Wha s he Aim of he Game?, Joural of Housig Ecoomics 6(2), Wallace, N.E. ad R.A. Meese (997), The Cosrucio of Resideial Housig Price Idices: A Compariso of Repea-Sales, Hedoic-Regressio ad Hybrid Approaches, Joural of Real Esae Fiace ad Ecoomics 4( 2), Wezlick, R. (952), As I See he Flucuaios i he Sellig Prices of Sigle Family Resideces, The Real Esae Aalys 2 (December 24), Wolvero, M.L. ad J. Seeza (2), Hedoic Esimaes of Regioal Cosa Qualiy House Prices, Joural of Real Esae Research 9(3), Wood, R. (25), A Compariso of UK Resideial House Price Idices, pp i Real Esae Idicaors ad Fiacial Sabiliy, BIS Papers No 2, Bak for Ieraioal Selemes, Washigo DC: The Ieraioal Moeary Fud. Wygarde, H. (927), A Idex of Local Real Esae Prices, Michiga Busiess Sudies Volume, Number 2, A Arbor: Uiversiy of Michiga. Zhu, H. (25), The Imporace of Propery Markes for Moeary Policy ad Fiacial Sabiliy, pp i Real Esae Idicaors ad Fiacial Sabiliy, Volume 2, Bak for Ieraioal Selemes (ed.). 76 Hadbook o Resideial Propery Prices Idices (RPPIs)

179 Idex Idex accuracy 9.35 rade-off bewee frequecy ad accuracy 9.38 (e) acquisiios approach (g) 3.5, 9.28 admiisraive daa 9. aggregae (g) aggregaio (g) firs-sage aggregaio examples of aggregaio sales versus socks of housig secod-sage aggregaio aicipaed iflaio raes (for srucures ad lad) 3.55, 3.59 askig price (g), 9.-3 assessed value or appraisal (g) 7.2, assessme-based mehods 3.23, 7.-6 axiomaic (es) approach (g) base period (g) balace shees 3.8 bias (g) omied variables bias 5.6 sample selecio bias 4.3, ui value bias 4.5 builder s model buyig ad sellig a propery process of buyig ad sellig ,.59 ime lie (Japa) buy-o-le marke 6.6 capializaio raio case sudies Caada.27-4 Colombia Germay.4-49 Idia.65-7 Japa.5-58 Souh Africa Uied Kigdom chai idex(g) characerisics (g) 3.8, 4-29, 5. addig srucures characerisics 8.-2 lad (or plo) size 4.34 srucure size 4.34 characerisics prices hedoic approach (g), ceral edecy measures 4.,.3- compoe (g) cosisecy i aggregaio (g) cosisecy of mohly wih quarerly esimaes cosrucio cos price idex 8.37 cosumer price idex (CPI) (g) comparabiliy (across couries) ,.3 cos of producio approach coverage (g), 9.6, 9.8, curre period, or compariso period (g) daa cleaig (g) 5.9, 6.-2, 7.22, 7.33 daa sources (i differe couries).2-3 decomposiio io lad ad srucures compoes deflaig (g) depreciaio (g) depreciaio rae 3.48, 8.5 e depreciaio 4.9, oe hoss shay (or ligh bulb) depreciaio 3.5 sraigh lie (or geomeric) depreciaio 3.5, developig couries discouig 3.43 domai (g) see scope drif (g) durable cosumpio good (g) 3.4 ecoomic approach (g) ediig (g) see daa cleaig elemeary aggregae (g) ex ae user cos 3.47 exisig dwelligs (g) exper opiio iformaio 9.22 family of resideial propery price idices 3.29 fiacial opporuiy cos approach 3.45 Fisher (ideal) price idex (g) 4.6-8,.9 fixed weigh idices (g) fixed base idices 4.8 frequecy of resideial propery price idices , geomeric Laspeyres idex (g) goods (g) gross capial formaio hedoic regressio (g) 3.22, examples of hedoic regressio mehods use of moooiciy resricios use of exogeous iformaio o srucures , hedoic impuaio approach (g) , ,.4-44 arihmeic impuaio idices double impuaio double impuaio Laspeyres idex 5.27, 5.66,.43 double impuaio Paasche idex 5.28, 5.67 double impuaio Fisher idex 5.29, 5.68 geomeric impuaio idices hedoic modelig parameric liear or logarihmic-liear) model 5.2,.28-3 sigle impuaio 5.27 hedoic qualiy adjusme i differe couries.8 qualiy adjusme for srucures households (g) housig sock (g) approximaio of housig sock value hybrid models (g) see repea sales mehod Hadbook o Resideial Propery Prices Idices (RPPIs) 77

180 Idex ideiy es (g) impued price (g) idex referece period (g) iefficiecy (of repea sales approach) iformal housig marke (g), , Jevos price idex (g) Laspeyres price idex (g) lad buildig lad price idex (Germay) decomposiio io lad ad srucures compoes price of lad 5.3 liear splies likig (g) Lowe price idex (g), lower-level idex (g) see (firs-sage) aggregaio life-cycle heories 6.6 mached models approach (g) marke value (g) mea idex (g) media idex (g).7 mea-daa.8, mix adjusme (g) see sraificaio moey oulays or paymes approach (g), moooiciy resricios morgage compaies movig average 4.45 Mudge-Soe framework mulicollieariy 5.8, 8.3, 8.24 e acquisiios approach (g), 9.28 offer price (g), opporuiy cos approach oulier (g) see daa cleaig ower-occupied housig (g) Paasche price idex (g) parameer sabiliy.37 paymes approach (g) 3.5 poolig (cross secio) daa 5.-2 price daa a differe sages price referece period (g) price relaive (g) producs (g) pure price chage (g) purpose-desiged saisics fiess-for-purpose of daa sources qualiy chage (g) qualiy adjused srucures 8.- qualiy adjused price idex for srucures 8.23 real esae ages regressio echiques ordiary leas squares regressio 5.5 oliar regressio 8.6 weighed leas squares regressio 5.5 weighed leas squares repea sales regressio 6.3, reproducibiliy 6.2 real equivalece approach (g) 3.5, 3.6 real cos (approximaio) 3.49 re o value (price) raio see capializaio raio repea sales mehod (g) 3.2, 6.-32,.45-56, arihmeic repea sales mehod 6.9 Gaussia radom walk 6.4 holdig period 6.7 hybrid models use of assessme iformaio 6.2 use of iformaio o maieace ad reovaio expediures 6.23 repea sales equaio 6.4 revisios 6.2 weighed leas squares echique represeaive propery (g) resideial propery (g) resideial real esae services idusry oupu revisios 5.7, revisio policy reweighig (g) rollig widow approach (g) , sample (g) sample probabiliy sample selecio bias (g) see bias samplig frame (g) scope (g), seasoal goods (g) seasoal adjusme , seasoaliy (reame i a esideial propery price idex) sellig (or rasacio) price (g) spaial depedece 5.7 specificaio (g) SPAR mehod (g) , arihmeic SPAR idex 7.-2 descripive regressio model 7.25 esimaor of sock-beased idex 7.3 geeralized regressio framework 7.28 model assumpios Paasche-ype SPAR idex 7.8 qualiy chage bias sale price appraisal raio (or relaive) 7.7 splies see liear splies sadardized propery 5.2 sarig problem (of idex series) 7.35 sock-based idex , , usig hedoic impuaio sraificaio mehod (g) 3.2, , i differe couries.7,.-6 marke segmeaio 4.-2, 5.37 sraified hedoic idices srucures price of srucures 5.3 superlaive idex (g).9 symmeric idex (g) 78 Hadbook o Resideial Propery Prices Idices (RPPIs)

181 Idex sysem of aioal accous (SNA) (g) framework for resideial propery price idices 3.6-4, 2.4 sysemaic error see bias ime dummy variable (hedoic) approach (g) 5.5, 5.-8 adjace-period echique ime dummy idex 5. liear ime dummy model liear ime dummy model wih qualiy adjused srucures log-liear ime dummy model , log-log ime dummy model imeliess 9.8 Törqvis-Theil idex.9 radiioal dwelligs (i developig couries), (fial) rasacio price from morgage compaies 9.8 from propery regisers ad ax offices rasacio coss 3.4 rasacio oise 6.8 urig poi 4.2 ui value or average value (g) 3.32, 4.5 ui value bias see bias user coss durable goods i geeral for ower occupied housig user cos approach (g) 3.5, simplified user cos approach 3.65 user requiremes 9.25 uses of resideial propery price idices compoe of wealh deflaor i aioal accous fiacial soudess idicaors ieraio ad ier-area comparisos macro-ecoomic idicaor 2.8- moeary policy ad iflaio argeig ower occupied housig i CPI 2.27 uses approach (g) valuaio price from morgage compaies from ax offices 9.2 value (g) weighs (g) daa sources for weighs weigh referece period (g) o-formal (iformal ad radiioal) housig.89-9 sales weighs 4.6 sock weighs 4.6 Hadbook o Resideial Propery Prices Idices (RPPIs) 79

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183 Europea Commissio Hadbook o Resideial Propery Prices Idices (RPPIs) Luxembourg: Publicaios Office of he Europea Uio pp. 2 x 29.7 cm Theme: Ecoomy ad fiace Collecio: Mehodologies & Workig papers ISBN ISSN doi:.2785/347 Ca. No KS-RA-2-22-EN-C

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186 KS-RA-2-22-EN-C Hadbook o Resideial Propery Prices Idices (RPPIs) For mos ciizes, buyig a resideial propery (dwellig) is he mos impora rasacio durig heir lifeime. Resideial properies represe he mos sigifica compoe of households expeses ad, a he same ime, heir mos valuable asses. The Resideial Propery Prices Idices (RPPIs) are idex umbers measurig he rae a which he prices of resideial properies are chagig over ime. RPPIs are key saisics o oly for ciizes ad households across he world, bu also for ecoomic ad moeary policy makers. Amog heir professioal uses, hey serve, for example, o moior macroecoomic imbalaces ad risk exposure of he fiacial secor. This Hadbook provides, for he firs ime, comprehesive guidelies for he compilaio of RPPIs ad explais i deph he mehods ad bes pracices used o calculae a RPPI. I also examies he uderlyig ecoomic ad saisical coceps ad defies he priciples guidig he mehodological ad pracical choices for he compilaio of he idices. The Hadbook primarily addresses official saisicias i charge of producig resideial propery price idices; a he same ime, i addresses he overall requireme o RPPIs by providig a harmoised mehodological ad pracical framework o all paries ieresed i he compilaio of such idices. The RPPIs Hadbook has bee wrie by leadig academics i idex umber heory ad by recogised expers i RPPIs compilaio. Is developme has bee co-ordiaed by Eurosa, he saisical office of he Europea Uio, wih he collaboraio of he Ieraioal Labour Orgaizaio (ILO), Ieraioal Moeary Fud (IMF), Orgaisaio for Ecoomic Co-operaio ad Developme (OECD), Uied Naios Ecoomic Commissio for Europe (UNECE) ad he World Bak.