A Framework For Analysing House Prices Using Time, Space And Quality Criteria *

Transcription

1 A Framework For Analysng House Prces Usng Tme, Space And Qualty Crtera * Shanaka Herath, Gunther Maer Research Insttute for Spatal and Real Estate Economcs WU Wen 1. Introducton An ncreasng number of theoretcal and emprcal studes have dealt wth the determnants of house prces over the last several decades. The hedonc prce method (HPM) s undoubtedly one of the most popular and most used methods employed n these studes. Most early hedonc models of house prces typcally ncluded several structural characterstcs of housng unts as exogenous varables. Subsequently, spatal hedonc models emerged wth the wdespread use of locatonal and neghbourhood concepts n urban economcs. Hedonc models were further expanded recently to nclude temporal dmenson as a result of ncreasng number of panel applcatons n real estate and urban economcs lterature. The extended model whch s known as the spatal panel model takes nto account both spatal and temporal dynamcs of house prces. The purpose of ths paper s to combne structural characterstcs of houses along wth spatal and temporal aspects wthn a sngle analytcal framework, and put forward an alternatve framework to the spatal panel models. The HPM s also known as the hedonc demand theory or the hedonc regresson. Ths methodology estmates the value of a commodty or alternatvely the demand for a commodty. The HPM s used n consumer and market research (e.g. Hrschman and Holbrook, 1982), calculaton of consumer prce ndces (e.g. Moulton, 1996), tax assessment (e.g. Berry and Bednarz, 1975), valuaton of cars (e.g. Cowlng and * The authors would lke to thank the partcpants of the doctoral research semnar on Regonal and Envronmental Economcs at Venna Unversty of Economcs and Busness for ther comments. We reman fully responsble for any errors. Venna Unversty of Economcs and Busness, Research Insttute for Spatal and Real Estate Economcs, Nordbergstrasse 15 (UZA4, Kern B, 4. Stock), A-1090 Venna, Austra, emal: shanaka.herath@wu.ac.at, tel: , fax: +43-(0)

2 Cubbn, 1972), computers (e.g. Whte et al, 2004) etc. n addton to real estate economcs and real estate apprasal, the topc dscussed n ths paper. The methodology has recently been used extensvely n real estate and housng market research: some of the most appled areas nclude correcton for qualty changes n constructng a housng prce ndex, assessment of the value of a property n the absence of specfc market transacton data, analyss of demand for varous housng characterstcs or housng demand n general, and testng assumptons n spatal economcs. The general dea of the HPM s as follows: commodtes are characterzed by ther consttute propertes, hence the value of a commodty can be calculated by addng up the estmated values of ts separate propertes. Accordng to ths nformal defnton, a couple of requrements need to be fulflled n order to be able to calculate hedonc prces. The frst requrement s that the composte good under consderaton could be reduced to ts consttuent parts. The second s there s a value for those consttuent parts n the market or at least t s possble to estmate an approxmate value. The dea of hedonc (mplct) prces has ts orgns n mcroeconomcs. Determnaton of demand of certan goods - partcularly of those that come as composte goods wth several ntrnsc features or characterstcs becomes ncreasngly dffcult. There were several dfferent applcatons that consdered ths mult-dmensonal nature of houses as a commodty, but Rosen (1974) was the frst to clearly refne the concept by mappng out how the hedonc prces represented the jont envelope of bds (from demand) and offers (from supply). Urban economsts demonstrate that not only physcal characterstcs, but also locatonal characterstcs partly determne the overall level of servces offered by a housng unt. Subsequent hedonc papers, therefore, ncorporate locatonal varables explctly n addton to structural characterstcs. A justfcaton for these locatonal determnants of house prces s very well artculated n the urban economcs lterature. For nstance, most of the scholarly work on urban monocentrc models nclude ether dstance to the cty centre, travel tme or travel cost n the model specfcaton to capture these prce dynamcs generated by locaton n space. Ths paper, among other thngs, examnes the wdely accepted hypothess that house prce s determned partly by locatonal characterstcs. 2

3 Most macroeconomc studes avalable on temporal dynamcs of house prces emphasse on changes of macroeconomc varables and ther co-movement wth house prces. A new class of hedonc models, spatotemporal housng models, on the other hand, consders spatal and temporal determnants of house prces smultaneously. In spatotemporal models, the hedonc model s augmented to nclude prevous values of the dependent and explanatory varables from nearby observatons or regons. These spatotemporal models deal wth change of explanatory varables X over tme and resultng change n house prces Y, and contan both tme as well as space-tme lags of the model varables. A detaled account of these spatal and spatotemporal models s provded by LeSage and Pace (2004) and Anseln et al. (2004). The man purpose of ths paper s to combne structural characterstcs, spatal attrbutes and temporal dynamcs of house prces wthn a sngle analytcal framework. The frst part of the paper deals wth the research queston what determnes house prces? Ths secton provdes a dscusson of theoretcal and methodologcal developments related to the hedonc regresson, spatal hedonc models, and temporal models of house prce dynamcs. The latter part of the paper deals wth a conceptual composte model that ncorporates these three pllars of house prce determnants,.e. structural characterstcs of houses, spatal attrbutes and temporal dynamcs. The research queston addressed n ths secton s whether the proposed composte model produces unbased and consstent estmates of mplct prce of characterstcs. If the error term of the composte model s stochastc wth ndependent and dentcally dstrbuted (d) characterstcs, then t provdes statstcal evdence that house prces are determned by a combnaton of structural characterstcs, spatal attrbutes and temporal dynamcs. The remander of the paper s structured as follows: Secton 2 presents a bref overvew of hstorcal developments related to the methodology as presented n prevous lterature. It also provdes an overvew of the urban economcs lterature on spatal dynamcs of house prces based on monocentrc and polycentrc models. Ths secton also looks at drvers of temporal change of house prces. Secton 3 revews dfferent estmaton technques and ssues related to functonal form and model specfcaton of the composte model. Secton 4 concludes the paper by provdng a summery of the dscusson. 3

4 2. Lterature revew Housng characterstcs and house prces The number and amount of dstnctve features a housng unt possesses determnes the qualty of servces that partcular housng unt provdes. Snce the HPM offers a bass to estmate demand and prces for composte commodtes, the method can be appled to estmate house prces takng nto account the specfc characterstcs of housng unts. The heterogeneous nature of real estate propertes n fact justfes the use of HPM for estmatng ther value and demand. The HPM has, therefore, been extensvely used n real estate and housng market research n the recent past. There s no consensus among scholars as to who frst ntroduced the method of hedonc regresson even though most of the scholars agree that t was Court (1939) who frst used the HPM. Accordngly, Bartk (1987), Goodman (1998), Robert and Shapro (2003) among many others argue that the frst actual estmaton of a HPM was a hedonc prce ndex for automobles by A.T. Court (1939). These scholars document that the methodology was popularsed by Zv Grlches n the early 1960s. One reason to consder Court s study as a sgnfcant contrbuton s that t deals wth problems of non-lnearty and wth changes n underlyng goods bundles (Goodman, 1998). Robert and Shapro (2003), commentng on Court s methodology, contend that mplct prce components for each of a bundle of product characterstcs are determned by a regresson procedure that expresses the prce of a product as a functon of the coeffcents assocated wth each characterstc. The prce of a new product (or dfferent product) can then be compared wth that of the prevously exstng product when one utlzes these coeffcents They further hghlght that Court (1939) and Grlches (1961) allow for tme dependence that does not requre any new methodology makng t possble to smply use the prevous tme-ndependent methodology restrctng the regresson to two consecutve perods. Ths wll calculate a measure of overall prce change for the hedonc commodty. A second group of scholars poneered by Colwell and Dlmore (1999) demonstrate that Haas (1922a, 1922b) conducted a hedonc study more than ffteen years pror to A. T. Court even though he never used the term hedonc. Haas analysed prce per acre adjusted for year of sale, road type, and cty sze, usng data on 160 sales 4

5 transactons gathered from farm sales n Mnnesota. The ndependent varables n the hedonc analyss ncluded deprecated cost of buldngs per acre, land classfcaton ndex, sol productvty ndex, and dstance to the cty centre. Colwell and Dlmore (1999) argue that Haas was nfluental but deny makng a comprehensvely strong case for Haas as the poneer to estmate a hedonc model. Surprsngly, ther alternatve hypothess s not Court (1939), but Wallace (1926), who used data aggregated by county to calculate comparatve farm land values n Iowa. Many other scholars contrbuted to the HPM over the years although the HPM s derved mostly from Lancaster s (1966) consumer theory and Rosen s (1974) model. The followng secton looks at the hstorcal development of the HPM. Houthakker (1952) takes nto account the problem of qualty varaton wthn the theory of consumer behavour. He leaves out a multtude of corner solutons necesstated by conventonal demand theory and assumes that consumers purchase only a neglgble fracton of all goods avalable to them. Ths treatment s preserved by many subsequent authors to mantan smplcty n the analyss. Ths early contrbuton of Houthakker was later developed and extended by Becker (1965), Muth (1966), and Lancaster (1966) to explctly take n to account the utlty bearng characterstcs n the context of consumer behavour. Grlches (1958) revved the HPM by further developng Court s work. Grlches s paper embedded technologcal change and nnovaton nto hedonc prces through qualty of goods. Ths hedonc model on demand for fertlzer contrbuted to popularse the HPM at the early stage. Demand for fertlzer relates prces and mxes of dfferent components of fertlzer (ntrogen, phosphorc acd and potash) to derve better weghts, whch n turn are used to develop a seres of constant qualty fertlzer quanttes and prces. Grlches s (1961) work on automoble prce ndces usng automoble models as unt of analyss attracted consderable attenton although t was publshed n an naccessble publcaton (Goodman, 1998). Most mportant theoretcal foundatons of the HPM are Lancaster s consumer theory and Rosen s model. These scholarly works are consdered early but sgnfcant contrbutons to the development of HPM. Lancaster (1966) establshes mcroeconomc foundatons for analyzng utlty-bearng characterstcs and apples that to a range of topcs ncludng housng market, fnancal assets, the labour-lesure 5

6 trade off, and the demand for money. In hs model quanttes of goods and quanttes of characterstcs are lnked by a fxed relatonshp called household producton functon. Whle households face a budget constrant defned over quanttes of goods, they derve utlty from the quanttes of characterstcs these goods do produce. Wth ths model, Lancaster (1966) focuses on the demand sde of the market. Rosen (1974) ntegrates the HPM nto standard economc theory. Inspred by work of Houthakker (1952), Becker (1965), Muth (1966), and Lancaster (1966), he derves bd functons of utlty maxmzng consumers and offer functons of proft maxmzng producers and shows that n equlbrum the hedonc prce functon represents the jont envelope of these functons. In ths form Rosen put forward a metculous explanaton of the mplct market and hedonc prces n the context of dfferentated products. Usng a vector of objectvely measured characterstcs representng a class of dfferentated products, he observes product prces and the amounts of characterstcs assocated wth each good to estmate a set of mplct or hedonc prces. Because of the jont dervaton of the hedonc prce functon from the supply and the demand sde, Rosen argued further that the entre set of mpled prces gudes both consumer and producer locatonal decsons n characterstcs space. Hs study extends to analyse buyer and seller choces, market equlbrum and the emprcal mplcatons of the HPM. Rosen s theoretcal foundaton leads to a two step approach, whch works as follows: frst, a hedonc equaton s estmated. Subsequently, the mplct prce of a characterstc s derved as the partal dervatve of the hedonc equaton wth respect to that characterstc. Dependng on the functonal form nvolved, ths dervatve has to be evaluated at a partcular bundle of characterstcs. In ths context, the emprcally derved prces are embedded n a system of demand and supply equatons. In Rosen s model, ncome s drectly ncorporated n the budget constrants of the consumer. Ths mples that the consumer s margnal wllngness to pay for a certan mplct attrbute may also change wth hs ncome. Buyers bd prce (or wllngness to pay) for an attrbute s a functon of the utlty level, the buyer s ncome, and other varables whch nfluence tastes and preferences ncludng educaton, age etc. An nverse demand functon can be estmated by usng the margnal prce as an endogenous varable n the second-stage smultaneous equaton. If t s possble to 6

7 trace back the nverse demand functon based on the mplct margnal prce functon, the utlty change wth respect to certan qualty changes can also be measured by ntegratng the nverse demand. Lancaster s and Rosen s deas dffer from each other bascally n two ways: the functonal form of hedonc regresson and the answer to the queston whether the consumers buy a bundle of goods or separate goods. The fact that a bundle of goods or separate goods are purchased have an mpact on the mplct market as follows. The Lancastran ndex (1966) s based on the dea that usefulness of goods depends on ther characterstcs, and goods can be arranged nto groups based on ther characterstcs. Consumers buy goods wthn groups based on the number of characterstcs they possess per dollar. Accordng to Lancaster, the consumer s utlty orgnates from the dfferent characterstcs (not just the quanttes of the dfferent goods) whch the goods themselves provde. Goods are members of a group and some or all of the goods n ths characterstc group are consumed n combnatons, subject to the consumer s budget. Accordngly, the Lancastran ndex s more approprate for consumer goods. Rosen s model (1974), on the other hand, has two dstnct steps: an ntal step nvolvng an estmaton of the margnal prce for the attrbute of nterest (by regressng the prce of a commodty or good on ts attrbutes), and a second step to dentfy the nverse demand curve (or the margnal wllngness to pay functon) from the mplct prce functon estmated n the frst stage. Rosen mantans that there s a range of goods, but that consumers typcally do not acqure preferred attrbutes by purchasng a combnaton of goods, rather each good s chosen from the spectrum of brands and s consumed dscretely. Accordngly, Rosen s model looks appealng to estmate demand for durable goods. Model specfcatons n these two theores dffer as well. Lancaster s consumer theory assumes a lnear relatonshp between the prce of goods and the characterstcs contaned n those goods. Implct prces are therefore constant over ther range of characterstc amounts, and only a change n the combnaton of goods consumed s possble. On the other hand, Rosen s model assumes a nonlnear relatonshp between the prce of goods and ther nherent attrbutes. The mplct prce s not a constant, but a functon of the quantty of the attrbute beng bought and of the quanttes of other 7

8 attrbutes assocated wth the good (dependng on the actual functonal form of the equaton) Spatal attrbutes ncludng locaton and accessblty The standard urban economc monocentrc model developed ntally by Alonso (1964) suggests that the prncpal varable causng varatons n constant-qualty house prces wthn a metro area s land prce. A typcal land rental equaton ncludes dstance from the CBD, agrcultural land rental, a converson parameter that depends on transport cost per mle and communty ncome suggestng that dstance to the CBD should be ncluded n any house prce model. Alonso s model has been emprcally tested by many scholars (Ball (1973) and Rchardson (1988) provde lterature surveys on ths topc). Fgure 1 The Monocentrc Model by Alonso (1964) Source: Authors notes Fgure 1 depcts the basc dea behnd the monocentrc model. The central part of ths model s accessblty as a determnant of value of land (or value of houses n the context of ths paper). Numerous papers have studed accessblty as a determnant of real estate value. Jackson (1979), for nstance, uses trend surface analyss to examne accessblty effects n a study of house prces n Mlwaukee. He found that a quadratc accessblty polynomal s preferred n explanng house prces and that 8

9 accessblty effects are sgnfcant. Rents peak at an area west of the CBD whch s well served by expressways. Despte early domnance of Alonso s model, the exstence of contradctory results n the expected sgns of the regresson model s coeffcents and, above all, wth regard to the accessblty varable s evdent. The multcentrc behavour of the urban spatal structure s probably what has motvated these contradctory results. In a study by Bender and Hwang (1985), the estmated coeffcent was postve on dstance from the CBD when a regresson was estmated for the entre study area of Chcago. When they subdvded the study area nto catchment areas for the employment centre of Chcago, the coeffcent on dstance to the relevant employment centre turned negatve. Smlarly, Dubn (1992) publshed that there s lack of emprcal support for the captalzaton of neghbourhood and accessblty effects probably because of the multcentrc nature of the cty (polycentrc rent gradents). In monocentrc theory, accessblty s measured as the dstance, cost or tme to the central busness dstrct (CBD). In the presence of other sub-centres n addton to the CBD, t becomes more complcated, because the exstence of those mult-centres also needs to be taken nto account. The polycentrc theory that deals wth multcentrc nature of ctes evolved n ths context. For example, Dubn & Sung (1987) allow for the exstence of non-cbd peaks n the rent gradent by usng a splne functon to estmate the rent gradent along four rays emanatng from the CBD. They demonstrate that centres such as the CBD, unverstes, and ndustral parks do nfluence rents but ths nfluence s lmted to propertes n close proxmty to the centre. Ther estmates show the effect of the CBD was lmted to a crcle wth radus 1.7 mles. The unverstes affected rents wthn a crcle of one mle radus. Dubn (1992) states that non-cbd peaks n the rent gradent cause tradtonal means of capturng accessblty effects to gve nconclusve results. He suggests a more flexble means of capturng neghbourhood and accessblty effects: one that allows for multple peaks n the rent surface. Accordng to Dubn (1992), n addton to polycentrc rent gradents, the measurement problems wth regard to neghbourhood qualty are also possble reasons for nconclusve results. The neghbourhood qualty s unobservable and must be addressed through the use of proxy varables. The proxes themselves are measured wth error due to the boundary problem, because the 9

10 concept of neghbourhood boundares s vague. Dubn and Sung (1987) also report that multcentrc nature poses several challenges wth regard to the selecton and spatal delmtaton of these sub-centres. Dubn (1992) subscrbes to a geostatstcal model when he omts all neghbourhood and accessblty measures from the set of explanatory varables and nstead models the resultng autocorrelaton n the error term to avod above mentoned complextes assocated wth the analyss. In addton to the ssue of measurement and neghbourhood boundares, Olmo (1995) put forward other dffcultes that emerge wth the multcentrc theory. One of them s the selecton and specfcaton of neghbourhood characterstcs. A second problem s that the parameters referrng to the neghbourhood characterstcs of the model are constant for the whole of the urban space, but a structural change test wll show otherwse n the majorty of cases. The presence of spatal autocorrelaton s the other mportant ssue n ths context: dependence of the neghbourhood characterstcs and the accessblty on the locaton. Implcaton of ths spatal dependence s the spatal heterogenety and autocorrelaton. If the space s omtted from the hedonc model, the estmated coeffcents wll be based and nconsstent. Olmo (1995) also suggests that the OLS estmator of the parameters of the hedonc model n the presence of spatal autocorrelaton s neffcent. Moreover, models wthout spatal varables tend to produce wrong standard errors of the estmates of the mplct prce of characterstcs. To control for these spatal effects, spatal dmenson was ncorporated nto hedonc models by Anseln (1998), Pace et al. (1998), Orford (2000), Bradford et al. (2004), and Brasngton (2004) and others Temporal dynamcs of house prces Even though t s wdely accepted that house prces are senstve to the temporal dynamcs, they are hardly ncorporated nto the hedonc models. Lterature related to temporal dynamcs of house prces justfy addng-n a tme varable as a determnant of house prces. Incluson of temporal dmenson allows capturng the tme related dynamcs of the market such as volatle prces generated by the persstent trend n the economy or the cyclcal behavour. 10

11 Most studes on temporal dynamcs of house prces are based on natonal level data. There are a number of studes that examne macroeconomc aspects of the housng market. For nstance, Poterba (1991) observes ntertemporal fluctuatons of house prces n partcular ctes or regons wth shfts n ncome and constructon costs, but provde evdence there s no mpact of aggregate demographc effects and user cost varatons. Hghly cted scholarly work of Mankw and Wel (1989), and Case and Shller (1990) mantan there are sgnfcant effects of populaton demographcs. There are also a consderable number of papers on house prce bubbles. Abraham and Hendershott (1993, 1996), for nstance, publsh support for speculatve bubbles n the housng market. The scholarly work on temporal changes of house prces belong to two man classes of studes. One class assumes that temporal trend, or the trend of market fundamentals s what drves house prces. Most of these are natonal level studes that take nto account the trend of the natonal economy,.e. real ncome, or trend of man fundamental varables such as constructon costs. On the other hand, the second class presumes that cyclcal component of the economy explans house prces for a certan extent. These studes consder busness cycle movements over tme, and nvestgate whether there s a relaton between the busness cycles and house prces. Several studes evaluate temporal changes of house prces usng panel data. Most common way of lookng at temporal changes of house prces n these models s to assess temporal as well as spatal changes smultaneously. Panel data model of Km (1993) reported that constructon costs, nterest rates, metro populaton, ncome, ncome growth and clmate have an mpact on house prces. Baltag and Chang (1994), usng a panel data set of Boston area predcted that crme rate, ar polluton, tax rate, pupl-teacher rato, proporton of the populaton n lower status, age of the house and the dstance from the employment centres determne medan house prces. In a separate study, Mendelsohn et al. (1992) used panel data on repeated sngle famly home sales n Massachusetts and found a sgnfcant reducton n housng values as a result of these houses proxmty to hazardous waste stes. 11

12 3. Methodology A cauton s n order before proceedng to the secton on conceptual model. The conventonal hedonc prce regresson equaton wth regard to the housng market s ether rent or house value aganst the characterstcs of the unt that determne the respectve rent or the value of the house. Majorty of scholars would argue that rent values do not represent actual value of real estate. On the one hand, the rent values may need adjustments for tax payments, deprecaton and other transactons costs etc. On the other hand, rents are based on current demand and supply condtons rather than the actual value of underlyng real estate. Snce t s almost mpossble practcally to obtan the actual values of real estate, most studes, n emprcal analyses, consder rent values to be proxes for value of the real estate. The frst hypothess of ths study s that house prce s determned by ts structural characterstcs. Secton 2 of the paper draws from lterature to support the argument that house prce s determned by structural characterstcs that houses hold. Lterature related to the HPM provded the foundaton and background knowledge to model ths econometrc relatonshp. The model can be extended to ncorporate the accessblty varable, dstance to the CBD, as a measure to rectfy spatal dependence and resultng spatal autocorrelaton. Ths possblty was justfed n urban economcs lterature n general, and n lterature related to monocentrc model and multcentrc model (or polycentrc model) n partcular. The follow-on hypothess n the second stage s that the house prce s determned by structural as well as locatonal characterstcs. Part 2 of secton 2 documents the foundatons of ths dea. The model can be extended once more wth a temporal varable to test the hypothess whether house prce s determned by structural, locatonal as well as temporal characterstcs. Part 3 of secton 2 provded detals about lterature related to ths thrd extenson. The conceptual model Most of the prevous analyses of house prces do not typcally take nto account the three dmensons,.e. housng characterstcs, accessblty and temporal dynamcs jontly so that the estmates produced are lkely to be based. The composte model suggested here wll reflect temporal and spatal dmensons n addton to the qualty 12

13 of the house represented by ts ntrnsc characterstcs (see conceptual model n Fgure 2). The estmates of the prospectve model, therefore, are lkely to be unbased. Fgure 2 The Conceptual Model Unt of analyss: House prce Mcroeconomc theory: Hedonc prce method *Characterstcs of of house Urban economcs theory: Monocentrc and polycentrc models *Locaton, accessblty and neghbourhood Macroeconomc theory: *Trend and busness cycles of the economy Source: Authors own work Regresson analyss related estmaton s the most popular estmaton approach among the scholars usng the HPM. Multple regresson analyss may ether be an OLS regresson or a maxmum lkelhood estmaton of the log-lkelhood functon derved from the hedonc functon. Both these estmaton technques try to fnd a vector of parameters that best matches the values of explanatory varables of observatons wth the respectve observed prce. They dffer by the crteron they use for dentfyng the best match. The explanatory varables may be the characterstcs values, or mathematcal transformatons thereof, dummy varables or panel varables makng t possble to allow for non-lnearty, varable nteracton, or other complex valuaton stuatons. As mentoned before, the conventonal hedonc prce regresson equaton wth regard to the housng market s ether rent or house value aganst the characterstcs of the housng unt that determne the respectve rent or the value of the house. The fundamental assumpton of regresson that the relevant determnants of the dependent 13

14 varable (rent, prce, or value n ths case) are known precsely and n advance s not volated. A classcal hedonc equaton s as follows: A sample of n ndependent observatons of house prce y, = 1,, n are lnearly related to structural characterstcs n a matrx X y = X β + ε ε ~ N(0, σ 2 ) = 1,..., n In practce, varous structural varables are employed based on prevous lterature, scholars preference or avalablty of data. Malpezz (2003) notes that experence from many studes suggests the followng structural varables often appear n hedonc prce analyses: Number of rooms and type of rooms (bedrooms, bathrooms, etc.) Floor area Category (sngle famly/ multfamly, attached/ detached, number of floors) Avalablty and type of heatng and coolng systems Age Structural features (presence of basement, freplaces, garages, etc.) Structural materal used, and qualty of fnsh The functonal form of the hedonc regresson equaton can ether be n lnear, semlog, or log-log form. Most common s the sem-logarthmc form whch has the advantage that the coeffcent estmates are proportons of the prce that are drectly attrbutable to the respectve characterstc. The advantage of the log-log form s that the hedonc regresson equaton estmates elastctes wth respect to each and every characterstc under consderaton. Takng logs of the dependent varable also takes nto account that prces are non-negatve. Ths property s at odds wth normalty assumptons n the case of a lnear specfcaton. If the error term of the hedonc regresson model s stochastc wth ndependent and dentcally dstrbuted (d) characterstcs, then t s possble to conclude that house prces are determned by structural characterstcs alone. It s hghly unlkely that 14

15 spatal characterstcs and temporal dynamcs do not play any role, but ths s an ndcaton that the estmated model wth structural characterstcs has captured most of the varaton of house prces. The second step takes nto account the spatal effects. There are alternatve ways of capturng spatal heterogenety and autocorrelaton usng lattce, geostatstcal and semparametrc models. The popular lattce models nclude spatal lag model and spatal error model. There are also dfferent ways to capture spatal dependence wthn these models; spatal dependency model and geographcally weghted regresson model are examples. Krgng method has been proposed as an nstrument to model and estmate house prces n the presence of spatal autocorrelaton. Olmo (1995) suggests usng the GLS estmator, because the OLS estmator of the parameters s neffcent n the presence of spatal autocorrelaton. The GLS estmator s consdered BLUE (best lnear unbased estmator), and as Cresse (1991) has shown, the co-varance matrx of the dsturbances V has to be known n advance n order to obtan ths estmator. Ths s normally unknown, but t s possble to obtan estmated GLS (EGLS) estmators by substtutng V for V*. An alternatve way of capturng the spatal dependence (and the resultng spatal autocorrelaton) s to nclude a spatal varable n the model as an exogenous varable. The smple and obvous way s to nclude dstance to the cty centre as an explanatory varable. Based on the monocentrc model, the expected coeffcent of ths varable should be negatve. Greater dstance to the cty centre would mean the prce of the house s lower. The extended model wth the accessblty varable s as follows: A sample of n ndependent observatons of house prce y, = 1,, n are lnearly related to structural characterstcs n a matrx X and to spatal characterstcs n a matrx Z y = X β + Z δ + ε ε ~ N(0, σ 2 ) = 1,..., n 15

16 If the error term of the extended hedonc regresson model s stochastc wth ndependent and dentcally dstrbuted (d) characterstcs, t s possble to conclude that house prces are determned by structural characterstcs and accessblty varables. If ths s the case, the noton that structural characterstcs and accessblty varables together explan most of the varaton of house prces wll be supported. It s also mportant to ensure that the dfferences of coeffcents from the prevous nonspatal model and the current spatal model are sgnfcant. The fact that dfferences of coeffcents from dfferent models are sgnfcant suggests ncluson of new varables consderably mproves the predctablty of the model. The thrd step ncorporates temporal dynamcs of house prces nto the extended model. The trend of the economy and the cyclcal movements of the economy are consdered possble canddates as explanatory varables. The mportant pont to note here s f the nvestgaton s at natonal level or regonal level. The man dstncton between the studes cted n the lterature secton and the present paper s that most prevous studes are macroeconomc analyses of house prces whle the present study provdes a framework to deal wth both house prces n a specfc country as well as n a specfc regon. If t s a study dealng wth a regonal housng market, the trend and the cyclcal movements of the regonal economy shall be consdered. If t s a natonal level study, the trend of the natonal economy and natonal level busness cycles shall be consdered. There are several ways to take nto account the temporal dynamcs of house prces. One way s to nclude a dummy varable startng from one and go up by one every year. For nstance, f there s a lst of housng sales transactons from the year 1990 untl 2010, the dummy varable for a house that was sold n the year 1990 takes the value 1, a house that was sold n the year 2000 takes the value 11, and a house that was sold n the year 2010 takes the value 21. There s an alternatve way of takng nto account the trend and cyclcal movements of the economy explctly usng the Hodrck and Prescott (HP) flter (1997). The HP flter s wdely used among macroeconomsts to obtan a smooth estmate of the longterm trend component of a seres. The HP flter s a two-sded lnear flter that calculates the smoothed seres s of y by mnmzng the varance of y around s, subject 16

17 to a penalty that constrans the second dfference of s. In other words, the HP flter chooses s to mnmze: T T 1 ( y ) 2 (( ) ( )) 2 t s t + λ s t + 1 s t s t s t 1, t = 1 t = 2 Where λ s the penalty parameter that controls the smoothness of the seres σ. The larger the λ, the smoother the σ. As λ=, s approaches a lnear trend. Snce annual data s used n ths analyss, a penalty parameter of 100 s recommended to smooth the seres. It s sensble to consder a fundamental varable such as real GDP, and use the Hodrck & Prescott flter (1997) to decompose the trend component and the cyclcal component. Our nterest n ths study s not only n the trend component of the data seres, but also n the cyclcal component; therefore both varables are ncluded as explanatory varables n the fnal composte model. For nstance, a transacton that was completed n 1990 wll have the relevant decomposed trend value and also the value of the busness cycle for that year produced by decomposton mechansm usng the HP flter. The composte model s as follows: A sample of n ndependent observatons of house prce y, = 1,, n are lnearly related to structural characterstcs n a matrx X, spatal characterstcs n a matrx Z, to a trend varable T, and to a cyclcal varable C y = X β + Z δ + Tλ + Cγ + ε ε ~ N(0, σ 2 ) = 1,..., n If the error term of the composte hedonc regresson model s stochastc wth ndependent and dentcally dstrbuted (d) characterstcs, then t s possble to conclude that house prces are determned by structural characterstcs, accessblty varables, and temporal dynamcs. If the trend varable or cyclcal varable s not sgnfcant, the partcular varable has to be excluded. If the trend varable s sgnfcant t s possble to emphasse that the trend of the economy, among other thngs, determnes house prces. It may also be nterestng to observe whether the 17

18 dfferences of coeffcents from non-spatal and spatal models are sgnfcant and how the coeffcents change wth addton of temporal varables. 4. Summery The HPM, derved mostly from Lancaster s (1966) consumer theory and Rosen s (1974) model mples that commodtes are characterzed by ther consttute propertes, therefore the value of a commodty can be calculated by addng up the estmated values of ts separate propertes. These hedonc prce ndces provde a bass to estmate house prces takng nto account the qualty or the characterstcs of a housng unt. Furthermore, the standard urban economc monocentrc model developed ntally by Alonso (1964) suggests that the prncpal varable causng varatons n constant-qualty house prces wthn a metro area s land prce. A typcal land rental equaton ncludes dstance from the CBD, agrcultural land rental, and a converson parameter that depends on transport cost per mle and communty ncome and hence suggests that dstance to the CBD should be ncluded n the house prce model. In addton, lterature related to temporal dynamcs of house prces justfy addng-n a temporal varable as a determnant of house prces. The temporal dynamcs are hardly ncorporated nto the hedonc models even though t s wdely accepted that house prces are senstve to them. Incluson of temporal dmenson allows capturng the tme related dynamcs of the market such as volatle prces generated by cyclcal movements of prces. Most of the prevous analyses of house prces do not typcally take nto account these three dmensons jontly so that the estmates produced are lkely to be based. The conceptual model suggested n ths paper wll reflect temporal and spatal dmensons n addton to the qualty of a house represented by ts ntrnsc characterstcs. The estmates of the prospectve model, therefore, are lkely to be unbased. Ths should be seen as an alternatve to the spatal panel or spatotemporal house prce models. 18

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