Previously Published Works UC Berkeley

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1 Previously Published Works UC Berkeley A Uiversiy of Califoria auhor or deparme has made his aricle opely available. Thaks o he Academic Seae s Ope Access Policy, a grea may UC-auhored scholarly publicaios will ow be freely available o his sie. Le us kow how his access is impora for you. We wa o hear your sory! hp://escholarship.org/reader_feedback.hml Peer Reviewed Tile: The divided pricig model: New evidece from he Korea housig marke Joural Issue: Joural of Real Esae Fiace ad Ecoomics, 32(3) Auhor: Hwag, Mi, Naioal Uiversiy of Sigapore Quigley, Joh M., Uiversiy of Califoria, Berkeley So, Jae-Youg, Kokuk Uiversiy Publicaio Dae: Series: UC Berkeley Previously Published Works Permalik: hp://escholarship.org/uc/iem/2xp84r Addiioal Ifo: The origial publicaio is available a i Joural of Real Esae Fiace ad Ecoomics. Keywords: housig price, re, prese value, asse prices Absrac: I is geerally coceded ha divided pricig models are poor predicors of asse prices. This fidig is someimes aribued o excess volailiy or o a divided process maipulaed by firm maagers. I his paper, we prese raher powerful pael ess of he divided pricig relaio usig a uique daa se i which divideds are se by marke forces idepede of maagers' prefereces. We rely o observaios o he marke for codomiium dwelligs i Korea-perhaps he oly marke i which iformaio o divideds ad prices is publicly ad coiuously available o cosumers ad ivesors. We exed he "divided-price raio model" o paels of housig reurs ad res differeiaed by ype ad locaio. We fid broad suppor for he divided pricig escholarship provides ope access, scholarly publishig services o he Uiversiy of Califoria ad delivers a dyamic research plaform o scholars worldwide.

2 model durig periods boh before ad afer he Asia Fiacial Crisis of , suggesig ha he marke for housig asses i Korea has bee remarkably efficie. Copyrigh Iformaio: All righs reserved uless oherwise idicaed. Coac he auhor or origial publisher for ay ecessary permissios. escholarship is o he copyrigh ower for deposied works. Lear more a hp:// escholarship provides ope access, scholarly publishig services o he Uiversiy of Califoria ad delivers a dyamic research plaform o scholars worldwide.

3 The Divided Pricig Model: New Evidece from he Korea Housig Marke * by Mi Hwag Joh M. Quigley Jae Youg So Naioal Uiversiy of Sigapore Uiversiy of Califoria Ko-Kuk Uiversiy Sigapore Berkeley rshm@us.edu.sg quigley@eco.berkeley.edu jyso@kokuk.ac.kr April 2005 Absrac I is geerally coceded ha divided pricig models are poor predicors of asse prices. This fidig is someimes aribued o excess volailiy or o a divided process maipulaed by firm maagers. I his paper, we prese raher powerful pael ess of he divided pricig relaio usig a uique daa se i which divideds are se by marke forces idepede of maagers prefereces. We rely o observaios o he marke for codomiium dwelligs i Korea perhaps he oly marke i which iformaio o divideds ad prices is publicly ad coiuously available o cosumers ad ivesors. We exed he divided-price raio model o paels of housig reurs ad res differeiaed by ype ad locaio. We fid broad suppor for he divided pricig model durig periods boh before ad afer he Asia Fiacial Crisis of , suggesig ha he marke for housig asses i Korea has bee remarkably efficie. Keywords: Housig price, re, prese value, asse prices * Previous versios of his paper were preseed a he Hog Kog-Sigapore Ieraioal Real Esae Research Symposium, Augus 2004, Hog Kog ad he meeig of he Hog Kog Ecoomic Associaio, Jauary We are graeful for he commes of Ashok Bardha, Yumig Fu, Chimoy Ghosh, Lok Sag Ho, Charles Ka Yui Leug, Sau Kim Lum ad Seow Eg Og.

4 I. Iroducio There is ow cosiderable research devoed o esig he implicaios of he divided pricig model. A geeral fidig is ha prese value models are o good predicors of he acual prices of shares raded i fiacial markes. This lack of fi is ierpreed as excess volailiy i prices, or aleraively as a failure of he maiaied hypohesis ha he discou rae for divideds is cosa. Cosiderable discreio i he payou of divideds is vesed i he maagers of firms who may follow rules of humb i awardig divideds. Maagers may also be reluca o icrease divideds uless hey expec ha he payou ca be maiaied subsequely 1. The failure of he prese value model ca hus be aribued o he divided process followed by firm maagers who exercise discreio over imig ad payou forms, ad whose behavior differs from he mechaical process assumed i ecoomeric models. I his paper, we prese raher powerful ess of he divided pricig relaio usig a uique body of daa o asses for which divideds are se by marke forces idepede of maagers prefereces. We rely, o upo observaios o shares raded o orgaized fiacial markes, bu o observaios ake from he marke for codomiium dwelligs i Korea perhaps he oly marke i which iformaio o divideds for idividual asses is publicly ad coiuously available o cosumers ad ivesors who rade hem over shor-erm iervals. We es he prese value model usig large paels of observaios o asse price movemes ad divideds. Secio II describes he Korea housig marke ad he uique isiuios ha provide precise daa which suppor our es of prese value models. Secios III ad IV oulie he 1 I addiio, ordiary divideds migh o represe rue cash flows; share repurchases ad ake-over disribuios are also releva cash flows for he pricig of shares. See Kleido (1986), Marsh ad Mero (1986) ad Acker ad Smih (1993). 1

5 aure of our ess ad repor he resuls. We prese hree kids of evidece. Firs, we describe he cross secioal characerisics of reurs o ivesme based o paels of virually ideical housig uis, differig by ype ad locaio, oig he imporace of lags ad aalyzig simple ivesme sraegies. Secod, we prese ess for he saioariy of divided price raios i each of our paels of dwelligs. Followig Craie (1993) ad geeralizig, we coduc a series of ui roo ess based upo paels of price-re raios, differeiaed by ype of housig, ivesigaig he saioariy of divided price raios. Wih he excepio of he period surroudig he Asia Fiacial Crisis of 1998, we fid ha he ime series are quie cosise wih saioary processes. The saioariy of divided price raios suppors our hird aalysis, a exesio of he divided-price raio model, origially proposed by Campbell ad Shiller (1988), o paels of housig reurs ad res, differeiaed by size ad locaio. I coras wih much of he exisig lieraure, we fid broad suppor for he divided pricig model i his more geeral framework. Take ogeher, hese resuls provide broad suppor for he divided pricig model as a predicor of asse prices ad hus for he efficiecy of he Korea housig marke. Secio V is a brief coclusio. II. The Korea Housig Marke A. Aparmes We es he prese value relaioship usig micro daa o he Korea housig marke durig he period from We divide he ime period io wo pars: 1990:Q1 hrough 1997:Q3, he period before he Asia Fiacial Crisis; ad 1999:Q1 hrough 2002:Q3, he period afer he ed of he crisis. We rely upo he daa o aparmes i he capial regio 2

6 surroudig. 2 Typically, aparmes (high-desiy aached dwelligs i high-rise buildigs) are buil i large complexes of muli-sory buildigs. The size of a aparme complex varies widely, bu i commoly coais hree or more ypes of dwelligs, differeiaed by size, ad cosiss of several hudred uis. Aparme cosrucio i Korea bega i eares i he early 1970s, ad soo hereafer became he domia housig developme paer i he coury. Aparmes accoued for 81 perce of all ew dwelligs cosruced i Korea bewee 1995 ad 2000, ad hey represeed almos half of he housig sock i he coury i Easy o mass-produce, he aparme has bee he ceral isrume i Korea housig policies aimed a providig subsidized aparmes o middle class cosumers. Public secor moopolies such as he Korea Lad Corporaio ad he Korea Naioal Housig Corporaio developed ad provided iexpesive lad o homebuilders, who i ur were required (uil 1998) o sell aparmes a regulaed prices. 3 Uder hese price regulaios, he developers objecive was o cram as may uis as possible o a give sie, usig sadard maerials ad approved desigs. As a resul, Korea aparmes i he same size classes are much more homogeeous ha are dwelligs i mos oher couries. Mos aparmes are buil for sale, ad each ui is ypically owed by a idividual. 4 The real marke for aparmes is acive ad lively, bu few aparme complexes have bee buil o provide permae real accommodaio. Raher, he real housig supply cosiss 2 The regio cosiss of he ciy of, he ciy of Icho, ad Kyuggi Provice. is capial of he coury, Icho a por ad idusrial ciy, ad Kyuggi Provice evelopes boh ciies. 3 Thus, he housig policy was ulimaely fuded by home-buyers, ad did o rely o a explici budgeary allocaio from he ceral goverme. This sraegy had major a weakess: he eglec of low-icome families who could o buy a home eve a regulaed prices. For deailed discussio of Korea housig policies, see So, e al. (2003). 4 I his sese, aparmes i Korea are similar o codomiiums i he U.S. 3

7 of uis which idividual owers choose o re, cusomarily o a fixed wo-year basis. A ower-occupied aparme ca be ured io a real ui, ad vice versa, ayime wihou cos. Aparme complexes buil specifically o provide real accommodaio do o exis i Korea excep for a small umber of aparmes for families wih very low icomes. This high degree of homogeeiy ad he fused real ad ower-occupied markes make he Korea aparme housig marke uusual i several respecs. Firs, sice floor plas, buildig maerials, ad ameiies are sadardized, marke paricipas have very good ideas of wha o expec abou ay specific dwellig for a give locaio, size, ad viage. This homogeeiy meas ha aparmes ca be easily raded ad reed, o oly for resideial, bu also for ivesme, purposes. I fac, persise price iflaio has made aparmes impora ad acively-raded asses i he wealh porfolios of middle-class households. The ivesme-asse aspec of aparmes may be more impora ha he durable-good cosumpio aspec. If here are iefficiecies i he marke, hey do o arise from hi markes; he marke is deep ad acive compared wih housig markes i mos oher couries. Secodly, sice aparmes are acively raded ad here are hudreds of similar virually ideical aparmes i ay eighborhood, referece prices ad res are easily foud, ad his iformaio flows fas ad freely. I is quie rouie o fid eighborhood brokers who ca provide daily movemes of prices, boh real ad sale prices. Several compaies regularly gaher such iformaio from local brokers ad regularly publish curre prices i 4

8 pri ad olie. 5 These surveys are cosidered o be a accurae reflecio of he marke, ad hey heavily affec he buy-, sell-, ad re-behavior of marke paricipas. For researchers, his iformaio provides a coiuous series of prices ad res o wellspecified asses a he micro-level, a rariy i oher couries. Third, aparme prices are quoed as a pair real prices (discussed below) ad sale prices sice he real ad ower-occupied markes are perfecly fused. Housig researchers i oher couries have difficulies i cosrucig re ad sale price daa which corol for he myriad differeces bewee real ad ower-occupied dwelligs (Meese ad Wallace 1994). Wih daa o Korea aparmes, oe ca mach he re o he sellig price of a ideical ui, ad idices of he re ad he sale price of aparmes ca be cosruced from he same se of dwelligs. Fially, rasacios coss are relaively low compared wih oher couries. Brokerage fees are ormally bewee oe half ad oe perce, ad he homogeeiy of aparmes keeps search coss low. Oly ax burdes are high; he axes payable a he ime of purchase are effecively bewee hree ad four perce of he price. I summary, may aribues which are hough o be he sources of iefficiecy i local real esae markes are abse i he Korea aparme marke. Ad may of he daa problems which preclude esig of he divided pricig model i fiacial markes are also abse. Ideed, his may be oe of few real propery markes where efficiecy holds ad oe of he 5 ad are marke leaders which provide aparme price iformaio hrough oher poral sies ad fiacial isiuios as well as hrough heir ow sies. Oe ca look up he laes re ad sale prices of ay arrowly specified ype of aparme (by locaio, size ad viage) from ay Korea iere poral, ad from he home pages of ewspapers ad fiacial isiuios. Recely, Kookmi Bak, he larges commercial bak, bega publishig is ow aparme price surveys. These ad oher providers usually updae heir prices weekly or bi-weekly. The populariy of aparme price iformaio reflecs he iese ieres amog Koreas o he ivesme poeial of aparmes. 5

9 few asse markes i which he lik bewee divideds ad prices ca be esed direcly. B. Chosei Real Coracs All segmes of he Korea real esae real marke, icludig resideial, commercial, ad eve idusrial secors, ivolve real coracs called Chosei. 6 Uder a Chosei real corac, he ea makes a sigle large deposi i lieu of mohly re paymes, ad he ieres icome ha accrues o he ladlord cosiues he re. A he ed of he real erm, he deposi is reured i full o he ea. As a isiuio, he Chosei real corac is ubiquious i he mid- ad upper- level resideial real marke. As of 2000, abou 30 perce of all dwelligs i Korea were i he real marke, ad wo-hirds of hese were o Chosei coracs. The real erm of a Chosei corac is legally se a wo years. The Chosei sysem of housig fiace combies wo separae rasacios i a sigle corac. The firs is a loa made by he ea o he ladlord, ad he secod is a lease by which he ladlord gras use of residece o he ea for impued ieres paymes o he Chosei deposi. If he ladlord does o reur he Chosei deposi a he ed of he real erm, he ea ca sue for a foreclosure sale o recover he deposi. 7 The coiuous housig price iflaio, he high ieres raes i Korea, ad is uderdeveloped bakig sysem explai he persisece ad he populariy of he Chosei sysem. Wih icreasig sale prices ad Chosei prices, eas eed seldom worry abou he safe reur of he deposi a he ed of he real erm. 6 We use Chosei deposi, Chosei re, ad Chosei price ierchageably. 7 These feaures of Chosei coracs are aalyzed by Ambrose ad Kim (2003). 6

10 C. Impacs of he Asia Fiacial Crisis Our daase covers he period of he Asia Fiacial Crisis ( ) which appears o have had subsaial impacs o Korea housig markes. The immediae impacs o he housig marke were rasmied from he bakig secor, which refused o roll over exisig debs o housig ad cosrucio secors. This, ogeher wih a sharp drop i disposable icome, led ew cosrucio o fall by 48 perce i 1998, compared o he previous year. Lad prices fell by 13.6 perce, he larges drop sice he goverme bega keepig records i I he meropolia area, housig prices experieced eve larger declies; sales prices of aparme codomiiums dropped by 22 perce ad Chosei prices dropped by more ha 40 perce i he firs half of However, i he mid 1990s aroud he ime of he crisis, he Korea housig marke was goig hrough oher impora srucural chages. 8 Korea housig markes were heavily regulaed i earlier years due o chroic shorages of available housig ad resulig iflaio i house prices. However, ogeher wih goverme-led massive cosrucio i he lae 1980s, may regulaios i he Korea housig marke were gradually elimiaed, ad he drives for privaizaio ad deregulaio were eve acceleraed durig he crisis -- as a par of he resrucurig package of he Korea macro-ecoomy. Reewed emphasis was placed o developig a adequae housig fiace sysem, sarig wih he slow iroducio of morgages ad morgage backed securiies i he lae 1990s o he privaizaio of Korea s Housig ad Commercial Bak, which specialized i fiacig housig cosrucio. 8 For deailed accous of he rece developme of Korea housig fiace sysem, see Kim (2000). 7

11 D. Daa ad Marke Treds Our daa come from surveys by he Real Esae Bak, 9 a major marke leader i he aparme iformaio busiess. The firm sared buildig a broker-reporer ework, publishig a biweekly price survey of aparmes i 1990, ad laer expaded coverage aioally. Currely, mos aparmes i major ciies are covered by is weekly eumeraio of sales prices ad Chosei deposis. A observaio (or record) i he daa is a ype of aparme, arrowly ideified by series of qualifiers: he locaio, he ame of he aparme complex (which sigifies viage), ad he size of he ui. The umber of disic ypes of aparmes i our daa icreases from 1,192 i 1990 Q1 o 3,354 i 1995 Q2 ad o 12,203 i 2002 Q3. Each ype may represe hudreds of similar uis. For example, each disic aparme ype i our daa i 2002 represes 177 uis o average. Thus, i 2002, our daa represe more ha 2,200,000 aparme uis i he capial regio. We use ed-of-quarer daa for capial regio aparmes from he firs quarer of 1990 o he hird quarer of We aalyze prices ad res for hese various housig ypes for seve geographical submarkes i he capial regio. These submarkes are raher disic i erms of hisory, idusrial composiio, ad housig marke developme. Figure 1 idicaes he seve submarkes: four are locaed wihi meropolia, wo are i Kyuggi provice, ad oe icludes he ciy of Icho. Appedix A describes hese geographical regios i more deail. Table 1 repors he disribuio of aparme ypes by submarke ad size. For ay size caegory ad regio, he umber of aparme ypes varies from 54, represeig 3,919 uis, o 769, represeig 9 8

12 143,535 uis. Alogeher here are more ha 12,000 ypes i he daa se, represeig more ha wo millio dwelligs i he capial regio. For various reasos, we do o have a coiuous ime series for all of he aparme ypes represeed i Table 1 for he period. 10 Table 2 repors he umber of housig ypes observed coiuously durig he sample period up o he Asia Fiacial Crisis of , ad he umber observed coiuously afer he ed of he crisis (i.e., sice 1999). We average he miimum ad maximum repored prices o ge quarer-ed Chosei deposis ad sale prices for each ype of aparme for each quarer. We use he average of oe-year ad hree-year Korea Idusrial Fiace bod raes o calculae he implici re from he Chosei deposi. 11 I addiio o he wo-year reur, we also compue quarerly reurs, usig he hree-moh CD rae. 12 Figure 2 repors reds i average sale prices, Chosei deposis ad implici res. 13 I shows ha he sharp housig iflaio of he lae 1980s coiued uil mid-1991, ad he declied hrough The declie of omial house prices was mild, bu i real erms, boh sale prices ad Chosei deposis fell subsaially from heir peak. A he ed of 1997, he aiowide sale price idex was 63.3 perce of is 1990 value, ad he Chosei idex was 84.7 perce i real erms. This paer of gradual declie i real housig prices was much 10 The daa collecio sared as a modes operaio a firs ad laer added more areas ad aparmes; may aparmes were ewly buil or demolished for re-cosrucio i his period; some observaios were deleed for suspeced errors i our verificaio process. 11 Neiher goverme bods or Bak of Korea bods of ay mauriy cover he eire daa period. Isead, we use bods issued by he Korea Idusrial Bak, owed by he goverme ad acceped as risk free i Korea bod markes. 12 Eve hough he ivesme horizo of wo years is by he legal cosrais o Chosei coracs, i is perfecly possible o ives i he housig marke wih a shorer horizo. The ower of a housig ui ca sell he house reed o a Chosei corac, ad he ew ower may simply ake over he exisig Chosei corac. 13 I Figures 2A ad 2B, he re is calculaed for wo-year iervals. The figure repors he uweighed mea of each variable. 9

13 differe from ha of Japa ad oher Asia couries, where a sharp rise ad sudde collapse of propery prices was aribued o a propery price bubble. The marke showed sigs of a boom i early 1997, bu he Asia ecoomic crisis hi hard i Korea lae ha year. From he las quarer of 1997 o he ed of 1998, he aiowide lad price idex fell by 13.8 perce; he aiowide house sale price idex ad he Chosei re idex fell by 13.2 perce ad 20.1 perce, respecively. New housig sars i 1998 were abou half of heir level i 1997, ad oher idicaors of he cosrucio marke, such as cosrucio ivesme, buildig permis, ad ew cosrucio coracs, all collapsed. Housig prices fell sharply for abou a year, bu rebouded sice lae 1999 wih he recovery of he geeral ecoomy. Movemes of Chosei deposis roughly follow hose of sale prices, wih some sigifica differeces. The asse price bubble for aparmes burs i 1991, bu here is o correspodig bulge i he Chosei red. I he mid-1990s, sale prices remaied sable, bu Chosei prices coiued o rise. Also, Chosei prices recovered much faser ha sale prices afer he ecoomic crisis of he lae 1990s. These differeces arise because Chosei prices reflec he marke for resideial services flows raher ha he socks of ivesme asses. Expeced capial gais affec sale prices, bu o Chosei deposis. The same logic (i.e., ha he real esae marke eds o be more sable ha oher asse markes) may explai he greaer sabiliy of he reds i implici res. As oed i he previous secio, he Asia Fiacial Crisis had a subsaial impac o Korea housig markes. Figures 3 hrough 5 repor he dramaic chages i re sales price raios, real growh raes, ad housig ivesme reurs durig he period of he 10

14 crisis. Figure 3 repors quarerly movemes of he average re-price raio, 1997Q3 1999Q1, i each pael, differeiaed by locaio ad dwellig size. Almos all he re-price raios show he same paer; re-price raios iiially rose ad he plummeed durig he secod quarer of Sice sales prices ad Chosei deposis boh fell afer he ose of he crisis i lae 1997, he figure illusraes how res fell furher ha asse prices, idicaig ha immediae impacs of he crisis fell o demad for housig service firs. Figure 4 shows average real growh raes i he various housig ypes. Cosise wih Figure 3, average res fell dramaically afer he secod quarer of Ideed, ha he level of average res i he laer period is abou 35 perce lower. The paers of re developme are quie similar amog differe paels. Figure 5 shows average housig reurs i differe paels aroud he crisis. Ulike re-price raios ad re growh raes, housig reurs show more diverse paers. Eve hough all he paels experieced losses, some housig ypes suffered greaer shor-erm losses (more ha e perce) ha ohers (as lile as wo perce). Tables 3, 4, ad 5 provide similar evidece of he srikigly differe performace of he marke before he Crisis of 1998 bega ad afer i had eded. Table 3 repors he average re-price raios of each pael before he crisis ad afer he crisis. The raio of mohly res o sellig prices for codomiiums averaged abou 1.5 perce durig he period before he fiacial crisis, ad oly abou 0.9 perce afer he crisis. I each of he various submarkes, re-price raios dropped afer he crisis, usually by fory or fify perce. There are much smaller differeces i housig reurs before ad afer he crisis. Before 1998, quarerly reurs averaged abou hree perce; afer 1998, hey averaged abou four perce. As oed i Table 5, here are cosise differeces i real growh raes for aparmes bewee he wo periods. The quarerly growh raes for res were almos wo perce durig he period ad were egaive durig he period. For each of he submarkes, 11

15 real growh before he Asia Fiacial Crisis exceeded he pos crisis growh raes. III. Cross Secioal Characerisics of Ivesme Reurs ad he Time Series Properies of Divided-Price Raios. A. Cross Secio We describe cross secioal characerisics of reurs o housig ivesme by a series of descripive regressios: R ( Pi, 1 Di, 1 ) + β 3 ( Pi, 1 Wi ) i, i, = β 0 + β S Si, + β L Li, + β1ri, 1 + β 2 + ε, (1) where is he wo-year reur (i logarihms) o housig ype i a, are dummy R i, S i, variables for sizes, L, are dummy variables for regios, ( P D ) is he logarihm of he i i, 1 i, 1 price-deposi raio (i.e., sellig prices divided by Chosei prices), ad ( W ) logarihm of he price per square foo. P i, 1 i is he The regressio is esimaed for each cross secio of wo-year reurs sarig from he firs quarer of Table 6 repors he resuls. The explaied variace for each cross-secio is subsaial, ragig bewee 0.2 ad 0.5. Excep for he periods durig he Asia Fiacial Crisis (1998), a subsaial porio of he cross secioal variaio ca be explaied by variables sigifyig housig ype, submarke, lagged reurs, ad prices. Secod, lagged reurs are geerally quie sigifica; his implies ha aparme ypes wih lower reurs i he previous period ed o have higher reurs i he curre period ha do aparme ypes wih higher reurs i he previous period. 14 Third, he lagged price/deposi raio also 14 I does o imply ha lower reurs for a give ype predic higher reurs for he same ype i he ex period. 12

16 sigificaly predics he curre reurs. The lagged price/deposi raio measures marke expecaios of fuure price appreciaio. Noe ha aparme ypes wih larger expeced appreciaio i prices ed o have higher price-deposi raios. If his expecaio were correc, he a higher price-deposi raio would be posiively correlaed wih he reurs i he ex period. However, he esimaed coefficies are cosisely egaive, implyig ha housig uis wih lower expeced reurs ed o ouperform hose uis wih higher expeced reurs. Fourh, coefficies o lagged price per square foo are also sigificaly posiive; uis wih higher prices las period ed o exhibi high reurs i he curre period. Take ogeher, hese cross secio regressios sugges a profiable ex-pos ivesme sraegy durig his period: Buy dwellig uis wih low curre reurs, low price/deposi raios ad high prices per square foo. The dummy variables classifyig he capial regio io seve submarkes are highly sigifica. Excep for he period of he Asia Fiacial Crisis (1998), he aparme ypes i he smalles size group exhibi he highes reurs. Moreover, size ad reurs ed o move i opposie direcios: he larger he aparme ypes, he lower he expeced reurs. The resuls sugges ha Regio 3, he area souh of he Ha River, cosisely geeraes he highes reurs wihi. The differece i reurs bewee his ad he oher regios also eds o grow larger over ime. Amog he o- regios, Kyuggi Regio 1 eds o geerae he highes reurs i early years, bu afer he Asia Fiacial Crisis, Icheo exhibis he highes ivesme reurs. B. Time Series : Ui Roos 13

17 As repored i Table 2, he sample icludes may paels of housig uis observed coiuously durig he period, ad a large umber of paels observed afer he Asia Fiacial Crisis of For each eleme i he various paels, we observe prices ad divideds quarerly. I his secio, we ivesigae he presece of ui roos i hese paels of divided price raios. There are may versios of pael ui roo ess; we adop he es proposed by Chag ad Sog (2003). Their procedure has several advaages for our purposes. I accous for cross secioal correlaios i iovaios ad he presece of coiegraio amog cross secioal uis. I addiio, he es ca also aalyze ubalaced paels, ad more sophisicaed hypoheses ca be formulaed. I esig for he presece of ui roos i our paels, we employ he ull hypohesis ha a leas e perce of he idividual aparme ypes have ui roos i price-re raios. (Noe ha his hypohesis is far more difficul o rejec ha he more ypical hypohesis ha all he idividual ypes have ui roos.) Tables 7A ad 7B prese pael ui roo ess for he housig ypes i each of he submarkes. Pael A refers o he period before he Asia Fiacial Crisis, , while Pael B refers o he period afer he crisis, For he former period, he presece of a ui roo i e perce or more of he series is soudly rejeced for 24 of he 28 submarkes. For hree of he oher submarkes, he hypohesis is rejeced a abou he 0.1 level. For oly oe of he submarkes, medium small aparmes i Regio 3, is he hypohesis clearly acceped (ρ=0.32) However, if he ull hypohesis is relaxed o es he hypohesis ha he log of price-re raios for less ha 25 perce of housig ypes i he marke have ui roos, hey hypohesis is rejeced by a comforable margi i 27 submarkes ad wih ρ=0.08 i he remaiig submarke. 14

18 The resuls are almos as srog for he period afer he Asia Fiacial Crisis. The hypohesis ha a leas e perce of he divided-price series have ui roos ca be rejeced a he five perce level i 15 of he 28 submarkes, a he 10 perce level i aoher 7 of he submarkes. I oly four of he submarkes, is he hypohesis clearly o rejeced. 16 IV. Tess of he Divided Price Raio Model For a give ivesme horizo ad for a idividual house, defie he expeced oal rae of reur e r 1 + a ime, where price is P ad he divided (re) is D + 1, compued as he proceeds from he risk free ivesme of he Chosei deposi received i he previous period. Re is received a he ed of he period, bu is k ow a he begiig of he period. r e + 1 ( r ) E ( P P ) + D = E + 1 =, (2) P I equilibrium, he expeced reur e r 1 + will reflec various risk facors ad coss associaed wih he ivesme. 17 Large rasacio coss ad limied liquidiy, high iformaio coss, ad high propery axes will all require higher expeced reurs from housig ivesme. Idividual houses may have disic risk-reur characerisics, bu similar dwelligs share he same risk-cos characerisics ad he same expeced rae of reur. Equaio (2) ca be solved forward o yield J 1 P + = E R J = 1 = j 1 1+ r J. (3) e + j 16 Eve here, if he ull hypohesis is relaxed o es he hypohesis ha he log of price-re raios for less ha half of he housig ypes i a submarke have ui roos, he hypohesis is rejeced by a comforable margi i 27 of he 28 submarkes. 17 For housig, equilibrium re equals he user cos of homeowership less he expeced capial gai, R+ 1 = [ δ + κ + ( 1 θ )( i + µ ) + α ] P E ( P + 1 P ) (N1) where δ is he depreciaio rae, κ is he maieace rae, θ is he margial icome ax rae, µ is he propery ax rae ad α is a risk premium. (See Poerba, 1984). 15

19 Wih cosa discou raes, his ca be simplified o R + J P = E. (3 ) J J = 1 ( 1+ r) There are may ways o es his relaioship i fiacial markes. 18 Here we es wheher he curre price is a adequae forecas of fuure divideds, followig Campbell-Shiller (1988). 19 The Campbell-Schiller es was origially applied i a uivariae coex usig U.S. sock marke idices over log horizo; we use paels of aparme ivesme reurs isead over shorer ime horizos. The major advaages from aalyzig paels of reurs are obvious: paels permi more powerful ess wih more observaios; paels permi he aalysis of cross secioal correlaios amog reurs. More imporaly, by usig paels, we ca mach res ad prices for he same dwelligs over ime, machig asse prices ad divideds exacly (see Meese ad Wallace, 1994, for he difficulies of umached samples). As demosraed i Secio III, ivesme reurs i Korea housig markes vary geographically ad by size of dwellig, ad here is a clea break wih he Asia Fiacial Crisis of Thus, i appears aural o defie paels by regio ad dwellig size. Also, as idicaed i Secio III, paels so cosruced do o exhibi ui roos i divided price raios. This makes he es of he divided-price raio model o hese paels quie aural (as he es relies upo saioariy i he divided-price raio). We aalyze quarerly reurs usig he paels summarized i Table 2. Cosider a es of he divided-price raio model. Le r +1 be he log of he gross reur o a aparme, r + 1 log( P D+ 1 ) log( P ) = p + 1 p + log ( 1+ exp( d + 1 p+ 1 )), (4) 18 For reviews of earlier ess, see LeRoy (1989) ad Gilles ad LeRoy (1991). 19 Diba ad Grossma (1984), Hamilo ad Whiema (1985), Campbell ad Shilller (1987), ad Craie (1993). 16

20 where P is a price, ad D is he divided impued from he Chosei deposi. By approximaig (4) aroud is mea, solvig he equaio forward ad adjusig for ucodiioal meas, d p = j= 0 j ρ ( r d ) + i+ j + 1+ j, (5) where 1 ρ = 1+ exp ( d p), ad where he bars represe ucodiioal expecaios. Sice (5) holds ex pos, for a give discou rae, d p = j= 0 j ρ E [ r d ] + i+ j + 1+ j. (6) To es (6) wih give discou raes, i is ecessary o specify he sochasic processes goverig divided price raios ad divided growh raes o compue he codiioal expecaios. Campbell ad Shiller (1988) propose a VAR approach o ideify hese codiioal exp ecaios. Assume x [ d p, r d ] follows a p-h order bi-variae VAR process, = p x = Ck x k + u, k = 1 (7) where C k is a 2x2 marix for k=1,2,,p. Equaio (7) ca be expressed as (Hamilo 1994) z = Az 1 + υ, (8) where [( d p ) L, ( d p )( r d ) ( r d )] z L ad is a (2p 1),, = p 1 p 1,, p 1 p 1 vecor. To ideify ( d p ) ad ( r d ) i z, we defie e p, a (2p 1) vecor whose p-h eleme is oe while r d = e p z, all he oher elemes are zero, so ha 17 d p = e1 z ad

21 e z 1 = j= 0 j ρ e p A z j+ 1. This oaio immediaely suggess a esable resricio, ( ) 1 e = e p A I ρ A = ( e p + ρ e 1 )A. (9) 1 or equivalely, R β = e 1, (10) = p p, β = [ A 1, Ap ], ad Ap is he p-h row of he coefficie marix A i (8). where R [ ρ I, I ] I is sraighforward o es equaio (10) i a pael coex. Sackig up he N aparme ypes, a pael versio of (10) is R 0 M 0 0 R M 0 L L M L 0 β1 0 β 2 = M M R β e e M 1 2 N e N (10 ) where β i is he coefficie vecor for he i-h aparme ype i he pael. The umber of resricios is 2 p N. To es (10 ) usig paels of aparme reurs, we adop a wo-sage procedure. I he firs sage, we esimae (8) separaely o paels of reurs by OLS for each idividual ype. I he secod sage, we esimae (8) o joily paels of idividual reurs, usig he variacecovariace marix of error erms esimaed from he error erms i he firs sage. We assume ha i each pael, he error erms for differe aparme ypes have a commo compoe Le ε be a vecor of error erms i a facor srucure, ε = Λf + υ, where f is a commo facor ad Λ is a marix of facor loadigs. The, uder he sadard assumpio ha he facors are idepedely ad ormally disribued wih zero meas ad ui variace, Σ, he covariace marix of ε, is Σ = ΛΛ' + Ψ, where Ψ = E( υυ' ). 18

22 Table 8A ad 8B repor he resuls of pael versios of he Divided Price Raio Tes, esimaed separaely for he period before ad afer he Asia Fiacial Crisis. We use he wo year Idusrial Fiace Bod rae as he discou rae (implicily assumig ha he risk premium i each period is cosa). We es he ull hypohesis ha all he aparme ypes i each submarke are priced by he prese value relaioship (PVR). The ables repor he Chi squared saisics for he es of he prese value relaioship ad he associaed ρ value. As oed i Table 8A, for he period precedig he Asia Fiacial Crisis, for oly oe of he 26 submarkes is he hypohesis rejeced a he.05 level. For oly oe oher submarke, is he hypohesis rejeced a he 0.10 level. The evidece seems clear: durig he period before he Asia Fiacial Crisis, he prese value of divideds does a very good job of explaiig he movemes i asse prices. Table 8B provides eve sroger evidece for he period afer he Asia Fiacial Crisis. For oly oe submarke -- small aparmes i oe regio of -- is he PVR pricig relaioships rejeced. For he oher 27 submarkes, he prices of asses are prediced by he prese value of divideds. For oher ess, o repored, based o VAR relaioships of differe leghs, he resuls are similar: asse prices are deermied by he prese discoued value of divideds. V. Coclusio Mos previous sudies esig he prese value relaioship (PVR) i fiacial markes have srogly rejeced he hypohesis of marke efficiecy. Bu hese sudies rely upo divideds 19

23 se by firm maagers. Oher sudies applyig he PVR model o housig (makig impuaios of divideds from he res of comparable dwelligs) have similarly rejeced he hypohesis of housig marke efficiecy. Bu hese laer sudies are ypically based o evidece from Norh America, where housig ad housig markes are quie heerogeeous ad where deailed observaios o res ad sellig prices for he same dwelligs are o available. I coras, we have exploied here he uique feaures of he Korea housig marke where dwelligs are homogeeous ad observaios o boh marke res ad sellig prices are available for each ui. We es several impora resricios implied by he prese value models usig paels of prices ad res i Korea codomiium submarkes. The resuls imply ha we cao rejec he hypohesis of marke efficiecy for Korea codomiium markes hroughou he 1990s ad early 2000s, for he period before or afer he Asia Fiacial Crisis of Iformaio o expeced housig reurs is refleced i he level of curre re as posulaed by he prese value model of asse pricig. Our resuls may also sugges ha he coclusios of previous sudies of housig marke efficiecy have bee compromised by iadequae iformaio o res ad values for dwelligs. 20

24 Refereces Acker, L., ad B. Smih (1993). Sock Price Volailiy, Ordiary Divideds, ad Oher Cash Flows o Shareholders, Joural of Fiace 48, Ambrose, Bre W., ad Suwoog Kim (2003). Modelig he Korea Chosei Lease Corac, Real Esae Ecoomics,31, Campbell, J. ad R. Shiller (1987). Coiegraio ad Tess of Prese Value Models, Joural of Poliical Ecoomy 95, Campbell, J. ad R. Shiller (1988). The Divided-Price Raio ad Expecaio of Fuure Divideds ad Discou Facors, Review of Fiacial Sudies 1, Capozza, D. R. ad P. J. Sagui (1996). Expecaios, Efficiecy ad Euphoria i he Housig Marke, Joural of Regioal Sciece ad Urba Ecoomics 26, Case, K. E. ad R. J. Shiller (1989). "The Efficiecy of he Marke for Sigle-Family Homes," America Ecoomic Review 79, Case, K. E. ad R. J. Shiller (1990). "Forecasig Prices ad Excess Reurs i he Housig Marke," Joural of he America Real Esae ad Urba Ecoomics Associaio 18, Chag, Y. ad W. Sog (2003). Pael Ui Roo Tess i he Presece of Cross Secioal Depedecy ad Heerogeeiy, Workig paper, Uiversiy of Houso. Clayo, J. (1996). "Raioal Expecaios, Marke Fudameals ad Housig Price Volailiy," Real Esae Ecoomics 24, Clayo, J. (1997). Are Housig Price Cycles Drive by Irraioal Expecaios? Joural of Real Esae Fiace ad Ecoomics 14, Cochrae, J. (1991). Volailiy Tess ad Efficie Markes: A Review Essay, Joural of Moeary Ecoomics 27, Cochrae, J. (1992). Explaiig he Variace of Price Divided Raios, Review of Fiacial Sudies 5, Craie, R. (1993). Raioal Bubbles: A Tes, Joural of Ecoomic Dyamics ad Corol 17, Diba, B. ad H. Grossma (1988). Explosive Raioal Bubbles i Sock Prices?, America Ecoomic Review, 78, Gilles, C. ad S. LeRoy (1991) "Ecoomeric Aspecs of he Variace-Bouds Tess: A Survey," Review of Fiacial Sudies 4, Hamilo, J. ad C. Whiema (1985). The Observable Implicaios of Self-Fulfillig Expecaios, Joural of Moeary Ecoomics 16,

25 Hamilo, J. (1994) Time Series Aalysis, Priceo Uiversiy Press, Priceo, New Jersey. Kim, S. (2000), The Srucural Chages i Korea Housig Marke ad New Housig Fiace Policy, Housig Sudies Review 8, Kleido, A. (1986). Variace Boud Tess ad Sock Price Valuaio Models, Joural of Poliical Ecoomy, 94, LeRoy, S. ad R. Porer (1981). The Prese Value Relaio: Tess Based o Implied Variace Bouds, Ecoomerica 49, LeRoy, S. (1989). "Efficie Capial Markes ad Marigales," Joural of Ecoomic Lieraure, 27 (4), Makiw, N., ad D. N. Weil (1989). "The Baby Boom, he Baby Bus ad he Housig Marke," Regioal Sciece ad Urba Ecoomics 19, Marsh, T. ad R. Mero (1986). "Divided Variabiliy ad Variace Bouds Tess for he Raioaliy of Sock Marke Prices," America Ecoomic Review 76(3), Meese, R. ad N. Wallace (1994). "Tesig he Prese Value Relaio for Housig Prices: Should I leave My House i Sa Fracisco?" Joural of Urba Ecoomics 35, Poerba, J. M. (1991). "House Price Dyamics: The Role of Tax Policy ad Demography," Brookigs Papers o Ecoomic Aciviies 2, Shiller, R. J. (1981). Do Sock Prices Move Too Much o be Jusified by Subseque Divideds? America Ecoomic Review, 71,

26 Table 1. Disribuio of Housig Types ad Housig Uis by Size ad Regio (Number of Housig Uis i Pareheses) 1990 Q Q3 Small Medium- Small Medium- Large Large Toal Regio 1 (3,919) (21,177) (45,658) (16,898) (87,652) ,591 Regio 2 (39,814) (93,801) (143,535) (30,957) (308,107) ,543 Regio 3 (67,559) (39,718) (116,167) (43,968) (267,412) ,597 Regio 4 (21,117) (65,126) (118,449) (31,526) (236,218) Kyuggi ,546 Regio 1 (15,884) (104,235) (138,939) (44,592) (303,650) Kyuggi 453 1,265 1, ,717 Regio 2 (110,680) (253,282) (269,270) (71,014) (704,246) Icheo Toal ,776 (52,949) (103,092) (122,002) (19,788) (297,831) 1,225 3,813 5,244 2,239 12,521 (311,922) (680,431) (954,020) (258,743) (2,205,116) Noes: Small aparmes are hose wih less ha 645 sq.f. Medium-Small are hose wih sq.f Medium-Large are hose wih sq.f Large are hose wih more ha 1430 sq.f 23

27 Table 2. Disribuio of Aparme Types ad Housig Uis Observed Coiuously: before he Asia Fiacial Crisis (1990 Q Q3) ad afer he Asia Fiacial Crisis (1999 Q Q3) Small Medium-Small Medium-Large Large Toal 5 (232) 11 (2,772) 23 (4,402) 12 (2,514) 51 (9,920) Regio 1 6 (272) 49 (9,032) 125 (23,084) 56 (7,752) 236 (40,140) 32 (10,128) 54 (14,396) 86 (20,254) 21 (2,988) 193 (47,766) Regio 2 93 (29,546) 208 (55,022) 363 (89,430) 94 (15,333) 758 (189,331) 52 (30,800) 44 (9,331) 154 (45,367) 136 (22,301) 386 (107,799) Regio 3 75 (48,756) 146 (27,695) 395 (90,336) 225 (34,688) 841 (201,475) 23 (5,997) 61 (6,093) 93 (16,199) 23 (3,351) 200 (31,640) Regio 4 49 (14,104) 156 (30,217) 299 (67,666) 95 (15,893) 599 (127,880) Kyuggi 8 (2,365) 5 (891) 0 (0) 0 (0) 13 (3,256) Regio 1 34 (7,162) 199 (52,263) 291 (64,133) 117 (17,341) 641 (140,899) Kyuggi 47 (13,299) 48 (8,252) 61 (14,753) 3 (526) 159 (36,830) Regio (72,167) 472 (104,898) 664 (147,763) 326 (41,497) 1702 (366,325) 2 (246) 7 (1,032) 9 (3,164) 3 (390) 21 (4,832) Icheo 48 (13,027) 131 (28,903) 203 (59,961) 70 (8,604) 452 (110,495) 169 (63,067) 230 (42,767) 426 (104,139) 198 (32,070) 1,023 (242,043) Toal 545 (185,034) 1,361 (308,030) 2,340 (542,373) 983 (141,108) 5,229 (1,176,545) Noes: The firs lie repors he umber of housig ypes i each submarke observed coiuously for he period 1990 Q1 hrough 1997 Q3. The secod lie repors he umber of housig ypes i each submarke observed coiuously for he period 1999 Q1 hrough 2002 Q3. I pareheses are he umber of uis i each submarke observed coiuously for he sample period. 24

28 Table 3. Average Re-Price Raios by Submarke ad Dwellig Size: Before he Asia Fiacial Crisis ad Afer he Asia Fiacial Crisis Small Medium- Small Medium- Large Large Toal Regio Regio Regio Regio Kyuggi Regio Kyuggi Regio Icheo Toal Noe: The firs lie for each regio ad size repors he average re-price raio for dwelligs durig he period 1990 Q1 hrough 1997 Q3. The secod lie repors he average re-price raios for dwelligs durig he period 1998 Q1 hrough 2002 Q3. 25

29 Table 4. Gross Quarerly Housig Reurs by Submarke ad Dwellig Size: Before he Asia Fiacial Crisis ad Afer he Asia Fiacial Crisis Small Medium- Small Medium- Large Large Toal Regio Regio Regio Regio Kyuggi Regio Kyuggi Regio Icheo Toal Noe: The firs lie for each regio ad size repors he average quarerly reur for dwelligs durig he period 1990 Q1 hrough 1997 Q3. The secod lie repors he average quarerly reur durig he period 1998 Q1 hrough 2002 Q3. Gross housig reur, r, is defied as, P + R where P represes sellig price ad R represes re. i, i, r i, = for quarer ad housig i, Pi, 1 26

30 Table 5. Quarerly Growh Rae i Res by Submarke ad Dwellig Size: Before he Asia Fiacial Crisis ad Afer he Asia Fiacial Crisis Small Medium- Small Medium- Large Large Toal Regio Regio Regio Regio Kyuggi Regio Kyuggi Regio Icheo Toal Noe: The firs lie for each regio ad size repors he average quarerly growh rae for re for dwelligs durig he period 1990 Q1 hrough 1997 Q3. The secod lie repors he average real growh rae durig he period 1998 Q1 hrough 2002 Q3. 27

31 Table 6. Cross Secioal Models of Ivesme Reurs i Korea Aparmes: 1994Q1 2002Q3 Size Medium-Small Medium-Large Large 1994:Q1 1996:Q1 1998:Q1 2000:Q1 2002:Q (7.28) (8.16) (2.77) (0.17) (12.67) (10.80) (10.25) (8.15) (2.96) (22.43) (8.82) (11.63) (4.43) (9.38) (33.17) Regio Regio 2 (2.93) (0.70) (4.02) (1.93) (3.10) Regio 3 (2.83) (10.46) (8.24) (14.85) (25.93) Regio 4 (2.58) (5.93) (7.33) (2.96) (12.06) Kyuggi Regio 1 (2.20) (4.58) (10.02) (6.17) (3.23) Kyuggi Regio 2 (4.11) (10.25) (16.25) (10.33) (8.93) Icheo (0.81) (6.61) (10.26) (9.67) (21.05) Lagged Reur (11.45) (3.97) (7.30) (17.92) (1.77) Lagged Price/Deposi (3.73) (7.07) (8.47) (10.46) (13.50) Lagged Price/Size (3.28) (9.86) (5.68) (14.40) (12.80) Adj R Number of Observaios Noe: Sadard errors are correced for heeroskedasiciy usig Whie (1985). T-saisics are give i parehesis. 28

32 Table 7A. Pael Ui Roo Tess o he Log of Price-Re Raios for Korea Aparmes 1990 Q Q3 (Oe Quarer Lag) Small Medium-Small Medium-Large Large Regio 1 (0.07) (>0.01) (>0.01) (>0.01) Regio 2 (0.10) (0.00) (0.00) (>0.01) Regio 3 (0.13) (0.32) (>0.01) (>0.01) Regio 4 (0.02) (>0.01) (>0.01) (>0.01) Kyuggi Regio 1 (0.10) (0.06) (>0.01) (>0.01) Kyuggi Regio 2 (0.08) (0.01) (>0.01) (0.12) Icheo (>0.01) (>0.01) (0.03) (0.04) Eries i he able are based o regressios for he -idividual aparme ypes i a give pael, y K 2 K i = β y, + β i y i + β i x K i + ε 1 1 1, 2, + i= 1 i= K + 1 where is he log of price-re raio, ad is he differece bewee he y discou rae ad re growh. The able repors ess of β1 = 1 ad Sog (2003). x, proposed by Chag For each cell, modified -saisics are provided for he ull hypohesis ha he log of price re raios for a leas e perce of housig ypes i he marke have ui roos. P-values are give i he parehesis. The umber of aparme ypes associaed wih each ery i he able is repored i Table 2. For more deailed iformaio o he pael ui roo es used, see Chag ad Sog (2003). 29

33 Table 7B. Pael Ui Roo Tess o he Log of Price-Re Raios for Korea Aparmes 1999 Q Q3 (Oe Quarer Lag) Small Medium-Small Medium-Large Large Regio 1 (0.51) (0.09) (0.11) (0.07) Regio 2 (0.05) (0.02) (0.00) (0.06) Regio 3 (0.20) (0.16) (0.03) (>0.01) Regio 4 (0.62) (0.03) (>0.01) (0.08) Kyuggi Regio 1 (0.07) (>0.01) (>0.01) (0.06) Kyuggi Regio 2 (0.02) (>0.01) (>0.01) (>0.01) Icheo (0.11) (0.06) (0.02) (0.02) Eries i he able are based o regressios for he -idividual aparme ypes i a give pael, y K 2 K i = β y, + β i y i + β i x K i + ε 1 1 1, 2, + i= 1 i= K + 1 where is he log of price-re raio, ad is he differece bewee he discou y rae ad re growh. The able repors ess of (2003). x β1 = 1, proposed by Chag ad Sog For each cell, modified -saisics are provided for he ull hypohesis ha he log of price re raios for a leas e perce of housig ypes i he marke have ui roos. P- values are give i he parehesis. The umber of aparme ypes associaed wih each ery i he able is repored i Table 2. For more deailed iformaio o he pael ui roo es used, see Chag ad Sog (2003). 30

34 Table 8A. Divided Price Raio Tess for Korea Aparmes 1990 Q Q3 Small Medium-Small Medium-Large Large Regio 1 (0.99) (0.71) (0.86) (0.89) Regio 2 (0.00) (0.68) (0.97) (0.99) Regio 3 (0.52) (0.84) (> 0.99) (> 0.99) Regio 4 (0.98) (> 0.99) (> 0.99) (0.95) Kyuggi Regio 1 (0.48) (0.76) - - Kyuggi Regio 2 (0.98) (> 0.99) (> 0.99) (0.34) Icheo (0.24) (0.97) (0.76) (0.09) Eries i he able are based o oe quarer VARs for he -h idividual aparme ype i a give pael, y = α K 2K 1,0 + α1, i y i + α1, i i= 1 i= K + 1 y x + K i K 2K 2,0 2, i i + α 2, i i= 1 i= K + 1 ad x = α + α y x, + K i where is log of price-re raio, ad is he differece bewee he growh i re ad he discou rae ad. Le β x = [ ] α, L, α, α, L α, ad R [ ρi, I ] 1,1 1,2K 2,1, 2, 2K =. We repor resuls from esig R 0 L 0 β1 e1 0 R L 0 β 2 e2 (*). = M M M M M M 0 0 L R β N e N Each cell repors he χ 2 -saisic for esig he resricio (*) above as well as he p-value, repored i parehesis. The umber of aparme ypes associaed wih each ery i he able is repored i Table 2. 31

35 Table 8B. Divided Price Raio Tess for Korea Aparmes 1999 Q Q3 Small Medium-Small Medium-Large Large Regio 1 (0.92) (> 0.99) (> 0.99) (> 0.99) Regio 2 (> 0.99) (> 0.99) (> 0.99) (> 0.99) Regio 3 (0.03) (> 0.99) (> 0.99) (> 0.99) Regio 4 (> 0.99) (> 0.99) (> 0.99) (> 0.99) Kyuggi Regio 1 (> 0.99) (> 0.99) (> 0.99) (> 0.99) Kyuggi Regio 2 (> 0.99) (> 0.99) (> 0.99) (> 0.99) Icheo (> 0.99) (> 0.99) (> 0.99) (> 0.99) Eries i he able are based o oe quarer VARs for he -h idividual aparme ype i a give pael, y = α where K 2K 1,0 + α1, i y i + α1, i i= 1 i= K + 1 x + K i K 2K 2,0 2, i i + α 2, i i= 1 i= K + 1 ad x = α + α y x, + K i y is log of price-re raio, ad x is he differece bewee he growh i re ad he discou rae ad. Le β = [ ] α, L, α, α, L α, ad R [ ρi, I ] 1,1 1,2K 2,1, 2, 2K =. We repor resuls from esig R 0 L 0 β1 e1 0 R L 0 β 2 e2 (*). = M M M M M M 0 0 L R β N e N Each cell repors he χ 2 -saisic for esig he resricio (*) above as well as he p-value, repored i parehesis. The umber of aparme ypes associaed wih each ery i he able is repored i Table 2. 32