1# RECORD c63f29dcdec077b7ee126d8f2c6b0bcc6611e6a72# TITLE: Spatial heterogeneity in implicit housing prices: evidence from Hangzhou, China3# YEAR: 2017.0 VENUE: nan DOI: 10.3846/1648715x.2016.12470214# AUTHORS: Hai-Zhen Wen; Yilan Jin; Ling Zhang5# PAGES: 14 CANDIDATE TABLE PAGES (1-based): [7, 8, 9]6# ABSTRACT: Estimated coefficients in hedonic price models are generally assumed to be constant throughout the entire study area. However, increasing evidence reveals that the marginal prices of housing characteristics may vary over space and that the spatial heterogeneity problem in implicit housing prices should be given attention. Taking Hangzhou, China, as an example, this study uses the micro data of 603 residential communities in 2014 to examine spatial heterogeneity in implicit housing prices. On the basis of the traditional hedonic price model, we establish spatial expansion and geographically weighted regression (GWR) models for comparative analysis. Results show that the spatial expansion and GWR models have excellent goodness of fit and can improve the traditional hedonic price model. The mixed geographically weighted regression (MGWR) model further reveals that the implicit prices of nine housing characteristics vary significantly over space and that the impacts of the four remaining housing characteristics on housing prices are fixed throughout the entire study area. Unlike the traditional hedonic price model and spatial expansion model, the GWR/MGWR model has the unique advantage of visually providing the spatial distribution of implicit housing prices and accurately describing spatial heterogeneity.789===== PAGE 1 (score 3, numeric-paren 0, table-words 0, var-words 3) =====1011Copyright © 2017 Vilnius Gediminas Technical University (VGTU) Press12http://www.tandfonline.com/tspm13SPATIAL HETEROGENEITY IN IMPLICIT HOUSING PRICES: 14EVIDENCE FROM HANGZHOU, CHINA15Haizhen WEN a, Yilan JIN a, Ling ZHANG a,*16a Center for Real Estate Studying, Department of Civil Engineering, Zhejiang University, 310058 Hang-17zhou China18Received 13 May 2015; accepted 4 April 201619ABSTRACT. Estimated coefficients in hedonic price models are generally assumed to be constant 20throughout the entire study area. However, increasing evidence reveals that the marginal prices of 21housing characteristics may vary over space and that the spatial heterogeneity problem in implicit 22housing prices should be given attention. Taking Hangzhou, China, as an example, this study uses 23the micro data of 603 residential communities in 2014 to examine spatial heterogeneity in implicit 24housing prices. On the basis of the traditional hedonic price model, we establish spatial expansion 25and geographically weighted regression (GWR) models for comparative analysis. Results show that 26the spatial expansion and GWR models have excellent goodness of fit and can improve the traditional 27hedonic price model. The mixed geographically weighted regression (MGWR) model further reveals that 28the implicit prices of nine housing characteristics vary significantly over space and that the impacts 29of the four remaining housing characteristics on housing prices are fixed throughout the entire study 30area. Unlike the traditional hedonic price model and spatial expansion model, the GWR/MGWR model 31has the unique advantage of visually providing the spatial distribution of implicit housing prices and 32accurately describing spatial heterogeneity.33KEYWORDS: Housing price; Spatial heterogeneity; Hedonic price model; Geographically weighted 34regression351. INTRODUCTION36With the acceleration of China’s urbanization pro-37cess, the real estate market has developed rapidly 38across many cities. Along with the rapid develop-39ment in Chinese housing market is the evident 40spatial differentiation of housing prices in some 41big cities, a topic that has attracted the attention 42of many scholars (Xu 1997; Wang, Zhu 2004; Zhou, 43Luo 2004; Zhou, Zhen 2008; Ma et al. 2008). Hang-44zhou, well known for the West Lake, is an impor-45tant central city of the Yangtze River Delta in 46Eastern China. The property market in Hangzhou 47is characterized by high supply, high demand, and 48sustainably rising prices, thus giving birth to the 49“Hangzhou phenomenon”, which is widely recog-50nized by the academia and the real estate industry 51in China (Wen et al. 2014a). The residential mar-52ket in Hangzhou has been ebullient during the last 53two decades, such that the average housing price 54once recorded 25840 RMB/m2 in 2010 as the top 55one in China (Hui et al. 2016). The housing mar-56ket of Hangzhou is typical in China, thus, the city 57represents a perfect context for investigating the 58spatial variation of housing price, which is a key 59issue worthy of study.60Currently, the hedonic price model is the main 61research method used to quantify the determi-62nants of housing prices and to estimate the im-63pacts of such determinants on housing prices. In 64the hedonic price model, the ordinary least squares 65(OLS) method is adopted to estimate the implicit 66prices of housing characteristics (Wang, Huang 672007; Hao, Chen 2007; Wen et al. 2010). However, 68overlooking the spatial fixity property of housing, 69the traditional hedonic price model assumes that 70housing prices are mutually independent in the 71spatial distribution. Such assumption may lead to 72bias in the model estimation results. As housing 73prices represent a type of spatial data, the topics of 74spatial dependence and heterogeneity have caught 75the attention of many scholars (Anselin 1988, 76* Corresponding author. E-mail: zlcivil@163.com77International Journal of Strategic Property Management78ISSN 1648-715X / eISSN 1648-9179792017 Volume 21(1): 15–28 80doi:10.3846/1648715X.2016.1247021818283===== PAGE 7 (score 44, numeric-paren 10, table-words 10, var-words 14) =====8485Spatial heterogeneity in implicit housing prices: evidence from Hangzhou, China862187In the empirical estimation of the GWR/88MGWR model, a spatial weight matrix needs to 89be introduced. The spatial weight function can 90be determined in several ways, such as through 91the threshold distance, inverse distance, bi-square 92function and Gaussian function. The results of 93GWR are sensitive to the choice of bandwidth. 94Besides assuming a predefined and fixed band-95width, an adaptive bandwidth has been proven to 96be highly suitable in practice (McMillen, Redfearn 972010). Therefore, we chose a Gaussian function as 98an adaptive spatial kernel that allows the band-99width to vary based on the density of house sales 100around each regression point, thus encapsulating 101a smaller area where data are rich and a larger 102area where data are sparse. To obtain the optimal 103bandwidth, Fotheringham et al. (2002) proposed 104that the GWR model has the best bandwidth when 105the value of the corrected Akaike Information Cri-106terion (AICc) or the cross-validation (CV) is at the 107minimum.1084. RESULTS AND DISCUSSION1094.1. Traditional hedonic price model110As the traditional hedonic price model, Model 1 111is estimated by the OLS method. The regression 112results are shown in Table 2. The analysis of vari-113ance results of the model show that the significant 114probabilities for the F value are less than 0.001, 115which confirms the validity of the equation and 116rejects the original hypothesis of all coefficients 117being zero. The value of the adjusted R2 is 0.567, 118which means that the independent variables can 119explain 56.7% of the variation of the dependent 120variable. The values of the variance inflation fac-121tor of all variables are between 1.272 and 4.203, 122which shows that the degree of collinearity among 123the independent variables is not serious.124Model 1 is a global model in which the implicit 125prices are held unchanged throughout the study 126area. Nine housing characteristic variables signifi-127cantly affect the housing price. Except for traffic 128condition, the other coefficients exhibit signs that 129match the theoretical expectations. The implicit 130price of traffic condition is negative, probably be-131cause private car ownership has grown rapidly 132during the rapid economic development period in 133Hangzhou and has thus reduced the dependence 134on public transport such as buses. The presence of 135buses around the residential area inevitably brings 136about some negative effects, such as traffic conges-137tion, exhaust pollution, and noise pollution. Hence, 138bus lines are likely to have a negative effect on 139housing price. The results are substantially con-140sistent with the findings of Wu et al. (2008) and 141Wen et al. (2014b), Wen and Tao (2015).142The regression coefficient of the nearby sub-143way variable does not pass the significance level 144of 10%, which indicates that the subway has no 145significant influence on housing price in the tradi-146tional hedonic price model. However, from a theo-147retical point of view, subways should have a signif-148icant impact at least on the surrounding housing 149prices. As the traditional hedonic price model can 150estimate only the average implicit price, the re-151gression coefficient of the nearby subway variable 152ultimately fails to reach the 10% significance level. 153Similarly, the building age variable in the tradi-154tional hedonic price model is not significant. Fur-155thermore, the statistics of Moran’s I for the spatial 156autocorrelation test is 0.387, and the significance 157level is below 0.001. These results show the obvi-158ous spatial effect of housing price on the regional 159distribution in Hangzhou, indicating that OLS pa-160rameter estimates are inefficient and t-ratios are 161biased (Dubin 2003). Therefore, We use the spatial 162extension and GWR models for further analysis.1634.2. Spatial expansion model164With the interaction terms between the 13 vari-165ables and the coordinates of the sample points, two 166spatial expansion models are estimated by OLS. 167Table 2. Regression results of the traditional hedonic 168price model169Variables170Coefficients171t172Constant17310.188***174117.612175ln(building age)176−0.011177−0.734178Inner environment1790.0131801.221181External environment1820.0081830.809184Property management1850.042***1865.328187Sports facility1880.031***1893.925190Nearby university1910.046***1922.979193Living facility1940.018**1952.208196Education facility1970.033***1983.390199Nearby subway2000.0202011.162202Traffic condition203−0.002***204−3.023205ln(distance to Wulin Square)206−0.067***207−3.429208ln(distance to the West Lake)209−0.221***210−12.694211ln(distance to the Qianjiang 212New Center)213−0.059***214−4.018215AICc216−468.846217Adjusted R22180.567219Note: ***,**, and * represent significance at the 1%, 5%, and 22010% levels, respectively.221222223===== PAGE 8 (score 74, numeric-paren 47, table-words 10, var-words 7) =====224225H. Wen et al.22622227The values of the variance inflation factor of all 228variables are less than 10, which show that the se-229rious collinearity is not present in the two expan-230sion models. We report only the coefficients that 231are at least significant at the 10% level.232The results for Model 2, the one-degree spatial 233expansion, are shown in the second and third col-234umns. The adjusted R2 is 0.671, which indicates 235that Model 2 can more effectively explain the vari-236ations of the dependent variable and demonstrate 237a more favorable goodness of fit compared with 238Model 1. Ten ‘‘base’’ housing characteristic vari-239ables have significant effects on housing prices, 240and five of these variables interact with location 241coordinates. Ten location–characteristic interac-242tion terms are significant at the 10% level, which 243indicates that spatial heterogeneity exists in the 244marginal prices of these housing characteristics. 245For example, the regression coefficients of Living 246facility is 0.032 which indicate that, in general, the 247value of Living facility increases by 1 unit and the 248housing prices will increase by 3.2%. The inter-249action term of U(living facility) is −0.007, which 250reveal that spatial heterogeneity exists in the hori-251zontal direction, and for the same quality of living 252facility, an additional 1 km from the Wulin Square 253(measured horizontally) will reduce an average 254community housing price by 0.7%.255Five variables, namely, building age, inner envi-256ronment, external environment, property manage-257ment, and sports facility, have significant effects 258on housing prices, but their interaction terms are 259not significant. This condition indicates that the 260marginal prices of these variables do not vary in 261the locational context. Furthermore, two variables, 262namely, nearby university and nearby subway, are 263not significant. However, their interaction terms 264are significant at the 10% and 5% significance lev-265els, respectively, indicating that the interaction 266terms still have space differences to some extent.267Table 3 also reports the results of Model 3, the 268quadratic spatial expansion model. The addition 269of the quadratic interaction terms in Model 3 re-270sults in an improvement in the explanatory power 271as the adjusted R2 increases from 0.671 to 0.704. 272A total of 15 out of the 65 interaction variables 273are significantly different from 0 at the 10% sig-274nificance level. The one-degree interaction terms 275of four variables and the quadratic interaction 276terms of seven variables have significant effects 277on the housing prices. This result provides strong 278evidence of implicit prices with complicated spatial 279distribution patterns.280Table 3. Regression results of spatial expansion models281Variables282One-degree term 283model284Quadratic term 285model286Coeffi-287cients288t289Coeffi-290cients291t292Constant29310.698 ***29491.87129510.699 *** 67.515296ln(building age)297−0.061 *** −3.765 −0.079 *** −3.247298Inner 299environment3000.022 *3011.6493020.029 ***3031.729304U(inner 305environment)3060.008 *3071.803308External 309environment3100.022 *3111.6533120.050 ***3132.616314U(external 315environment)316−0.015 **317−2.526318Property 319management3200.036 ***3213.4903220.033 **3232.267324V2(property 325management)326−0.001 *327−1.718328Sports facility3290.032 ***3304.0343310.055 ***3324.131333V2(sports 334facility)335−0.001 *336−1.877337V(nearby 338university)3390.007 *3401.792341Living facility3420.032 ***3433.043344U(living facility)345−0.007 **346−2.445 −0.010 **347−1.984348Education 349facility3500.050 **3512.461352U2(education 353facility)354−0.003 **355−2.471356Nearby subway357−0.209 *** −3.208358U(nearby 359subway)3600.053 ***3612.587362V(nearby 363subway)3640.018 **3652.3873660.081 ***3673.232368UV(nearby 369subway)370−0.013 **371−2.493372Traffic condition373−0.005 *** −3.585 −0.004 **374−2.037375U(traffic 376condition)3770.001 *3781.818379V(traffic 380condition)3810.001 ***3823.6823830.001 *3841.952385ln(distance 386to the Wulin 387Square)388−0.087 *3891.786390−0.168 **391−2.149392Uln(distance to 393Wulin Square)3940.033 **3952.2123960.128 ***3973.099398Vln(distance to 399Wulin Square)4000.019 *4011.898402U2ln(distance to 403Wulin Square)404−0.021 **405−2.547406ln(distance to 407the West Lake)408−0.269 *** −7.596 −0.336 *** −6.557409Vln(distance to 410the West Lake)411−0.022 **412−2.413413V2ln(distance to 414the West Lake)415−0.008 *416−1.648417ln(distance to 418the Qianjiang 419New Center)420−0.185 *** −4.028 −0.237 *** −3.061421Uln(Distance to 422the Qianjiang 423New Center)424−0.015 *425−1.716 −0.076 **426−2.505427U2ln(distance to 428the Qianjiang 429New Center)4300.017 ***4313.134432AICc433−605.089434−657.128435Adjusted R24360.6714370.704438Note: ***,**, and * represent significance at the 1%, 5%, and 43910% levels, respectively.440441442===== PAGE 9 (score 39, numeric-paren 14, table-words 8, var-words 9) =====443444Spatial heterogeneity in implicit housing prices: evidence from Hangzhou, China44523446The results of the two spatial expansion mod-447els confirm that spatial heterogeneity exists in the 448implicit prices of the housing characteristics of the 449Hangzhou market. For example, the variables of 450inner environment, external environment, nearby 451subway, and building age are insignificant in the 452traditional hedonic price model, but their interac-453tion terms are significant in Models 2 and 3. This 454result indicates the influence of the four variables 455on housing price and their tendency to still change 456over space. No significant residual dependence on a 4570.01 level is detected by the Moran’s I, which indi-458cates spatial expansion models can capture the spa-459tial effect and be used to improving the misspecifi-460cation problem, which lead to inefficient parameter 461estimations in the traditional hedonic price model.4624.3. Geographically weighted regression 463model464With a Gaussian kernel, CV determines an opti-465mal adaptive bandwidth that includes 182 obser-466vations. Sensitivity analysis with alternative ker-467nels (i.e. bi-square kernel) shows no significant dif-468ferences. The values of VIF of all variables are less 469than 5, which do not suggest a problem of collin-470earity among the independent variables. Table 4 471shows the regression results of Model 4 (GWR). 472The adjusted R2 is 0.757, which is significantly 473better than that in the traditional hedonic price 474model and the two spatial expansion models. This 475improvement reflects that the GWR model can ef-476fectively explain the relationship between housing 477prices and the explanatory variables and provide 478strong evidence that spatial heterogeneity plays 479an important role in the Hangzhou housing mar-480ket. The GWR parameter estimates, which vary 481at each observation point, are described by their 482minimum, median, and maximum values, as well 483as by their interquartile range.484For example, the lower quartile of the regres-485sion coefficients of the distance to the West Lake 486is −0.421 and the upper quartile is −0.171. These 487values indicate that in a certain space location, the 488distance to the West Lake increases by 1% and the 489housing prices decline by 0.421%. Meanwhile, in 490another space location, the distance to the West 491Lake increases by 1% while the housing prices 492decline by 0.171%. The magnitude of change is 4930.25%. One advantage of GWR is that the spatial 494patterns of the parameter estimates can be eas-495ily mapped and visualized. Figure 1 reveals the 496spatial effect of the distance to the West Lake on 497housing price. Almost all samples reach the signifi-498cance level of 1% by P value. Hence, the distance 499to the West Lake has an important influence on 500the housing prices throughout the entire study 501area. As expected, the estimates are negative and 502exhibit localized spatial patterns. The highest es-503timates are found within North Hangzhou, where 504the housing prices are relatively lower than that 505in other areas, resulting in the rapid decrease 506of the price gradient of the distance to the West 507Lake. The estimates are the smallest and exhibit 508Table 4. Results of GWR model509Variables510Min511Lwr Quartile512Median513Upr Quartile514Max515Constant5165.3735179.80451810.520***51910.84852012.687521ln(building age)522−0.180523−0.107524−0.061**525−0.0245260.006527Inner environment528−0.0345290.0295300.043**5310.0665320.097533External environment534−0.042535−0.0055360.015*5370.0285380.103539Property management540−0.0155410.0065420.016***5430.0265440.051545Sports facility546−0.0195470.0155480.028***5490.0435500.076551Nearby university552−0.104553−0.0155540.015***5550.0505560.210557Living facility558−0.087559−0.0175600.012***5610.0475620.092563Education facility564−0.068565−0.0155660.010***5670.0475680.155569Nearby subway570−0.170571−0.0045720.021**5730.0485740.164575Traffic condition576−0.009577−0.004578−0.002***5790.0005800.005581ln(distance to Wulin Square)582−1.295583−0.151584−0.034***5850.1245861.159587ln(distance to the West Lake)588−1.224589−0.421590−0.280***591−0.1715920.083593ln(distance to the Qianjiang New Center)594−1.317595−0.272596−0.131***5970.0825982.775599AICc600−714.328601Adjusted R26020.757603Note: ***,**, and * represent significance at the 1%, 5%, and 10% levels, respectively.604605606===== PAGE 10 (score 26, numeric-paren 0, table-words 9, var-words 8) =====607608H. Wen et al.60924610relatively smooth spatial trends within Central 611Hangzhou (the eastern region of the West Lake), 612which belongs to the traditional downtown area 613with convenient public facilities. The housing pric-614es in this area are relatively high. In other words, 615the GWR model shows that the implicit prices of 61613 housing characteristics are not entirely fixed in 617space but exist with spatial heterogeneity. These 618results verify that the global/average estimation by 619the traditional hedonic price model may be flawed.620Model 5 is the MGWR. Compared with the 621GWR model, the MGWR model divides independ-622ent variables into two types: global variables with 623fixed estimated coefficients (see Table 5) and lo-624cal variables that change over space (see Table 6). 625Following the test statistic of Leung et al. (2000a), 626we find that four independent variables in the 627study are global variables while the remaining 628nine variables are local variables. Again, applying 629a Gaussian kernel function, CV results in an opti-630Fig. 1. P value and regression coefficients for the distance to the West Lake variable631Table 5. Regression results for global variables632Variables633Coefficients634t value635Critical value 636(10%)637Critical value (5%)638Inner environment6390.0486404.1766411.6486421.965643Nearby university6440.0406452.635646Sports facility6470.0216483.246649Property management6500.0126511.722652Table 6. Regression results for local variables653Variables654Min655Lwr Quartile656Median657Upr Quartile658Max659Constant6603.4016619.88766210.35466310.87966413.094665ln(building age)666−0.214667−0.113668−0.079669−0.0306700.033671External environment672−0.055673−0.0066740.0156750.0316760.109677Living facility678−0.107679−0.0166800.0116810.0516820.105683Education facility684−0.094685−0.0156860.0256870.0456880.194689Nearby subway690−0.205691−0.0136920.0076930.0426940.254695Traffic condition696−0.011697−0.004698−0.0026990.0007000.005701ln(distance to Wulin Square)702−1.739703−0.160704−0.0037050.1207061.515707ln(distance to the West Lake)708−1.328709−0.403710−0.307711−0.1427120.142713ln(distance to Qianjiang New Center)714−1.594715−0.279716−0.0697170.0727183.862719AICc720−756.902721Adjusted R27220.766723