# RECORD 2344ebd24eeebb31c33011f3e72a12383c3c1e88 # TITLE: Hedonic Price Modeling of New Residential Property Values in Xi’an City, China # YEAR: 2015.0 VENUE: nan DOI: 10.11114/ijsss.v5i9.2510 # AUTHORS: Kai Liu; T. Ichinose # PAGES: 15 CANDIDATE TABLE PAGES (1-based): [4, 8, 9] # ABSTRACT: This study analyzed new residential property values of Xi’an City in March, 2014. Results show that accessibility indices, such as distance to CBD, have been well capitalized into the residential property values. Particularly, a within-zone housing unit is sold 9.4% more than if it was outside the attendance zone of a Key Primary School, i.e. home buyers have how much willingness-to-pay for the high-quality educational resource. Another corollary is got that the accessibility to subway stations has not significantly been capitalized, only with a low premium reflecting in the real estate market of Xi’an City. Considered that spatial local singularities caused by unobserved variables or estimation bias can be associated with multi-regression errors, this study herein has explored an unconventional viewpoint to residual problem, which combines the regional differences (coming from real world) and the spatial distributions of singularities (feedback from data). Furthermore, whole samples are classified into 5 agglomerations for revealing the underlying reasons about the future trend and variation of real estate market within each region. It is effective to provide scientific basis of decision making for the real estate investors and planners. ===== PAGE 1 (score 14, numeric-paren 0, table-words 0, var-words 14) ===== International Journal of Social Science Studies Vol. 5, No. 9; September 2017 ISSN 2324-8033 E-ISSN 2324-8041 Published by Redfame Publishing URL: http://ijsss.redfame.com 42 Hedonic Price Modeling of New Residential Property Values in Xi’an City, China Kai Liu1 & Toshiaki Ichinose2, 3 1Doctoral Program in Geoenvironmental Science, University of Tsukuba, Tsukuba City, Japan 2Center for Social and Environmental Systems Research, National Institute for Environmental Studies, Tsukuba City, Japan 3Graduate School of Environmental Studies, Nagoya University, Nagoya City, Japan Correspondence: Kai Liu, Doctoral Program in Geoenvironmental Science, University of Tsukuba, 1-1-1 Tennodai, Tsukuba City, 305-8577 Ibaraki, Japan. Received: June 23, 2017 Accepted: July 20, 2017 Available online: September 1, 2017 doi:10.11114/ijsss.v5i9.2510 URL: https://doi.org/10.11114/ijsss.v5i9.2510 Abstract This study analyzed new residential property values of Xi’an City in March, 2014. Results show that accessibility indices, such as distance to CBD, have been well capitalized into the residential property values. Particularly, a within-zone housing unit is sold 9.4% more than if it was outside the attendance zone of a Key Primary School, i.e. home buyers have how much willingness-to-pay for the high-quality educational resource. Another corollary is got that the accessibility to subway stations has not significantly been capitalized, only with a low premium reflecting in the real estate market of Xi’an City. Considered that spatial local singularities caused by unobserved variables or estimation bias can be associated with multi-regression errors, this study herein has explored an unconventional viewpoint to residual problem, which combines the regional differences (coming from real world) and the spatial distributions of singularities (feedback from data). Furthermore, whole samples are classified into 5 agglomerations for revealing the underlying reasons about the future trend and variation of real estate market within each region. It is effective to provide scientific basis of decision making for the real estate investors and planners. Keywords: Hedonic price modeling, new residential property values, residuals 1. Introduction Residential property value is one of the most important indicators of urban economic development, and it concerns everybody in a city. Especially in recent years, residential problem in major Chinese cities has generated global interest among investors, policy makers, scholars and journalists (Wu, Deng, & Liu, 2014). In Chinese cities, variations of housing price are directly affected by macroeconomic and policy, apparently showing characteristic of spatial disproportion. Cities with location and resource superiority have a comparatively higher and more rapidly growing housing price, and this brings a bigger pressure on the housing market in the area near the quality public resource and local public goods such as Key Primary Schools (see Note 1), main stations, etc. (Hu, Zheng & Wang, 2014). Zheng and Kahn (2007) proved that subway stations, schools, green spaces and other public resources can be able to explain a quarter of the spatial differences about residential property values in Beijing. Chinese scholars also found that property values of residences inside a Key school's attendance zone had a higher and faster growth rate in Shanghai (Wang, Ge, & Zhang, 2010; Shi & Wang, 2014; Liu & Sun, 2015). In addition, transportation infrastructures, high schools, parks and other amenities have also been proved to be the important determinants of housing prices (Kim & Zhang, 2005; Zheng & Kahn, 2007). Certainly, extensive researches about the impact of public rail transit on housing price and land use pattern have been done in Beijing, Shanghai and various other cities, where the appreciation effect is observed and premiums caused by local public goods are quantitatively estimated (Wang, Zhu, & Zhang, 2004; Pan, Ren, & Yang, 2007). Wei, Wei, & Jiang (2014) exposed that development of urban rail transport has a marked impact on real estate industry. In short, properties bought and sold on real estate market are a kind of compound commodities, whose values are usually influenced by the following two key factors: commuter cost and education environment. It is because that these factors can contain the main part of implicit price used to embody property buyers' convenience will and willing-to-pay for these location accessibilities. Moreover, lower commuter cost and quality education environment are ===== PAGE 4 (score 18, numeric-paren 0, table-words 3, var-words 8) ===== International Journal of Social Science Studies Vol. 5, No. 9; 2017 45 a typical case for making quantitative analyses to estimate the capitalization effect of local public goods such as CBD, subway stations and Key Primary Schools. 2.2 Structure of the Hedonic Pricing Model Before using hedonic pricing model, the form for the hedonic price function must be chosen. Housing is not usually considered as a homogeneous commodity (McLeod, 1984). A house buyer purchases both a dwelling and a set of site characteristics. The price at which a residence is traded is depending on lots of factors: housing structure, location, neighborhood, and environmental characteristics. The household must find the dwelling with the best combination of features at the most apposite price (O’Sullivan, 2002). The implicit prices of spillover benefits (premium) from the factors can be inferred based on the hedonic hypothesis (Rosen, 1974). Consequently, the traditional hedonic pricing model takes the following form: 𝑃= 𝑓(𝐿,𝑆,𝑁) (1) where P is market price of the housing. Here we defined total price of a new residence as the dependent variable P. L, S, N denotes independent variables, which represents location characteristics, structure characteristics, and neighborhood characteristics, respectively (Ridker & Henning, 1967). In this study, 11 variables were chosen as hedonic price indices. Data with detailed descriptions and descriptive statistics, can be found in Table 1. Table 1. Selection of variables used to be added into the hedonic pricing mode and results of descriptive statistics* Dependent variable Unit Description Mean SD Min. Max. Expected sign** P 10,000RMB The total price of a new residence 92.25 109.92 17.70 1230.00 Independent variable DC km A measure of the ease of accessibility to CBD, i.e. straight-line distance to central business district 8.58 4.88 1.06 32.89 - DSX km A measure of the ease of accessibility to railway station, i.e. straight-line distance to Xi'an Station 8.75 4.73 1.30 30.58 - DS km A measure of the impact of the nearest subway station which is a straight-line distance from the residence 1.37 1.60 0.10 15.73 - DR km A measure of the integrated impact of the nearest river or lake from the residence to the boundary of the nearest river or lake 1.63 1.15 0.01 6.63 - S m2 Gross Floor Area 110.86 48.66 24.02 456.00 + BR individual Number of bedroom 2.47 0.79 0.00 5.00 + LR individual Number of living room 1.93 0.36 1.00 5.00 + WR individual Number of washroom 1.43 0.64 1.00 4.00 + HB Dummy variable Whether the residence is in a high-rise building above 12 floors or not 0.67 0.47 0.00 1.00 - SN Dummy variable Whether the residence is a south facing house or not 0.86 0.35 0.00 1.00 + E Dummy variable A measure of education environment. Ed=1, where d is the radius of buffer made by a Key Primary School when the residence is located into this area; or Ed=0, when the residence is located outside this buffer. 0.61 0.49 0.00 1.00 + * Data source from biggest Chinese homepage of real estate website named An Ju Ke. (https://xa.anjuke.com) ** + and - represent increasing and decreasing effects on the housing price, respectively. The hedonic pricing model employed in the evaluation of resources typically uses multiple regression techniques to relate property price details to diverse characteristics of differing properties, and sort out the different contributions. Many economists have stressed that economic theory does not suggest an appropriate functional form for hedonic price equations (Rosen, 1974; Freeman, 1979; Halvorsen & Pollakowaski 1981; Cassel & Mendelsohn 1985). Consequently, it is necessary to try reasonable functional forms to each variable and utilize a multiple regression equation (Cassel & Mendelsohn 1985). Halvorsen and Pollakowaski (1981) recommend the use of the Box-Cox flexible functional form in ===== PAGE 5 (score 7, numeric-paren 0, table-words 2, var-words 3) ===== International Journal of Social Science Studies Vol. 5, No. 9; 2017 46 hedonic analysis, which would measure best performance with goodness-of-fit. This form is commonly applied in the literatures using the hedonic pricing model (Shultz & King 2001, Kong et al., 2007). However, Cassel and Mendelsohn (1985) had pointed out a disadvantage of this methodology: that using a best-fit criterion to choose functional forms does not necessarily lead to more accurate estimates of characteristic prices. Maurer et al. (2004) thought that simplicity of the model and explanatory in economics are more important comparing to the accurate Box-Cox conversion. In general, this study just considers coefficient of determination (R2) as the indictor to judge whether the function form of hedonic pricing model has measured better performance with goodness-of-fit. Equation 1 is a very classical defined formula which is frequently referenced. However, as Rosen (1974) pointed out, there is no reason to expect the relationship between the price and factors to be liner. Another situation is that different factors based on different units and orders of magnitude. In most cases, non-liner is to be expected, because purchasers cannot treat individual housing attributes as discrete items from which they can pick and mix until the desired combination of characteristics ID is found (Morancho, 2003). Thus following previous studies (Harrison & Rubinfeld 1978; Can, 1992; Zheng & Kahn, 2013), this study employs a function form combining with logarithmic and semi-logarithmic form, which can be respectively defined as follows: 𝐿𝑛(𝑃) = 𝑎0 + ∑ 𝑎𝑖𝐿𝑛(𝑍𝑖) + 𝜀 𝑖 𝑛=1 (2) 𝐿𝑛(𝑃) = 𝑎0 + ∑ 𝑎𝑖𝑍𝑖+ 𝜀 𝑖 𝑛=1 (3) where Zi denotes explanatory variables, a0 denotes a constant, ai denotes regression coefficients, and ε is the residual error term. This study applies a form which is combined with Equation 2 &3 to deal with a variety of situations which happened correspondingly for the selected variables as the case may be. In other words, some variables must be regarded as dummy variables (0 or 1). This is because logical variables or category variables cannot make logarithmic transformation (Li, Silva, & Bo, 2011). This detail and regression process will be brought to light in the next Section. In this study, real estate transaction prices were collected for Mar. 2014 in Xi’an City. Based on the hedonic pricing model, this study attempts to estimate the capitalization effect of location characteristic such as CBD, subway stations and Key Primary Schools. At the same time, implicit prices (premium) for characteristics specific to the housing itself and neighborhood characteristics are also estimated. Figure 2. Study area ===== PAGE 8 (score 25, numeric-paren 0, table-words 7, var-words 6) ===== International Journal of Social Science Studies Vol. 5, No. 9; 2017 49 Table 2. Collinearity diagnostics Start End Variable Collinearity Statistics Variable Collinearity Statistics Tol VIF Tol VIF Ln_DC 0.212 4.720 Ln_DC 0.638 1.567 Ln_DSX 0.234 4.278 Ln_DS 0.697 1.434 Ln_DS 0.721 1.386 DR 0.951 1.052 DR 0.957 1.045 Ln_S 0.234 4.281 Ln_S 0.829 1.206 BR 0.311 3.215 LR 0.694 1.441 WR 0.422 2.367 HB 0.888 1.126 HB 0.894 1.118 SN 0.824 1.213 SN 0.846 1.182 E 0.822 1.217 E 0.853 1.172 Table 3. Judgment process of variable selection Variable selection in the model Coefficient of determination (R2) Remarks Every variable is added. 0.81 Start Every variable Except Ln_DC 0.77 Hold Ln_DC Every variable Except Ln_DSX 0.80 Drop Ln_DSX Hold Ln_S and remove BR,LR & WR 0.78 Hold Ln_S Hold BR and remove Ln_S, LR & WR 0.57 Drop BR Hold LR and remove Ln_S, BR & WR 0.38 Drop LR Hold WR and remove Ln_S, BR & LR 0.63 Drop WR and end 3.4 Focusing on a Key Primary School As Section 3.2 announced, there is a remaining problem about variable E. Owing to the value of dummy variable E is determined by the size of d-meters buffer drawn in GIS software, the radius d needs to be done some adjustments through changing the threshold value at several times, for the purpose of quantifying the capitalization of premium from a Key Primary School in the hedonic pricing model, also must meet the condition passing in T-test at statistically significance (Table 4). Finally when setting an 825-meters buffer, we can get the best regression result with statistical significance at 5% level. This study had tried 8 times and finally found a certain threshold value, 825 meters. Results prove that, within a scope of 825-meters, Key Primary Schools, as one of the most representative local public goods, have the strongest impact on new residential property values in Xi’an City. As noted in Sections 3.3 and 3.4, this study had selected 7 variables and simplified the model successfully. Table 4. Adjustment for the variable E E Coefficients t-Ratio Degree of confidence in T-text Passed or not E_1000 0.018 0.692 51.1% (<<95%, try to set d<1000) Resolutely not passed E_800 0.040 1.620 89.4% (become better, try to set d<800) Not passed E_600 0.020 -0.169 Regression failed Resolutely not passed E_700 0.027 1.079 71.9% (worse than d=800) Not passed E_750 0.025 1.024 69.4% (even worse than d=700, must set d>800) Not passed E_900 0.042 1.605 89.1% (become better, but worse than d=800, try to set 80095% (It means when d=825, variable E works best in hedonic pricing model) Passed T-test at the 5% level and can be added into the regression 4. Results of Hedonic Pricing Model Results of parameter estimates are presented in Table 5. The estimated coefficients generated using hedonic pricing model exhibits signs in accordance with expectations. They provide a clear indication that factors of housing area, CBD; floors; subway station; Key Primary School and south facing do exert a significant impact on new residential property values. Final regression equation denoting the whole results can also be created (Equation 4). ===== PAGE 9 (score 29, numeric-paren 1, table-words 8, var-words 9) ===== International Journal of Social Science Studies Vol. 5, No. 9; 2017 50 Table 5. Regression results after eliminating collinear variables, dependent variable: Ln (P), where P is total price Independent variables Regression parameters (R2 =0.782, adjusted R2 =0.779, F-value=267***, No. of Obs.=378) Coefficient t-Ratio P-value Constant 1.413 5.139 0.000 Ln_S*** 1.245 32.311 0.000 Ln_DC*** -0.268 -0.924 0.000 HB*** -0.142 -4.538 0.000 Ln_DS*** -0.061 -3.174 0.002 E** 0.090 2.097 0.037 SN* 0.044 1.690 0.092 *, ** and *** indicate statistical significance at 10%, 5% and 1% level, respectively 𝐿𝑛(𝑃) = 1.413 + 1.245𝐿𝑛(𝑆) −0.268𝐿𝑛(𝐷𝐶) −0.142𝐻𝐵−0.061𝐿𝑛(𝐷𝑆) + 0.90𝐸+ 0.044𝑆𝑁 (4) From the value of every coefficient, the calculation based on the regression equation can be completed, in order to quantify the estimation value of capitalization corresponding every variable, respectively. Premiums can be calculated according to series of processes of anti-logarithmic transformation. Main findings are summarized as follows: 1. P (total price in 10,000 RMB) increases by 1.245% along with S (Area in m2) increases by 1%. According to the average level of hosing prices got from the 378-samples (922,500 RMB), this is equivalent to about 11,500 RMB more expensive. 2. P decreases by about 0.268% along with DC (distance to CBD in km) becomes 1% farther, which is about 2500 RMB cheaper. Generally, between a residence and CBD there exist strong distance decay effects. 3. A residence at the floors which is above 12th (≧12) is 14.2% cheaper than one at a lower floor below 12th (<12). According to PCDI (per capita disposable income) of Xi’an in 2013 (see Note 6), two ratiocinations can be generalized that: 1) a high premium caused by the number of the floor; 2) home-buyers should pay more about 121,800 RMB to buy a low-rise residence, which is equivalent to nearly 3.7 times the amount of PCDI in Xi’an in 2013. 4. When distance to the nearest subway station (in km) becomes 1% farther, housing price will become 0.061% cheaper, correspondingly. It means that about 560 RMB cheaper at the average level. Comparing with other metropolis cities that have well-developed rail transportation, Xi’an is during a period of the initial stage (until 2014 at least) as a developing city because of a low-level premium (see Note 7). In contrast, Metropolis cities like Beijing, Shanghai or Guangzhou, there are much higher premium about the factor of rail transportation (Gu & Zheng, 2010). Li et al. (2011) found that inside CBD within 8km of Beijing, premiums caused by subway station is not significant and cannot be passed in regression processing, that is to say the factor of subway station failed to join the hedonic pricing model because the result of T-test is substandard. Only outside the area which is 8km far from the CBD, premiums on the housing price caused by subway station seemed to be statistically significant. This contradiction can be considered relating to the commuting cost. The metro rail transit is more inclined to give scope to its advantages about commuting cost in the suburban districts far from the CBD (Dong, Ding, & Zhao, 2009). Conversely, taking other modes of transportation like bus is cheaper and more efficient than taking subway rails for commuting activities happening around the CBD. 5. With regard to the premium from a Key Primary School, three arguments can be supported: 1) In the case that when setting an 825-meter buffer of a Key Primary School, the best regression results can be got with statistical significance at 5% level. For the future study, another approach named matching regression can be used to specifically investigate the so-called Xue Qu Fang problem (Hu et al., 2014); 2) a within-zone housing unit is sold 9.4% more than if it was outside the attendance zone of a Key Primary School; 3) At average, premiums are nearly 86,900 RMB from the factor, a Key Primary School, which is about 2.6 times the amount of 2013 year’s PCDI of Xi’an. It also indicates that educational resources have been well capitalized into the residential property value. 6. For the factor about the situation of North and South transparent, there is a slight premium, which is only 41,500 RMB. Moreover, the regression result is roughly statistically significance at only 10% level (strictly speaking it is normal at least 5% in statistics). This is because the vast majority of new residences are south facing, which can be clearly read from the raw data. Therefore, it seems that data set are lack of comparison samples (not N-S facing houses) when just discussing about new residential property values. 7. After T-text, all of these chosen variables in the hedonic pricing model yield good explanatory power and can also reflect the preferences of homeowners in Xi’an City. However, during the regression process, there is a meaningless variable, DR, which was dropped in the regression process. In general, housing price trends to become higher when the residence is closer to a river or lake according to the expectation. But the regression coefficient of DR got a positive number, which is out of expected results and the actual situation. Perhaps, this situation is related to the limitation of the ===== PAGE 10 (score 4, numeric-paren 0, table-words 1, var-words 2) ===== International Journal of Social Science Studies Vol. 5, No. 9; 2017 51 samples, or else unobserved variables or errors. Thence, this study has proved a mathematical corollary that omitted variables may result in regression failure and estimated bias. Besides, water system in Xi’an City is very complicated, which may cause geographical recognition errors, such as the Xi’an Moat surrounding the City Wall and the Weihe Reservoir. So nearest neighborhood analysis done by GIS may also cause accidental and systematic errors. Additionally, for these new residential properties which located in the undeveloped suburban areas in Xi’an, the impacts of water on housing price are relatively weak, even though they are near a river or lake with a very low price but a closed distance to some suburban rivers (see Note 8). Furthermore, real estate development is faster but development of urban infrastructure lags behind. So this factor failed to join and estimate the regression equation. All of these above situations could not be controlled; consequently, it is necessary to employ the approach of residual analysis, which will be brought to light in Chapter 5. 5. Residual Analysis According to the above work, firstly the reasons why residual analysis is necessary need to be discussed: 1. Variable DR failed to join the hedonic pricing model and was dropped by using stepwise regression method, caused by spatial local singularities or data limitations. 2. Unobserved variables are existent. Quantity of residual can reflect the effectiveness of regression fitting, as well as residuals are related to the existence of unobserved variables in a sense. 3. Positive or negative numbers of residuals indicate smaller or larger biased estimate of regression equation, respectively. 4. It provides a reference for future studies using residual analysis. Specifically, through the process of residual analysis, we can try to explain what places have more caused residuals and the reason in consideration of city layout of Xi’an. 5. According to the results running in SPSS software, we can probe the local singularity from a table of residuals. Distribution of residuals was approximately following the Normal distribution, and this indicated that the chosen variables in the hedonic pricing model yielded good explanatory power and residuals were under a reasonable situation. Herein, map of the location of residuals can be illustrated in Figure 4a. Moreover, sample cases with a high residual are picked out and visualized by deviation multiples (Predictive values / observed values), can used for reflecting and quantifying the local singularities (Figure 4b). Figure 4. Spatial distribution of regression residuals (left: a) and local singularities (right: b) On Figure 4a, we can find that most of residuals are located in the developing area between 2nd Ring Road and 3rd Ring Road, which have more real estate development and appreciation space. Even though these areas are about 4km-8km far from the CBD, more and more new residences have been built in recent years. In other words, in these places effects of unobserved variables on the housing price are more significant. So, the results of hedonic pricing model show a situation of smaller biased estimates. Eight of the local singularity points that have the highest residual is illustrated in Fig. 4b. They are located in three areas in Xi’an City. First area (A) in the southwest of the 2nd Ring Road, High-tech New Development Zone is located. It seems that homeowners in High-tech New Development Zone can