1# RECORD 3bbf88ea5271189e3329337f57932674d7aa341e2# TITLE: The Spatial Dimension of House Prices3# YEAR: 2017.0 VENUE: Architecture and the Built Environment DOI: 10.59490/abe.2017.4.17474# AUTHORS: Yun-Long Gong5# PAGES: 206 CANDIDATE TABLE PAGES (1-based): [54, 55, 56, 76, 80, 81, 83, 90, 106, 108, 118, 130, 132, 134, 135, 139, 140, 148, 168, 169]6# ABSTRACT: The economic reform in China, launched in the late 1970s, gradually promotes the free mobility of capital and labour between rural and urban areas, and between cities. The following housing market reform in the late 1990s thoroughly terminates the socialist allocation of housing and introduces market forces into the housing sector. Such institutional shifts have profound effects on the evolution of the Chinese interurban housing market. Yet, little is known about the spatial behaviour of house prices across cities in the post-reform era. How do the housing markets of different cities organise across space? What is the relationship between the house price dynamics of different cities? To answer these questions, this research performs economic and econometric analysis of the spatial dimension of the Chinese interurban housing market. In addition, this research also concerns the construction of a reliable house price index in the presence of spatial heterogeneity and dependence in the urban housing market of China. A reliable house price index is essential to the analysis of house price dynamic behaviour. However, owing to the data problem, this part is conducted based on the housing market of a Dutch city.7This research discovers the spatial regularities of house prices across Chinese prefecture cities in an economic common area and investigates the underlying formation process. It reveals an uneven distribution of house prices across cities, with those large and/or higher-tier cities and their neighbours having significantly higher house prices. Such an uneven pattern of house prices demonstrates the agglomeration spillovers in the interurban housing market. Two forms of spillovers are empirically examined. The first is the urban hierarchy distance effect, which is related to the position of a city in a hierarchical urban system. In general, the distance penalty of higher-tier urban centres is confirmed, that is, all else being equal, the further away a city is from the higher-tier city, the lower the house price. The second form of spillovers relates to a city’s position in a city network system, in which no hierarchical structure is imposed. In such a situation, the spillovers arise from the interaction with neighbouring cities and it is found that a city that has larger neighbours tends to have higher house prices. These two forms of spillovers are somewhat correlated with each other because a higher-tier city is always associated with a larger urban size.8It i91011===== PAGE 1 (score 0, numeric-paren 0, table-words 0, var-words 0) =====1213The Spatial Dimension of 14House Prices15Yunlong Gong1604172017181920===== PAGE 54 (score 57, numeric-paren 30, table-words 10, var-words 0) =====2122TABLE 2.223Estimation of central-city house price gradient24Linear/Dist25Linear/Time26Semi-log/Dist27Semi-log/Time28Log-log/Dist29Log-log/Time30House price31House price32Ln(House price)33Ln(House price)34Ln(House price)35Ln(House price)36Constant376699.1337***38(9.66)396636.7919***40(8.25)418.7021***42(82.59)438.7009***44(73.12)459.0524***46(45.59)479.0272***48(48.71)49Distance to central city50-3.672051(-1.24)52–53-0.0011***54(-2.84)55–56–57–58Ln(Distance to central city)59–60–61–62–63-0.1198**64(-2.58)65–66Travel time to central city67–68-3.531369(-0.89)70–71-0.0012**72(-2.27)73–74–75Ln(Travel time to central city)76–77–78–79–80–81-0.1156***82(-2.62)83Dummy: Jiangsu84-2893.4657***85(-2.79)86-3018.9746***87(-3.04)88-0.4331***89(-3.08)90-0.4702***91(-3.40)92-0.4260***93(-2.93)94-0.4428***95(-3.10)96Dummy: Anhui97-3670.9179***98(-2.75)99-3917.2915***100(-3.04)101-0.6136***102(-3.56)103-0.6767***104(-4.03)105-0.7090***106(-4.73)107-0.7308***108(-5.04)109Time effect110Yes111Yes112Yes113Yes114Yes115Yes116F-stats11730.2711829.5111969.1712064.7312163.2212261.92123R21240.5121250.5061260.7061270.6921280.6871290.682130Adj.R21310.4921320.4861330.6791340.6651350.6601360.656137AIC1383832.4901393835.20014076.9014186.6414290.0414393.03144Sample size145210146210147210148210149210150210151Notes: ** and *** denote significance at the 5% and 1% level, respectively. The t values shown in parentheses are calculated based on clustered standard152errors that are robust to serial correlation of the same unit and heteroskedasticity over time.15334154The Spatial Dimension of House Prices155156157===== PAGE 55 (score 53, numeric-paren 24, table-words 11, var-words 2) =====158159The results shown in Table 2.3 reveal that both central and subcentral cities have160significantly negative distance effects on house prices when using the semi-log/log-log161form and log-log/semi-log functional form. Those results also show that the162semi-log/log-log form is the best one in terms of adjusted R2 and AIC criteria.163However, the distance penalties are no longer significant, even at 10% significance164level, for the central city in the log-log/log-log model or for the subcentral city in the165semi-log/semi-log model. Thus, it is certainly correct to infer that the log-log function166is more appropriate than the semi-log function for subcentral cities. It should be kept167in mind that the central city always has a macro-effect that influences a larger radius168while the subcentral city only has a local micro-effect. In that light, it seems that the169choice of functional form is sensitive to the influence sphere of the centre. The log-log170function performs beɦer when the area of influence is relatively small, while the171semi-log function is more appropriate if the area is larger. These findings are in line172with those of Osland et al. (2007), who found that the exponential (semi-log) function173performs best when the estimation is based on a large area, while the power (log-log)174function performs best if the data is restricted to a small area.175TABLE 2.3176Distance effects of both central and subcentral cities177Semi-log/178Semi-log179Semi-log/180Log-log181Log-log/182Semi-log183Log-log/184Log-log185Ln(House186price)187Ln(House188price)189Ln(House190price)191Ln(House192price)193Constant1948.7260***195(80.38)1968.9212***197(115.18)1988.9805***199(59.59)2009.0699***201(43.06)202Distance to central203city204-0.0008***205(-1.98)206-0.0008***207(-2.03)208–209–210Ln(Distance to211central city)212–213–214-0.0779**215(-2.06)216-0.0607217(-1.27)218Distance to219subcentral city220-0.0006221(-0.93)222–223-0.0010*224(-1.69)225–226Ln(Distance to227subcentral city)228–229-0.0701***230(-4.60)231–232-0.0746***233(-4.66)234Dummy: Jiangsu235-0.4339***236(-3.06)237-0.4142***238(-2.99)239-0.4269***240(-2.89)241-0.4196***242(-2.96)243Dummy: Anhui244-0.6733***245(-4.01)246-0.6530***247(-3.84)248-0.7598***249(-5.24)250-0.7454***251(-5.18)252Time effects253Yes254Yes255Yes256Yes257F-Stats25861.7825972.3226060.0326165.76262Adj.R22630.6802640.7102650.6752660.693267AIC26875.10226951.0627079.3827165.70272Sample size273210274210275210276210277Notes: *, ** and *** denote significance at the 10%, 5% and 1% level,respectively. The t278values shown in parentheses are calculated based on clustered standard errors that are279robust to serial correlation of the same unit and heteroskedasticity over time.280Unlike the semi-log model that only includes the effect of the central city, adding the28135282Interurban house price gradient: Effect of urban hierarchy distance on house prices283284285===== PAGE 56 (score 71, numeric-paren 42, table-words 9, var-words 4) =====286287effects of subcentral cities raises the adjusted R2 from 0.679 to 0.710. Their added288effects explain 3% more variance in interurban house prices and decrease the289magnitude of the distance penalties of the central city by about 27%. Since we use290different functional forms for central and subcentral cities, we cannot compare the291magnitudes of their distance penalties directly.292TABLE 2.4293House price and wage gradient after controlling for city amenities and294characteristics295House price model296Wage model297Regional298dummies299Amenities300+ Regional301dummies302Amenities +303Location variables304Amenities +305Location variables306Ln(House price)307Ln(House price)308Ln(House price)309Ln(Wage)310Constant3118.4666***312(77.39)3137.6520***314(17.77)3158.0267***316(22.26)31711.0058***318(45.97)319Dummy: Jiangsu320-0.4895***321(-3.46)3220.0946***323(0.66)324–325–326Dummy: Anhui327-0.8410***328(-6.90)329-0.1816330(-1.34)331–332–333Coastal city334–3350.3230**336(2.32)3370.3523***338(3.98)3390.0227340(0.45)341Winter temperature342–3430.0791**344(2.58)3450.0627*346(1.72)347-0.0086348(-0.40)349Smoke and dust350emissions351–352-0.0008353(-1.56)354-0.0013***355(-2.73)3560.0004357(0.60)358Doctor359–3600.0010**361(2.58)3620.0008***363(2.72)3640.0004*365(1.79)366Student/teacher ratio –367-0.0050368(-0.38)369-0.0022370(-0.15)371-0.0354***372(-3.46)373Arable land374–375-0.0003*376(-1.83)377-0.0003378(-1.33)379-0.0004**380(-2.38)381Distance to central city–382–383-0.0008***384(-2.80)385-0.0003*386(-1.67)387Ln(Distance to388subcentral city)389–390–391-0.0329*392(-1.72)393-0.0131394(-1.20)395Time effects396Yes397Yes398Yes399Yes400F-Stats40161.0440285.5840389.4740463.22405Adj.R24060.6224070.7884080.7944090.746410Sample size411210412207413207414207415Notes: *, ** and *** denote significance at the 10%, 5% and 1% level,respectively. The t416values shown in parentheses are calculated based on clustered standard errors that are robust417to serial correlation of the same unit and heteroskedasticity over time.418§ 2.5.3419House price gradient after controlling for city amenities and characteristics420.............................................................................................................................42136422The Spatial Dimension of House Prices423424425===== PAGE 57 (score 10, numeric-paren 0, table-words 3, var-words 4) =====426427As suggested by the theoretical model, the negative house price gradient with respect428to higher-tier cities should persist after controlling for city amenities and429characteristics. Before estimating this, we first investigate the compensating house430price differentials for urban amenities and characteristics. As noted earlier, the average431house prices in Zhejiang, Jiangsu and Anhui provinces differ significantly from each432other. This observation is further supported by the estimation results of column 1 in433Table 2.4, which only contains two regional dummy variables. We assume that the434observed house price differentials across provinces are actually proxies for the435differences in amenities. The result of testing this hypothesis is shown in column 2 of436Table 2.4. After including the variables of city amenities and characteristics, the437regional effects of Jiangsu and Anhui province fall dramatically and are no longer438significant, which offers some support for our hypothesis.439The six variables of city amenities and characteristics, together with the two regional440dummy variables, account for nearly 80% of the house price variance. As a group, the441amenity and characteristic variables are statistically highly significant at the 1%442significance level (the joint F-statistic is 39.98 where the 1% critical value is 2.90), and443each has the anticipated sign. Among these variables, winter temperature, bordering444an ocean and number of doctors have significantly positive effects, while arable land445per capita has a negative effect at a significance level of 10% or beɦer. The unpleasant446effect of smoke and dust emissions is marginally insignificant.447The third column of Table 2.4 reports the estimation results of the model with both448amenity variables and two distance measures. The two distance variables in which we449are most interested still have significantly negative effects: distance to the central city450is significant at the 1% level, while distance to the subcentral city at the 10% level.451Compared to the semi-log / log-log model that only includes two distance variables452and two regional dummies, the magnitude of the central-city house price gradient in453this model does not change, but the distance penalties of the subcentral city decrease454by about 50%. The point estimates of city amenities and characters are quite robust as455they do not differ much from the results in column 2. Perhaps the most obvious change456is that the negative effect of particulate maɦer becomes highly significant.457.............................................................................................................................458§ 2.6459Decomposition of interurban house price gradient460.............................................................................................................................461The previous section has provided estimates of the impact of urban hierarchy distances462on house prices. According to the theoretical model, the decline in the interurban463house price gradient could be aɦributed either to productivity disadvantages or464amenity disadvantages. This section will empirically decompose the interurban house465price gradient based on Equation (7) and reveal which component contributes more to466the negative price effects of remoteness from higher-tier cities.46737468Interurban house price gradient: Effect of urban hierarchy distance on house prices469470471===== PAGE 76 (score 107, numeric-paren 71, table-words 11, var-words 5) =====472473TABLE 3.2474Estimates of nonspatial model and SLX model475Dependent variable = Ln(House prices)476Pooled model477OLS478RE479ML480SLX_G(RE)481ML482(W = W0-160483G484)485SLX_T(RE)486ML487(W = W0-150488T489)490Winter temperature4910.0617***492(5.14)4930.0262***494(2.74)4950.0258***496(2.75)4970.0260***498(2.77)499Ln(Smoke and dust500emission)501-0.1231***502(-5.24)503-0.1396***504(-4.37)505-0.1297***506(-4.12)507-0.1325***508(-4.22)509Ln(Student/Teacher510ratio)511-0.4662***512(-3.82)513-1.3482***514(-7.24)515-1.1673***516(-6.21)517-1.1815***518(-6.39)519Doctor5200.0358***521(6.01)5220.0253***523(2.69)5240.0268***525(2.93)5260.0243***527(2.66)528Coast5290.2537***530(4.78)5310.3009**532(2.54)5330.2230*534(1.93)5350.2104*536(1.78)537Ln(Arable land)538-0.0082539(-0.11)540-0.0160541(-0.13)542-0.0497543(-0.40)544-0.0856545(-0.71)546Ln(Population density)5470.1561***548(5.29)5490.1712***550(2.91)5510.1181*552(1.87)5530.1006*554(1.63)555Ln(Land)5560.1721***557(4.93)5580.1817**559(2.55)5600.1897***561(2.72)5620.1630**563(2.36)564W × Ln(Population565density)5660.2719***567(3.04)5680.2795***569(3.17)570W × Ln(Land)5710.2590**572(2.00)5730.1691574(1.35)575Constant5766.4704***577(8.23)5789.2550***579(6.48)5805.3201**581(2.38)5826.6990***583(3.21)584R-Squared5850.8235860.9235870.9255880.925589Corr-Squared5900.7645910.7855920.787593Log-likelihood59424.54459559.04359663.84959763.973598CD test59919.551***6007.6129***6017.955***6028.051***603Sample size604210605210606210607210608Notes: Corr-Squared is the squared correlation between fiɦed and actual value. t-values are609reported in the parentheses. W0-160610G611and W0-150612T613denote the spatial interaction structure614between a city and its neighbouring cities within the distance band 0 – 160 km and within615the travel time band 0 – 150 min, respectively. The CD test, which detects the global cross-616sectional dependence of residuals, tends to standard normal distribution under the null617hypothesis. ***, ** and * indicate a 1%, 5%, 10% significance level, respectively.61856619The Spatial Dimension of House Prices620621622===== PAGE 77 (score 9, numeric-paren 1, table-words 0, var-words 8) =====623624capita which implies no significant influence of land supply constraint. After controlling625for random city-specific effects, the results in the second column do not show any626noticeable changes compared to the results of pooled model. In general, a warmer627winter, less industrial smoke and dust emission, a beɦer education and healthcare628condition, and bordering to an ocean increases the house price of a city. Note that the629estimated effect of education quality in the random effect model is much higher than630that in the pooled model, while the influence of winter temperature is weakened631drastically. As expected, the two variables measuring urban size have statistically and632economically significant effects on house prices in both models. Interestingly, an633increase in urban density has almost the same effect as an expansion in urban scale. A6341 percent increase of urban population of a city will drive up house prices by around6350.17%. The fixed effects estimation, including only the time-variant variables, also636confirms the importance of climate, education quality and urban population density in637determining the house prices.638Overall, the explanatory variables we have chosen perform satisfactorily as indicated by639a relatively high Corr-Squared statistic (0.764) which represents the squared640correlation between actual and fiɦed value. However, the CD test (Pesaran 2004)641detects significant global cross-section dependence in residuals, suggesting the642existence of cross-city spillovers7.643§ 3.6.2644Results of spatial models645.............................................................................................................................646Estimation of SLX model647The spatial weights matrix W is vital to measuring the city network spillovers as W648carries the underlying spatial interaction structure. In this paper, we expect that the649network externalities are only noticeable within a certain radius; at some farther650distance between the two cities, network spillovers vanish.651Such spatial interaction structure can be captured by different weight matrixes. Based652on geographical distance, we first divide the cities surrounding city i into three distance653bands, namely 0 – 160 km, 160 – 320 km and 320 – 480 km. A spatial weight matrix654for each distance band is then constructed. For instance, for a city j within distance655band 0 – 160 km, the spatial weight wij of W0-160656G657is defined as658wij,i̸=j = d−2659ij ,660for6610 ≤dij < 160.662(7)663Geographical distance has some intrinsic pitfalls; it does not take into account the664physical obstacles, such as mountains and bays. So we have also constructed spatial6657666The CD test is constructed based on the average of pair-wise correlations of the residuals of each cross-sectional667unit. As N →∞, this test tends standard normal distribution under the null hypothesis of no cross-sectional668correlation.66957670Network externalities in Chinese housing markets: A spatial econometric approach671672673===== PAGE 80 (score 21, numeric-paren 6, table-words 5, var-words 5) =====674675error correlation in the SLX_G model based on different spatial weight matrixes.676Assuming the remaining dependence structure is still confined to the neighbours in677physical distance space, the SDM model is a beɦer choice and the results will be678discussed laɦer. On the other hand, if a city is assumed to interact with the cities that679are nearby on the economic-geographical space, the LM tests are in favor of the SDEM680specification.681TABLE 3.4682LM tests on residuals of SLX model683Residuals of SLX_G model estimated in Table 3.2684LM spatial lag685Robust LM spatial686lag687LM spatial error688Robust LM spatial689error690W0-160691G69257.784*69359.056*69418.162*6959.434*696W0-1.5697EG6980.0916991.76070017.504*70119.173*702Notes: For the definition of matrix W0-160703G704, see notes of Table 3.2. W0-1.5705EG706has the similar707definition but are constructed based on economic-geographic distance. The LM and robust708LM tests, developed by Anselin et al. (2008) and Elhorst (2010b) for the spatial panel data,709are based on the residuals of SLX_G model estimated in Table 3.2 and follow the χ2(1)710distribution under null hypothesis. * denotes the 1% significance level.711The SDEM model is estimated by a ML procedure suggested by Elhorst (2014); the712results are reported in second column of Table 3.510. For the sake of comparison, the713first column replicates the estimates of SLX_G model. Based on the714economic-geographical distance matrix, we find a highly significant spatial715autoregressive process in residuals of the SLX_G model. After controlling for the spatial716error correlation, the influence of population density on its own house prices becomes717highly significant at 1% significance level. The point estimates of population density718and land area as well as their spillovers effects are almost in line with the estimates of719SLX_G model, showing the robustness of SLX_G model in measuring the720agglomeration spillovers. In contrast, the estimates for the local-specific721characteristics show a noticeable discrepancy between the two models. For example,722smoke and dust emission and the ratio of students to teacher no longer significantly723affect the house prices, whereas land supply constraint becomes an important house724price determinant in SDEM model. This discrepancy might be due to the fact that the725spatial paɦern of some local-specific variables is closely related to the spatial paɦern of726the residuals of SLX_G model.727Estimation of SDM and SAR model728As previously discussed, if the spatial interaction of house prices after controlling for72910730The following random effects SDM and SAR model are also estimated by ML procedure. The matlab routine can731be found at hɦp://www.regroningen.nl/elhorst/.73260733The Spatial Dimension of House Prices734735736===== PAGE 81 (score 111, numeric-paren 71, table-words 13, var-words 4) =====737738TABLE 3.5739Estimates of SDEM, SDM and SAR models740Dependent variable = Ln(House prices)741SLX_G (RE)742ML743(W = W0-160744G745)746SDEM_G (RE)747ML748(W = W0-160749G750)751(M = W0-1.5752EG753)754SDM_G(RE)755ML756(W = W0-160757G758)759(M = W0-160760G761)762SAR_G763ML764(M = W0-160765G766)767Winter temperature7680.0258***769(2.75)7700.0601***771(3.14)7720.0122773(1.52)7740.0126775(1.57)776Ln(Smoke and dust777emission)778-0.1297***779(-4.12)780-0.0219781(-0.74)782-0.0409783(-1.54)784-0.0420785(-1.59)786Ln(Student/Teacher787ratio)788-1.1673***789(-6.21)790-0.6218***791(-3.07)792-0.7090***793(-4.33)794-0.7080***795(-4.29)796Doctor7970.0268***798(2.93)7990.0026800(0.31)8010.0065802(0.85)8030.0069804(0.90)805Coast8060.2230*807(1.93)8080.1560*809(1.68)8100.1793*811(1.91)8120.1671*813(1.77)814Ln(Arable land)815-0.0497816(-0.40)817-0.2906**818(-2.40)819-0.1091820(-1.09)821-0.1178822(-1.24)823Ln(Population density)8240.1181*825(1.87)8260.1278***827(2.65)8280.2042***829(3.95)8300.1909***831(4.10)832Ln(Land)8330.1897***834(2.72)8350.1702***836(2.80)8370.1737***838(3.07)8390.1757***840(3.12)841W × Ln(Population842density)8430.2719***844(3.04)8450.2493***846(2.91)847-0.0686848(-0.85)849W × Ln(Land)8500.2590**851(2.00)8520.2490**853(2.02)854-0.0564855(-0.52)856M × Error8570.7364***858(14.25)859M × Ln(House prices)8600.5510***861(9.48)8620.5280***863(9.96)864Constant8655.3201**866(2.38)8675.5096**868(2.67)8694.4485**870(2.43)8713.8541***872(3.05)873R-Squared8740.9258750.9408760.9488770.948878Corr-Squared8790.7858800.7888810.8198820.812883Log-likelihood88463.84988582.07388695.10888794.721888Sample size889210890210891210892210893Notes: Corr-Squared is the squared correlation between fiɦed and actual value. t-values are894reported in the parentheses. For the definition of the various spatial matrixes, see notes of895Table 3.2. The SDEM, SDM and SAR models are estimated by the ML procedure introduced in896Elhorst (2014). ***, ** and * indicate 1%, 5%, 10% significance level, respectively.89761898Network externalities in Chinese housing markets: A spatial econometric approach899900901===== PAGE 82 (score 10, numeric-paren 0, table-words 3, var-words 4) =====902903network spillovers occurs based on geographical proximity, the SDM model is a beɦer904specification. The third column of Table 3.5 shows the ML estimates of SDM model.905Again, the point estimate of spatial lag of house prices is statistically significant,906suggesting the existence of remaining dependence arising from other channels.907Compared to the SDEM model, which models the spatial interaction in the residuals,908the magnitude of the direct effect of population density in the SDM model increases909from 0.13% to 0.21%. Most importantly, the spatial lags of population density and910land area have negative signs, which finding contradicts network spillovers, but these911effects are not statistically significant. In this case, the SDM model collapses to the SAR912model which only includes the spatial lag of house prices. The SAR model estimates913presented in the fourth column of Table 3.5 are largely in line with the results of SDM914model. The results of the SDM and SAR models suggest that the spatial lag of house915prices also contains the information of network spillovers, which cannot be916distinguished from other mechanisms that can result in spatial dependence.917§ 3.6.3918Network spillovers919.............................................................................................................................920All of the four models, SLX, SDEM, SDM and SAR, can be used to model the network921spillovers in the housing markets. The first two models directly reflect our theoretical922foundation and generate local network spillovers whereas the last two models generate923global spillovers which are not easy to justify11. Table 3.6 summarizes the direct and924spillovers effects of the four models. For the SLX and SDEM model, the direct and925spillover effects are the corresponding point estimates. On the other hand, the partial926derivative approach is needed to calculate the direct and spillover effects for the SDM927and SAR models.928The direct effect of land area is almost the same among the four spatial models, while929the direct effect of population density estimated by the SDM and SAR models is much930more pronounced than that in the SLX and SDEM models. In contrast, the SDM and931SAR models estimate much lower network spillovers of both population density and932land area than the SLX and SDEM models do. In the SDM specification, there is no933significant network spillover at all. Since the spatial lag of house prices mixes various934sources of spatial interaction, and because the global spillovers assumption is not935consistent with our theoretical foundation, our interpretation is based on the SLX and936SDEM models, and in particular on the laɦer model which considers the remaining937spatial dependence in residuals.93811939Local spillovers are those spillovers occuring only between a city and its neighbouring cities connected by a940spatial weight matrix. In contrast, global spillovers are those spillovers that originate from a city and transmit941to all other cities.94262943The Spatial Dimension of House Prices944945946===== PAGE 83 (score 55, numeric-paren 34, table-words 6, var-words 5) =====947948TABLE 3.6949The estimated direct effects and spillovers950RE951SLX952SDEM953SDM954SAR955Direct effects956Ln(Population density)9570.1712***958(2.91)9590.1181*960(1.87)9610.1278***962(2.65)9630.2148***964(3.90)9650.2059***966(3.84)967Ln(Land)9680.1817**969(2.55)9700.1897***971(2.72)9720.1702***973(2.80)9740.1832***975(2.68)9760.1914***977(3.01)978Spillovers979Ln(Population density)9800.2719***981(3.04)9820.2493***983(2.91)9840.0941985(0.66)9860.1989***987(3.07)988Ln(Land)9890.2590**990(2.00)9910.2490**992(2.02)9930.0895994(0.38)9950.1850***996(2.56)997Notes: For SLX and SDEM model, the direct effect and network spillovers are998exactly the point estimates, whereas the partial derivative approach is used for999SDM and SAR model. The inferences of direct effects and spillovers in SDM and1000SAR model are based on 1000 simulations using the variance-covariance matrix1001implied by the ML estimates (LeSage and Pace 2009; Elhorst 2010a). t-values are1002reported in the parentheses. ***, ** and * indicate 1%, 5%, 10% significance level,1003respectively.1004The direct effect of the SDEM model shows that the influence of land area is bigger1005than the effect of population density, suggesting that, in current China, city growth is1006likely to be characterized by an expansion of urban scale rather than an increase in1007intensity. The network spillover is even more noticeable. If a city becomes 1% denser1008and larger, the total house price increases of neighbouring cities are about 0.25%,1009whereas its own house price only rises by 0.13% and 0.17%, respectively. Considering1010that each city on average has 8 neighbours within the radius of 160 km, the network1011spillover on each neighbouring city is by average around 0.03%, which is much lower1012than the magnitude of the direct effect.1013§ 3.6.41014Discussion1015.............................................................................................................................1016As previously discussed, the estimation of network spillovers depends on the choice of1017spatial weight matrix because this matric reflects the underlying interaction structure.1018In this paper, the distance band used for constructing the spatial weight matrix is1019somewhat arbitrarily chosen. To check the robustness of our findings, we replicated our1020analysis based on 4 distance bands: 120, 200, 240 and 280 km. Table B1 in the1021appendix reports the SDEM estimation of direct effect and network spillovers based on1022different matrixes. Clearly, the estimation of the direct effect is very robust to the1023choice of spatial matrix. The estimation of network spillovers, on the other hand, shows1024some variation, though small. When the definition of neighbours is restricted to the1025radius of 120 km, the network spillovers decrease substantially with the spillover of1026land area becoming insignificant. As we include more cities as neighbours, the1027631028Network externalities in Chinese housing markets: A spatial econometric approach102910301031===== PAGE 84 (score 3, numeric-paren 0, table-words 0, var-words 3) =====10321033magnitude of network spillover becomes a bit larger (see the results of distance band1034240 and 280 km), which is in line with our expectation. Nevertheless, given that the1035spatial weight matrix is based on a squared inverse distance function, the majority of1036the network spillovers still falls into the nearby neighbours despite the total number of1037neighbours being increased. In this sense, we believe that the evidence on network1038spillovers presented in this paper is reliable.1039The existence of network spillovers means that, all else being equal, house price in a1040city surrounded by large cities are much higher than those in a city that has small1041neighbours. If we see high house prices as a sign of the ‘triumph of the city’, our1042findings would indicate a core-periphery structure in our study area. We checked this1043implication using Moran’s I plot, which is based on a spatial weight matrix which1044assumes that every city within the 160 km radius of a specific city has the same1045influence on that city (a bit different from the matrix defined by equation (7))12. The1046global Moran’s I plot (Figure C1 in the Appendix) clearly shows a positive correlation1047between a city’s house price and the neighbouring cities’ urban population13. In1048particular, almost all of the cities that are surrounded by small cities have relatively1049lower house prices. The local Moran’s I map, also known as local indicators of spatial1050association (LISA) (Anselin 1995), depicts a detailed clustering paɦern. In general, we1051find a ‘successful’ group (high prices – high population) in the east of the study area1052and a ‘lost’ group (low price – low population) in the western part. There is one1053exception: a coastal city (Nantong) in the east with large neighbours is characterized by1054relatively low prices. Yet, the paɦern that a city surrounded by small cities has high1055house prices is not supported. A lesson learned is that the vast number of ‘lost’ cities in1056the western part will not flourish in the near future, since they are unable to benefit1057from network spillovers of big cities.1058.............................................................................................................................1059§ 3.71060Concluding remarks1061.............................................................................................................................1062Most studies aɦributed the spatial variation of interurban house prices to local-specific1063characteristics. However, the spatial clustering paɦern of house prices cannot be fully1064explained by these local-specific variables, pointing to the importance of spillovers. To1065account for spatial interaction, spatial econometrics is becoming the standard toolbox1066in the analysis of house prices. In particular, the spatial model with spatial lag of house1067prices has been widely used by researchers. Nevertheless, SAR-type models have been1068heavily criticized because the endogenous interaction is difficult to justify.1069121070Both the global Moran’s I plot and the LISA map are calculated by the software ‘Geoda’ which is available at1071hɦps://geodacenter.asu.edu.1072131073The Moran’s I statistic is 0.193. Based on the distribution of 999 simulations of spatially random distributed1074data, it is significant at 5% significance level.1075641076The Spatial Dimension of House Prices107710781079===== PAGE 90 (score 74, numeric-paren 47, table-words 9, var-words 4) =====10801081Appendix B.Tables1082.............................................................................................................................1083TABLE B11084Direct effect and spillovers based on different spatial weight1085matrixes, SDEM1086W0-1201087G1088W0-1601089G1090W0-2001091G1092W0-2401093G1094W0-2801095G1096Direct effects1097Ln(Population density)10980.1228***1099(2.60)11000.1278***1101(2.65)11020.1348***1103(2.80)11040.1319***1105(2.65)11060.1361***1107(2.74)1108Ln(Land)11090.1412**1110(2.32)11110.1702***1112(2.80)11130.1753***1114(2.85)11150.1716***1116(2.77)11170.1770***1118(2.78)1119Spillovers1120Ln(Population density)11210.1198*1122(1.78)11230.2493***1124(2.91)11250.2484***1126(2.70)11270.2765***1128(2.76)11290.2894***1130(2.69)1131Ln(Land)11320.05891133(0.63)11340.2490**1135(2.02)11360.2504*1137(1.93)11380.2747*1139(1.94)11400.3127*1141(1.93)1142Notes: The direct effects and network spillovers are estimated by the spatial Durbin1143error model specified in equation (3), with M = W0-1.51144EG1145. The spatial weight1146matrixes are defined in the same way as those defined in Table 3.2. t-values are1147reported in the parentheses. ***, ** and * indicate 1%, 5%, 10% significance level,1148respectively.1149TABLE B21150Fixed effects estimation of time-variant variables1151Dependent variable = Ln (House prices)1152Winter1153temperature1154Ln (Smoke and1155dust emission)1156Ln (Student1157/Teacher ratio)1158Doctor1159Ln (Population1160density)1161R-squared11620.0226***1163(0.0065)11640.02001165(0.0337)1166-1.0950***1167(0.3369)11680.00881169(0.0142)11702.0576***1171(0.3739)11720.7301173Notes: The robust standard errors are reported in the parentheses. ***, ** and *1174indicate 1%, 5%, 10% significance level, respectively.1175701176The Spatial Dimension of House Prices117711781179===== PAGE 91 (score 0, numeric-paren 0, table-words 0, var-words 0) =====11801181Appendix C.Figures1182.............................................................................................................................1183FIGURE C11184Global Moran’s I plot1185FIGURE C21186LISA cluster map1187711188Network externalities in Chinese housing markets: A spatial econometric approach118911901191===== PAGE 106 (score 21, numeric-paren 10, table-words 4, var-words 1) =====11921193structure reasonably well. The average distances between the housing markets within1194Cluster 1 and Cluster 2 are 136.53 and 184.02, respectively, much smaller than the1195sample average distance (221.54). The extremely low standard deviations of Cluster 11196and Cluster 2 also confirm such findings.1197TABLE 4.21198Cluster membership and statistics based on Euclidean distance and JKL1199divergence1200Euclidean distance1201JKL divergence1202Membership1203Average1204within1205distance1206Membership1207Average1208within1209distance1210Average1211monthly1212growth rate1213(%)1214Cluster 1 2,3,4,5,6,7,8,9,13,15,121517,18,19,20,21,22,121625,26,27,28,29,30,121731,32,33,3412189.101219(1.49)12202,3,4,5,6,7,8,9,13,15,122117,18,19,20,21,22,122225,26,27,28,29,30,122331,32,33,341224136.531225(68.24)12260.351227(0.09)1228Cluster 2 1,10,11,14,16,23122910.701230(1.57)12311,11,12,14,16,231232184.021233(45.72)12340.501235(0.13)1236Cluster 3 2412372412380.781239Cluster 4 1212401012410.411242Sample124310.791244(3.05)1245221.541246(173.21)12470.391248(0.13)1249Notes: For the cluster membership, only the ID of the city is presented. Readers can refer to1250Table B1 for the names of the cities. The numbers in parentheses are the standard deviations.1251The average within distance is the mean of all city-pair distances within the same cluster.1252After obtaining the mean monthly growth rate for each city throughout the sample period, the1253average monthly growth rate reported in the table is the average of mean growth rate across1254cities in the same cluster.1255In a broad sense, the classification results can reduce to a two-cluster solution. One is1256Cluster 1, which contains mainly slow-growing markets with an average monthly1257growth rate of 0.35%. The other combines Clusters 2, 3 and 4, which contain markets1258with relatively higher appreciation rates (see Table 4.2) and are considered to be1259“red-hot” markets. There is a much higher degree of heterogeneity within these1260red-hot markets, however. Compared to the difference in house price appreciation1261rates, the most striking divergence between the two broad groups is that, referring back1262to Figure 4.2, the red-hot markets experienced tremendous house price appreciation1263in the second half of the period, whereas house price growth during the first half of the1264period makes the most important contribution for the cities in Cluster 1. One can also1265easily identify a spatial paɦern in the house price dynamics of cities with red-hot1266markets located in Eastern China, as well as others that are mainly in the remaining1267“peripheral” regions.1268861269The Spatial Dimension of House Prices127012711272===== PAGE 107 (score 13, numeric-paren 1, table-words 5, var-words 2) =====12731274FIGURE 4.51275Spatial distribution of sample cities and their membership based on JKL1276divergence1277§ 4.5.31278Do structural changes maɢer?1279.............................................................................................................................1280The classification analysis of the whole period relies on the premise that the housing1281market structure of a city does not change. In other words, the relationship between1282any two cities’ housing markets is stable throughout the sample period. This1283assumption may not hold given the evolving conditions of the nascent Chinese housing1284market. To explore whether structural changes affect previous classification results, I1285split the sample into subsamples and perform the classification analysis on each1286subsample. If there is no structural change, the classification results will be highly1287consistent among the subsamples, as well as with the clusters presented in Table 4.2.1288Otherwise, some quite different cluster demarcations will be observed.1289The house price appreciation trajectories depicted in Figure 4.1 indicate that house1290price changes among sample cities are quite volatile during the first half of the period1291and the recent period. Thus, I divide the sample period into three sub-periods:12922005–2010 (66 observations), 2011–2013 (36 observations) and 2014–2016 (301293observations). For each sub-period, the JKL divergence is calculated based on an AR(3)1294specification. The average JKL distances between cities as well as the associated1295standard deviations are reported in the last row of Table 4.3. The average distance1296between housing markets in the period 2014–2016 (196.79) is much larger than the1297871298The clustering paɢern of Chinese house price dynamics129913001301===== PAGE 108 (score 28, numeric-paren 19, table-words 2, var-words 1) =====13021303average distance in the first (92.14) and second periods (71.23), indicating a1304remarkable divergence of housing markets in the recent period. While the overall1305housing market difference throughout the whole sample is approximately 220, as1306measured by JKL divergence, it can be concluded that the highly divergent market1307conditions in the third period account for the most important component.1308The hierarchical clustering method is then applied to the three subsamples, providing1309more details about the structural evolution of housing markets. To obtain comparable1310clusters across the different periods, the dendrograms of these three periods should be1311cut at a common “height” (divergence threshold). To do this, I first determine the1312appropriate number of clusters (k) for the 2014–2016 sample, which should be 51313according to Figure A2. This demarcation requires a minimum height (h)1314approximately 94.87. I then cut the dendrograms of the first and second period at the1315same height and obtain 3 clusters for both of the periods. According to the elbow plots1316in Figure A2, the 3-cluster demarcation is not the optimal solution for the first two1317periods. But only in this way can the demarcation solutions of the three sub-periods be1318directly compared with each other.1319TABLE 4.31320Cluster membership and statistics for different sample periods13212005-201013222011-201313232014-20161324k = 3,h = 94.871325k = 3,h = 94.871326k = 5,h = 94.871327Membership1328Average1329within1330distance1331Membership1332Average1333within1334distance1335Membership1336Average1337within1338distance1339Average1340monthly1341growth rate1342(%)1343Cluster 1 1,2,3,4,5,6,13447,8,9,11,12,134513,14,15,16,134617,18,19,22,134723,24,25,26,134827,28,29,30,134931,32,33,34135072.161351(45.72)13522,3,4,5,6,7,13538,9,11,14,135415,16,17,18,135520,21,22,25,135626,27,28,29,135730,31,32,33,135834135941.661360(24.42)13613,4,5,6,7,8,13629,19,22,25,136326,27,28,29,136430,31,32,33,136534136629.861367(11.96)1368-0.121369(0.09)1370Cluster 2 20,21137136.371372(20.21)137312,13,19137452.861375(30.65)13762,13,15,17,137718,20,21137852.711379(26.38)13800.211381(0.12)1382Cluster 3 1013831,10,23,24138434.671385(11.24)13861,10,12,23138746.411388(24.12)13890.561390(0.27)1391Cluster 4139211,14,16139347.651394(16.20)13950.891396(0.16)1397Cluster 513982413991.821400Sample140192.141402(73.90)140371.231404(66.48)1405196.791406(275.54)14070.171408(0.46)1409Notes: The same notes as Table 4.2.1410In both the 2005–2010 period and the 2011–2013 period, one observes highly1411881412The Spatial Dimension of House Prices141314141415===== PAGE 109 (score 10, numeric-paren 0, table-words 5, var-words 0) =====14161417integrated, homogeneous cross-city housing markets. Most of the cities are classified1418into the same cluster, with a few exceptions, Shanghai(10) for instance. The most1419remarkable structural change between these two periods could be that a few developed1420eastern cities, such as Beijing(1), Shenzhen(24), Guangzhou(23) and Hangzhou(12),1421began to deviate from the main group during the 2011–2013 period.1422When turning to the 2014–2016 period, the interurban housing market diverges1423much more. House price growth in Shenzhen(24), where the average monthly growth1424rate is 1.82%, obviously stands out from the other cities. Aside from the red-hot1425markets that are already separated in the 2011–2013 period (1, 12 and 23 for1426example), a few more rapid-growth markets with monthly growth rates of 0.89%1427(Cluster 4), such as Hefei(11), Fuzhou(14) and Xiamen(16), are also isolated from the1428main group. Furthermore, there is another cluster (Cluster 2) that deviates from the1429main group but not by much; this group has a relatively low average monthly growth1430rate (0.21%) and mainly contains some lower-tier centres in Eastern and Central1431China, such as Ningbo(13), Fuzhou(15), Nanchang(16) and Wuhan(21). Note that a1432parsimonious three-cluster solution for the 2014–2016 housing markets, which1433merges Cluster 1 with Cluster 2, and fuses Cluster 3 with Cluster 4, is highly consistent1434with the classification results based on the whole period (Table 4.2). By grouping1435Cluster 1 and Cluster 2 in Table 4.3, one obtains precisely Cluster 1 in Table 4.2.1436Similarly, Cluster 2 in Table 4.2 is almost identical to the combination of Clusters 3 and14374 in Table 4.3.1438To summarize the findings, the Chinese interurban housing market in the early periods1439(2005–2013) can be considered a homogeneous market; only a few markets have1440distinctive dynamic paɦerns of house prices. In the recent period (after 2014), the1441interurban housing market begins to diverge; not only do the markets of the most1442important centres of the three main economic regions stand out remarkably, the1443markets of some lower-tier centres are also isolated. Given this sudden structural1444change, it is not surprising to see that the clustering paɦern of the 2014–2016 period1445almost determines the classification results based on the whole period.1446§ 4.5.41447The effectiveness of geographical and economic divisions1448.............................................................................................................................1449The classification results suggest that geography seems to play a role in the1450homogeneous clustering of the city-level housing markets. In this section, I will test the1451effectiveness of the traditional geographical demarcation in describing the interurban1452housing market structure. This classification scheme was introduced by NBSC in 20111453and divides all of China into four regions: Eastern, Central, Western and Northeast1454China (see Figure 4.5). In addition, I also examine whether the city-tier system of1455demarcation based on economic factors can produce meaningful groups of housing1456markets. There are presently several versions of the city-tier division system available,1457891458The clustering paɢern of Chinese house price dynamics145914601461===== PAGE 118 (score 119, numeric-paren 100, table-words 2, var-words 0) =====14621463Appendix C.The AR(3) estimation1464.............................................................................................................................1465TABLE C11466The AR(3) estimation of selected cities1467Lag 11468Lag 21469Lag 31470Intercept1471R-squared1472BG test1473Tianjin14740.6423***1475(0.088)1476-0.03551477(0.105)14780.2180**1479(0.093)14800.0922*1481(0.052)14820.50414838.30**1484Taiyuan14850.2663***1486(0.084)1487-0.05021488(0.087)14890.3104***1490(0.081)14910.08471492(0.055)14930.179149427.64***1495Shenyang14960.4988***1497(0.089)14980.06111499(0.098)15000.13951501(0.087)15020.09221503(0.057)15040.38015053.331506Changchun15070.4762***1508(0.089)15090.05761510(0.097)1511-0.04141512(0.085)15130.1743**1514(0.075)15150.249151626.12***1517Shanghai15181.0636***1519(0.090)1520-0.2565*1521(0.130)15220.07151523(0.090)15240.0772*1525(0.040)15260.80115271.651528Ningbo15290.7572***1530(0.089)1531-0.05721532(0.111)15330.07771534(0.089)15350.07681536(0.051)15370.58015383.001539Hefei15400.7352***1541(0.087)15420.2850***1543(0.102)1544-0.1992**1545(0.097)15460.09821547(0.065)15480.640154913.24***1550Nanchang15510.5306***1552(0.089)15530.05661554(0.100)15550.11141556(0.089)15570.1336**1558(0.061)15590.38915601.011561Zhengzhou15620.5888***1563(0.089)15640.01471565(0.103)15660.14321567(0.090)15680.1086**1569(0.047)15700.44715714.301572Changsha15730.5207***1574(0.088)15750.2283**1576(0.095)1577-0.10191578(0.082)15790.1517**1580(0.070)15810.41815826.321583Guangzhou15840.5805***1585(0.089)15860.2104**1587(0.102)1588-0.03481589(0.091)15900.1422*1591(0.080)15920.51215933.811594Chengdu15950.5154***1596(0.089)15970.2242**1598(0.096)15990.00241600(0.088)16010.0686*1602(0.041)16030.47116042.071605Guiyang16060.5804***1607(0.089)1608-0.04761609(0.103)16100.02991611(0.089)16120.1588***1613(0.061)16140.31816155.891616Xian16170.07921618(0.087)16190.2755***1620(0.084)16210.2213**1622(0.086)16230.1492*1624(0.078)16250.17916262.791627Yinchuan16280.1882**1629(0.090)16300.4658***1631(0.081)16320.06231633(0.090)16340.0922*1635(0.054)16360.36916371.381638Notes: The standard errors are reported in the parentheses. The BG test represents the1639Breusch-Godfrey test, following the χ216403 distribution under the null hypothesis of no serial1641correlation of order up to 3. ***, ** and * indicate 1%, 5%, 10% significance level, respectively.1642981643The Spatial Dimension of House Prices164416451646===== PAGE 119 (score 2, numeric-paren 0, table-words 0, var-words 2) =====1647164851649Spatial interrelations of Chinese housing markets:1650Spatial causality, convergence and diffusion1651Published as: Gong, Y., Hu, J., Boelhouwer, P., 2016. Spatial interrelations of Chinese1652housing markets: Spatial causality, convergence and diffusion. Regional Science and1653Urban Economics, 59:103-117.1654Abstract: This paper comprehensively tests the spatial interrelationships of 10 housing1655markets in the Pan-Pearl River Delta (Pan-PRD) in China, including the properties of1656spatial causality, convergence and diffusion paɦerns. The pairwise Toda-Yamamoto1657Granger causality tests suggest widely existing leading-lag relationships between1658housing markets; a unidirectional causal flow from the eastern-central area to western1659China can be tentatively confirmed. However, there is a lack of sufficient evidence1660supporting pairwise long-run cointegration and convergence, indicating a diverged1661interurban housing market in the Pan-PRD. In the short run, the spatial-temporal1662diffusion model manifests the importance of the spillover effect from neighbouring1663cities in predicting one city’s house price changes. Furthermore, the generalized1664impulse response functions (GIRFs) clearly depict the transmission paɦern of shocks to1665one chosen city. The diffusion paɦern is characterized by the fact that the shocks first1666spread to nearby cities with cities further away taking a longer time to respond.1667Keywords: Spatial causality, long-run convergence, ripple effect, diffusion, house1668prices, China1669JEL: C31, C33, R21, R311670.............................................................................................................................1671§ 5.11672Introduction1673.............................................................................................................................1674After the financial crisis in 2008, many governments have been aɦempting to1675stimulate depressed housing markets through policy interventions. However, whether1676the interventions can work as expected relies heavily on our understanding of housing1677markets. To provide deeper insights into house price behaviour, many scholars1678advocate an investigation into a series of interrelated regional markets rather than a1679single national market (Meen 1996; Yunus and Swanson 2013). Indeed, the structure1680991681Spatial interrelations of Chinese housing markets: Spatial causality, convergence and diffusion168216831684===== PAGE 130 (score 15, numeric-paren 1, table-words 3, var-words 2) =====16851686are integrated of order one, i.e., I(1). The ADF tests provide preliminary evidence that1687house prices of different cities are integrated of different orders.1688The ADF test has very low power in distinguishing highly persistent stationary1689processes from non-stationary processes; the power is lower when a deterministic1690trend is included in the test. Thus, an efficient unit root test, the Dickey-Fuller1691generalized least square (DF-GLS) test proposed by Ellioɦ et al. (1996), is also1692conducted. The results in the second and fifth column of Table 5.1 are largely1693consistent with the ADF test, except that the level house price determination of1694Xiamen is a unit root process.1695TABLE 5.11696Unit root test1697level16981st difference1699ADF1700DF-GLS1701KPSS1702ADF1703DF-GLS1704KPSS1705Guangzhou -3.886(2)** -3.361(2)** 0.080(9)1706-3.467(1)** -3.494(1)** 0.056(8)1707Shenzhen1708-2.179(1)1709-2.209(1)17100.121(9)*1711-3.477(0)** -3.510(0)** 0.078(8)1712Fuzhou1713-2.538(2)1714-1.399(2)17150.157(9)**1716-3.642(1)** -3.574(1)*** 0.085(8)1717Xiamen1718-3.391(2)*1719-2.404(2)17200.103(9)1721-3.784(1)** -3.642(1)*** 0.086(8)1722Nanchang1723-1.411(1)1724-0.957(1)17250.199(9)**1726-6.037(0)*** -5.233(0)*** 0.051(8)1727Changsha1728-1.852(1)1729-0.962(1)17300.226(9)***1731-6.596(0)*** -3.899(0)*** 0.046(8)1732Nanning1733-2.188(1)1734-0.862(1)17350.248(9)***1736-4.579(0)*** -4.382(0)*** 0.083(8)1737Guiyang1738-1.044(1)1739-0.745(1)17400.286(9)***1741-6.289(0)*** -5.908(0)*** 0.042(8)1742Kunming1743-1.365(1)1744-1.764(1)17450.148(8)**1746-7.070(0)*** -5.161(0)*** 0.092(7)1747Chengdu1748-2.623(2)1749-2.144(2)17500.127(9)*1751-3.628(1)** -3.347(1)** 0.055(8)1752Notes: All the models include an intercept and a deterministic trend. Numbers shown in1753parentheses are the lag length or bandwidth. For the Augmented Dickey-Fuller (ADF) test1754(Dickey and Fuller 1979), the lag length for level variables is selected using the Bayesian1755Information Criterion (BIC) with the maximum lag length being set to 12. DF-GLS unit1756root tests (Ellioɦ et al. 1996) use the same lag length chosen for ADF test. For KPSS1757test (Kwiatkowski et al. 1992), the bandwidth is selected by Newey-West method. In1758all the cases, the lag length for first difference variables equals to the lag length for level1759variables minus one. The null hypothesis for ADF and DF-GLS tests is having a unit root,1760but stationary for the KPSS test. *, ** and *** indicate significance at the 10%, 5% and 1%1761level, respectively.1762Table 5.1(column 3 and 6) also presents the results of the KPSS test (Kwiatkowski et al.17631992), which has the null hypothesis of stationary. The KPSS results support that1764Xiamen’s house price series is I(0), in accordance with the ADF test but in1765contradiction to the DF-GLS test. The evidence for the integration order of the Xiamen1766price series appears to be mildly confusing. Given that the KPSS statistic is very close to1767the 10% critical value (0.119), it is reasonable to assume Xiamen’s price process to be1768I(1) for the following analysis 10.1769101770One reviewer pointed out that house prices are very likely to display an asymmetric adjustment, reducing the17711101772The Spatial Dimension of House Prices177317741775===== PAGE 131 (score 6, numeric-paren 0, table-words 2, var-words 2) =====17761777Because not all the house price series are integrated of the same order, the pairwise1778Toda-Yamamoto Granger causality procedure is preferable in this analysis. According1779to information criteria, such as AIC and BIC, the optimal lag lengths for most of the1780city-pair VARs are 2 and 3. To largely ensure that the residuals are close to white noise,1781we proceed using the VAR(3 + d) system in which d is the maximum integration order1782of the city pair.1783The results of Toda-Yamamoto Granger causality tests are reported in Table 5.2, where1784the null hypothesis is that column cities do not Granger cause row cities. Overall, in1785most of the city pairs, we find significant evidence of bilateral or unidirectional1786leading-lag relations; however, the causality paɦern is very complicated 11. Certain1787literature focusing on housing market interaction, such as Clapp et al. (1995) and Chen1788et al. (2011), has claimed that the house price interrelation (or causality) only occurs1789between neighbouring markets. Our results cast doubt on this conclusion because1790leading-lag relationships are found in many city pairs where the two cities are1791separated by very long distances. Conversely, there is no spatial causality in certain1792short-distance city pairs, such as Xiamen and Fuzhou. Similarly, Pollakowski and Ray1793(1997) and Luo et al. (2007) also found significant causality between non-contiguous1794regions. Such complicated causality paɦerns may be largely due to economic relations1795rather than behavioural reasons (Pollakowski and Ray 1997).1796To further examine the results, the cities in the system are divided into two groups: the1797eastern-central group including the first six cities in Table 5.2 and the western group1798containing the remaining cities. We tentatively find a general unidirectional causal flow1799from the eastern-central area to western China. The historical house price information1800of all eastern-central cities, except Xiamen, can significantly contribute to predicting1801the house prices of western cities. The opposite, conversely, can hardly be true given1802the largely insignificant Granger causality test results in the lower-left panel. However,1803among the four western cities, the housing markets of Kunming and Chengdu appear1804to play a role in predicting house price behaviours in eastern-central cities. The above1805findings are closely related to the socio-economic disparities between eastern, central1806and western China. Considering that eastern-central cities are generally more1807developed than western ones, it can be expected that their market dynamics can lead1808housing market behaviours in the remaining cities. Chengdu is an exception in western1809cities, given its status as the financial and economic centre of western China.1810Consequently, the mutual leading-lag relationships between Chengdu and most1811power of traditional unit root tests. Thus, we employed the momentum threshold autoregressive (MTAR)1812asymmetric unit root test proposed by Enders and Granger (1998) to test the integration order of 10 cities’1813house price indexes. However, the results, which are available upon request, do not turn over the finding that all1814the cities are I(1) process except for Guangzhou.1815111816It should be noted that, throughout the paper, when we say “a market leads or causes another market in the1817Granger sense”, we cannot exclude the possibility that such correlation is caused by common shocks.18181111819Spatial interrelations of Chinese housing markets: Spatial causality, convergence and diffusion182018211822===== PAGE 132 (score 169, numeric-paren 149, table-words 1, var-words 0) =====18231824TABLE 5.21825Toda-Yamamoto Granger causality test1826Guangzhou Shenzhen1827Fuzhou1828Xiamen1829Nanchang1830Changsha1831Nanning1832Guiyang1833Kunming1834Chengdu1835Guangzhou183625.63***1837(0.000)18386.47*1839(0.091)184050.54***1841(0.000)184211.13***1843(0.011)184414.10***1845(0.003)184611.25***1847(0.010)18489.47**1849(0.024)18504.411851(0.220)18529.16**1853(0.027)1854Shenzhen185513.821856(0.003)18579.14**1858(0.027)185918.93***1860(0.000)18616.05*1862(0.109)186318.76***1864(0.000)18658.25**1866(0.041)186714.14***1868(0.003)18696.22*1870(0.101)18718.23**1872(0.041)1873Fuzhou18742.001875(0.572)18761.521877(0.678)18787.52*1879(0.057)18805.041881(0.169)18827.97**1883(0.047)18848.52**1885(0.036)18866.49*1887(0.090)18888.26**1889(0.041)18906.78*1891(0.079)1892Xiamen189318.73***1894(0.000)18952.321896(0.510)18973.381898(0.336)18994.101900(0.251)19012.821902(0.420)19035.281904(0.153)19052.011906(0.570)19070.281908(0.963)19090.941910(0.815)1911Nanchang19124.471913(0.215)19147.90**1915(0.048)19168.25**1917(0.041)19186.42*1919(0.093)192014.61***1921(0.002)192212.22***1923(0.007)192417.52***1925(0.001)192611.44***1927(0.010)192811.55***1929(0.009)1930Changsha19311.031932(0.794)19335.311934(0.150)19357.48*1936(0.058)19376.11*1938(0.106)19396.74*1940(0.081)194113.36***1942(0.004)194334.22***1944(0.000)194513.29***1946(0.004)19477.99**1948(0.046)1949Nanning19508.91**1951(0.031)195214.22***1953(0.003)19544.921955(0.178)19563.521957(0.318)19585.081959(0.166)19609.51**1961(0.023)196219.42***1963(0.000)19648.64**1965(0.035)19668.70**1967(0.034)1968Guiyang19690.411970(0.938)19712.371972(0.500)19732.321974(0.509)19750.671976(0.880)19775.311978(0.150)19795.071980(0.167)19815.291982(0.152)19831.381984(0.711)19857.46*1986(0.058)1987Kunming19887.27*1989(0.064)199011.59***1991(0.009)19921.791993(0.616)19945.961995(0.113)19967.30*1997(0.063)199827.03***1999(0.000)20008.31**2001(0.040)200211.68***2003(0.009)200410.32**2005(0.016)2006Chengdu20075.572008(0.135)20095.242010(0.155)201116.81***2012(0.001)201317.69***2014(0.001)201515.25***2016(0.002)20178.21**2018(0.042)20196.20*2020(0.102)20217.24*2022(0.064)20237.19*2024(0.066)2025Notes: Toda-Yamamoto Granger causality test is performed under VAR(3+d) system where d is the maximum integration order of house price2026processes in the city pair. Both intercept and deterministic time trend are included in the VAR system. The null hypotheses are that house prices2027in column cities do not Granger cause house prices in row cities. The asymptotic Wald statistics are reported, and the corresponding p-values are2028shown in parentheses. *, ** and *** indicate significance at the 10%, 5% and 1% level, respectively.20291122030The Spatial Dimension of House Prices203120322033===== PAGE 133 (score 2, numeric-paren 0, table-words 0, var-words 2) =====20342035eastern-central cities are no surprise. Furthermore, within either the eastern-central or2036western group, the significant leading-lag relationship (at least for one direction) can2037be found in every city pair.2038Given the leading position of Guangdong in the Pan-PRD, we expect that the housing2039markets of the two cities under its territory, namely Guangzhou and Shenzhen, will lead2040the markets in other cities. Indeed, Guangzhou and Shenzhen impose a significant2041leading influence on nearly all the other housing markets, and they are less predictable2042on the basis of previous information from other markets. However, these cities’2043dominant role is not unique. Certain other cities appear to also have similar2044‘exogenous’ properties, such as Nanchang.2045.............................................................................................................................2046§ 5.52047Long-run properties2048.............................................................................................................................2049§ 5.5.12050Cointegration and convergence test2051.............................................................................................................................2052The previous section reveals that the 10 cities’ housing markets in the Pan-PRD are2053interrelated with each other. In this section, we go further to ask the question of2054whether these markets are tied together in the long-run, i.e., if they hold a long-run2055equilibrium relationship. To answer this question, the long-run cointegration and2056convergence properties of house prices are investigated.Two I(1) house price series p1t2057and p2t are said to be cointegrated if a linear combination of p1t and p2t is stationary.2058Since we are interested in the pairwise cointegration of house price indexes of two2059cities, the Engle-Granger (EG) two-step procedure (Engle and Granger 1987) is2060employed in this paper, which has been applied by, for example, MacDonald and Taylor2061(1993) to a similar question.2062The first step is to estimate the long-run equilibrium relationship by the following2063equation2064pit = D + βp2t + ut2065(3)2066where D is deterministic terms that may contain a constant, a deterministic trend or2067both. The cointegration test involved in the second step is then based on testing the2068unit root of residual series ut. If ut is stationary, we say that p1t and p2t are cointegrated2069with (1,−β). Because of the spurious regression under the null hypothesis of2070non-cointegration in the first stage, the residual-based ADF test in the second stage2071does not have the standard Dickey-Fuller distribution. Therefore, critical values for2072cointegration test simulated by MacKinnon (1996) are used in this paper.2073As noted by Holly et al.(2011) and Abboɦ and Vita (2013), conditional on2074cointegration, the long-run convergence of house prices necessitates two additional20751132076Spatial interrelations of Chinese housing markets: Spatial causality, convergence and diffusion207720782079===== PAGE 134 (score 38, numeric-paren 17, table-words 2, var-words 3) =====20802081conditions: (1) the cointegrating vector corresponding to house price series being2082(1,-1), and (2) the lack of a deterministic trend being presented in cointegration space.2083The long-run convergence property is tested by the so-called pair-wise approach, which2084has been used by Holmes et al. (2011) and Abboɦ and Vita (2013). Specifically, the2085cointegrating vector is pre-specified with form (1,-1), and then any standard unit root2086test can be directly used to test the stationarity of cointegrating residuals.2087TABLE 5.32088Engle-Granger pairwise cointegration results2089Shenzhen Fuzhou2090Xiamen2091Nanchang Changsha Nanning2092Guiyang2093Kunming Chengdu2094Shenzhen2095-0.6332096-3.0942097-2.0532098-13.7062099-0.8372100-4.4132101-0.5322102-2.0922103-0.5202104-1.5572105-0.9192106-3.9672107-0.7232108-2.7182109-0.0672110-0.2802111Fuzhou2112-0.2212113-1.2892114-0.8552115-3.6832116-2.0942117-5.5532118-1.7162119-5.9632120-1.9812121-7.0772122-2.2042123-9.3712124-2.2392125-7.2012126-2.7112127-10.0442128Xiamen2129-1.8752130-13.7282131-1.1292132-4.6922133-0.7912134-2.3902135-1.3622136-5.6422137-1.2482138-3.8002139-1.4822140-5.8852141-1.3392142-4.2002143-0.8312144-3.5912145Nanchang -0.5012146-3.2662147-2.4232148-6.4212149-0.6042150-1.9182151-3.792*2152-27.395**2153-2.1362154-6.5072155-3.086*2156-19.217*2157-3.1722158-14.1872159-2.6152160-14.0582161Changsha -0.0252162-0.1292163-1.7742164-6.2342165-1.2792166-5.7482167-3.722*2168-26.892**2169-1.6572170-3.2872171-3.331*2172-20.505*2173-4.069**2174-20.546*2175-2.3812176-11.2132177Nanning21780.30921791.2252180-1.7622181-6.2342182-0.6932183-2.1552184-1.6932185-5.0072186-1.1622187-2.1892188-1.9882189-6.3422190-1.9382191-5.0582192-1.5932193-4.2862194Guiyang2195-0.5802196-3.2312197-2.3872198-10.2492199-1.4982200-6.5882201-3.086*2202-19.214*2203-3.435*2204-21.148*2205-2.4532206-8.0412207-2.9072208-14.0282209-2.6802210-15.7412211Kunming -0.5112212-2.3692213-2.7932214-8.8152215-1.4382216-4.6082217-3.470*2218-15.2072219-4.479**2220-22.088*2221-2.8562222-7.3902223-3.1182224-14.7792225-3.1692226-13.7682227Chengdu 0.33022281.6492229-2.9192230-10.7532231-0.6612232-2.9362233-2.5692234-13.7142235-2.4202236-11.2872237-2.0172238-5.4442239-2.6012240-14.8932241-2.8432242-12.4652243Notes: The two statistics in each cell are, respectively the τ statistic and z statistic of ADF test with the2244null hypothesis of no cointegration. The MacKinnon (1996) critical values are used. In each cointegration2245equation, the row cities are defined as dependent variables. The constant is included in the cointegration2246space in all city pairs except the Nanchang-Guiyang pair, in which the constant is not significant. * and **2247indicate the 5% and 1% significance level, respectively.2248§ 5.5.22249Empirical results2250.............................................................................................................................2251Table 5.3 demonstrates the results of the pairwise Engle-Grange cointegration test.2252Guangzhou is excluded from cointegration analysis because it is I(0) according to our2253unit root test results. A brief view of the results indicates that cointegration2254relationships rarely exist between cities, in contrast to the widely existing leading-lag2255relationships. Among the city pairs that are tied together in the long-run, three cities,2256Nanchang, Changsha and Guiyang, form a ‘cointegration club’ within which every city2257cointegrates with each other. In addition, the significant long-run equilibrium2258relationship can also be observed in the city pair of Changsha-Kunming. We also note2259that none of the three eastern cities, namely Shenzhen, Fuzhou and Xiamen, is22601142261The Spatial Dimension of House Prices226222632264===== PAGE 135 (score 25, numeric-paren 11, table-words 3, var-words 1) =====22652266cointegrated with each other or with the remaining central and western cities. This2267might indicate that in the long-run, the housing market conditions in eastern cities still2268significantly differ from the markets of the remaining cities, although much effort has2269been made to promote the integration process of Pan-PRD’s economy.2270TABLE 5.42271Pairwise convergence results with pre-specified coefficients (1,-1)2272Shenzhen Fuzhou2273Xiamen2274Nanchang Changsha Nanning Guiyang Kunming Chengdu2275Shenzhen2276-0.9192277-1.8382278-1.0712279-0.8752280-0.6672281-1.07722820.56322831.0402284Fuzhou2285-0.6422286-1.0602287-0.7962288-0.9402289-1.0092290-1.44822910.14622921.0442293Xiamen2294-2.1092295-0.9272296-0.8402297-1.0472298-0.8802299-1.51023000.80323011.1092302Nanchang -0.8532303-1.8432304-0.7332305-0.5462306-0.6122307-2.994** 0.20623080.5882309Changsha -1.1442310-1.6072311-1.5292312-2.7292313-0.6482314-0.46523150.34823160.6142317Nanning2318-0.4802319-2.1442320-1.1322321-2.0902322-0.5942323-0.57723240.17423250.3922326Guiyang2327-0.8822328-2.1702329-1.4682330-3.075*2331-2.900*2332-2.4512333-0.0092334-0.0562335Kunming -0.4802336-3.383* -1.4642337-3.550** -4.012** -3.770** -2.949*2338-1.1542339Chengdu 0.5092340-4.018** -0.4912341-1.8102342-2.973*2343-3.443* -1.5422344-2.1242345Notes: The null hypothesis of no convergence is tested based on the residual from pit −pjt. The2346results of ADF test (Dickey and Fuller 1979) are reported in the lower triangle, whereas the upper2347triangle shows the results of DF-GLS tests (Ellioɦ et al. 1996). In the unit root test process, the2348constant is included, and the lag length (not reported) is automatically selected by the Bayesian2349Information Criterion (BIC). * and ** indicate the 5% and 1% significance level, respectively.2350After examining the cointegration, we proceed to test the more restricted long-run2351convergence properties. The pairwise cointegration results with pre-specified2352coefficients (1,-1) are shown in Table 5.4. The ADF test in the lower triangle suggests2353that among the four cointegration city pairs, there are three convergent pairs:2354Nanchang-Guiyang, Changsha-Guiyang and Changsha-Kunming. In addition, another2355seven city pairs, which are not cointegrated in the Engle-Granger cointegration test are2356found to be significantly converged. Considering that cointegration is a necessary2357condition of convergence, the convergent results of these seven pairs are a surprise.2358These contradictory results might be due to the low power of the ADF test in detecting2359the unit root. To verify the ADF test, we also perform the more efficient DF-GLS test,2360the results of which are reported in the upper triangle of Table 5.4. This time we find2361only one significantly convergent pair, the Nanchang-Guiyang pair, which is also2362cointegrated. Note that regardless which unit root test we used, city pairs that are2363convergent are rare. Therefore, it is reasonable to conclude that cointegration or2364convergence is unlikely to widely exist among the nine cities, which indicates a diverged2365interurban housing market in the Pan-PRD.2366To check the robustness of the cointegration and convergence test results based on the2367two-step procedure, we also conduct two additional tests: the pairwise Johansen2368cointegration test and the two-step convergence test based on the momentum2369threshold autoregressive (MTAR) unit root test (Enders and Granger 1998) which can2370allow an asymmetric adjustment. The trace statistics of the Johansen procedure,23711152372Spatial interrelations of Chinese housing markets: Spatial causality, convergence and diffusion237323742375===== PAGE 136 (score 9, numeric-paren 0, table-words 4, var-words 1) =====23762377computed based on a VAR(3) specification with unrestricted intercept and no trend in2378VAR, are reported in the lower triangle of Table A1. The null hypothesis is that the2379column city is not cointegrated with the row city. For those cointegrated city pairs, the2380upper triangle of Table A1 reports the results of the log-likelihood ratio (LR) test, which2381is used to test the cointegrating vector restriction (1,-1). Table A2 displays the pairwise2382cointegration results with pre-specified coefficients (1,-1) based on the MTAR unit root2383test. Both of these two powerful methods identify a similar cointegration and2384convergence paɦern between cities with the two-step procedure does; the results are2385largely in line with the lower triangle results of Table 5.4. Thus, we are confident of the2386previous finding that only very few city pairs are found to be cointegrated or convergent.2387For the following analysis, we mainly rely on the results of the two-step procedure.2388.............................................................................................................................2389§ 5.62390House price diffusion paɢern2391.............................................................................................................................2392§ 5.6.12393Spatial-temporal house price diffusion model2394.............................................................................................................................2395Previous analysis suggests that most of the city pairs do not hold a long-run2396equilibrium relationship; however, a few pairs do. When modelling the house price2397dynamics of a city, we should consider the interrelation with both the cointegrated2398cities and the non-cointegrated cities. In other words, we should consider the influence2399from the cities that can impose a long-term effect and the cities that only have a2400transitory effect. In addition, the spatial dimension should also be considered because2401it is likely that the effect imposed by nearby cities is stronger than the influence of2402distant cities. The spatial-temporal house price diffusion model adopted in this paper2403can fully capture the characteristics along both spatial and temporal dimensions. This2404model is a variant of spatial-temporal diffusion model proposed by Holly et al. (2011)2405(the Holly model), which has been applied to investigating the effects of language2406border on the diffusion of house prices in Belgian markets by Helgers and Buyst (2016).2407However, unlike the Holly model, we do not designate a ‘dominant’ city, which is2408assumed to have contemporaneous effects on non-dominant cities. The reason for2409abandoning the ‘dominant’ city from our model specification is that the general lack of2410pairwise long-run cointegration relationships between cities found previously suggests2411that there is no city that can be seen as the long-run forcing for other cities. In our2412model specification, the house price series in the system excluding pit is split into two2413groups because of the existence of a ‘cointegration club’: one group (denoted by C)2414being cointegrated with pit and the other (denoted by O) not. A first order error2415correction specification for pit is given by2416∆pit = ϕi02417(2418pi,t−1 −βi¯pC2419i,t−12420)2421+ai + ai1∆pi,t−1 + bi1∆¯pC2422i,t−1 + ci1∆¯pO2423i,t−1 + ϵit,2424(4)24251162426The Spatial Dimension of House Prices242724282429===== PAGE 139 (score 13, numeric-paren 6, table-words 3, var-words 0) =====24302431provide significant evidence of cointegration for Nanchang, Changsha and Kunming. In2432the case of Guiyang, we cannot reject the null hypothesis of no cointegration at the 5%2433significance level; however, the statistics are marginally significant at the 10% level.2434The third column of Table 5.5 reports the estimated long-run relationships (βi). The2435estimated βi are approximately distributed around the value of unity, except for2436Kunming.2437TABLE 5.52438Cointegration between the four cointegrating cities and spatial2439lag of their cointegrated counterparts2440τ statistic2441z statistic2442β2443Nanchang2444-3.561*2445-25.128*24460.8434412447Changsha2448-4.541**2449-34.150**24501.2879452451Guiyang2452-3.0892453-18.20924540.8712912455Kunming2456-4.069**2457-20.546*24580.6022302459Notes: The test is based on one equation regression in which we take column cities2460as dependent variables and the spatial lags of their cointegrated counterparts as2461independent variables. The first two columns report the τ statistic and z statistic of2462ADF test with the null hypothesis of no cointegration. The third column reports the2463estimation of β. Note that the t-ratio for β is invalid in this case. * and ** indicate2464the 5% and 1% significance level, respectively.2465With βi being determined, the spatial-temporal house price dynamic model for each2466city can be estimated using ordinary least squares (OLS). The estimation results are2467summarized in Table 5.6 where the lag-orders are set to 2. These models perform2468reasonably well because the Breusch-Godfery test suggests no serial correlation in each2469regression’s residuals at least at the 5% significance level.2470The error correction terms, which appear in the model specification of four cities, are all2471significant at the 10% significance level, three of which are significant at the 5% level or2472above. That is, the four cities’ short-run dynamics are influenced by the deviation from2473the long-run equilibrium relationship. The coefficient ϕi0 indicates that the house price2474of Changsha responds to the disequilibrium much more rapidly than that of the other2475three cities.2476We now turn to the influence of short-term dynamics. Not surprisingly, the first-lag2477price changes are significantly positive in all equations. The second-order lagged price2478dynamics also play a role in the price equation for Fuzhou and Xiamen. Similarly, the2479lagged price changes from neighbouring cities (either from the cointegration group or2480the non-cointegration group) are also found to be statistically significant in all2481equations, except for Changsha and Kunming. This confirms the existence of cross-city2482spillover effects from the neighbouring cities, which is in accordance with the findings2483of Holly et al. (2011) for the UK market and Helgers and Buyst (2016) for Belgian2484housing markets.24851192486Spatial interrelations of Chinese housing markets: Spatial causality, convergence and diffusion248724882489===== PAGE 140 (score 112, numeric-paren 94, table-words 2, var-words 0) =====24902491TABLE 5.62492Estimation results of the spatial-temporal house price diffusion model2493City2494Constant2495Error2496correction2497Own lag effects2498Lag effects of2499cointegration group2500Lag effects of non-2501cointegrated group2502Adjusted2503R22504Serial2505correlation2506ϕi02507ai12508ai22509bi12510bi22511ci12512ci22513Guangzhou25140.00072515(0.001)2516–25170.4326***2518(0.098)25190.07652520(0.108)2521–2522–25230.6540***2524(0.182)2525-0.3067*2526(0.161)25270.51425285.4522529Shenzhen25300.00112531(0.001)2532–25330.6464***2534(0.106)2535-0.00382536(0.106)2537–2538–25390.9324**2540(0.197)2541-25420.7141***2543(0.200)25440.52725456.0352546Fuzhou25470.00052548(0.001)2549–25500.3074***2551(0.100)25520.2321*2553(0.097)2554–2555–25560.5384***2557(0.140)2558-0.22312559(0.141)25600.54825610.5882562Xiamen25630.00082564(0.001)2565–25660.1673*2567(0.096)25680.1624*2569(0.093)2570–2571–25720.7223***2573(0.167)2574-0.15772575(0.180)25760.47725772.3442578Nanchang25790.0548*2580(0.028)2581-0.0755*2582(0.040)25830.3530***2584(0.104)25850.07232586(0.108)25870.07372588(0.098)2589-0.04362590(0.096)25910.3720**2592(0.171)2593-0.04302594(0.174)25950.42525964.7082597Changsha2598-25990.2594***2600(0.062)2601-26020.2006***2603(0.048)26040.3654***2605(0.093)26060.07262607(0.092)26080.14372609(0.158)2610-0.09342611(0.159)26120.17632613(0.192)26140.16282615(0.195)26160.54126171.2712618Nanning26190.00032620(0.001)2621–26220.4869***2623(0.106)26240.02442625(0.101)2626–2627–26280.3624**2629(0.171)26300.09282631(0.170)26320.61526333.1112634Guiyang26350.0414**2636(0.020)2637-26380.0696**2639(0.034)26400.4129***2641(0.095)2642-0.02582643(0.092)26440.4800***2645(0.109)2646-0.2064*2647(0.111)26480.09762649(0.155)2650-0.04132651(0.165)26520.46726537.778*2654Kunming26550.1915***2656(0.059)2657-26580.1092***2659(0.034)26600.3423***2661(0.102)2662-0.05462663(0.098)26640.13232665(0.109)2666-0.14762667(0.106)26680.38472669(0.263)26700.00622671(0.232)26720.25826730.8552674Chengdu2675-0.00022676(0.000)2677–26780.2419**2679(0.099)26800.04202681(0.098)2682–2683–26840.3315***2685(0.120)26860.17532687(0.124)26880.55026891.9342690Notes: The estimation results are based on equation (4) with lag-orders being set to 2. For the cities except Nanchang, Changsha, Guiyang and2691Kunming, we eliminate the error correction term and the term ‘lag effects of cointegration group’ because these cities do not have cointegrated2692counterparts. The “serial correlation” column reports the Breusch-Godfery serial correlation statistic test that distributes approximately as χ226933 under2694the null hypothesis of no residual serial correlation. *, ** and *** indicate the 10%, 5% and 1% significance level, respectively.26951202696The Spatial Dimension of House Prices269726982699===== PAGE 141 (score 7, numeric-paren 0, table-words 3, var-words 1) =====27002701The regression results of spatial-temporal diffusion models presented in Table 5.62702depict a complicated dynamic system in which the historical house price changes of a2703city not only affect its own price changes but also influence the price changes in other2704cities directly or indirectly through their neighbouring cities, or through the long-run2705equilibrium. To intuitively illustrate the diffuse nature of house prices in a complicated2706system, we provide the generalized impulse response functions, which can trace the2707time profile of shocks both over time and space.2708FIGURE 5.32709Generalized impulse responses of a positive unit shock (one standard2710error) to Shenzhen house prices2711Figure 5.3 plots the generalized impulse responses of all the cities to a positive unit2712shock (one standard error) to the house prices of Shenzhen, one of the most developed2713cities in the Pan-PRD. The positive shock gradually diffuses to the remaining cities,2714significantly raising the house prices in the whole area (being confirmed by the2715bootstrap confidence interval in Figure B1 in the Appendix). However, the magnitude2716of the spillover effect differs across the region. Given the one standard error shock to2717Shenzhen, its own house prices soar approximately 3.5%, followed by Guangzhou,2718which rises by approximately 2%. Conversely, the increases of the other cities’ house2719prices are approximately 1%. This indicates a diverged interurban housing market2720between developed and less-developed cities. For the sake of comparison, Figure 5.42721portrays the responses to a positive stand error shock to Changsha, a city in Central2722China and cointegrating with the other three cities. It is clear that the unit shock to2723Changsha generates relatively homogenous effects on all other cities’ house prices2724(house prices increases are approximately between 0.8% and 1%), except for Shenzhen2725and Kunming. The effect on Shenzhen house prices is not significant, as indicated by2726the bootstrap error bounds shown in Figure B2 (refer to the Appendix). This2727information further supports our conclusion regarding the divergence of a few cities’27281212729Spatial interrelations of Chinese housing markets: Spatial causality, convergence and diffusion273027312732===== PAGE 148 (score 28, numeric-paren 16, table-words 2, var-words 0) =====27332734.............................................................................................................................2735Appendices2736.............................................................................................................................2737Appendix A2738.............................................................................................................................2739TABLE A12740The results of pairwise Johansen cointegration test2741Shenzhen Fuzhou2742Xiamen2743Nanchang Changsha Nanning Guiyang Kunming Chengdu2744Shenzhen2745Fuzhou27467.6027471.952748Xiamen27498.6927507.442751Nanchang 7.25275211.1127539.0527547.19**27550.1627561.572757Changsha 10.0227589.8327597.27276020.27**27614.45*27628.80**2763Nanning276410.74276512.6627669.01276712.77276810.2627692.052770Guiyang27716.81277214.52277310.30277418.03*277518.22*277613.7427770.012778Kunming 2.40277913.2027806.46278116.89*278225.04**278318.55*278417.07*2785Chengdu 6.75278616.61*27874.12278815.46278913.93279012.94279115.03279213.222793Notes: The lower triangle cells report the trace statistic of the pairwise Johansen cointegration test2794under the null hypothesis H0 : r = 0. The test is based on a VAR(3) specification, with unrestricted2795intercept and no trend in VAR. For the co-integrated city pairs, the upper triangle cells report the2796log-likelihood ratio (LR) test for the cointegrating vector restriction (1,-1). * and ** denote 5% and27971% significance level, respectively.2798TABLE A22799Pairwise convergence with pre-specified coefficients (1,-1) base on the MTAR2800unit root test2801Shenzhen Fuzhou2802Xiamen2803Nanchang Changsha Nanning Guiyang Kunming Chengdu2804Shenzhen2805Fuzhou28062.08(1)2807Xiamen28083.72(1)28090.70(2)2810Nanchang 1.54(1)28111.43(1)28120.48(1)2813Changsha 3.19(1)28143.93(2)28151.40(2)28164.87(1)2817Nanning28180.18(1)28192.76(1)28201.96(2)28212.15(1)28220.32(1)2823Guiyang28241.90(1)28252.38(1)28261.55(2)28274.73(1)28284.66(1)28293.03(1)2830Kunming 0.91(1)28315.17*(1) 2.17(1)28327.81**(1) 8.29**(1) 6.01*(1) 4.10(1)2833Chengdu 0.24(1)28344.34(1)28354.60(2)28361.67(1)28373.72(1)28385.96*(1) 1.20(1)28392.71(1)2840Notes: The null hypothesis of no convergence is tested based on the residual from pit −pjt. In all2841the models a constant is included, and the lag length is shown in the parentheses. The 5% and28421% critical values are 5.02 and 7.10, respectively. * and ** denote 5% and 1% significance level,2843respectively.28441282845The Spatial Dimension of House Prices284628472848===== PAGE 149 (score 3, numeric-paren 0, table-words 1, var-words 1) =====28492850Appendix B: Bootstrap GIRF confidence intervals2851.............................................................................................................................2852The methods for computing the bootstrap confidence intervals of the generalized2853spatial-temporal impulse response functions are borrowed from Holly et al.(2011). The2854estimated model (7) is first used to generate B bootstrap samples. The bth bootstrap2855sample can be obtained by the following Data Generation Process (DGP)2856p(b)2857t2858= ˆa + ˆΦ1p(b)2859t−1 + ˆΦ2p(b)2860t−2 + ˆϵ(b)2861t2862,2863(B.1)2864where ˆϵ(b)2865t2866= ˆΣ28671/2v∗(b)2868t2869. The elements of v∗(b)2870t2871are recursively replaced by the values that2872are randomly drawn from the transformed residual matrix ˆΣ2873−1/2 (ˆϵ1, ˆϵ2, . . . , ˆϵt). Note2874that in equation (B.1), the first 2 observations are replaced by the original data.2875When obtaining the bootstrap sample p(b)2876t2877, we estimate the model (7) again and2878produce the bth bootstrap GIRF2879g(b)2880i2881(h) =2882ˆΨ2883(b)2884h2885ˆΣ2886(b)ei2887√2888ˆσ(b)2889ii2890,2891for2892i = 1, · · · , n; h = 0, 1, · · · , H.2893(B.2)2894The lower and upper bands of 100(1 −α)% confidence interval are equivalent to the2895α/2 and 1 −α/2 quantiles of B g(b)2896i2897(h) for each i and h.28981292899Spatial interrelations of Chinese housing markets: Spatial causality, convergence and diffusion290029012902===== PAGE 168 (score 66, numeric-paren 54, table-words 2, var-words 3) =====29032904When estimating the MGWR model, we used the adaptive bi-square function to2905construct the weighting scheme, given that the transactions were not evenly2906distributed across space. In this case, the bandwidth is generally referred to as the2907window size, and the choice of window size is equivalent to the choice of the number of2908nearest neighbors. To find the optimal value, we varied the window size from 10% to290995% using a 5% interval and selected the size that yielded the lowest CV score as given2910by equation (18). Each annual sample has a unique optimal window size. The CV2911scores indicated that a 10% window size was preferred for most of the years, except for29121999, 2000 and 2002, with an optimal size of 15%, and 2003, with an optimal size of291330%. However, for the construction of price indexes, we would prefer using the same2914window size for all years, especially since the number of sales is almost evenly spread2915across the whole period. So we chose a window size of 10% for each year, leading to 602916nearest neighbors that were used in the estimation of the annual MGWR models.2917TABLE 6.12918Parameter estimates for structures characteristics, 20072919OLS2920OLSD2921MGWR2922Intercept29231480.70***2924(46.93)29251405.41***2926(53.71)29271395.76***2928(57.51)2929Building period:1960-19702930-370.48***2931(25.94)2932-389.50***2933(36.67)2934-398.40***2935(41.75)2936Building period:1971-19802937-311.17***2938(23.36)2939-261.50***2940(33.96)2941-323.50***2942(41.75)2943Building period:1981-19902944-232.93***2945(23.37)2946-173.08***2947(32.59)2948-226.14***2949(42.87)2950Building period:1991-20002951-58.64***2952(21.64)2953-49.34*2954(26.55)2955-115.13***2956(37.26)2957Terrace2958-285.65***2959(35.17)2960-264.34***2961(35.24)2962-187.28***2963(37.32)2964Corner2965-281.36***2966(31.77)2967-274.54***2968(31.18)2969-192.85***2970(34.07)2971Semidetached2972-122.89**2973(47.96)2974-149.50***2975(47.57)2976-96.93**2977(48.73)2978Duplex2979-151.08***2980(30.60)2981-147.24***2982(30.17)2983-104.56***2984(31.03)2985Notes:Standard errors are reported in parentheses; ***, ** and * denote significance at the 1%2986, 5% and 10% level, respectively.2987As an illustration, Table 6.1 shows the 2007 parameter estimates for the structures2988characteristics. Almost all of the estimates differ significantly from zero at the 1% level.2989To some extent they vary across the different models. For example, the OLS intercept2990term is relatively high compared to the OLSD and MGWR intercepts. Note that, since2991dummy variables for houses built after 2000 and for detached houses were not2992included, the intercept measures the price in euros of structures per square meter of2993living space for detached houses built after 2000. In accordance with a priori2994expectations, detached dwellings are more expensive than other types of houses. For29951482996The Spatial Dimension of House Prices299729982999===== PAGE 169 (score 17, numeric-paren 0, table-words 3, var-words 3) =====30003001all models, there is a clear tendency for the structures to become less expensive as they3002are geɦing older.3003TABLE 6.23004Summary statistics for estimated land prices3005OLS3006OLSD3007MGWR3008Mean3009S.D.3010Min3011Max3012Median3013Mean3014S.D.301519983016116.803017131.50301831.14301972.303020231.033021122.663022125.49302328.66302419993025154.643026178.50302734.853028105.953029223.663030174.073031167.77303230.39303320003034239.773035239.41303636.243037138.533038319.323039251.343040241.83304144.27304220013043214.543044235.58304547.593046110.413047295.013048229.523049226.70305048.77305120023052234.773053245.11305438.413055156.153056323.633057255.053058242.23305940.89306020033061166.073062185.11306344.23306482.123065248.233066179.933067172.26306844.55306920043070186.403071197.19307229.753073104.953074254.203075197.703076195.41307733.78307820053079226.133080224.11308136.553082127.533083299.743084214.193085205.89308635.17308720063088202.843089195.77309030.853091125.903092274.243093207.433094201.27309532.05309620073097214.873098236.73309927.963100141.463101286.913102235.073103229.25310430.993105Notes: For OLS, the land price estimates are reported. For OLSD, the columns show the3106weighted mean and standard deviation of the estimated land prices for 9 postcode areas where3107the weights are equal to the share of transactions within each postcode area. For MGWR, the3108columns provide summary statistics for the land price estimates of all transacted properties.3109Table 6.2 contains summary statistics for the estimated price per square meter of land3110from the three models. The three average land price series exhibit a similar paɦern3111over time, which differs substantially from the changes in the average transaction price3112of the properties (see Table A1 in the Appendix). After a sharp increase in 1999, the3113estimated average land price fluctuated during a couple of years, experienced a3114dramatic drop in 2003, and then increased again.3115As mentioned earlier, a virtue of MGWR is that it allows us to plot a continuous map3116with estimated prices of land per square meter. For the year 2007, such a map is3117depicted in Figure 6.1 for the city of “A”, where the land prices have been rescaled to3118the range [0,1]. The postcode areas are indicated as well. While the spatial paɦern in3119Figure 6.1 is largely consistent with the paɦern found using the OLSD model (shown in3120Figure A1 in the appendix), the MGWR land prices estimates do vary within some of3121the areas. This suggests that the use of postcode dummies, as in the OLSD model, is a3122rather crude strategy to incorporate spatial variation of land prices.3123To formally compare the performance of the three hedonic models, two statistics were3124calculated, the Corrected Akaike Information Criterion (AICc) and the Root Mean3125Square Error (RMSE). The AICc takes into account the trade-offbetween goodness of fit3126and degrees of freedom. The AICc expressions for the OLS and OLSD models can be3127found in Hurvich and Tsai (1989). And for MGWR models, it is defined by3128AICc = 2nln(ˆσ) + nln(2π) + n3129(3130n + tr(S)3131n −2 −tr(S)3132)31331493134Accounting for spatial variation of land prices in hedonic imputation house price indexes: A semi-parametric3135approach313631373138===== PAGE 170 (score 3, numeric-paren 0, table-words 1, var-words 1) =====31393140FIGURE 6.13141Price of land per square meter, 20073142where ˆσ is the estimated standard deviation of the error term and tr(S) the trace of the3143hat matrix described in section 6.3.2. The RMSE measures the variability of the3144absolute prediction errors of the models and is given by3145RMSE = 13146n3147√∑3148i3149(pi −ˆpi)2.3150Table 6.3 shows the AICc and RMSE and their differences for the three models. A rule3151of thumb states that if the difference in the AICc for two models is larger than 3, a3152significant difference exists in their performance (Fotheringham et al. 2002). It can be3153seen that the OLSD model performs much beɦer than the OLS model in all years, as we3154would expect, and in turn that the MGWR model outperforms the OLSD model (except3155for 2003, when the difference is insignificant). The same ranking is found if the RMSE3156is used to assess the various models. These results confirm the earlier finding that land3157prices vary across space, both across and within postcode areas.3158Although MGWR is obviously beɦer suited to model the variation of land prices and to3159predict property prices, the OLSD model does a surprisingly good job. In several years,31601503161The Spatial Dimension of House Prices3162