Housing Investment in Urban China: Evidene from Chinese Household Survey Yujin Cao, Jidong Chen, Qinghua Zhang Deember 15, 2016 Abstrat What explains the rapidly inreasing housing investment demand in China? This paper onjetures that higher expeted housing apital gains drive higher investment demand. Due to the finanial fritions prevalent in China, suh demand takes plae not only through households owning multiple houses, but also through their owning a larger primary living residene if they are onstrained from buying multiple houses. We develop a simple framework to study how expeted apital gains impat households' housing investment deisions when subjet to finanial onstraints. Our empirial findings, based on 2010 and 2011 household survey data, are onsistent with our theoretial preditions. Speifially, we find that (1) households are more likely to own multiple houses when expeting higher apital gains; (2) the primary housing demand of those households who are onstrained from owning multiple houses inreases with the expeted apital gains; while (3) the primary residene demand of those who are not onstrained does not inrease with the expeted apital gains. Furthermore, we find that wealthier households are more sensitive to hanges in expeted apital gains. Speifially, the marginal effet of apital gains on housing investment is higher for wealthier households. This links the booming housing market to widening inome inequality whih is a typial growth pain in a developing ountry like China. JEL Code: O12, O18, R1, R21 Key Words: Housing investment, Finanial Frition, Expeted Capital Gains, Chinese Housing Market We would like to thank the editor and two reviewers for very useful suggestions and omments. We would also like to thank Hongbin Cai, Jimmy Chan, Edward Coulsen, Shihe Fu, Vernon Henderson, Yi Lu, Mingzhe Tang, Matthew Turner, Jianfeng Wu, Siqi Zheng, Guozhong Zhu, and seminar partiipants at Business Shool of Beijing Normal University, Fudan Shool of Eonomis and Wenlan Shool at Zhongnan University of Eonomis and Law for helpful omments and suggestions. Zhang aknowledges support from China s Natural Siene Foundation Grant #71273017. Any remaining errors are our own. The views expressed in the paper are those of the authors and do not neessarily represent those of the authors' affiliated institutions. Institute of Eonomi Researh, National Development and Reform Commission. Email: aoyujin777@126.om. Business Shool, Beijing Normal University. Email: gdonghen@gmail.om Guanghua Shool of Management and IEPR, Peking University. Correspondene: zhangq@gsm.pku.edu.n 1
1 Introdution The privatization reform of the housing setor in 1998 triggered the rapid development of real estate markets in urban China. Sine the early 2000s, the unit prie of residential housing aross 35 major Chinese ities has been growing at an average annual rate of 9.29% 1. In partiular, for those ities whose prie levels were in the top 90 perentile in 2002, the average housing prie inreased from 5,168 RMB per square meter in 2002 to 25,564 RMB per square meter in 2013, an average inrease of 15.6% per year. Furthermore, the housing prie appreiation has aelerated in reent years, reahing an annual rate of 18.7% between 2006 and 2013 for those top 90 perentile ities. This fast growth in housing pries ould be driven by rising demand. On the one hand, the privatization reform released huge onsumption demand for housing servies whih were previously filled by old and unomfortable subsidized housing provided by work units. The massive urbanization proess also brings out tremendous onsumption demand as well. On the other hand, households in China often buy extra-large primary living houses and/or buy a seond or a third house for investment purposes. Suh investment demand auses wide onern beause it may lead to overly hot housing markets and inrease the risk of housing bubbles. This is espeially relevant in a fast-growing eonomy like China s where real estate investment aounts for approximately 22% of the total fixed asset investment of the whole eonomy. Therefore, a better understanding of both the driving fore behind housing investment and its available hannels bears important poliy impliations. This paper studies housing investment in urban China. We show that higher expeted apital gains drive higher investment demand. Due to the finanial fritions prevalent in China, suh demand takes plae not only through households owning multiple houses, but also through their owning a larger primary living residene if they are 1 The alulation is based on the quality-ontrolled housing prie indies released by Tsinghua University s Hang Lung Center for Real Estate. 2
onstrained from buying multiple houses. There have been few works in the literature that study both of these hannels of housing investment and provide empirial evidene. There has been substantial researh on China s urban housing markets (e.g., Wu, et al., 2012 and Wang and Zhang, 2014). However, there are few studies on housing investment demand based on miro-level data (espeially household survey data) in the literature exept for Gan (2014) and Coulson and Tang (2013). Both of the above-mentioned papers fous on just one hannel of investment, i.e., owning multiple houses. Moreover, they do not study expeted apital gains a key driving fore behind housing investment. This paper fills in the gap by studying both the driving fore behind housing investment and its available hannels based on 2010 and 2011 household survey data of China. Speifially, we address three main questions. The first question is how muh the expeted apital gains influene housing tenure hoies. The seond question is, when there are higher expeted apital gains with finanial frition, whether households inrease housing investment through the hannel of owning multiple housing units or through the hannel of owning a larger primary living residene. The third question is whih group of owners has a greater apital-gain effet on housing investment. Sine sensitivity to expeted apital gains is a prominent feature of housing investment, the answers to the above questions will help provide evidene of both the magnitude and omposition of housing investment. We first develop a simple model to illustrate households housing tenure hoies and investment portfolio deisions when there is a finanial onstraint. Our model generates three main testable preditions: 1) A household's likelihood of owning multiple housing units inreases in response to higher apital gains. 2) For those households who only own their primary residene, their demand for primary housing inreases with the expeted apital gains. The intuition for this is that those 3
households are onstrained from buying a seond house, so their extra investment demand, indued by higher expeted apital gains, would be diverted into greater investment in primary housing. 3) Among those who already own more than one housing unit, the demand for primary residene does not inrease with the expeted apital gains, while the additional demand for other houses does inrease with the expeted apital gains. This is beause those households are less onstrained from investing in multiple housing units and are already satisfied with their primary residene. Therefore, as the expeted apital gain inreases, they will invest more in extra housing units to fulfill their investment purpose. In addition, the theoretial model also demonstrates that the expeted-apital-gain effet is stronger for wealthier households. Speifially, an inrease in expeted apital gain makes a wealthier household more likely to own multiple housing units, or to own a larger residene unit if the tenure status remains unhanged. In other words, for the households with only one housing unit whose tenure status is unaffeted by the inreased expeted apital gain, the inreased demand for primary residene is higher among riher households. To test the main impliations, we use both the 2010 household survey data provided by the Institute of Soial Siene Survey at Peking University and the 2011 China Household Finane Survey provided by the Survey and Researh Center for China Household Finane at Southwestern University of Finane and Eonomis. For our researh purposes, we use only the sub-sample of urban households in 19 major ities nationwide for whih we have histori housing prie information. We measure households' expetation of future housing apital gains by using the average prie growth rate in the three years just before they purhase a primary residene. 2 Our data provides the purhase-year information for households' primary residene. Case (2000) and Piazzesi and Shneider (2009) study households' subjetive views about housing and the eonomi environment using the U.S. survey 2 For renters, we use the average growth rate in the three years just before the survey year to measure their expetation. 4
data. Case finds that households tend to hold a more optimisti view regarding housing pries around the peaks of the past housing booms in the U.S. Piazzesi and Shneider show that during the late phase of the last housing boom in the U.S. (after 2004), more households beame optimisti about future housing prie appreiation after observing that housing pries had gone up for several onseutive years. Consistent with their findings, we assume that households form adaptive expetations of future returns based on the housing appreiation rate prior to the purhase year of the primary residene. As robustness heks, we assign different weights to different years prior to the purhasing year in alulating the expeted apital gains in our empirial analysis. In their study of housing investment, Dusanski and Ko (2007) use the housing prie in the survey year to measure the expeted return on housing investment, assuming the expeted future return has been apitalized into the urrent housing prie. When there are transation osts 3 in housing markets (suh osts are high in China), households annot freely adjust their housing investments, espeially their primary residene. Beause of this, expetations formed in the purhase year of the primary residene are likely to be more influential on the demand for a primary residene than the prie in the survey year. In addition, beause different households may purhase primary residenes indifferent years, there are variations in the expeted returns alulated based on purhase year even for households in the same ity in the same survey year. This enables us to ontrol for a ity fixed effet, whih addresses many ity-speifi fators suh as the urrent ity-level housing prie and rent, and the osts of owning and maintaining houses in the ity. We first study the effet of expeted apital gains on households' tenure hoies, whih is measured in three disrete ategories: renters, owners who own just one housing unit and owners who own more than one housing unit. We then investigate 3 These osts inlude not only transation fees and moving osts, but also institutional barriers aiming to prevent speulative transations. 5
their housing demand separately, aiming to understand the hannels of housing investment. We alulate the housing demand by dividing the housing value by eah ity s hedoni housing prie level as provided by Tsinghua University's Hang Lung Center for Real Estate. The demand measure thus obtained ontrols for the housing quality fator and is more aurate. The major findings are: 1) Households are more likely to own multiple houses if the expeted apital gains from housing investment are higher; an inrease of one standard deviation in the expeted apital gains will inrease the likelihood of owning multiple housing units by 3.54%. Moreover, the value of housing assets other than the primary residene inreases signifiantly with apital gains.2) For homeowners who own just one housing unit, the expeted apital gains have a positive effet on their demand for primary housing; an inrease of one standard deviation in the expeted apital gains will ause the demand for primary housing to inrease by 11.51%. 3) The demand for primary housing among home owners who own multiple housing units does not inrease with the expeted apital gains. In sum, in response to an inrease in expeted prie, households inrease their housing investments not only through owning multiple housing units but also through owning a larger primary residene if they are onstrained from owning multiple housing units. The results are onsistent with our theoretial preditions. Furthermore, we find that the apital-gain effet on housing investment beomes muh greater for wealthier households who have stronger investment needs and are less likely to be finanially onstrained. Speifially, among households whose predited net wealth is above the 50 th perentile of all households, the likelihood of owning multiple housing units inreases by 7.97% in response to an inrease of one standard deviation in expeted apital gains. Suh an inrement is higher than the average effet of the whole sample whih, as mentioned above, was 3.54%. Similarly, for households who own just one housing unit, when there is a one-standard-deviation inrease in expeted apital gains, their subdued investment need will be diverted into 6
greater demand for a primary residene whih will in turn inrease by 15.9%. Suh an inrement is also higher than the effet of the whole sample (i.e., 11.51%). Related Literature This paper is related to the literature on optimal portfolio hoies in the presene of housing (e.g., Flavin and Yamashita, 2002, Fisher and Stamos, 2013, and Corradin et al., 2014).This lass of literature studies how a representative household hooses between housing investment and investment in other risky finanial assets assuming exogenous house pries. Following Kiyotaki et al. (2011), Sommer et al. (2013), Iaoviello and Pavan (2013), our theoretial framework imposes a borrowing onstraint on households. We also emphasize that housing investment takes plae not only through households owning multiple houses, but also through their owning a larger primary living residene if they are onstrained from buying multiple houses. That means in our theoretial model, the household an hoose to buy either one housing unit or multiple ones. In addition, we also inorporate another important feature of China's real estate market: the minimum size onstraint of housing units. Although these features are not unique to China, together they play a very important role in shaping the pattern of housing market outomes given China s peuliar institutional bakground. Our model s inlusion of these three features enrihes the appliability of the lassial models and helps build an analytial framework that is more suitable for the study of housing markets in China. The latter two features of the above three make the household s optimization problem deviate from the standard onvex optimization in housing investment. Tehnially, now it is the optimization of a non-onneted (or non-onvex) spae. The addition of the finanial frition onstraint further ompliates suh an optimization. Lukily, even with suh tehnial hallenges, we are able to analytially demonstrate the main results onerning the expeted-apital-gain effet. 7
Few works in the urrent literature study housing markets with both finanial fritions and the hoie of owning one or multiple units. Dusanski and Ko (2007) investigate the apital-gain effet on housing demand in the U.S. They show that inreases in the expeted apital gains positively influene the owner-oupied housing investment. However, neither their model nor their empirial analysis studies the hoie of owning multiple houses. Coulsen and Tang (2013) study how various household harateristis influene housing investment through owning multiple housing units. Gan (2015) alulates the housing vaany rate for different ities using information on owners of multiple housing units. Our paper omplements their work by showing that under finanial onstraints, the investment need may be met by demanding a larger primary residene instead of owning multiple houses. As suh, it may lead to misalloation of resoures in real estate development as developers may build more large houses than is soially effiient. This paper also omplements the lassi literature on household tenure hoies and housing demand by studying an important driving fator of housing investment demand, that is, individual households' expetations of future apital gains. For example, Henderson and Ioannides (1983) develop a model of housing tenure hoie and in several subsequent papers (1986, 1987) they estimate housing tenure hoie and housing demand as joint deisions. Ioannides and Rosenthal (1994) estimate housing tenure status using an ordered probit model and examine both onsumption demand and investment demand. However, none of the above works investigate the effet of expeted housing apital gains on household demand. Finally, our paper has broad impliations for the relationship between housing markets and wealth inequality. Favilukis (2016) and Zhang (2016) offer a linkage between housing prie formation and inome inequality. Our empirial analysis provides some miro-level evidene. Our results suggest that wealthier households have stronger investment inentives for housing, whih implies that investment motivation among wealthy households will play a key role in the formation of future 8
housing pries. This links the booming housing market to a widening wealth and inome inequality whih is a typial growth pain in a developing ountry like China. The rest of the paper is organized as follows. Setion 2 presents the model and the analytial results. Setion 3 desribes the data. Setion 4 ontains empirial analysis. Setion 5 onludes. 2 Theoretial Framework In this setion, we build a theoretial model to haraterize a household s housing demand and tenure hoies. Our model inorporates fritions suh as minimum house size and down-payment requirements in the housing market. Under some appropriate assumptions, we haraterize the optimal hoie and the omparative statis, based on whih we derive three testable preditions. 2.1 Model Setup Following Henderson and Ioannides(1983), we assume that a representative household (heneforth she or her) lives for two periods. The household s first period utility depends on the onsumptions of both a numeraire non-housing good x and the primary residene housing servies h. The seond period utility V ( i) is a funtion of the household's net wealth, whih depends on her investment deision. Her total utility is thus u(x, h ) + V ( i ). 4 The household has initial wealth w > 0 in the first period and inome y > 0 in the seond period. For simpliity, we assume that the first-period utility is separable in onsumption and housing onsumption, namely, u(x, h ) = φ ( x) + φ ( h ). 1 2 We assume that φ ( i) : (0, + ) R is a ontinuously differentiable, stritly inreasing i 4 In general, the utility ould be written as u(x, h ) + βv ( i ), where β (0,1] is the disount fator. The introdution of β does not qualitatively hange the main results of the omparative statis. 9
and stritly onave funtion with ' lim φi ( x) + x 0 ' = + and lim φ ( x) = 0, for i=1,2. V ( i ) is x + i a ontinuously differentiable, stritly inreasing and weakly onave funtion. Throughout the benhmark model, we fous on a quasi-linear environment, i.e., V ( x) = x. 5 We use h I to denote the total amount of housing investment. Throughout the model, we assume that the household an hoose to rent a house without owning one, or to own one or more housing units. 6 (I) To rent a house, a renter hooses numeraire non-housing onsumption x, housing onsumption h and savings q 0 to maximize her two-period utility. In the seond period, a renter's total wealth is (1 + r) q0 + y, where r is the interest rate. Formally, we have u h + E V + r q 0 + y x 0, h 0, q0 max (x, ) [ ((1 ) )] s. t. x + sh + q w 0 (II) To buy house(s), a household faes a first-period budget onstraint (Equation (1)) and a liquidity onstraint (Equation (2)): p h + x w + s( h h ) q,(1) 0 I I 0 (1 δ ) p h + q 0. (2) 0 I 0 The left-hand side of the budget onstraint inludes the expenditure for total housing investment p0h I, and numeraire non-housing onsumption x. The right-hand side of 5 For a more generalized funtional form of V(.), we present simulation results in the Appendix demonstrating that the main results still hold in a reasonable parameter spae. 6 Our model an be extended to apture another option for households: renting a housing unit for residene while owning housing units in other plaes. Speifially, in the renter's hoie we an allow her to also make an investment in owning housing units. However, adding this hoie will ompliate the analysis without adding further insight into the main preditions of the model. 10
the budget onstraint inludes the initial wealth w, the benefit of renting out the houses other than the primary residene s( h h ),and the money she borrows from the bank q0. I The liquidity onstraint reflets the fat that the initial payment p0hi ( q0) for the total housing investment must make up at leastδ proportion of the total housing value p0h I. 7 Throughout the paper, we assume that p0 down-payment ratio is not negligible. δ > s so that the requirement of the Beause real estate developers must build housing units subjet to a minimum-size onstraint, a homeowner's housing asset must satisfy the feasibility onstraint and hi h h if she owns additional houses (i.e., hi h > 0 ). h > 0 h h, is the minimum housing size available to buy. In the seond period, she an earn p 1 h I by selling the owned houses. p 1 as a random variable reflets the future prie of the houses. She also needs to pay bak the debt ( q0 ) to the bank with interest rate r. Therefore, her seond period total wealth is p h + (1 + r) q + y. 1 I 0 The household hooses non-housing good x, houses for primary residene housing investment h, total h, and bank loans I q to maximize her expeted utility. Hene 0 a house owner's optimization problem beomes: u h + E V p h 1 I + + r q 0 + y x 0,h, hi, q0 max (x, ) [ ( (1 ) )] s. t. p h + x w + s( h h ) q, 0 I I 0 (1 δ ) p h + q 0, 0 I 0 h [ h, + ), ( h h ) {0} [ h, + ). I 7 In China, buying a seond house involves a higher down-payment ratio. We ould inorporate this assumption in the model. However, this would make the optimization problem more ompliated. 11
To make an optimal deision (on whether to be a renter, an owner of one house or an owner of more than one), a household ompares the above two optimization problems and hooses the one with the highest utility. 8 We use { h, h, x, q } to denote the household's optimal hoie. I 0 There are three possible types of tenure status in equilibrium. The household an be a renter that does not own any houses, i.e., h > 0, h = 0. She an also own a single house both for primary residene and investment, without making any other additional housing investments, i.e., h = h h. Furthermore, she an also own a house for her I primary residene as well as other houses ( h h ) as additional investments, i.e., I I h h and h h h. I 2.2 Charaterizing the Tenure Choie and Housing Demand In Proposition 1, we first haraterize how tenure hoie (i.e., whether to be a renter, to own just one housing unit, or to own more) is affeted by prie expetation. In the orollaries following the proposition, we further quantify the effet of expeted apital gain and investigate how suh an effet is shaped by finanial fritions. Then in Propositions 2 and 3, we analyze the effet of prie expetation on primary housing demand and investment demand for different types of housing demands. Proposition 1 (Tenure Choie) A household s status on the tenure hoie ladder is inreasing in her expeted apital gain E( p 1). Speifially, there exist two utoff points k k (1 + r)( p s) (whih depend on minimum size h, household 1 0 0 wealth w and the down payment ratio δ ), suh that with a relatively lower expeted apital gain, i.e., with E ( p ) < k, the household is a renter that owns no housing units; 1 0 8 When the two optimization problems indue the same expeted utility, we assume that she hooses the one with the highest housing investment. 12
with a moderate expeted apital gain, i.e., with k E ( p ) < k, the household owns 0 1 1 only one housing unit as her primary residene, i.e., h = h h ; and with a relatively high expeted apital gain, i.e., with E ( p ) k, the household owns more than one unit, i.e., h h h. (See the Appendix for the proof.) I 1 1 I Proposition 1 demonstrates that a household s status on the tenure ladder is inreasing in her expetation of future housing prie. Expansion of housing demand takes various forms. Not only may a household hoose a larger primary living residene, but she also may hoose to own multiple houses. As her expeted apital gain inreases, she is more likely to be an owner than a renter, and is more likely to own more than one housing unit. The ost of buying a housing unit is p 0, whereas the benefit E( p ) 1 1 + r + s is derived from the value of selling the unit in the future and the rental gain in the urrent period. When the expetation of future prie is suffiiently low, e.g., E( p1 ) < (1 + r)( p0 s), it is therefore not profitable to buy any housing unit. Thus (1 + r)( p0 s) is a lower bound of the ut-point k that separates renters and owners. The following orollary identifies a ondition under whih k reahes its 0 lower bound and equals (1 + r)( p0 s). 0 Corollary 1 (Quantifying Tenure-Choie Cut-points )When the minimum size is not suffiiently large, i.e., q h min{ h, h }, where { h, q } is a solution of the 0 0 δ p0 s renter s problem, the lower ut-point reahes its minimum value, i.e., k = (1 + r)( p s) ; in addition, we also have k > k if 0 0 1 0 13
( δ p s) h + G( h; δ p s) < G(0; δ p s), where 0 0 0 G( x; A) = Maxφ ( w ( δ p s) x δ p h ) + φ ( h ) + Ah. 9 h h 1 0 0 2 (See the Appendix for the proof.) The above orollary shows that the ut-point k that differentiates renters from owners 0 an reah its lower bound and equal (1 + r)( p0 s), provided that the minimum size is not suffiiently large. In this ase, the equation stating that E( p1 ) = (1 + r)( p0 s) serves as a no-arbitrage ondition under whih the household is indifferent between renting a housing unit and owning one. Furthermore, the orollary also quantifies a ondition under whih the proportion of owners having exatly one housing unit is not negligible, that is, the two ut-points do not trivially oinide with eah other, i.e., k > k. The following orollary shows the role of finanial frition in shaping the 1 0 tenure hoie. Corollary 2 (Tenure-Choie, Finanial Frition and Wealth) (1) The borrowing onstraint pulls the household s status downward along the tenure hoie ladder. Namely k and 1 k are weakly inreasing in the down-payment ratioδ. 0 (2) The family wealth pulls the household s status upward along the tenure hoie ladder. Namely k and 1 k are stritly dereasing in the initial wealth w. 0 (See the Appendix for the proof.) As the down-payment ratio beomes higher, the household faes a tighter borrowing onstraint, so she is more likely to be pulled down along the tenure status ladder. In other words, with an inrease in finanial fritions, the proportion of households with multiple housing units shrinks; meanwhile the proportion of renters expands. The fat 9 For example, whenφ 1 ( x) = φ 2 ( x) = ln x, w < 2 and δ p0 ( δ p s) h + G( h; δ p s) < G(0; δ p s) is satisfied. 0 0 0 14 is suffiiently lose to s, the ondition
that k and 1 k are inreasing in the down-payment ratio δ also suggests that the 0 expeted apital gain and the finanial frition substitute for eah other in determining the housing tenure hoie. A household with a relatively higher expeted apital gain might not make additional housing investments due to the relatively higher finanial fritions. Instead, she may hoose to improve her living ondition by replaing the original residene with a larger one. The seond part of the orollary indiates that the initial wealth of the household and the finanial fritions have opposite impats on the tenure hoie. As household wealth inreases, the proportion of those holding multiple housing units inreases. This is beause an inrease in wealth mitigates the distortion indued by finanial frition so that the repressed investment demand gets partially released. Given the same inrement of expeted apital gain as the two ut-points move downward, the household is more likely to move upward along the tenure hoie ladder. Speifially, the marginal effet of the expeted apital gain on tenure hoie is inreasing in the wealth. In addition to finanial frition and wealth, the minimum size requirement ould also distort a household s inentive for investment. An inrease in the minimum size requirement may fore the household to divert the additional investment demand into buying a larger primary residene 10. We haraterize how the expeted apital gain affets the housing demand of suh a household in the following proposition. Proposition2 (Expeted-Capital-Gain Effet for Home Owners without Additional Investments) The demand of the house owners who don t have additional investments (i.e., h = h h ) is weakly inreasing in the expeted prie E( p 1) and the wealth I w. Furthermore, the expeted-apital-gain effet is higher for wealthier households, h i.e., I is weakly inreasing in w, provided thatφ 1 ''( i ) and 1 E( p ) φ ''( i ) are stritly 1 inreasing. (See the Appendix for the proof.) 10 In Proposition 4 of the Appendix, we formally haraterize how the tenure hoie is affeted by the minimum size requirement. 15
If the household has extra investment demand indued by higher expeted apital gains, yet at the same time is prevented from buying a seond house by requirements for minimum house size and down-payment, she will divert the additional investment demand into buying a larger primary residene. Proposition 2 shows that suh a household s demand is jointly affeted by her expetation of future prie and her initial wealth. An inrease of either fator an potentially drive up the residene demand, as long as the inrement of the fator is not suffiiently large. Aording to Proposition 1 (and its orollaries), a suffiiently large inrease of either expeted prie or wealth will make the household invest in another housing unit instead of remaining as own1. Furthermore, a wealthier household s response to an inrease in expeted apital gain is more sensitive. Speifially, the marginal effet of the expeted apital gain is higher for wealthier households. It suggests that the expeted apital gains and the wealth omplement eah other in shaping the housing demand. Although we do not diretly model the transition from owner to owner (i.e., selling the urrent housing unit and buying a large one to live in) in our theory, the omparative statis of the model helps us to understand suh a transition. Suppose that originally the exogenous parameters of the model are suh that the household owns only one housing unit. Aording to Propositions 1 and 2, if there is a positive shok (i.e., an inrement) to family wealth (e.g., owning a fang-gai housing unit originally an be thought of as a subsidy leading to an inrease in wealth), as long as suh an inrement is not large enough for the household to have suffiient finanial ability to afford a seond housing unit, she would hoose to have a larger demand for primary residene housing. Substantively this an be interpreted as the ation of upgrading, that is, selling the original fang-gai housing unit and buying a larger unit for residene. Empirially, we onsider the impat of fang-gai housing on housing investment in Setion 4.5.2. In the following, we haraterize the expeted-apital-gain effet for households with multiple housing units. Proposition 3 (Expeted-Capital-Gain Effet for Households with Multiple Units) (1) The total investment demand h of the households having multiple housing I 16
investments (i.e., h h h ) is weakly inreasing in the expeted prie E( p 1). I (2) However, the residene demand h of suh households is weakly dereasing in the expeted prie E( p 1). (See the Appendix for the proof.) When the onstraints of minimum house size and down-payment requirement do not prevent a household from buying a seond house, the household s investment demand inreases with the expeted apital gains, as suggested by the above proposition. With an inrease in the expeted apital gain, she is not going to improve the primary residene beause she is already satisfied with it. Instead, suh a less-finanially onstrained household will invest more in extra housing units to fulfill her investment purpose. 3 Data We use the 2010 household survey data provided by the Institute of Soial Siene Survey at Peking University and the 2011 household finane survey data supplied by the Survey and Researh Center for China Household Finane at Southwestern University of Finane and Eonomis. The 2010 data overs 14,798 households and the 2011 data overs 8,438 households. All households are randomly seleted from aross the nation, inluding both rural ounties and urban distrits. The 2010 survey data overs 25 provines in mainland China, exluding Xinjiang, Tibet, Qinghai, Inner Mongolia, Ningxia and Hainan. The 25 provines represent 94.5% of the total population in China, so the 2010 survey an be deemed to be a representative sample of mainland China. With similar sampling methods, the 2011 survey randomly and uniformly selets 80 muniipalities from 2,585 muniipalities nationwide. The muniipalities in the sample over 25 provines in mainland China, exluding Xinjiang, Tibet, Fujian, Inner Mongolia, Ningxia and Hainan. This survey is also a representative sample of mainland China. We ombined the two independent data sets by pooling all of their observations together in our regression analysis. Regarding the housing information that is key to our analysis, the 2011 data inludes a 17
variable indiating whether a household owns a housing unit or not (i.e., if she is a house owner or renter), and another variable representing the total number of housing units owned. The 2010 data inludes a variable indiating the status of eah household's primary residene unit. For example, the unit an be rented, owned by the household, or provided (by the government, employer, parents, or other relatives or friends) for free. We exlude those housing units provided for free by employers or relatives from our data set beause these are not traded in the market. In addition, the 2010 survey asks the households how many extra housing units they own (if any). Notie that both data sets provide information on the purhasing year of eah household's primary residene if the household is a homeowner. For our researh purposes, we use a sub-sample that inludes only urban households in 19 major ities nationwide for whih we have histori housing prie information. Speifially, ity-level housing prie data is provided by Tsinghua University's Hang Lung Center for Real Estate, whih reports the hedoni pries of residential housing for 35 major Chinese ities from 1998 through 2013. 11 The ity overage is the same as that of the housing prie index published by China's National Statisti Bureau. One advantage of knowing this prie is that housing quality is ontrolled for. During this time period, the mean hedoni prie is 5,036 RMB. The average annual hedoni prie growth rate is 7.76%. The mean of the hedoni prie in survey years 2010 and 2011 is 7,783RMB and 8,843RMB respetively. Other ity-level data suh as the GDP per apita and population growth rate (both for the entral ity, alled Shixiaqu) are from the Urban Statistial Yearbook published by China's National Statisti Bureau. We merge the ity-level data with the household survey data using eah household s primary residene ity and the year she purhased her primary residene. By doing so, we obtain the housing prie and growth rate as well as other variables of ity aggregate eonomy for the years around the primary residene purhase year for eah homeowner. 11 Note that 1998 is the year when China launhed the privatization reform of housing markets. 18
There are a small number of households that rent one house while owning another house somewhere else. In our analysis, we exlude this small group beause it is speial and most of those households are in mega ities like Shanghai, Beijing, Hangzhou, and Shenzhen. 12 The remaining sample size is 2,851.In Table 1-b, for our working sample, we learly speify the distribution of observations by ity from eah of the two data sets. 13 The four statuses in our merged data are mutually exlusive. Note that rent_own has been exluded from our sample for analysis in Table 1-. The table shows the sample distribution by tenure status. For the 2,851households sampled, 60% own only one house, 14.5% own more than one house and 25.5% are renters. Furthermore, the data ontains detailed housing information for homeowners. We know the floor area, purhase value and market value of eah homeowner's primary residene, as well as the total number, total area and total market value of all the other housing units or apartments owned by the household if there are any. In partiular, the survey data reports the purhase year of eah homeowner s primary residene. The data inludes omprehensive information on eah household s harateristis, inluding the survey year, gender, age, eduation level, Hukou status (urban Hukou vs. rural Hukou) 14 and marital status of the household head, household size, whether an elderly family member (aged over 60) is part of the household or not, whether the household inludes a young hild (aged below 6) or not, various ategories of household inome, assets and debts, and the geo-information about the household s urrent residene (whih we refer to as the primary residene) suh as the distane to the nearest bus stop and the time to the nearest shopping enter. 12 We will have more disussions and a robustness hek in Setion 4.5.3 to deal with suh type of households. 13 We did a robustness hek by taking into aount the differenes between the two surveys and ontrolling the survey year effet in our regressions. Most of the main results are similar. 14 In China, Hukou refers to the household registration system. If one is registered in the urban areas, she or heis said to have an urban Hukou; otherwise, she or he has a rural Hukou. 19
Table 1-a explains the meaning of the explanatory variables used in the regression equations. Table 2-a presents the summary of statistis for non-homeowners. Table 2-b presents the summary of statistis for homeowners. Compared to non-homeowners, homeowners have higher inome and wealth, and are more likely to be married. Their families are larger, and their household heads are older. Homeowners are less eduated than renters. 15 In addition, the perentage of households working in the government or in government-related institutions is higher for homeowners than for renters. Tables 2- and Table 2-d report the summary statistis for homeowners with just one house and for those with multiple houses, respetively. 4 Empirial Analysis In this setion, we study the relationship between housing demand and expeted apital gains. We first examine households' (disrete) tenure hoies. We then investigate the ontinuous hoie of housing demand by fousing on homeowners. Speifially, we break the owners into two tenure groups: one group onsists of those who own only one housing unit (i.e., own1) and the other group onsists of those who own more than one housing unit (i.e., own2). We investigate their housing demand separately, aiming to understand different hannels of housing investment. 4.1 Housing tenure hoie 4.1.1 Speifiation In this part, we examine how a household s tenure hoie is related to expeted housing apital gains as well as to the household s harateristis. We first run a probit regression on the hoie of whether to own a house or not. We then run an ordered probit regression inorporating the hoie of owning multiple houses. 15 In our sample, renters are relatively younger than homeowners. Therefore, they are more likely to enjoy the inreased opportunity for ollege eduation after the mid-1990s reform. Note that after the mid-1990s, China substantially inreased the ollege admission quota so that more high-shool graduates ould enter ollege. 20
We assume that eah household forms an expetation of apital gains based on the weighted average of housing prie growth rates in the three years before she purhases her primary residene. For homeowners, the survey data we use provides information on the purhase year of eah household's primary residene. The purhase years range from 1998 to 2010. There are a few observations before 1998. We exlude them from the regressions beause 1998 is the year when housing privatization reform was launhed, whih triggered the development of housing markets in a real sense. For non-homeowners, we alulate the expeted apital gains as the weighted average of housing prie growth rates in the three years before the survey year. Let p denote t, the hedoni prie in year t in ity where household i 's primary residene is loated. Let ti denote the purhase year of household i 's primary residene. The expetation of apital gains that household i holds is measured as g i = 100 2 ς (ln pt, ln 1, ) / ( 1) i k pt i k k + k = 0 i, (3) 2 k= 0 1 ( k + 1) ς where g is the weighted growth rate of housing pries, i 1 ( k + 1) ς is the weighting fator, and k is the time lag from the purhase year. ς > 0 means that the weighting dereases as time gets further away from the purhase year. ς < 0 means that as time gets further away from the purhase year, the weighting inreases. In our main regressions, we hoose ς = 0.1.We also try different values of ς as a robustness hek. 16 The probit regression speifiation is as follows: 16 We try different weights ς [0.05,0.2] to form apital gains expetations and re-run all the regressions. The results all show patterns that are fairly similar to those of our main regressions. Results are omitted from the paper in order to save spae, however, they are available upon request. 21
TS i 1, if TSi = α + β1gi + β2x i + β3zi + β4wi + u + εi > 0 = (4) 0, otherwise where i is the index for individual household and is the index for the household s ity of primary residene. TS i is a dummy variable indiating the tenure status of interest (i.e., own1 or own2) for household i, and g i is the household's expetation of apital gains as defined earlier. We ontrol for the ity fixed effet u in ase some ity fators simultaneously influene both the expeted apital gains and the housing demand of individual households. Other ontrols are desribed below. X i is a vetor of household harateristis that may influene households' housing demand, suh as inome, wealth, family struture, and household head information. Inome is the sum of wage inome, rental inome, interest inome, pension and soial seurity inome, gift and other misellaneous inome. Wealth is total assets minus debt. Household total assets inlude housing assets, finanial assets (the sum of bonds, stok shares, funds and bank deposits), insurane ompensation to be paid and money lent out. Household debt inludes borrowing from banks suh as for mortgage loans, borrowing from informal finanial setors, borrowing from friends and relatives and other borrowing. Guided by our theory, the wealth measure as an explanatory variable should be total wealth net of various debts inluding mortgage. However, there is a potential endogeneity problem. Speifially, housing investment hoie may affet net wealth. To deal with this problem, following the literature (e.g., Ioannides and Rosenthal, 1994; Dusanski and Ko, 2007), we first run an OLS regression of wealth on all the exogenous variables in our main regressions inluding some personal harateristis of the household head, suh as age, sex, eduation, and body height. 17 We then use the predited wealth WHAT as our measurement for family wealth in our main regressions. 18 17 Various findings in labor eonomis suggest that body height an be used to predit labor market performane and earnings (e.g., Persio, Postlewaite and Silverman, 2004, Case and Paxson, 2008). 18 We also did a robustness hek and diretly use the wealth exluding housing assets as a measure. It does not 22
Family struture harateristis inlude family size, whether there are any family members aged over 60 living in the household and whether there are any hildren aged below 6 in the household. Household head harateristis inlude age, eduation, marital status (unmarried, married or ohabiting, divored or widowed.) and Hukou status (i.e., urban Hukou or rural). We also ontrol for a dummy variable indiating whether the household head works for the government or a government-related institution beause government employees may have subsidies or privileges when buying primary residenes in China (Fang, Gu and Zhou, 2014). We use Z to denote the hedoni housing prie level of household i s primary i residene ity in the purhase year of the household s primary residene. This fator varies aross different households in different ities. It is possible that there are some other ity-wide time-varying fators that may influene both an individual household's housing investment demand and the ity's housing prie growth around the purhase year of the household's primary residene. Therefore, we inlude two additional ontrols in our regressions: one is the log of the ity's GDP per apita in the purhasing year; the other is the ity's population growth rate in the purhasing year. We use Wi to denote the vetor of these fators. We do not inlude the survey year hedoni housing prie or rental prie at the ity level in our benhmark analysis beause we have ontrolled for the ity fixed effet. Other ity-level time-invariant ost fators related to owning houses suh as taxes and mortgage loan interest are aptured by the ity fixed effet as well. In addition to the probit regression, we also run an ordered probit regression following Ioannides and Rosenthal (1994). We break the housing tenure status into three ladders: hange the main results, although the signifiane of the effets beomes weaker. 23
renter, own1 and own 2. The explanatory variables are the same as those in the previous probit regressions. 4.1.2 Findings The results are shown in Table 3. In olumn 2, we an see whih fators are important in a household s deision as to whether to purhase a home or not. First of all, the expeted apital gains have no signifiant impat here. The housing prie level at the purhase year has a negative effet as expeted. Households with higher inome, a male head and larger size, and households whose heads work for government-related institutions are more likely to own a house. If a household head is older, the household s probability of owning a house inreases, although at a dereasing rate. The results of the ordered probit regressions are shown in olumn 1 of Table 3. Higher expeted apital gains help households move up the housing tenure status ladder. Combined with the finding from the previous probit regression that expeted apital returns have no signifiant effet on households' deision as to whether to own a house, this suggests that an inrease in expeted apital returns would inrease the likelihood that they own multiple houses. Meanwhile, households with higher inome or larger size and households whose heads work for government-related institutions are more likely to have a higher housing tenure status. 4.2 Housing investment of homeowners who only own a primary residene In this subsetion, we investigate one hannel of housing investment. This hannel is through the primary residene. 4.2.1 Speifiation and Strategy The housing demand of homeowners who own just one housing unit is equal to their primary residene. There are 1,907 own1 households out of 2,344 total homeowners. 24
This housing demand is a mix of the onsumption demand and the investment demand in the sense that it may apture part of the potential investment need that has been subdued by finanial onstraints as illustrated in the theory setion. We will examine how the housing demand of own1 households responds to hanges in expeted apital gains, whih is indiative of their investment need. We will also hek how the responses differ among different wealth groups. To onstrut the housing demand measure, we divide the market value of a household s primary housing by the hedoni housing prie level of the residene ity in the survey year. The demand measure is therefore the housing servies demanded with the quality fator ontrolled. We examine how housing demand is related to expeted apital gains and household harateristis. Our baseline regression is speified as follows: y = α + β g + β X + β Z + β W + u + d + ε, (5) i 1 i 2 i 3 i 4 i 2010i i where y i is the housing investment demand for household i. The explanatory variables and the ontrol variables are the same as those in Equation (2). For example, g i is a household s expetation of apital gains as defined in setion (4.1).We ontrol for the ity fixed effet u beause there may be ity fators that simultaneously influene both the expeted apital gains and the housing demand of individual households. We also inlude the survey year effet d 2010 i beause we have two survey years, 2010 and 2011. (Remember that eah year overs different households.) Beause our regression is based only on the sample of own1 homeowners, we utilize a Hekman seletion model to deal with the possible endogenous sample seletion problem. Beause it is very hard to find a variable that influenes the housing tenure hoie but not the housing demand, in the first stage seletion regression (probit), we 25
utilize the same set of explanatory variables as in the main regression, following Ioannides and Rosenthal (1994). This means we rely only on the non-linearity of the probit model for identifiation. We run Hekman regressions and find that the rho is insignifiant, suggesting that the sample seletion issue is not severe. 4.2.2 Findings In Table 4, we report the regression results. From olumn 1, higher expeted apital gains inrease the housing demand signifiantly. When the expeted return on housing investment inreases by one standard deviation (i.e., by 8.85 perentage points), the housing demand inreases by 11.51%. It is worth noting that in China s urban housing markets, households fae a substantial down-payment ratio requirement 19 along with minimum size onstraints for housing units. 20 When expeted apital gains inrease, households have greater housing investment need. However, if they annot afford to buy a seond house due to the aforementioned finanial onstraints, they will alternatively buy a larger primary residene unit. An inrease in hedoni housing prie level in the purhase year of the primary residene redues the demand, but its effet is not very signifiant. Inreased household inome inreases the demand signifiantly. When the log inome inreases by one standard deviation (i.e., the log inome inreases by 1.35 perentage points), the housing demand inreases by 10.13%. Inreases in household wealth also have a positive effet on housing demand. As for the effets of the other household harateristis, households with larger family sizes demand larger primary residenes, as do households with higher eduation levels. Moreover, households with urban Hukou own 39% larger primary residenes on average than those without. This indiates that the Hukou restrition is still a hurdle that redues rural migration into ities. 19 The down-payment ratio for purhasing the first housing unit is 20-30%. In order to urb possible speulative behavior in the housing market, ity governments in China impose higher down-payment requirements for purhasing additional housing units. 20 A single bedroom apartment typially has a minimum size of 30 square meters, and a studio apartment typially has a minimum size of 22 square meters. In reent years, the government of China has started to implement poliies that aim to enourage land developers to build and sell smaller apartments. 26