A panel regression method for quantifying the convergence of house prices

Transcription

1 Bon Universiy Conference Papers 36h Ausralasian Universiy Builing Eucaors Associaion (AUBEA) Conference A panel regression meho for quanifying he convergence of house prices Le Ma Deakin Universiy Chunlu Liu Deakin Universiy Follow his an aiional works a: hp://epublicaions.bon.eu.au/aubea_211 Recommene Ciaion Ma, Le an Liu, Chunlu, "A panel regression meho for quanifying he convergence of house prices" (211). Conference Papers. Paper 43. hp://epublicaions.bon.eu.au/aubea_211/43 This Conference Paper is brough o you by he 36h Ausralasian Universiy Builing Eucaors Associaion (AUBEA) Conference a epublicaions@bon. I has been accepe for inclusion in Conference Papers by an auhorize aminisraor of epublicaions@bon. For more informaion, please conac Bon Universiy's Reposiory Coorinaor.

2 A Panel Regression Meho for Quanifying he Convergence of House Prices Le Ma an Chunlu Liu School of Archiecure an Builing Deakin Universiy, Geelong, Ausralia ABSTRACT The convergence among house prices has arace much aenion from researchers. Previous research mainly uilise a ime-series regression meho o invesigae convergences of house prices, which may ignore he heerogeneiy of houses across ciies. This research evelope a panel regression meho, by which he heerogeneiy of house prices can be capure. Seemingly unrelae regression esimaors were also aape o eal wih he conemporary correlaions across ciies. Invesigaion of he convergence among house prices in he Ausralian capial ciies was carrie ou by using he evelope panel regression meho. Resuls suggese ha house prices converge in Syney, Aelaie an Hobar bu iverge in Darwin. KEYWORDS Convergence, panel regression, uni roo es, house prices INTRODUCTION Variaions in house prices may cause significan impacs on economy a boh naional an regional levels. The variaions may also poenially influence in migraion an invesmen mobiliy across regions. Therefore, i is imporan o unersan wheher a long run equilibrium relaionship exis beween house prices across a counry. In oher wors, here is consierable value o fin ou wheher house prices across regions will converge. The convergence in regional house prices in he Unie Kingom was early suie by using he Kalman filer/ime varying parameer esimaion meho (Drake 1995). Meen (1999) poine ou ha he regional house prices shoul move proporionaely. This suppors ha he ifferenial raios beween regional house prices an a benchmark price level, such as a naional price level or he price level of a ominan region, will converge o equilibrium in he long run. Much research aresse o he above issue by carrying ou a ime-series regression meho. I can be generae ha uni roo ess, vecor auoregression moels an vecor error correcion moels were wiely use in previous research (Maysami an Koh 2, Cook 25, Luo e al. 27, Chien 21). However, hose ime-series regression mehos fail o capure he heerogeneiy of house prices, 572

3 which is regare as an imporan characerisic cause by he immobiliy of houses. The ignorance of heerogeneiy may lea o unreliable esimaions of he regressions. In aiion, conemporary correlaions across regions canno be capure eiher by an orinary leas square (OLS) esimaion meho applie in previous research. Holmes an Grimes (28) inrouce a panel regression meho o improve he convenional uni roo ess. The convergence of house prices across he U.K. was invesigae. I was suggese ha he panel regression meho some avanages in measuring long run convergence among regional house prices. This research use a panel regression meho o esablish he moel for quanifying he house price convergence. The heerogeneiy of house prices coul be aken ino accoun by allowing he esimae parameers in he panel sysem varying across regions. In orer o capure he conemporary correlaions beween regions, a seemingly unrelae regression (SUR) esimaor was aape o esimae he moel. This evelope moel was applie o invesigae he convergence among house price inices in he Ausralian capial ciies. The nex secion of his paper illusraes he mehos use o es convergence. The following secions inrouce he Ausralian house price inices use in his research, an repor he convergence among house prices in Ausralian capial ciies. The final secion forms he conclusion. A PANEL REGRESSION METHOD FOR CONVERGENCE INVESTIGATION Convergence for a regional house price is efine as is saionary propery. Once a regional house price series is confirme as saionary, i will have a seay sae in he long run. The convenional invesigaion meho is base on he saionariy es for a ime-series. The Dicky-Fuller (ADF) uni roo es is one of he mos wiely use echniques o es he uni roo of ifference beween he house price in a specific region an a benchmark (Dicky an Fuller 1979). Denoe p po, where p an san for he house prices of a specific region an he benchmark respecively, a ime. The saionary properies of p inicaes he house price in ha region shall move proporionally wih he behaviour of he benchmark in he long run. The calculaion of he es is expresse as follows: q 1 s s (1) s1 The saisic is hen employe o examine he significance of he esimae coefficien, wih he null hypohesis of. The rejecion of he null hypohesis suggess ha 573

4 is saionary, which also inicaes ha shoul converge o a seay equilibrium. On he oher han, he accepaion of he null hypohesis rejecs ha is saionary an convergen in he long run. The curren value of a ime-series is always correlae wih he previous values. I will lea he auocorrelaions beween he isurbers. The series auocorrelaions may cause he resuls of he saisics o be unreliable. This problem can be resolve by he emporal lagge erm, number of lags. s s, where he subscrip s enoes he Alhough he series correlaion can be filere by emporal lags, he heerogeneiy of house prices across regions canno be eal wih. Holmes an Grimes (Holmes an Grimes 28) exene he echniques by inroucing he panel aa regression. The panel regression moel ADF uni roo ess is expresse as D D D 1 1 (2) D ( 1 2 ) N, A ( 1 2 ) N an ( 1 2 ) N, while 1 2 N, 1 2 N. This proceure is able o aress he problems associae wih he presence of crosssecional epenency among he regional house prices. Seen from Eq. (2), heerogeneiy beween house prices are capure ifferen he esimae parameers across regions. Moreover, he SUR esimaion assumes he error erms of ifferen equaions,, shoul be correlae wih each oher conemporarily. Tha means he variance-covariance of he error erms shoul be calculae by E( i js 2, s ). Therefore, he panel, oherwise regression meho is more powerful han he iniviual regression wih an OLS meho. DESCRIPTION OF HOUSE PRICES IN AUSTRALIAN CAPITAL CITIES This research use he House Prices Inices (HPI) o represen he house prices in Ausralian capial ciies. The HPI of he eigh sae capial ciies of Ausralia were collece from he publicaions of he Ausralian Bureau of Saisics (ABS 29). The 574

5 perio chosen was from he December quarer 1989 o he December quarer 28. The inices are consruce by using a sraificaion approach. In each perio he meian price movemen is calculae for each sraum an use o consruc a sraum level price inex (ABS 25). The aggregae inex is calculae by weighing ogeher he iniviual sraum inex, where he weighs represen he relaive significance of he sock of wellings in each sraum. The inices are base on he quarerly house prices for esablishe an newly erece wellings an each capial ciy s house price inices base on =1. The reference base of he publishe HPI change for he 23-4 financial year afer he Sepember quarer 25 (ABS 25). In orer o mainain consisency, he ol reference base (1989-9) was use in his research. The meho use o conver he re-reference aa o he previous base is escribe as HPI 899 w HPI3 4, where 899 HPI enoes he house price inex on he base = 1, HPI 34 enoes he house price inex on he base 23-4 =1, an w is he convering facor. The aa use in his empirical suy are available from he auhors upon reques (Ma 21). CONVERGENCE INVESTIGATION FOR HOUSE PRICES IN AUSTRALIAN CAPITAL CITIES This research use he ADF uni roo es o invesigae he saionariy of raios beween he HPI an he naional level in he Ausralian capial ciies. The null hypohesis of nonsaionariy is performe a a 5% significance level. Three forms of ADF uni roo es base on Eq. (1) were calculae, he resuls of which were repore in Table 1. Three forms inclue a es conaining no inercep or ren, an inercep bu no ren, an an inercep an a ren. The resuls show ha none of he eigh ciies house prices are saionary a levels. Accoring o he resuls of he ADF ess in he hree forms, raios beween local house price inices an he naional level are no saionary in mos of he capial ciies. The raio in Canberra is foun saionary when he ess wihou ren were applie. This suggese ha house price inices shoul move wih he naional house price level bu he house price inices in he oher ciies shoul no converge in he long run perspecive. 575

6 Table 1 The uni roo ess for house prices in Ausralian capial ciies Types of ess ciies ADF es a level -saisic Sig. level Lag Aelaie Na 1 Brisbane Na 1 Canberra ** Na 1 No inercep an Darwin Na 2 ren Hobar Na 2 Melbourne Na Perh Na 1 Syney Na 2 Aelaie Na Brisbane Na 1 Canberra ** Na Inercep wihou Darwin Na 2 ren Hobar Na Melbourne Na Perh Na 1 Syney Na 2 Aelaie Na Brisbane Na 1 Canberra Na 1 Inercep wih ren Darwin Na 2 Hobar Na Melbourne Na Perh Na 1 Syney -.21 Na Noe: Criical value of null hypohesis a he 5% significance level is Since lile evience can be foun o suppor he convergence in an iniviual ciy, he evelope panel regression approach base on Eq. (2) was applie o ienify he proporional convergence in he Ausralian capial ciies. Table 2 repors he esimaions of he moel base on Eq. (2), which inicaes ha he house price inex in a capial ciy will move ogeher wih he naional house price inex in he long run. The house prices, in Syney, Aelaie, Brisbane an Hobar, are foun proporionally move ogeher wih he behaviour of he naional level. On he oher han, he house prices of Canberra an Darwin are likely o move away from he naional price level, as suggese by he posiive coefficiens in hese wo ciies. There is lile evience o suppor a price raio convergence in Melbourne an Perh. Therefore, he iea can be generae ha house price raio convergence may be presen in some capial ciies of Ausralia, when he conemporary correlaions across he regions are involve in he invesigaion moel. However, he raios of Canberra an Darwin may iverge. The properies in Melbourne an Perh are uncerain. 576

7 Table 2 Invesigaion of house price ifferenial raio convergences Ciies Coefficiens saisics Aelaie ** Brisbane * Canberra Darwin ** Hobar ** Melbourne Perh Syney ** Noe: * an ** enoe he significances a 1% an 5% respecively. Moreover, he half-lives associae wih eviaions from long run seay saes are illusrae in Table 3, inicaing he convergence spees in each ciy. The half-life is calculae by (ln.5)/ln(1 ), where is he esimae coefficiens in he panel i regression moel. The half-lives are foun o range from 2.75 years in Syney o over 7 years in Perh. This inicaes ha he ajusmen spees of house prices owars he naional level are faser in Syney an Aelaie. Relaively slower spees are experience by he house prices in Perh. I akes aroun 5 years for Brisbane, Hobar an Melbourne agains he naional level converge o he seay sae in he long run. Table 3 Convergence spees Ciies Half-lives (year) Aelaie 2.85 Brisbane 5.1 Canberra N/A Darwin N/A Hobar 4.88 Melbourne 5.4 Perh 7.4 Syney 2.75 The long run convergence characerisics of regional house prices can only be invesigae in Canberra by an iniviually esimae ADF es. When heerogeneiy an conemporary correlaions beween regions are consiere, he house price ifferenial raios of Syney, Aelaie, Brisbane an Hobar are prove o move proporionaely wih he naional price level, while he raios of Darwin an Canberra iverge. CONCLUSIONS This research carrie ou an ADF uni roo es o invesigae he saionary characerisics of house prices in a specific ciy. A panel regression moel, wih SUR esimaors, was 577

8 evelope o explore he proporional convergence saus of a series of regional house prices base on a common benchmark. The panel regression meho can capure heerogeneiy of house prices across ciies, by allowing house prices o have heir own uni roos. The SUR esimaors are able o ake he conemporaneous correlaions among he isurbances, in he equaion of each ciy, ino accoun. In pracice, boh he ADF an panel ADF ess were applie on he house price inices in he Ausralian capial ciies. Lile evience coul be obaine from he ADF es o suppor he convergence among he house prices in he Ausralian capial ciies. However, he convergences of he price raios, aking he Ausralian naional house price level as a benchmark, were foun in some ciies. I showe ha he house prices of Syney, Aelaie an Hobar were moving proporionally wih he naional price. The house price of Canberra an Darwin iverge. Relaively faser convergence spees were experience by house prices in Syney an Aelaie. REFERENCES ABS. (25) Renovaing he esablishe house price inex. Ca no Ausralian Bureau of Saisics, Canberra. ABS. (29) House price inexes: eigh capial ciies. Ca no Ausralian Bureau of Saisics, Canberra. Chien, M.S. (21) Srucural breaks an he convergence of regional house prices. Journal of Real Esae Finance an Economics, 4 (1), Cook, S. (25) Deecing long-run relaionships in regional house prices in he UK. Inernaional Review of Applie Economics, 19 (1), Dicky, D.A. an Fuller, W.A. (1979) Disribuion of he esimaors for auoregressive ime series wih a uni roo. Journal of he American Saisical Associaion, 74 (336), Drake, L. (1995) Tesing for convergence beween UK regional house prices. Regional Suies, 29 (4), Holmes, M.J. an Grimes, A. (28) Is here long-run convergence among regional house prices in he UK? Urban Suies, 45 (8), Luo, Z.Q., Liu, C. an Picken, D. (27) Housing price iffusion paern of Ausralia's sae capial ciies. Inernaional Journal of Sraegic Propery Managemen, 11 (4), Ma, L. (21) Spaial an emporal variaion of house prices. Disseraion for PhD egree. School of Archiecure an Builing, Deakin Universiy, Geelong. Maysami, R.C. an Koh, T.S. (2) A vecor error correcion moel of he Singapore sock marke. Inernaional Review of Economics & Finance, 9 (1),

9 Meen, G. (1999) Regional house prices an ripple effecs: a new inerpreaion. Housing Suies, 14 (6),