Estimates of the Price Elasticity of New Housing Supply, and Their Determinants: Evidence for China

Estimates of the Price Elasticity of New Housing Supply, and Their Determinants: Evidence for China Songtao Wang 1,2, Su Han Chan 3 and Bohua Xu 4 1 Hang lung Center for Real Estate, Tsinghua University, Beijing 100084, P.R. China. 2 Department of Construction Management, Tsinghua University, Beijing 100084, P.R. China. 3 Department of Real Estate, Baruch College, City University of New York, New York, NY 10010, US 4 Department of Landscape Architecture, School of Architecture, University of Southern California, Los Angeles, CA 90007, US Abstract: Despite a growing recognition of the importance of housing supply studies, empirical work on housing supply outside the U.S. is still scarce. This paper adds to this literature by providing a first look at estimates of housing supply elasticities in China, at both the aggregated (national) and disaggregated (city) level. Using a stock adjustment model as in Malpezzi and Maclennan (2001), we estimate the price elasticity of housing supply using panel data for 35 cities in China over a 12 year period from 1998 to 2009, finding that the average price elasticity ranges from 2.82 to 5.64. Our analysis at the city-level suggests that land availability, urban built-up area and its growth rate, population and its growth rate, housing price as well as governmental regulation are all important determinants of variations in the housing supply elasticity measure across the cities. Our findings have implications to understanding how and why the housing market in China may differ in supply responsiveness from other markets. Keywords: price elasticity of housing supply, housing price, stock-adjustment model, panel data, China 1 Introduction Many cities around the world have experienced a rapid growth in housing prices since the late 1990s, raising the issue of a housing bubble as a major policy concern. To identify the key factors driving up housing prices, an increasing number of studies have attempted to explain the variation in housing price dynamics across countries or metropolitan areas (Glaeser et al., 2008; Wheaton and Nechayev, 2008). Although strong economic growth and 1

intensified housing financial support along with other demand side factors played a role in the recent run up in housing prices prior to the financial crisis that started around 2007, these demand side factors alone are hardly sufficient to capture the variations in the regional price dynamics. Hence, an increasing number of supply side studies have begun to surface to shed light on the other side of the coin in explaining housing price dynamics. It is not unusual that the supply side of the housing market has attracted more attention than other commodity markets. One obvious reason is the zero or negligible price elasticity of housing supply in the short run given the lag in construction process. In the medium to long run, however, housing supply becomes more responsive to demand shocks. The magnitude of a change in housing prices as well as the time taken to restore a new level of price equilibrium due to an unexpected shock in housing demand are greatly affected by the price elasticity of housing supply. This explains why early research in the 1960s and 1970s focused on drawing inferences or directly estimating housing supply elasticity from reduced form estimation models (Muth, 1960; Follain, 1979; Whitehead, 1974; Maclennan, 1978; Mayes, 1979). The price elasticity of housing supply, a behavioral parameter, has already become a focal point of housing supply research. Researchers employ various empirical models and use data at the national or metro level to analyze this parameter. The bulk of the research focuses on the U.S. housing market research(dipasquale and Wheaton, 1994; Bramley and Watkins, 1996; Mayer and Somerville, 1996; Malpezzi and Mayo, 1997; Blackley, 1999; Malpezzi and Maclennan, 2001; Evenson, 2001; Harter-Dreiman, 2004; Malpezzi and Wachter, 2005; Green et al., 2005; Glaeser et al., 2006; Glaeser et al., 2008), while only a handful of studies estimate the parameter for non-u.s. housing markets (Peng and Wheaton, 1994; Mayo and Sheppard, 1996; Malpezzi and Mayo, 1997; Malpezzi and Maclennan, 2001; Meen, 2005; Vermeulen and Rouwendal, 2007).Despite a growing body of empirical work on housing supply, the results vary and there is yet to be a consensus, on theestimation method of the price elasticity of housing supply..research. Two related research questions stem from the above housing supply elasticity studies. The first concerns the extent to which supply elasticity impacts housing price dynamics (Malpezzi and Wachter, 2005; Wheaton, 2005; Gyourko et al., 2006; Glaeser et al., 2008; Grimes and Aitken, 2010; Davidoff, 2010). Most findings on this issue confirm an inverse relationship, that is, a more elastically supplied housing market tends to have lower price levels as well as smaller price volatilities than a market with less elastic supply. Other studies, 2

however, do not find this to be the case (e.g., Aura and Davidoff,2006; Davidoff, 2010).. More recently, some researchers even extended the casual linkage to even broader implications, like the indirect impact from housing supply to economic stability (OECD, 2004), regional employment (Vermeulen and Ommeren, 2009) and social capital investment at the community level (Hilber et al., 2010). The second research question concerns the empirical finding of variations in the estimated price elasticity of housing supply across different countries (Mayo and Sheppard, 1996; Malpezzi and Mayo, 1997; Malpezzi and Maclennan, 2001; Vermeulen and Rouwendal, 2007) or across different regions within a country (Goodman, 1998; Harter-Dreiman, 2004; Green et al, 2005). This variation in supply-side elasticity contrasts with the stability of demand elasticities observed across countries or regions., thereby raising a question as to what are the factors influencing housing supply elasticity. Different researchers have proposed different factors, most of which can be categorized into either institutional, economic or geographical factors. However, none of the past studies has examined all the three groups of determinants simultaneously. Further, there is no consensus on the potential determinants of housing supply elasticity. This question, up till now, is understudied. In this paper, we focus on estimating the price elasticity of housing supply as well as identifying the important determinants of the variations in regional housing supply elasticity in China. We will not examine the linkage between supply elasticity and housing price dynamics since other studies on China (e.g., Wang, 2009) have found a negative connection between the two variables, which is consistent with U.S. results. Instead, this paper will contribute to the international comparative literature on housing supply by providing new insights on how the heterogeneous supply elasticities of different regional markets are shaped. In 1998, China s welfare housing system was substituted by a market- oriented housing system and since then the restrained housing demand is gradually released. Statistics shows that from 1998 to 2008, new immigrants to Chinese cities add up to more than 100 million and the urbanization rate increased from 30.42% to 45.68%. Under such demand shifts, most of the urban housing markets across China enjoyed a sustained price increase over the past decade as the economy boomed. Figure 1 shows the housing price dynamics of Beijing, Shanghai, Guangzhou and Shenzhen, the largest four urban housing markets in China 1. 1 These housing price data are all from China Real Estate Index System (CREIS). The housing price index data bank was constructed in November 1994 and used 1000 as the base point. The indices are transaction based and are designed to take into account the quality variations in the sample. Thus, they are currently the best available indices on China s 3

Statistics show that the annual appreciation rate of Shanghai s and Beijing s housing price indexes are 12.02% and 20,42%, respectively, from December 2002 to December 2009.In mid-2003, fearing that a potential bust in housing prices would undermine the sustained growth of the economy, the central government began to launch a wide range of regulatory policies (including mortgage and reserve rates adjustments, tax rate adjustments, housing price regulation, land use right transaction reform and supply structure regulation 2, 3 ) with the hope to restrain the rising residential prices (Wang and Yang, 2010). The supply side policy measures utilized during the intervention period are aimed at improving the responsiveness of the housing supply environment as well as providing more affordable housing for the low and medium income households. Wang (2009) found that, although demand-side government regulations have rather limited effects, supply side interventions are more successful in curbing the price appreciations. 3200 Beijing 2700 Shanghai Guangzhou 2200 Shenzhen 1700 1200 700 2000-12 2001-12 2002-12 2003-12 2004-12 2005-12 2006-12 2007-12 2008-12 2009-12 Figure1. Housing prices of Beijing, Shanghai, Guangzhou and Shenzhen in east China Data source: The housing price data are from China Real Estate Index System housing market. Since the index only covers ten important cities in China, in the empirical part of this paper, we will use another type of housing price index (which is a transaction-based price index for newly built houses) for 35 large scale cities published by the National Bureau of Statistic and National Development and Reform Commission. 2 With regard to land use right, on 31st March 2004, the Ministry of Land and Resources (MLR) of China promulgated Notification No. 71. This notification requested that after 31st August 2004, all state-owned urban land for real estate development should be granted through tender auction, oral auction, or listing auction. Before this date, most of the transactions are conducted through private negotiations. 3 With regard to supply structure, the State Council launched a policy in May 2006, requiring that units with floor area less than 90 square meters must cover 70% of the total floor area in all newly registered or constructed projects. 4

5000 All East Middle West 4000 RMB 3000 2000 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Figure2. Housing prices dynamics in east, middle and west China Data source: The housing price data are published by the National Bureau of Statistic and National Development and Reform Commission Apart from some hot regional markets, which have triggered nation-wide government intervention, China s housing market also has an obvious regional pattern across the east, middle and west. Figure 2 illustrates the regional housing price levels from 1998 to 2009 4. Basically, housing price has a faster price appreciation rate in the East group(18 cities, 35.58%) than in the Middle group (7 cities, 20.13%) and the West group (10 cities, 24.27%). Although the averaging process within each group in figure 2 has masked the potential differences between housing prices of different cities, yet by comparing Figures 1 and 2, we can still conclude that there exist quite different housing price patterns across different regions and cities. Since neighboring cities confront similar demand shocks, different price dynamics shall be a reflection of different price elasticity of housing supply. Thus we assume there are regional variations in housing supply elasticities due to different features in each submarket. The first objective of our paper is to estimate a nation-wide housing supply elasticity for China, which will serve as the basis for cross-country comparisons. To utilize the wealth of data in the regional markets, we employ the panel data technique as in Harter-Dreiman (2004) who imposed a common coefficient on the price elasticity of housing supply across the 76 Metropolitan Statistics Areas (MSAs) in a panel data setting to derive the national supply 4 We categorized our 35 cities into three groups: East, Middle and West. Wulumuqi, Xining, Lanzhou, Yinchuan, Xi an, Chengdu, Chongqing, Guiyang, Kunming and Nanning are 10 cities in the West group. Huhhot, Taiyuan, Zhengzhou, Hefei, Wuhan, Nanchang and Changsha are 7 cities in the Middle group. The remaining 18 cities are in the East group. The price level data are published by the National Bureau of Statistic and National Development and Reform Commission. 5

elasticity. A similar procedure is also employed by Saiz (2010) who imposed a common coefficient on inversed supply elasticity in panel data analysis. In such a way, the estimated elasticity could be deemed as an average price elasticity of housing supply in all the regional markets. For the aggregated level measure, we employ the stock-adjustment model as proposed by Malpezzi and Maclennan (2001).. Kim et al. (2010) point out that such stockflow model is relatively simple and uses the reduced form housing price equation and estimates of demand elasticities to calculate the supply elasticity. In addition, the Malpezzi and Maclennan (2001) model has been widely used in past studies of supply elasticity, and using this model at the aggregated level will foster an identical methodology for crosscountry comparisons. To make the traditional Malpezzi and Maclennan (2001) model more realistic and to get a more accurate estimation, we extend the model by incorporating the real cost of homeownership into the demand equation and introducing lagged housing prices, construction cost as well as capital cost into the housing supply equation. Our sample covers the largest 35 cities in China, most of which are provincial capital cities, (the geographical locations of these cities are presented in Appendix A) and the period from 1998 to 2009. We find that the average supply elasticity is within the vicinity of 2.82 to 5.64. Comparing to the supply elasticity estimates by prior studies for the U.S. and other markets, our finding suggests that China has a moderately elastic housing supply environment. We then explore the determinants of price elasticity of housing supply. The Malpezzi and Maclennan model is not a good choice for estimating the city-level supply elasticity considering the limited observations compared to the high degrees of freedom. As such, the estimated coefficients will suffer from low power of estimation. In addition, in order to explain the determinants of the disaggregated supply elasticity estimates, we need to find point estimates rather than range estimates derived from the Malpezzi and Maclennan (2001) model. To get city-level supply elasticity, we directly estimate new housing constructions in response to changes in housing prices, controlling for important cost shifters as in Topel and Rosen (1988) and Green et al (2005). Using the city-specific point estimate of the price elasticity of housing supply as the dependent variable and related factors as independent variables in the estimation model, we find the land availability, urban built-up area and its growth rate, population and its growth rate, housing price as well as governmental regulation are important determinants of the housing supply elasticities. It is noteworthy that we incorporate geographical information into our model through a developable land ratio 6

variable (as Saiz, (2010) did to explain the housing supply elasticity). By so doing, we can examine the determinants of housing supply simultaneously from geographical, economic and institutional perspectives, thus extending Green et al. s (2005) empirical findings, which excludes a geographic perspective. Generally speaking, the current literature on the China housing market has focused primarily on demand side factors to explain housing price dynamics while largely overlooking housing supply elasticity.. This study fills this gap in the literature and enriches our understanding of the housing market from the supply side. The remaining of the paper is organized as follows. Section two reviews the related literature. Section three discusses the estimation models and the data as well as estimates the nation-wide price elasticity of housing supply. Section four uses a simple cross-sectional regression method to find the important factors that could have an impact on the price elasticity of housing supply. Section five concludes. 2 Previous Research 2.1 Defining the price elasticity of housing supply In housing economics, the price elasticity of housing supply is an elasticity defined as a numerical measure of the responsiveness of housing supply to a change in housing price. Such a textbook definition is not sufficient to fully understand the feature of housing supply elasticity. At least three more questions need to be answered.. (1) How to measure housing supply? In a broader perspective, all the unit (or measured in housing service) of the total housing stock are potential housing supply, which is a stock variable, but often the housing supply is regarded as the new supply of housing, which is a flow variable. Rydell (1982), Dipasquale and Wheaton (1994), Mayer and Somerville (1996, 2000b) have distinguished a stock price elasticity of housing supply from a flow counterpart. The magnitude of the flow supply elasticity should be larger than the stock supply elasticity. For example, Mayer and Somerville (1996) derived a flow supply elasticity of 6 and a stock supply elasticity of 0.08 for U.S. housing market. In practice, residential investment, newly built number of units and the housing start permit issuance are commonly used variable to depict housing supply. (2) How long is the time horizon to measure the housing supply elasticity? Theoretically speaking, in the immediate short run, the supply elasticity is equal to zero while in a enough long time horizon, the housing supply elasticity could be pretty large. This feature reveals that housing supply elasticity is a time-variant variable and it is important to specify the time horizon when define a supply elasticity. Topel and Rosen (1988) first proposed short-run and 7

long-run supply elasticity concept and define the former to be around 1 year while the latter around 3 years. Evenson (2001) calculated supply elasticity for 47 MSAs in U.S. with time horizon of 3, 6, 9 and 12 years. The estimated supply elasticities increase monotonically over time horizon. Pryce (1999) estimate supply elasticity at consecutive boom and bust period and find housing supply elasticity is noticeably smaller in the boom (0.58) than in the slump (1.03). (3) Is housing supply elasticity a real term or a nominal term? Actually, most of the market indicator shall be in real term to have economic interpretation, so does housing supply elasticity. Housing supply elasticity is derived from both the housing supply variable and housing price variable. When estimating the elasticity, it is essential to utilize the real term variables within the model. In this paper, we examine the real flow supply elasticity with a fixed time horizon of one year which is short-run supply elasticity. 2.2 Estimation methods for the price elasticity of housing supply There are three main different theoretical models for estimating housing supply elasticity with different econometrical techniques. The first type of model is based on the Tobin s q- theory which implies that the level of housing investment is a positive function of the ratio of housing prices to construction cost. Houses will be built when the total cost of building a new house is less than the cost of purchasing an existing identical property (replacement cost). Muth (1960), Follain (1979), Follain et al (1993), Vermeulen and Rouwendal (2007), Green et al (2005), Grimes and Aitken (2010) are some examples of using q-theory. Most of empirical settings among the above studies are reduced form equations with price and cost shifters on the right hand side. Typical cost shifters include land cost, material cost, labor cost and various interest cost. The second type of model is based on stock-flow adjustment theory which implies a stock adjustment process to equilibrate housing demand and supply. Newly housing supply adds to meet the increasing housing demand and make up the gap for potential demolishment in the housing stock, however, the current stock adjust to the long run desired housing stock with certain speed (not necessarily clear the market within one year). Topel and Rosen (1988) and Blackley (1999) first incorporated the stock adjustment process (one year lagged housing stock) in their theoretical and empirical research 5. Malpezzi and Mayo (1997) as well as Malpezzi and Maclennan (2001) proposed models to indirectly estimate housing supply elasticity in a flow adjustment and stock adjustment settings based on several demand elasticity and price elasticity. Both models and their extensions have been widely used in international comparative studies, for example, Mayo and Sheppard (1996), 5 Although Topel and Rosen (1988) s theoretical model is based on stock-flow theory, yet its empirical model did not include a housing stock proxy, which make it more like a q-theory empirical model. 8

Harter-Dreiman (2004), Malpezzi and Watcher (2005), Goodman (2005), Goodman and Thibodean(2008) and Wang (2009). This strand of literature is also reduced form model in nature and there is always housing stock on the right hand side as an independent variable. The third type of model is structural model mainly based on urban spatial theory which explicitly accounts for land as an input of housing construction. Mayer and Somerville (1996, 2000a, 2000b) use models of residential construction based on the theory of urban land development presented in Capozza and Helsey (1989). Dipasquale and Wheaton (1994), Peng and Wheaton (1994) also extend the traditional stock-flow model with urban spatial theory. Aura and Davidoff (2006) and Saiz (2010) separately endogenize land supply in their theoretical models to estimate housing supply elasticity. Among this type of structural models, Poterba (1984) proposed a structural asset market model. Evenson (2001) use conditional vector auto-regression (CVAR) to explain housing price and housing stock simultaneously. When estimating price elasticity of housing supply, another widely discussed issue is whether it is proper to use housing price level or change in the empirical models. Mayer and Somerville (2000b) argued that since housing price is a stock variable while newly housing supply is a flow one, it is proper to use the price change which is also a flow variable to explain the dynamics of housing supply. Of course, this argument focuses on the time-series property of the data to avoid spurious regression. Grimes and Aitken (2010) conciliated Mayer and Somerville (2000b) s argument with many previous studies using price levels by arguing that the existence of co-integration relationship between housing supply and its explanatory variables are the key issue rather than specify the format of variables. In this paper, we will do co-integration before estimating the supply elasticity. 2.3 Estimated price elasticity of housing supply The earliest attempt to estimate the price elasticity of housing supply was conducted by Muth (1960). He stated that if housing supply is perfect elastic, housing price should be independent from new housing supply, because housing supply will respond to all demand shocks immediately. His empirical study based on reduced model supports this assumption, and finds that U.S. has highly elastic housing supply between the First World War and the Second World War. Follain (1979) used 1947-1975 data to get a similar estimation of perfect elasticity while Poterba (1984) gets an estimate between 0.5 to 2.9. Dipasquale and Wheaton (1994) employed urban spatial model to estimate the elasticity of housing supply from 1963 to 1990 in U.S. and found the value lied within the vicinity between 1.0 to1.2 for new 9

housing construction while 1.2~1.4 for housing Stock. Malpezzi and Maclennan (2001) found that the housing supply elasticity of newly built market was 4~10 in U.S. and 1~4 in U.K. before the Second World War, while it was 6~13 in U.S. and 0~1 in U.K. after the Second World War. Blackley (1999) estimated the newly built elasticity of housing supply to be 1.6~3.7. More recently, Harter-Dreiman (2004) proposed VEC model to estimate the range of supply elasticity of U.S. urban housing market to be within the vicinity of 1.8 to 3.2. Green et al (2005) estimate supply elasticity of 45 cities in the U.S. and find a diverged distribution from highest 29.9 in Dallas to lowest -0.30 in Miami. Goodman (2005) based on 317 U.S. suburban area s data in 1970s, 1980s and 1990s to estimate supply elasticity within the vicinity of 1.26-1.42. Goodman and Thibodean (2008) used similar stock-flow models for 133 U.S. MSAs from 1990 to 2000 and find largest supply elasticity 2.98 in Las Vegas and the smallest supply elasticity -1.37 in Harrisburg. Saiz (2010) provides the most recent estimates of supply elasticities. Using his topographically-derived estimates of developable land ratio along with the local regulation data from Gyourko et al (2008), he provides housing supply elasticity estimation around 1.54 on average for U.S. metropolitan area and a 5.45 upper limit in Wichita while a 0.60 lower limit in Miami. In addition, there are also estimations of housing supply elasticity for counties other than the U.S. Whitehead (1974) found the newly built elasticity of housing supply was from 0.5 to 2 in the U.K during 1955 to 1972. Mayo and Sheppard (1996) find Malaysia s supply elasticity is between 0 to 1.5, Thailand near infinite and Korea from 1 to 1.5. Malpezzi and Mayo (1997) s estimate find Malaysia s supply elasticity is between 0 and 0.35, Korea is between 0 to 0.17 while Thailand also near infinite. Vermeulen and Rouwendal (2007) conclude zero elasticity in Netherland both in the short run and long run. Peng and Wheaton (1994) find supply elasticity to be 1.1 in Hong Kong, P.R. China. In general, the above studies gave a wide range of estimation on housing supply elasticity both within a country like U.S. or across different countries. From one side, this is in line with earlier argument that the definition of supply elasticity, specification of estimating model, research time horizon as well as the phase in the market cycle are different. From the other side, this implies great differences embedded in determinants of supply elasticity in different regional markets. 2.4 Determinants of price elasticity of housing supply A majority of literature has focused on the regulatory stringency s impact on housing supply 10

elasticity (Mayo and Sheppard, 1996; Mayer and Somerville, 2000a; Quigley and Raphael, 2005; Green et al, 2005; Malpezzi and Wachter, 2005; Zabel and Paterson, 2006; Vermeulen and Rouwendal, 2007; Glaeser and Ward, 2009). These studies developed different indicators to measure the stringency of government regulation on housing or land market. Malpezzi and Wachter (2005) used a simple addictive index of REGTEST developed by Malpezzi (1996) which incorporated approval time, issue of permits and acreage of land zoned for a single family housing et al. Similar index has also been developed by Gyourko et al (2008) called WRLURI which incorporate more information from a national survey. Evenson (2001) use the number of permit issuing authorities as a measure of the regulatory environment while Quigley and Raphael (2005) use the number of regulation policies as indicator. Mayer and Somerville (2000a) use months to receive subdivision approval, number of growth management technique as well as a development fee dummy variable to depict the regulatory framework. Most of above studies found statistically significant negative effects from tighter regulation on housing supply elasticity. Some studies also explore the economic factors of local market on housing supply elasticity. Evenson (2001) found that an area s population densities, historical employment growth rate, region of jurisdiction along with government regulation are important determinants of its supply elasticity and housing price response. Malpezzi and Wachter (2005) found that housing market with more liberal regulatory environments, or less natural constraint or greater access to infrastructure would have bigger price elasticity of housing supply. Green et al (2005) estimated supply elasticities for 45 U.S. metropolitan areas and found through cross section regression that population level, population change, population density, housing price level as well as government regulation are important in shaping regional housing supply elasticity, though some of regressed coefficients have unexpected signs. In current literature, only Saiz (2010) testify that physical land constraints is important in explaining housing supply elasticity by using satellite-generated data on terrain elevation and presence of water bodies. He proposed a model to endogenize developable land ratio with respect to price elasticity of housing supply. Empirical research finds significant impact from developable land ratio on housing supply elasticity. It is clear that geographical factor, along with economic and institutional factors are important in determining the supply elasticity of housing market, but up to now there is no research to examine all the three aspects of housing supply elasticity. This paper will give a thorough consideration of potential determinants from these three dimensions. 11

3 Estimating the price elasticity of housing supply in China 3.1 Models Stock adjustment model from Malpezzi and Maclennan (2001) Malpezzi and Maclennan (2001) provided a simple stock-adjustment model to estimate housing supply elasticity. We extend his model as follows. * Qdt ( Kt Kt 1) * Kt 0 1HPt 2INCt 3POPt 4OwnCostt Qst 0 1HPt 2HPt 1 3HPt 2 4HPt 3 5ConCostt 6MRate Qdt Qst (1) where, HP is the long-term price level of standard housing service, INC is household income, POP is total population, OWNCOST is the real cost of home ownership, * K is the long-term housing demand reflected by housing service, Kt 1 is the stock of housing service with a one period (year) lag, ConCost is the construction cost and MRate is the mortgage interest rate. All the variables in equation (1) are in logarithmic form but OWNCOST and MRate. Therefore 1 is the price elasticity of housing supply. Compare with the standard Malpezzi flow-adjustment model, equation (1) have three extensions. First, it incorporates real cost of homeownership into the demand equation since this variable is quite influential on housing demand. Second, we introduce lagged housing prices in the supply equation since housing construction process is lengthy and historical prices can be more influential to housing supply than current price. In our model, we first arbitrarily assume that housing prices during past three years can impact on current housing supply but will check the detailed lag periods in empirical study. Third, it further incorporates construction cost and capital cost into the housing supply equation since both are important indicators influencing housing supply decision. Equation (1) can be transformed into equation (2). HP INC POP K HP 0 0 2 3 2 t t t t 1 t 1 1 1 1 1 1 1 1 1 1 1 HP HP ConCost MRate 3 4 5 6 t 2 t 3 t t 1 1 1 1 1 1 1 1 (2) Since the parameters on the right side of equation (2) can not be identified directly, Malpezzi estimates 1 indirectly assuming 1 and 2 are given. Equation (2) can be estimated by OLS method as equation (3) when incorporating stochastic term. 12

HP INC POP OwnCost HP t 0 1 t 2 t 3 t 4 t 1 HP HP ConCost MRate K 5 t 2 6 t 3 7 t 8 t 9 t 1 t (3) Compared equation (2) with equation (3), the price elasticity of housing supply 1 is estimated as equation (4). ( ) (4) 2 1 1 1 Where, is the parameter of stock adjustment speed which can be assigned artificially. In Malpezzi and Maclennan (2001) s empirical study, they set the benchmark value of as 0.3 or 0.6, depicting a moderate speed of adjustment. As Malpezzi and Mayo (1997) stated, the elasticities of housing demand and housing prices are relatively stable across nations or regions. It makes the Malpezzi s models efficient to estimate the price elasticity of housing supply indirectly with reasonable simplicity. However, as argued by Kim et al (2010), the accuracy of the estimates for supply elasticity depends on the specification of the reduced form house price equation and the estimates of the demand elasticities. In this paper, we extend the Malpezzi and Maclennan (2001) model by incorporating cost of homeownership, cost of housing construction, cost of investment capital and lags in housing prices, which makes the models more realistic. 3.2 Data Data description The data used in this study covers macro-economic indicators as well as housing market variables in 35 major Chinese cities from 1998 to 2009. Due to the limited length of timeseries available, major cities are pooled to create a panel dataset. Thus, there are 35 cross sections and 12 years in our panel data, the total observations are 420 in each pooled variable. Actually, in panel data estimation, longer cross sections and shorter time period is good data formation as in Dreiman (2004) where there are 76 MSA cross section and 19 years. The variables and their descriptive statistics are shown in Appendix B.1. HP i is housing price level which is calculated according to Real Estate Price Index of 35 major cities published by National Bureau of Statistics (NBS) and National Development and Reform Commission (NDRC). This housing price index is transaction-based index and is the best available annual housing price data in China for its larger coverage of sample cities as well as its length. HStock i is housing stock estimated by multiplying per capita floor area and residential 13

populations of the year 1999 6. Using the housing completed floor areas as flow amount, the housing stock in the following years is estimated accordingly. disposable income per capita, completed floor area of residential housing, POP i is total residential populations, housing which we use as a proxy for housing demand. INC i is urban household NewStart i is newly SaleArea i is newly sold floor area of residential ConCost i is the construction cost of housing development. We divide the annual value of completed housing units over annual completed floor area to obtain a proxy estimation of construction cost which is a rough reflection of the structure cost. INF i stands for local inflation rate which are calculated from local Consumer Price Indices (CPI). Since all the interest rates are identical cross different urban housing market, we extracted local inflation rate from nominal benchmark lending rate to get MRate i, real rate of five-year lending. Actually, in China, dynamics of real cost of homeownership appreciation 7. We will use MRate i to replace the MRate i can capture the OwnCost t if we neglect the expected housing price OwnCost t in theoretical models in following empirical study. All the nominal variables are also adjusted by local Consumer Price Indices. Our data source includes China Monthly Economic Indicators, China City Statistical Yearbook and Statistic Yearbook in various cities. The data structure is panel data. In our model, we assume there are no structural changes across sections. Therefore, fixed effect panel data model is employed in our empirical study. Unit root test of panel data Similar to time series model, we should conduct unit root test of panel data to examine whether the data is stable in level or to check the degree of integration. Several panel unit root tests have been published and widely used recently. In our paper, we employ Im et al. (1997) (IPS) test to check the unit root in panel data 8 since IPS test touts particular usefulness for situations in which time-series are short and cross sections are relative plentiful. The test results are demonstrated in Table 1. 6 7 Series after the year 1999 is computed by adding newly built floor areas. To make the calculation easy, we assume there is no deterioration in the housing stock. Traditional cost of homeownership is equal to e OwnCost NominalMRate Maintain Pr opertytax Inflation HP / HP. In China, the maintenance cost does not vary much across time and region. There is no enacted property tax during the sample period. If we also assume a constant rate of expected housing price appreciation across time and region, then the real rate of lending (MRate=NominalMRate- Inflation) will fully capture the dynamics of home ownership cost (OwnCost). 8 IPS test is put forwards by Im et al (1997), which relaxed the assumption of cross section unit root homogeneity, and conducts ADF test respectively to each section, assuming there is different unit root on different cross section as the null hypothesis. 14

Table 1 Unit root test of panel data Level First Difference Variables IPS test Order of IPS test Order of stat P value integration stat P value integration ln(hp) -2.158 0.016 I(0) / / / ln(inc) 0.581 0.719 I(1) 5.481 0.000 I(0) ln(pop) -5.178 0.000 I(0) / / / ln(newstart) -0.124 0.451 I(1) 5.849 0.000 I(0) ln(salearea) -1.634 0.051 I(0) / / / ln(hstcok) 0.371 0.645 I(1) 0.964 0.067 I(0) INF -8.839 0.000 I(0) / / / MRate -8.148 0.000 I(0) / / / ln(concost) -1.284 0.100 I(0) / / / The results reveal that housing price, population, sale area, local inflation, real mortgage lending rate and housing construction cost are integrated at levels, while the other three series are integrated at the first order. Generally speaking, two panel data series with same degree of integration would be cointegrated (Greene, 1993). However, in order to give robust check on cointegration relationship in panel data, we have to conduct panel cointegration test. 3.3 Estimating the average price elasticity of housing supply First we will estimate the price elasticity ( 1 ) and income elasticity ( 2 ) of housing demand. Then we will estimate the income elasticity ( 1 ) of housing prices. With commonly used arbitrary settings of coefficient, we will get a range estimation of the price elasticity of housing supply ( 1). This method is intrinsically the same as Harter-Dreiman (2004) who also used panel data model to estimate 1. Estimating the price elasticity and the income elasticity of housing demand The price elasticity of housing demand 1 and the income elasticity of housing demand 2 should be given before calculating the housing supply elasticity. In extant literature about Chinese housing market, Zheng (2007) estimated both the coefficients using micro survey 15

data. Her empirical results indicate that the price elasticity is -0.505 and the income elasticity is 0.670 for Chinese urban housing market. However, her sample only covers three provinces including Liaoning, Guangdong and Sichuan. In order to acquire more information from panel data of 35 major cities, our study also estimates a reduce-form housing demand function as equation (5). We use sold floor areas, SaleArea, as a proxy for housing demand. ln( SaleArea ) ln( HP ) ln( INC ) ln( POP ) MRate (5) it 0i 1 it 2 it 3 it 4 it it Cointegration test of panel data model is conducted before estimating above formula. We employ the methods of Kao test and Pedroni test to empirically check whether the five variables within equation (5) are cointegrated. The null hypothesis of Kao and Pedroni test are that there is no cointegrated relationship between the variables. The results revealed that the both Kao and Pedroni test reject the null hypothesis 9, so we conclude that the variables used in equation (5) are cointegrated or in other words, they at least have one cointegration vector. Therefore, a Pool Generalized Least Square method is used to estimate the equation taking account of cross-section fixed effect and period fixed effect. Table 2 gives the detailed regression report. Table 2 regression result of equation (5) Variable Coefficient Std. Error T-Statistic P value Intercept *** 9.818 2.267 4.331 0.000 LOG(HP) *** -0.765 0.150-5.084 0.000 LOG(INC) *** 0.437 0.143 3.055 0.002 LOG(POP) *** -0.451 0.168-2.677 0.008 MRate ** -2.358 0.944-2.499 0.013 Adj. R square 0.969 D.W. Statistics 1.075 F-statistic 266.866 Prob (F-statistic) 0.000 Notes: Fix effects of each cross section and time dummy are not displayed here. ***significant at the 1% level, **significant at the 5% level, *significant at the 10% level Our results indicate that the price elasticity of housing demand in urban cities is -0.765, and the income elasticity is 0.437. The estimation is basically in accordance with Zheng (2007) s inference. We will use estimations of this paper to proceed with later calculation. Estimating the income elasticity of housing prices In this section, we employ fixed-effect panel data model to estimate equation (3). Cointegration test of panel data model is also conducted beforehand, and both Kao test and 9 The detailed test reports will be provided up on request. 16

Pedroni test indicate that there shall at least have one cointegration vector which is in line with the panel unit root test in table 1. Therefore, a Pool Generalized Least Square method is employed to do the estimation. Table 3 demonstrates the estimated results. Housing Price Model Table 3 Regression result of equation (3) Dependent Variable: log housing price Independent Var I II III 0 ln( INC) : ln( POP) : MRate : 3 1 ln( HP) : 2 t 1 4 ln( HP) : ln( HP) : ln( ConCost) : ln( HStock) : 0.037 (0.17) 0.030 ** (2.11) -0.010 (-0.25) 0.678 *** (6.52) 0.875 *** (34.09) t 2 5 / 0.713 *** (3.22) 0.043 *** (3.09) -0.001 (-0.04) 0.548 *** (5.48) 1.268 *** (25.16) -0.483 *** (-9.45) t 3 6 / / 8 7 0.008 (0.71) 0.074 *** (3.75) 0.005 (0.44) 0.063 *** (2.80) 0.948 *** (3.73) 0.045 *** (2.79) 0.026 (0.95) 0.402 *** (3.43) 1.225 *** (19.26) -0.513 *** (-5.18) 0.046 (0.71) 0.001 (0.08) 0.046 * (1.60) Adjusted R 2 0.993 0.995 0.995 D.W. sat 1.075 1.847 1.984 F Statistics 1277 1527 1376 AIC -4.067-4.352-4.356 ***significant at the 1% level, **significant at the 5% level, *significant at the 10% level. We estimate three scenarios with different lags. In model I, we only incorporate one year lagged housing prices while in model II and III, we incorporate both two year and three year lags respectively. It shows that the estimated coefficients are stable in all the regressions, but three year lags are insignificant. This reveals that only housing prices in previous two years are important in supply decision making during the sample period in China. Since model II have smaller AIC and bigger adjusted R 2, we therefore take the results in model II as the estimation result which suggests that the income elasticity of housing price, 1, is 0.043. Estimating the average price elasticity of housing supply 17

Based on the given parameters of 1, 2 and 1, we conduct our estimation of the elasticity of housing supply according to equation (4). The results in table 4 show that the elasticity of housing supply is estimated to be within the vicinity of 2.82 to 5.64 according to extended stock-adjustment model (equation (1)) with changes from 0.3 to 0.6 (when is 0.3, we get the lower limits of supply elasticity, while is 0.6, we derive the upper limits). It is worth noting that this estimation result should be interpreted as the average price elasticity of housing supply for Chinese urban housing market. This is the same as in Saiz (2010) where the author imposed a common inverse supply elasticity parameter for all cities in his panel data model to represent a national average. Table 4 Estimation of the average price elasticity of housing supply in 35 major Chinese cities Price elasticity of housing demand Price elasticity of housing demand 1 0.765 Income elasticity of housing demand 2 0.437 Equ(8): 1 0.043 0.3 2.82 Equ(8): 1 0.043 0.6 5.64 We further make an international comparative study with the other findings using the same theoretical models as shown in table 5. The results reveal that the elasticity of housing supply in Chinese major cities from 1998 to 2009 is moderately elastic. Among the nations in table 5, Thailand and U.S. (especially during the prewar period) have highly elastic housing supply environment, while Korea and Malaysia have seriously inelastic housing supply. Our estimation results indicate that the price elasticity of housing supply in China is higher than U.K., Korea and Malaysia, and is less than that of Thailand and U.S. Table 5 Comparison of supply elasticity across countries Countries Period Data Sources Elasticity Estimated Category Prewar period National data Malpezzi and Maclennan (2001) 4.40~10.40 highly elastic U.S. Postwar ~1994 National data Malpezzi and Maclennan (2001) 5.60~12.70 highly elastic 1980~1998 City-level data Hart-Dreiman (2004) 1.80~3.20 moderately elastic U.K. Prewar period National data Malpezzi and Maclennan (2001) 1.40~4.30 moderately elastic Postwar ~1995 National data Malpezzi and Maclennan (2001) 0.00~0.50 inelastic Korea 1970~1986 National data Malpezzi and Mayo (1997) 0.00~0.17 seriously inelastic Malaysia 1970~1986 National data Malpezzi and Mayo (1997) 0.07~0.35 seriously inelastic Thailand 1970~1986 National data Malpezzi and Mayo (1997) highly elastic mainland China 1998~2009 City-level data This paper 2.82~5.64 moderately elastic 18

Alternative Estimation methods as robust check If we utilize essentially the same model as Malpezzi and Maclennan (2001), then in equation (3), there are no Owncost, Concost, Mrate as well as lagged housing price terms. We estimate the same equation again with Cochrane Orcutt correction (including both AR(1) and AR(2) to eliminate the serial correlation) 10. The estimated income elasticity of housing price is 0.091 and the housing supply elasticity lies in the vicinity of 1.21 to 2.42. This suggests that if we do not extend the stock-flow model, the estimated range of supply elasticity would be downward biased. In addition, as mentioned beforehand, the utilization of the q-theory model would suffer from limited observations and regression power. We do a robust check to model the log national newly completed floor area of residential building as a function of log national housing price, log construction cost, log wage of construction worker as well as real five-year mortgage rate. The result demonstrates that only housing prices and real mortgage rate are statistically significant and the estimated supply elasticity is 3.24, which is well included into the estimated vicinity by using extended stock-flow model. 4 The determinants of housing supply elasticity 4.1 Estimating the price elasticity of housing supply for each city In sector three, we estimate the average housing supply elasticity for Chinese cities and give a general picture of the housing supply environment in China. However, as stated before, the housing supply elasticity have large regional variances due to different topology status, housing market maturity and regulatory framework et al. In this sector, we firstly estimate the supply elasticity of the 35 large scale Chinese cities. Then, we will try to explain the determinants of these supply elasticities from geographical, economic and institutional dimensions. Although we can utilize the abundance of regional housing market data and pool those data together to inference the national level supply elasticity by stock adjustment model as used in Malpezzi and Maclennan (2001), yet when estimating the supply elasticity at the city level, the extended stock adjustment model would have two limitations. Firstly, the stock adjustment speed parameter will determine the range of supply elasticity. In order to obtain the point estimation of supply elasticity for later regression, it is essential to estimate 10 Malpezzi and Maclennan (2001) used Cochrane Orcutt correction to solve serial correlation problem by adding AR(1) into the model. 19

the parameter in different cities. However, the speed of stock adjustment shall depend greatly on the market fundamentals which again have great regional variance. It is thus quite unrealistic to impose an identical or artificially assign a value to estimate the supply elasticity of a city. Secondly, the length of dataset limits our estimation using the extended stock-adjustment models too. When considering two lags in the supply equation, extended stock-adjustment models in our paper will have fourteen regression coefficients (or degree of freedom) 11. Since we only have twelve observations in each city, we could not use such model in regional supply elasticity estimation. However, a popular alternative method is to directly estimate housing starts or new housing construction in responses to changes in housing prices controlling for some other cost shifters based on the Tobin s q-theory (Kim et al, 2010). Particularly, Green et al (2005) modeled housing starts as a function of housing prices over 18 years (1979-1996) to obtain the point estimation of housing supply elasticity for 45 U.S. metropolitan areas. Topel and Rosen (1988) s empirical model incorporated a vector of cost shifters, including real interest rate, expected inflation, median time on the market, construction and wage costs, to estimate the national housing supply elasticity during 21 years horizon (1963-1983). It is noted that in order to avoid the endogenous problem, both studies used lagged housing prices as instrumental variables. As stated by Topel and Rosen (1988), all demand-side effects should be embodied in housing prices in an ideal market, so we do not include demand variables in our estimation. Following the Green et al (2005) as well as Topel and Rosen (1988) s specification, we incorporate a construction cost shifter ConCost and a capital cost shifter MRate into the regression model as shown in equation (6) where 1i is the supply elasticity for city i. Our sample period is from 1998 to 2009. ln( NewStart ) ln( HP ) ln( ConCost ) MRate (6) it 0i 1i it 2i it 3i it it In equation (11), we restrict the coefficients on ConCost and MRate to be identical across areas reflecting shared underlying preferences 12. Thus 2i is equal to 2 while 3i is equal 11 If we do not extend the standard Malpezzi flow-adjustment and stock-adjustment model, there will be seven and eight coefficients. Though we can estimate these coefficients in the standard malpezzi model, but I do not have confidence with such a short time series. 12 China s interest rate is modulated by People s Bank of China. Since the bank lending mortgage rate is identical across different regions and any change in the rate is released simultaneously, we believe there is similar impact from mortgage rate on supply decision across regional markets. In addition, although the construction cost varies in level, but they do share a common trend and takes up approximately similar share in the total housing prices. So we assume that they also 20