What Drives the Housing Markets in China: Rent, Cost of. Capital, or Risk Premium of Owning relative to Renting?

Transcription

1 Wha Drives he Housing Markes in China: Ren, Cos of Capial, or Risk Premium of Owning relaive o Rening? Chen Sichong 1 Chen Yingnan 2 (1.School of Finance, Zhongnan Universiy of Economics and Law; 2.Hang Lung Cener for Real Esae, Tsinghua Universiy) Preliminary draf Absrac: We combine he sandard Campbell and Shiller (1988) presen-value model wih he classical user cos of housing model o decompose he renal yield ino hree componens: expeced fuure ren growh, cos of capial and risk premium of owning relaive o rening. We hen apply a quarerly daase of four major ciies (Beijing, Shanghai, Guangzhou and Shenzhen) o explore he quesion of wha forces have driven he movemen of China s housing marke. Specifically, using he variance decomposiion approach o examine quaniaively how much he variaion in renal yield comes from he above-menioned hree componens. Our resuls show ha cos of capial is playing a vial role in all he four major ciies, while he fuure ren growh is no a driving force as significan as he cos of capial in he flucuaion of he renal yield. Moreover, we find ha anoher facor -- he risk of owning relaive o rening a house -- is accouning for a large par of housing marke movemen in China. I is also worh noing ha he risk of rening relaive o owning a house seems o be rising rapidly in China over he recen years. Key Words: Renal Yield; Dynamic Gordon Growh model; User Cos of Housing Model; Variance Decomposiion; China JEL Classificaion: G12, R31 1

2 1. Inroducion The housing marke in China s major ciies has surged for almos 1 years since 23 unil early 211, wih some signs of moderaion recenly. Wha economic forces drive he large swings in he China s housing marke? Does i prelude furher declines or good prospecive reurns in he fuure? Or does i simply reflec a gloomy oulook abou fuure ren ha can be generaed by housing service? Asse pricing heory ries o answer hese quesions by relaing he price o enire fuure uncerain cash flow, usually in he form of presen-value saemen. The renal yield, he equivalen of he dividend-price raio in he housing marke, is of paricular imporance in assessing he housing marke based on his presen-value framework, because i reveals agen s expecaions abou fuure reurns and ren growh in housing marke. In oher words, he changes in renal yield mus capure he ime variaion in expeced reurns and/or expeced ren growh raes. In his work, we would like o sar by he sandard presen-value model of renal yield pioneered by Campbell and Shiller (1988) ha decomposes he movemen of renal yield mainly ino wo componens: changes in expeced fuure reurns and fuure ren growh. Campbell and Shiller (1988) originally use his framework o explore he dynamics of aggregae sock marke reurns. Since hen, his framework has been applied by researchers o many oher areas in finance, such as individual sock reurns (Vuoleenaho, 22), fixed income securiies (Shiller and Belrai, 1992; Campbell and Ammer, 1993), inernaional financial adjusmens (Gourinchas and Rey, 27), and real esae marke (Campbell, Davis, Gallin and Marin, 29; Plazzi, Torous and Valkanov, 21). For example, Campbell, Davis, Gallin and Marin (29) and Hieber and Sydow (211) use he same framework o sudy he flucuaions in he real esae markes for he U.S. and EU, respecively. To our bes knowledge, his is he firs research o examine he driving forces of mainland Chinese housing marke wihin he presen-value model of renal yield. More imporanly, we would go beyond he sandard presen-value model of renal yield o incorporae feaures in he housing markes hrough he user cos of housing model (Hendersho and Slemrod, 1983; Jorgenson, 1963; Poerba, 1984) o gain furher economic insighs ino he presen-value model of renal yield. In oher words, we would be able o gain furher economic insighs ino he presen-value model of renal yield, if addiional srucure is imposed on he dynamics of reurns and/or ren growh raes. We would ake an approach similar o Binsbergen and Koijen (21) and Plazzi, Torous and Valkanov (21), who impose addiion srucure on he specificaion of expeced reurns and expeced dividend (ren) growh process guided by he empirical properies of sock and real esae s daa. However, unlike Binsbergen and Koijen (21) and Plazzi, Torous and Valkanov (21), who specify exogenously a ime-series saisical model, we would like o impose srucure wihin a presen-value model of renal yield base on an economic model of user cos of housing in order o invesigae in more deail he economic properies of he housing marke. In his sense, 2

3 our work is more relaed o Campbell, Giglio and Polk (21), who impose he cross-secional resricions of he iner-emporal capial asse pricing model (ICAPM) on asse reurns. In shor, we are looking a he quesion of wha forces have driven he movemen of China s housing marke, by combining he sandard presen-value model wih he classical user cos of housing model, o decompose he renal yield ino hree componens: he expeced fuure rens, coss of capial, and risk premium of owing relaive o rening. We would like o idenify which forces have played he mos significan par in he movemen of he China s housing marke. Afer using he vecor auoregressive mehodology o consruc empirical proxies for he relevan expecaions in our presen-value model, we can employ he variance decomposiion approach o examine quaniaively how much he variaion in renal yield comes from he above-menioned hree componens. Specifically, we would firs build a heoreical model by combining he sandard Campbell and Shiller (1988) presen-value model wih he classical user cos of housing model o decompose he renal yield ino hree componens: expeced fuure ren growh, cos of capial, and risk premium of owning relaive o rening. And hen, based on our heoreical model, we would like o exploi a daase compiled by he Chinese Mainland DTZ, a global real esae adviser, for he four Chinese firs-ier ciies (Beijing, Shanghai, Guangzhou and Shenzhen) o explore he quesion of wha forces have driven he movemen of China s housing marke. Our resuls show ha cos of capial is playing an imporan role in all he four major ciies, while he fuure ren growh is no a driving force as significan as he cos of capial in he flucuaion of he renal yield. Moreover, we find ha anoher facor -- he risk of owning relaive o rening a house is accouning for a large par of housing marke movemen in China. I is also worh noing ha he risk of rening relaive o owning a house seems o be rising rapidly in China over he recen years. The res of our work is organized as follows. The nex secion oulines he log-linearized presen-value model of renal yields ha combines he sandard Campbell and Shiller (1988) presen-value model wih he classical user cos of housing model. Secion 3 presens our implemenaion of he presen-value model of renal yields, including daa descripion and empirical mehodology. Secion 4 repors he empirical resuls of variance decomposiion showing how each componen of he model in driving housing marke movemens of he four major ciies in China. The final secion concludes. 3

4 2. The Model The presen-value model of renal yield Following Campbell and Shiller (1988), we sar wih he definiion of one-period holding reurns in housing markes o derive a presen-value model of renal yield (also called a dynamic Gordon growh model ha is a dynamic generalizaion of he Gordon growh model for housing prices wih consan expeced reurns and ren growh). This presen-value model of renal yield provides a useful organizing principle for empirical work o divide he underlying driving forces in housing markes mainly ino wo pars: one is changes in expeced cash flow; he oher is changes in expeced reurns or discoun raes. In paricular, we define he one-period holding reurn in housing markes as follows: R P L i, 1 i, 1 i, 1, (1) Pi, where P i, is he price of a house in ciy i a he end of ime, Li, 1 is he ren paid o he corresponding housing holder in ciy i over he period from he end of o he end of period 1, Ri, 1 is he realized gross reurn held in ciy i from he end of o he end of period 1. Afer aking logs of boh sides of he above defined one-period holding reurn, we can derive an approximaed log-linearized ideniy as follows using firs-order Taylor expansion: + r l, (2) i, i, 1 i, 1 i, 1 where l indicaes he firs difference of log ren, denoes he log of renal yield, r is he log of one-period holding reurn, is a parameer ha equals 1 1 exp{e[ ]}, is a consan erm in he log-linear approximaion. We can ierae he Eq. (2) h periods ahead o express renal yield as a discouned sum of fuure holding reurns, ren growh and renal yield as follows: 4

5 h 1 h h j1 j1 h +. (3) 1 r l i, i, j i, j i, h j1 j1 If we impose he condiion ha renal dividend yield is saionary, he las erm of Eq. (3) would disappear as we ierae forward o he infinie-horizon limi: + r l. j1 j1 i, i, j i, j 1 j1 j1 (4) Eq. (4) holds ex pos, bu i also holds ex ane as well since i is an approximaed ideniy, Thus, afer aking expecaions of boh sides of Eq. (4) and noing ha, we can express renal yield as a presen-value model of infiniely discouned sum of fuure ren growh and holding reurns in housing markes: r l j1 j1 + E E, (5) i, i, j i, j 1 j1 j1 where he expecaion operaor E can refer o any informaion se ha includes renal yield. I deserves noing ha Eq. (5) shows renal yield reveals agen's expecaion abou expeced fuure reurns and expeced fuure ren growh in housing markes. If renal yield varies a all, i mus mechanically come from he changing expeced fuure reurns or ren growh or boh, given ha renal yield is saionary. On he one hand, invesors would bid up house prices relaive o curren ren, if hey expec fuure ren will be higher han hey are oday. Then, oday s low renal yield forecass he subsequen rise in rens. On he oher hand, house prices can also be high if expeced reurns are low. Tha is, he same rens in he fuure are discouned a a lower rae. Then, oday s low renal yield forecass low reurns in he fuure. In addiion, we can follow he approach of Campbell and Shiller (1988) o use he dynamic accouning ideniy derived in Eq. (5), o decompose he variance of he renal yield ino he sum of variance and covariance erms as follows by aking ino accoun he possible correlaion among various componens: var, var E j, var E j, cov E j,, E j i ri j li j ri j li, j. j1 j1 j1 j1 (6) Specifically, we need firs o employ appropriae mehod o consruc empirical proxies for corresponding erms in he righ hand side of Eq. (5). And hen, we can 5

6 compue he variance or sandard deviaion of each erm o examine quaniaively how much he variaion in renal yield comes from changes in expeced reurns, and how much is due o changes in expeced ren growh. The relaive conribuion of differen componens o he movemen of he curren renal yield could hen be measured by he variance of ha componen, calculaed as he percenage share of he variance of he curren renal yield. I is also worh noing ha he presen-value model of renal yield is a dynamic accouning ideniy wih minimum assumpions such as saionariy. In oher words, we are only using dynamic ideniies ogeher wih and he variance decomposiion approach o derive our empirical resuls. Therefore, our resuls are robus on inferring relaive imporance of fuure expeced reurns and ren growh in driving he variaion in renal yield. Imposing he housing user cos model as a resricion condiion However, he srengh is also he weakness. Alhough he presen model enables us o uncover he proximae causes of changes in renal yield, i does no clarify why he expeced reurns and profiabiliy change so much, and so never really provides an economic explanaion of fundamenal facors driving he variaion in housing markes. Moreover, here is a large lieraure documening ha almos all asse price movemens, eiher in socks or real esae, are due o changing expeced reurns raher han o changing expecaions of fuure cash flow. I also holds in China s housing marke, as we will show laer in his work. I hus implies ha we have o aribue a large porion of housing marke movemen o ime-varying discoun raes ha is harder for people o capure, raher han easier-o-undersand ren growh. In order o open he black-box like discoun raes, we may need o go beyond he sandard he presen-value model of renal yield o incorporae feaures in he housing markes. In oher words, we would be able o gain furher economic insighs ino he presen-value model of renal yield, on if addiional srucure is imposed on he dynamics of reurns and/or ren growh raes. In wha follows, we would ake an approach similar o Binsbergen and Koijen (21) and Plazzi, Torous and Valkanov (21), who impose addiion srucure on he specificaion of expeced reurns and expeced dividend (ren) growh process guided by he empirical properies of sock and real esae s daa. However, unlike Binsbergen and Koijen (21) and Plazzi, Torous and Valkanov (21), who specify exogenously a ime-series saisical model, we would like o impose srucure wihin a presen-value model of renal yield based on an economic model of housing user s cos in order o invesigae in more deail he economic properies of he housing marke. In his sense, our work is more relaed o Campbell, Giglio and Polk (21), who impose he cross-secional resricions of he ineremporal capial asse pricing model (ICAPM) on asse reurns. 6

7 In real esae economics lieraure (eg. Jorgenson, 1963; Hendersho and Slemrod, 1983; Poerba, 1984), he classical user cos of housing model assumes ha he housing marke is an efficiency marke wihou fricion. There is a no arbirage condiion meaning ha he marginal benefi which is he renal price, mus be equal o he marginal cos, namely, he user cos of housing. L, i, 1 UCi, 1 (7) where Li, 1 is he ren paid o he homeowner in ciy i over he period from he end of o he end of period 1, UCi, 1 is he cos of owning a house of corresponding homeowner in ciy i over he period from he end of o he end of period 1, which is known as user cos or impued ren. As defined by lieraure, he user cos is he sum of several componens, usually can be divided ino hree caegories. The firs elemen is he cos of capial. People can use a leverage o buy a house, hus, he homeowner has o pay a morgage and/or loose a reurn on an alernaive invesmen. We consider he capial cos as he sum of ineres paymen of a morgage 1 paymen 1 rf Pi, LTVi, ri, 1 and he opporuniy cos of he insall rf Pi, LTVi, ri, 1. Thus he capial cos PC i, i, 1 is he weighed average rf m of risk-free deposi raes ( ri, 1 ) and morgage raes ( ri, 1 ), wih loan-o-value raio (,1 LTV ) as he weigh: P,, 1, (1, ) rf m i Ci P i LTVi ri, 1 LTVi, r i, 1. The second elemen of user s cos of owning a house includes depreciaion, mainenance coss, and risk premium. Following he lieraure, we assume ha boh he depreciaion and mainenance coss are invarian over ime as a fracion of curren housing prices, i.e., Pi, i Pi, i. On he oher hand, according o Sinai and Souleles (25), he risk premium is no only ime-varying, bu can also be posiive or negaive. Thus, we follow he lieraure o assume he risk premium of owning relaive o rening as a changing fracion of curren housing prices Pi, i, 1. In sum, he cos of reaining a house can be denoed as Pi, Mi, 1 Pi, i, 1 i i. Third, since he homeowner have he opion o resale he house in he fuure, a poenial capial gain or loss should also be aken ino accoun: P E i, 1 P i,. 7

8 In some oher counries, owning a house can be eniled o some ax benefis ha should be deduced, such as he deducibiliy of morgage ineres from income ax. Meanwhile, he homeowner can also be obliged o paying propery ax. Forunaely, our sample is immune from hose ax consideraions. Therefore, he housing user cos model applied o our sudy can be wrien as followings: Li, 1 Pi, Ci, 1 Pi, Mi, 1 E Pi, 1 P i,. (8) If we rewrie he above Eq. (8), we can obain: L E i, 1 i, 1 P i, P 1 C M. (9) i, 1 i, 1 Provided ha he rens is deermined or paid in advance ha is ypical in he renal marke, he renal price for he nex period would be included in he informaion se a ime, so ha we have Li, 1 E Li, 1. Since he informaion se a ime.. also includes he housing price P i,, he lef side of he Eq. (9) can be rewrien as E L P i, 1 i, 1 P i,. Then, we can have: Taking logs of boh sides, we can obain 1 : E R 1 C M. (1) i, 1 i, 1 i, 1 E r c m. (11) i, 1 i, 1 i, 1 where ri, 1 log Ri, 1 is he log of one-period reurns, ci, 1 log 1Ci, 1 denoes he log of capial cos, log 1 m C M c is he cos of i, 1 i, 1 i, 1 i, 1 reaining a house mainly reflecing he changing risk premium. 1 Of course, ER 1 exp Er 1, because E f x f Ex log E R 1 E r 1 2 disribuion, we haveer exp Er r 2. Since r Er 8. Bu, we can derive approximaely. For example, if he housing reurn R follows log-normal 2 such as r r r ER exp Er 2 2 E E 2 holds approximaely. is small, he higher order erms,, would be small enough o be ignored. As a resul, he equaliy

9 Having obained he housing user cos model in he form of Eq. (11),we can hen nes i wihin a presen-value model of renal yield, in order o furher decompose he discoun rae ino wo componens: he cos of capial and he risk premium of owning relaive o rening. In oher words, we can impose he above Eq. (11) as a resricion condiion ino Eq. (5) o acquire: + E c m l. (12) i, 1 j1 j1 i, j i, j i, j Eq. (12) shows ha we can decompose he renal yield ino hree componens: he expeced fuure rens, coss of capial, and risk premium of owing relaive o rening. Similar o Eq. (6), we can examine quaniaively how much he variaion in renal yield comes from he above-menioned hree componens, by decomposing he variance of he renal yield ino he sum of variance he hree componens ogeher wih he covariance erms among hem. j1 j1 var i, var E ci, j var E mi, j j1 j1 j1 + var E li, j covariance erms j1 (13) Below, we would apply he presen-value model of renal yield in Eq. (12) o a quarerly daase of four major ciies in China, in order o explore he quesion of wha forces have driven he movemen of China s housing marke. Specifically, by employing he variance decomposiion approach, we can examine quaniaively he relaive imporance of differen forces in driving he variaion in renal yield over ime. 3. Empirical Implemenaion Daa We apply a vecor auoregression(var) sysem o consruc ime-series esimaes of expeced housing reurns, cos of capial and ren growh by using four empirical proxy variables 2 : (1)renal yield, (2)housing reurn, (3)cos of capial and (4)ren growh rae. House prices, rens and renal yield 2 For he variable of risk premium of rening relaive o buying, we use a similar mehod which applied in Campbell and Shiller (1988) abou aking dividend as he residual erm of model, and hrough he model equaion (13) o consruc i. However, we should bear in mind ha his mehod is easy o overesimae he impac of risk premium; because residual erm includes he linear approximaion error and oher no esimaed facors. We will discuss hese problems laer in his secion and find ha hese effecs are no worhy of oo much worry. 9

10 The residence daa se we use in our sudy is house pricesp i, and rens indexli, of four major ciies (namely Beijing, Shanghai, Guangzhou, Shenzhen) 3 and is provided by DTZ 4. The residenial prices and rens index in each ciy are corresponding ransacions daa of secondhand high-end residence in a given quarer. 5 The index daa is on a quarerly basis, and he available ime period of Shanghai, Guangzhou and Shenzhen is beginning in he firs quarer of 1991(1991:Q1) and ending in he firs quarer of 211(211:Q1), while he ime span of Beijing's price index is from 1993:Q2 o 211:Q1 and ren index also covers he sample period 1991:Q1 o 211Q:1. All index series are convered in 1993:Q3 as he base period. To he bes of our knowledge, he DTZ index is he only kind of housing marke index ha can capure one housing price cycle in China, especially a a ciy-level, and his novel advanage is essenial for our analysis. Given he advanage of DTZ index, we are he firs o consruc ciy-level ime series daa of renal yield in China. To obain a series in levels for he renal yield, we hen use daa of a survey from China Inernaional Capial Corporaion Limied (CICC) o benchmark he level of he renal yield in 26:Q1. And we work wih log renal yield: i, L =log P i, i,. Housing reurns Based on four ciies' house price indexes from DTZ and renal yield which we consruc above, he log housing reurns are calculaed as: Ren growh raes +1 Ri, =log P i, i, i, -1 P. The log ren growh raes are compued as: li, log Li, log Li, -1. Cos of Capial As we defined earlier in his paper, he uni cos of capial C i, is (1 LTV, -1) rf m i ri, LTVi, -1 r i,. We use 1-year deposi ineres rae and 5-year above loan ineres rae respecively as he proxy variables of risk free ineres rae and morgage 3 The praciioners ofen refer o hese four ciies as firs-ier ciies in China. Real esae developmen of hese four ciies is apparenly ahead of oher ciies in China. 4 DTZ is a global real esae adviser founded in 18 h cenury UK and enered Chinese mainland marke in DTZ will no announce deails abou how hey consruc heir daa series. To he bes of our available informaion, he sample of DTZ's index is coninuous and comparable across ciies and over ime. 1

11 loan ineres rae. The ineres rae daa is from he People's Bank of China (PBoC). For convenience of analysis, we assume he down paymen raio is 2%, and corresponding LTV raio is 8% 6. Table (1) presens he descripive saisics on he above four variables, prior o log and demean. We repor ime series averages, sandard deviaions, maximum and minimum. From Table 1 we can see ha he averages of renal yield of four ciies ranging from.47(shanghai) o.85(beijing), wih he sandard deviaions varying from.25(shanghai) o.48(beijing); which means ha he valuaion level of Shanghai's housing marke is he highes and Beijing is he lowes on average, while he volailiy of housing marke in Beijing is higher han oher ciies and Shanghai is he lowes. The volailiy of housing reurns of four ciies is very close, bu Shanghai's reurn is relaive lower han he oher hree ciies. Boh means and sandard deviaions of ren growh rae of four ciies are close plus means are negaive, indicaing ha hese ciies' renal growh rends are generally declining in he sample period. I is worh o menion ha he volailiy of cos of capial and renal yield of hese ciies is similar. Table 1 Descripive saisics for variables included in VAR sysem Variables Saisics Beijing Shanghai Guangzhou Shenzhen i, r i, l i, c i, Max Min Mean Sd.dev Observaion Max Min Mean Sd.dev Observaion Max Min Mean Sd.dev Observaion Max Min Mean Sd.dev Observaion Noes:This able repors summary saisics for renal yield (), reurns (r), ren growh ( l) and cos of capial (c) of four ciies. The able liss he max, he min, he mean, he sd.dev and he observaion. The sample is quarerly observaions of four ciies from 1991:Q1 o 211:Q1, excep 6 Zhu(26) also considers he upper value of morgage rae in China is 8%. 11

12 ha Beijing's house price index is from 1993:Q2 o 211:Q1. Mehodology Since he expecaions variables in Eq. (5) and (12) are unobservable, we need o consruc empirical proxies for he expecaions o implemen he decomposiion of renal yields. We adop he VAR mehodology, proposed by Campbell (1991) and Campbell and Ammer (1993), and hen applied in housing markes by Campbell e al (29) and Hieber and Sydow (211), o creae proxies for relevan expecaions. We follow Campbell e al (29) o specify a firs-order VAR for he sake of parsimony 7 : Z A Z (14), 1 1 where ' Z l, r, c, is a 4-dimenional vecor of sae variables including ren growh ( l ), reurns ( r ), coss of capial ( c ), and renal yields ( ); A is he coefficien marix; 1 is he forecasing error. Noe ha all he variables in his VAR model are demeaned so ha we specify he VAR model wihou consan erms. In oher words, we focus only on he variaion of variables under quesion in he form of deviaions from heir equilibrium values. The consans in he log-linearized presen-value model are also ignored. Having obained he proxies for expecaions variables in hand, we could use he dynamic accouning ideniy defined in Eq. (5) o decompose he renal yield ino he discouned sum of expeced fuure ren growh and reurns, or we can use he dynamic user cos of housing model derived in Eq. (12) o decompose he renal yield ino hree componens: he expeced fuure rens, coss of capial, and risk premium of owing relaive o rening. Then, he relaive conribuion of differen componens o he movemen of he renal yield in China s four major ciies could hen be measured by he variance of ha componen, calculaed as he percenage share of he variance of he curren renal yield. Given he VAR model we jus specified, we can obain he fuure forecass of sae variables a any ime horizon as follows: h A Z, E Zh (15) 7 Alhough he BIC crierion would selec 2 lags for he cases of Shanghai and Shenzhen, we confirm ha adding more lags would no change our resuls qualiaively. No only will i be unable o improve he forecasing abiliy of our VAR model, bu also has lile impac on he empirical resuls of variance decomposiion. 12

13 where h is he lengh of forecasing horizon. Then, we have he Eq. (5) wrien as j1 j1 j1 j j1 j E ( j ) E ( j ) r A Z l A Z j1 j1 j1 j1 r l e e 1 1 r l r l e A I A Z e A I A Z, (16) where e i is a uni vecor ha selecs he corresponding variable of 4-dimenional vecor Z. For example, given ha ren growh is he firs elemen of he VAR sysem, he selecion vecor in he case of firs-order VAR is jus he forh column of a 4x4 ideniy marix, denoed e l. Similarly, e r, e c and reurns, coss of capial and renal yields, respecively. e denoe he selecion vecor of 4. Empirical Resuls VAR esimaes Table (2) repors he esimaion resuls of he forecasing equaions of he ren growh, reurn, cos of capial, and renal yield in our VAR model for all he four major ciies in China. Table (2) consiss of four panels wih each summarizing he resuls for a ciy of Beijing, Shanghai, Guangzhou, and Shenzhen. In addiion o he coefficien esimaes and heir associaed sandard errors, each panel also repors he p values of Wald ess ha none of he forecasing variables are significan ogeher wih adjused R, in order o gauge he forecasabiliy of endogenous variables in our VAR model. The Wald ess for he join significance of he forecasing coefficiens appear o indicae ha all he endogenous variables in our forecasing VAR are predicable. However, he adjused R saisics seem o sugges ha he exen o which variables are predicable would vary a lo from one variable o anoher. Table 2: VAR Esimaion Resuls Ciy Indep Dep l r c Ciy Indep Dep l r c BJ l -1 r (.17).141 (.129).115 (.143).193 (.199).29 (.13).13 (.16).262 (.136).1 (.143) SH l -1 r (.92) (.15) (.17) (.165).38 (.13).4 (.11).197 (.146).225 (.215) 13

14 c (.367) -.32 (.15).737 (.423).19 (.19).928 (.49). (.1) -.33 (.425) 1.4 (.21) c (.347) (.364) (.32) (.16) (.17) (.1) -.41 (.399) 1.14 (.18) Wald.... Wald Adj. R Adj. R GZ l -1 r 1 c (.145).32 (.98) -.28 (.243) -.18 (.12).31 (.111).328 (.98) -.23 (.215).31 (.17).21 (.14).19 (.1).969 (.25). (.1) -.5 (.144).69 (.124) -.16 (.294) 1.9 (.18) SZ l -1 r 1 c (.15) (.13) (.1) (.84) (.84) (.11) (.161) (.178) (.27) (.14) (.15) (.1) -.24 (.129) (.124) (.222) 1.8 (.18) Wald.... Wald Adj. R Adj. R Noe: The sample is quarerly observaions of four ciies from 1991:Q1 o 211:Q1, excep ha Beijing's house price index is from 1993:Q2 o 211:Q1. The Wald ess repor he associaed p values. In parenheses are heeroskedasiciy-auocorrelaion consisen sandard errors. On he one hand, we find ha only a small porion of he variabiliy can be accouned for by our forecasing VAR for boh he ren growh and reurn. While he ren growh appears o be mainly forecas by is own lag in Beijing and Shanghai, is predicabiliy is mainly due o oher forecasing variables han is own lag in Guangzhou and Shenzhen. Conrary o ren growh, he holding reurns show some degree of persisence in Guangzhou and Shenzhen markes bu no in Beijing and Shanghai. On he oher hand, our resuls show ha a subsanially large amoun of flucuaions in renal yield and cos of capial can be capured by he VAR model. In paricular, boh he renal yield and cos of capial seem o follow a highly persisen AR(1) process in eiher cases wih a coefficien of more han.9. Consisen wih he heoreical model, higher renal yield would no only forecas economically and saisically significan higher fuure holding reurns, bu also end o be associaed wih lower ren growh in he fuure. Acual and esimaed renal yield Before using he one-period VAR esimaes o conduc he variance decomposiion analysis, we would like o examine how well he presen-value model of renal yield ogeher wih he one-period VAR forecasing resuls can be fied ino our sample of four Chinese major ciies. Despie he solid jusificaion for he dynamic accouning 14

15 ideniy in Eq. (5), he esimaed renal yield (sum of he expeced fuure ren growh and reurns) can differ from he acual renal yield a leas for he following wo reasons. Firs, our log-linearized model of Eq. (5) is an approximaed accouning ideniy, so ha i has he chance o involve significan approximaion errors, and he errors can even pile up a longer horizons as we ierae he approximaed one-period ideniy forward o express he renal yield as a presen-value model of discouned sum of fuure ren growh and holding reurns. Second, i is also possible ha he one-period forecasing VAR model may no be adequae in capuring he long-horizon dynamics of ren growh and reurns. For example, our esimaes of renal yield may no equal o he acual renal yield if invesors do no form forecass of expecaion variables according o he one period VAR model specified in Eq. (14). 1 Beijing 1 Shanghai Guangzhou 1 Shenzhen Realized Renal Yield Esimaed Renal Yield Difference Figure 1: Acual and esimaed renal yield Given he esimaes of VAR coefficiens marix ( A ), we can compue he esimaed renal yield by adding up he wo erms a he righ hand side of Eq. (5). We hen compare he esimaed renal yield wih he acual renal yield in Figure (1). Our resul seems o sugges ha he esimaed renal yield based on one-period VAR can capure he movemens of acual renal yield prey well hroughou our sample period for all for major ciies, in he sense ha he wo erms a he righ hand side of Eq.(5) almos add up o he acual renal yield. For he sake of clariy, we also plo he difference beween acual and esimaed renal yield. I appears ha he difference is no only small in scale, bu also highly sable. In sum, he evidence indicaes ha errors in approximaion process and one-period VAR-based esimaes of expecaion variables seems no o be he main driver of movemens in renal yield for China s housing markes. Therefore, we can conclude ha he presen-value model of renal yield ogeher wih he one-period VAR esimaes can perform quie well empirically in racking he movemen of renal yield for all he four major ciies in China. Variance decomposiion of renal yields Table (3) repors he resuls of variance decomposiion of log renal yields based on 15

16 he dynamic Gordon growh model of Eq. (5). The variance of renal yields is decomposed ino he sum of wo variance componens relaed o expeced presen value of ren growh and reurns, ogeher wih he covariance beween hem. The firs row of each ciy panel repors he oal conribuion, while he second row shows he conribuion as a percenage of he variance of renal yields. In general, i is eviden from he able ha expeced reurns played he mos significan role in he movemen of renal yields in all he four major ciies. The ren growh, of course, also have conribued o he variaion in renal yields, bu no as imporan as expeced reurns. In oher words, our resuls abou he informaion conen of he variaion in renal yields hrough ime in China s four major ciies, are more similar o hose of he U.S. as repored by Campbell e al. (29) raher han he Euro area counries (e.g. Hieber and Sydow, 211). Table 3: Variance decomposiion of renal yield based on he dynamic Gordon growh model Ciy l r VAR l Ciy r VAR (Frac) (.197) (.499) (1.) (Frac) (.98) (1.379) (1.) STD STD BJ (Frac) (.444) (.76) (1.) (Frac) (.313) (1.175) (1.) SH Corr Marix: Corr Marix: l l r r VAR VAR (Frac) (.44) (.575) (1.) (Frac) (.189) (.572) (1.) STD STD GZ (Frac) (.21) (.758) (1.) (Frac) (.435) (.756) (1.) SZ Corr Marix: Corr Marix: l l r r Noe: This able repors he variance decomposiion of he renal yield ( ) ino he sum of wo variance componens relaed o expeced presen value of ren growh ( l ) and reurns ( r ) ogeher wih he covariance beween hem, based on he dynamic Gordon growh model of Eq. (5). A four-variable firs-order quarerly VAR is employed o consruc he empirical proxies for he relevan expecaions in our presen-value model. The rows of VAR ( STD ) repor he variance (sandard deviaions), while he rows of Frac show he conribuion as a percenage of he variance of he renal yield. 16

17 Alhough ren growh played only a moderae role in he variaion of renal yields, comparing o he expeced reurns ha accouned for he greaes par of housing marke movemen, he relaive imporance of ren growh and expeced reurns can vary among ciies. For example, in Beijing, while he variaion in expeced reurn is he dominan force wih explaining 5 percen of he ime varying movemen of renal yields, changes in expeced ren growh can sill accoun for abou 2 percen of he variaion in renal yields. However, in Shanghai, he expeced reurn explains almos all variaion in renal yields, wih lile remaining ha could be aribued o ren growh. Table (4) repors he resuls of variance decomposiion of log renal yields for he four major ciies over he period based on he dynamic user cos model of Eq. (12), which is derived by imposing housing user cos model as a resricion ino he dynamic Gordon growh model. In oher words, we furher decompose he black-box like discoun rae ino wo componens: he cos of capial and he risk premium of owning relaive o rening. Therefore, employing he same variance decomposiion approach, he variance of renal yields could be decomposed ino he sum of hree variance componens relaed o expeced presen value of ren growhs, coss of capial and he risk premia of owning relaive o rening, ogeher wih he covariance beween hem. We repor he resuls using he same layou as Table (1). In addiion, we also plo in Figure (2) he movemen acual renal yields over he period, ogeher wih is hree componens relaed o expeced ren growh, cos of capial, and risk premium of owning of rening, respecively. Table 4: Variance decomposiion of renal yield based on he dynamic user cos model Ciy l c l Ciy c VAR VAR (Frac) (.197) (.23) (.121) (1.) (Frac) (.98) (1.334) (.166) (1.) STD STD (Frac) (.444) (.451) (.347) (1.) (Frac) (.313) (1.155) (.48) (1.) BJ Corr Marix: SH Corr Marix: l l c c VAR VAR GZ (Frac) (.44) (.56) (.451) (1.) (Frac) (.189) (.74) (.636) (1.) STD SZ STD (Frac) (.21) (.748) (.672) (1.) (Frac) (.435) (.839) (.797) (1.) 17

18 Corr Marix: Corr Marix: l l c c Noe: This able repors he variance decomposiion of he renal yield ( ) ino he sum of wo variance componens relaed o expeced presen value of ren growh ( l ), capial cos ( c ), and risk premium of owning relaive o rening ( ), ogeher wih he covariance beween hem, based on he dynamic user cos model of Eq. (12). A four-variable firs-order quarerly VAR is employed o consruc he empirical proxies for he relevan expecaions in our presen-value model. The rows of VAR ( STD ) repor he variance (sandard deviaions), while he rows of Frac show he conribuion as a percenage of he variance of he renal yield. 1 Beijing 1.5 Shanghai Guangzhou 1 Shenzhen Renal Yield Capial Cos Ren Growh Risk Premium Figure 2: Decomposiion of renal yield based on dynamic user cos model We have hree main findings from he decomposiion of renal yields based on he dynamic user cos model. Firs, we can find ha he erm of cos of capial is he primary source of variabiliy in renal yields across all he four major local housing markes. Remember ha he cos of capial reflecs a combinaion of morgage raes and deposi raes, which are deermined mainly by he People's bank of China. Therefore, our resuls sugges ha moneary policy in China can exer grea influence over he housing marke movemen. Second, we find ha here seems o be some heerogeneiy in he relaive imporance of cos of capial o oher facors across four major ciies in China. Of he four major local housing markes, changes in expeced coss of capial played a much more imporan role in Shanghai, followed by Shenzhen, Guangzhou and Beijing. Changes in expeced coss of capial are a much more relevan driving force in Shanghai markes han oher wo facors hree. Measured eiher in variance or sandard deviaion, he variabiliy of coss of capial is several imes higher han he 18

19 volailiy of expeced ren growh. I can be observed even more clearly from Figure (3) ha he movemen of he cos of capial erm is almos idenical o ha of renal yields. On he oher hand, he relaive conribuion of expeced ren growh shows as almos equivalen imporance as he role of coss of capial in Beijing. Finally, we find ha he variaion of risk premia of owning relaive o rening is also an imporan source of variaion in renal yields. Owning o he dynamic housing user cos model, we are capable of measuring he influence of changing risk premia, alhough he risk premium of owning relaive o rening is no direcly observable. Specifically, aking a similar approach of Campbell and Shiller (1988) who rea he expeced fuure dividend growh as a residual, he erm of risk premia of owning relaive o rening can be obained as a residual using Eq. (12). Consisen wih o he earlier findings of Sinai and Souleles (25), our resuls show clearly ha he risk premium of owning relaive o rening in China s four major ciies is no ime-varying, bu also an imporan deerminan of housing marke variabiliy. There are pros and cons of our measure of risk premia of owning relaive o rening. On he one hand, conrary o Sinai and Souleles (25) who use an ad-hoc proxy of he risk premium, we derive a measure of risk premia of owning relaive o rening based on an economic model. On he oher hand, i is also worh of noing ha we end o oversae he variabiliy of risk premium if he VAR undersaes he predicabiliy of oher relevan variables or here exiss some errors in log-linear approximaion, since our approach reas he risk premium componen as a residual of he esimaion. Risk premium of owning relaive o rening In order o examine he dynamics profile of risk premia of owning relaive o rening, we plo in Figure (3) he changes of risk premia compued from Eq. (12) for all he four major ciies over he pas wo decades. We can find wo main resuls from he Figure. Firs, here seems o be some heerogeneiy across he four housing markes. While Shanghai, Guangzhou and Shenzhen markes show much larger up and downs in he flucuaions of risk premia of owning relaive o rening, he risk premium of owning relaive o rening in Beijing appears o be rending down over he las wo decades wih only moderae spikes, suggesing he housing price risk bear by residens in Beijing relaive he ren risk have declined consisenly. Second, all he four major housing markes in China exhibi key similariies in he movemen paerns of risk premia of owning relaive o rening ha sugges he changes of invesor s preference in housing markes are closely relaed o macro facors. Specifically, he risk premia of owning relaive o rening declined early 199s, followed by a period of bounce back in he lae 199s. Around 2, he risk premia of owning relaive o rening sared declining again in all he four major housing markes. From lae 28 o early 29, probably because of he increased risk aversion of housing marke invesors due o global financial crisis and/or he rising macroeconomic risks due o he surging of house prices in several pas years, he risk 19

20 premium of owning relaive o rening has ever reversed is declining rend. Bu soon i once again end o decline since 21, suggesing ha he ren risk faced by residens in Beijing relaive he housing price risk have been back o he rising rend..4 Beijing.4 Shanghai Guangzhou.6 Shenzhen Figure 3: Risk premium of owning relaive o rening 5. Conclusions There are mainly wo approaches in he lieraure concerning he variaion in renal yield in he housing marke. The firs one is from he perspecive of asse pricing. Usually, his sring of researches would employ a presen-value model o examine he informaion conen of he variaion hrough ime in renal yields, wihou aking ino accoun he characerisics of housing markes. The oher one is, on he oher hand, based on he saic user s cos model of real esae economics ha is derived from he no-arbirage condiion beween he rening and purchasing a house. However, his approach would suffer from no only he inabiliy of capuring he ime-varying aspec of renal yield, bu also he quaniaive examinaion of relaive imporance of differen forces in driving he variaion in renal yield. In his paper, we combine he sandard Campbell and Shiller (1988) presen-value model wih he classical user cos of housing model o decompose he renal yield ino hree componens: expeced fuure ren growh, cos of capial and risk premium of owning relaive o rening. We hen apply he presen-value model of renal yield o a quarerly daase of four major ciies in China o explore he quesion of wha forces have driven he movemen of China s housing marke. Our resuls are hree-fold: Firs, we find ha he presen-value model of renal yield performs quie well in our sample period for he four major ciies. The approximaion errors seem no o be he main driver in he variaion of renal yields. Second, using he variance decomposiion approach, we find ha he expeced reurn in he fuure can explain a large porion of variaion in he renal yield, while he role of expeced ren growh is limied. Third, when furher imposing he housing user cos model as a resricion condiion ino he presen-value 2

21 model, our resuls show ha cos of capial is playing a vial role in all he four major ciies, followed by he risk of owning relaive o rening a house ha is also accouning for a large par of housing marke movemen in China. Forh, similar o he previous lieraure using ad-hoc measures, our model-based measure of risk premium of rening relaive o owning a house in four major ciies of China is also ime-varying. I is also worh noing ha he risk of rening relaive o owning a house seems o be rising rapidly in China over he recen years. Our resuls herefore have wo imporan implicaions for he Chinese housing marke. Firs, he moneary policy or credi policy can exer is leverage over he housing marke, since he capial cos is he mos imporan facor in deermining he ime-varying changes in he housing marke. Therefore, he moneary policy insead of adminisraive measures may be a more appropriae ool in conaining he heaing housing marke in China. Second, alhough he ren growh can only have limied impac on he housing marke direcly, i can influence he variaion in renal yield indirecly hrough he changes in risk premia of rening relaive o owning a house. Therefore, he developmen and improvemen of he rening marke, such as he effecs o esablish a public housing sysem o provide decen, safe and sable renal housing for eligible families, could be a sabilizing facor for he Chinese housing marke. Reference: Binsbergen J. H. and R. S. J. Koijen, 21, Predicive Regressions: A Presen-Value Approach, Journal of Finance, 65(4), Campbell J. Y. and R. J. Shiller, 1988, The Dividend-Price Raio and Expecaions of Fuure Dividends and Discoun Facors, Review of Financial Sudies, 1(3), Campbell J. Y. and J. Ammer, 1993, Wha Moves he Sock and Bond Markes? A Variance Decomposiion for Long-erm Asse Reurns, Journal of Finance, 48(1), Campbell S. D., M. A. Davis, J. Gallin, and R. F. Marin, 29, Wha Moves Housing Markes: A Variance Decomposiion of he Renal yield, Journal of Urban Economics, 66(2), Cochrane J., 28, The Dog ha Did No Bark: A Defense of Reurn Predicabiliy, Review of Financial Sudies, 21(4), Cochrane J., 211, Presidenial Address: Discoun Raes, Journal of Finance, 66(4), Gordon M., 1962, The Invesmen, Financing, and Valuaion of he Corporaion, Irwin, Homewood, IL. Gourinchas PO and H. Rey, 27, Inernaional Financial Adjusmen, Journal of Poliical Economy, 115(4), Hendersho P. and J. Slemrod, 1983, Taxes and he User Cos of Capial for Owner-Occupied Housing, Journal of he American Real Esae and Urban Economics Associaion, 1(4),

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