# RECORD c63f29dcdec077b7ee126d8f2c6b0bcc6611e6a7
# TITLE: Spatial heterogeneity in implicit housing prices: evidence from Hangzhou, China
# YEAR: 2017.0  VENUE: nan  DOI: 10.3846/1648715x.2016.1247021
# AUTHORS: Hai-Zhen Wen; Yilan Jin; Ling Zhang
# PAGES: 14  CANDIDATE TABLE PAGES (1-based): [7, 8, 9]
# ABSTRACT: Estimated coefficients in hedonic price models are generally assumed to be constant throughout the entire study area. However, increasing evidence reveals that the marginal prices of housing characteristics may vary over space and that the spatial heterogeneity problem in implicit housing prices should be given attention. Taking Hangzhou, China, as an example, this study uses the micro data of 603 residential communities in 2014 to examine spatial heterogeneity in implicit housing prices. On the basis of the traditional hedonic price model, we establish spatial expansion and geographically weighted regression (GWR) models for comparative analysis. Results show that the spatial expansion and GWR models have excellent goodness of fit and can improve the traditional hedonic price model. The mixed geographically weighted regression (MGWR) model further reveals that the implicit prices of nine housing characteristics vary significantly over space and that the impacts of the four remaining housing characteristics on housing prices are fixed throughout the entire study area. Unlike the traditional hedonic price model and spatial expansion model, the GWR/MGWR model has the unique advantage of visually providing the spatial distribution of implicit housing prices and accurately describing spatial heterogeneity.


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Copyright © 2017 Vilnius Gediminas Technical University (VGTU) Press
http://www.tandfonline.com/tspm
SPATIAL HETEROGENEITY IN IMPLICIT HOUSING PRICES:  
EVIDENCE FROM HANGZHOU, CHINA
Haizhen WEN a, Yilan JIN a, Ling ZHANG a,*
a Center for Real Estate Studying, Department of Civil Engineering, Zhejiang University, 310058 Hang-
zhou China
Received 13 May 2015; accepted 4 April 2016
ABSTRACT. Estimated coefficients in hedonic price models are generally assumed to be constant 
throughout the entire study area. However, increasing evidence reveals that the marginal prices of 
housing characteristics may vary over space and that the spatial heterogeneity problem in implicit 
housing prices should be given attention. Taking Hangzhou, China, as an example, this study uses 
the micro data of 603 residential communities in 2014 to examine spatial heterogeneity in implicit 
housing prices. On the basis of the traditional hedonic price model, we establish spatial expansion 
and geographically weighted regression (GWR) models for comparative analysis. Results show that 
the spatial expansion and GWR models have excellent goodness of fit and can improve the traditional 
hedonic price model. The mixed geographically weighted regression (MGWR) model further reveals that 
the implicit prices of nine housing characteristics vary significantly over space and that the impacts 
of the four remaining housing characteristics on housing prices are fixed throughout the entire study 
area. Unlike the traditional hedonic price model and spatial expansion model, the GWR/MGWR model 
has the unique advantage of visually providing the spatial distribution of implicit housing prices and 
accurately describing spatial heterogeneity.
KEYWORDS: Housing price; Spatial heterogeneity; Hedonic price model; Geographically weighted 
regression
1. INTRODUCTION
With the acceleration of China’s urbanization pro-
cess, the real estate market has developed rapidly 
across many cities. Along with the rapid develop-
ment in Chinese housing market is the evident 
spatial differentiation of housing prices in some 
big cities, a topic that has attracted the attention 
of many scholars (Xu 1997; Wang, Zhu 2004; Zhou, 
Luo 2004; Zhou, Zhen 2008; Ma et al. 2008). Hang-
zhou, well known for the West Lake, is an impor-
tant central city of the Yangtze River Delta in 
Eastern China. The property market in Hangzhou 
is characterized by high supply, high demand, and 
sustainably rising prices, thus giving birth to the 
“Hangzhou phenomenon”, which is widely recog-
nized by the academia and the real estate industry 
in China (Wen et al. 2014a). The residential mar-
ket in Hangzhou has been ebullient during the last 
two decades, such that the average housing price 
once recorded 25840 RMB/m2 in 2010 as the top 
one in China (Hui et al. 2016). The housing mar-
ket of Hangzhou is typical in China, thus, the city 
represents a perfect context for investigating the 
spatial variation of housing price, which is a key 
issue worthy of study.
Currently, the hedonic price model is the main 
research method used to quantify the determi-
nants of housing prices and to estimate the im-
pacts of such determinants on housing prices. In 
the hedonic price model, the ordinary least squares 
(OLS) method is adopted to estimate the implicit 
prices of housing characteristics (Wang, Huang 
2007; Hao, Chen 2007; Wen et al. 2010). However, 
overlooking the spatial fixity property of housing, 
the traditional hedonic price model assumes that 
housing prices are mutually independent in the 
spatial distribution. Such assumption may lead to 
bias in the model estimation results. As housing 
prices represent a type of spatial data, the topics of 
spatial dependence and heterogeneity have caught 
the attention of many scholars (Anselin 1988, 
*	Corresponding author. E-mail: zlcivil@163.com
International Journal of Strategic Property Management
ISSN 1648-715X / eISSN 1648-9179
2017  Volume  21(1): 15–28 
doi:10.3846/1648715X.2016.1247021


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Spatial heterogeneity in implicit housing prices: evidence from Hangzhou, China
21
In the empirical estimation of the GWR/
MGWR model, a spatial weight matrix needs to 
be introduced. The spatial weight function can 
be determined in several ways, such as through 
the threshold distance, inverse distance, bi-square 
function and Gaussian function. The results of 
GWR are sensitive to the choice of bandwidth. 
Besides assuming a predefined and fixed band-
width, an adaptive bandwidth has been proven to 
be highly suitable in practice (McMillen, Redfearn 
2010). Therefore, we chose a Gaussian function as 
an adaptive spatial kernel that allows the band-
width to vary based on the density of house sales 
around each regression point, thus encapsulating 
a smaller area where data are rich and a larger 
area where data are sparse. To obtain the optimal 
bandwidth, Fotheringham et al. (2002) proposed 
that the GWR model has the best bandwidth when 
the value of the corrected Akaike Information Cri-
terion (AICc) or the cross-validation (CV) is at the 
minimum.
4. RESULTS AND DISCUSSION
4.1. Traditional hedonic price model
As the traditional hedonic price model, Model 1 
is estimated by the OLS method. The regression 
results are shown in Table 2. The analysis of vari-
ance results of the model show that the significant 
probabilities for the F value are less than 0.001, 
which confirms the validity of the equation and 
rejects the original hypothesis of all coefficients 
being zero. The value of the adjusted R2 is 0.567, 
which means that the independent variables can 
explain 56.7% of the variation of the dependent 
variable. The values of the variance inflation fac-
tor of all variables are between 1.272 and 4.203, 
which shows that the degree of collinearity among 
the independent variables is not serious.
Model 1 is a global model in which the implicit 
prices are held unchanged throughout the study 
area. Nine housing characteristic variables signifi-
cantly affect the housing price. Except for traffic 
condition, the other coefficients exhibit signs that 
match the theoretical expectations. The implicit 
price of traffic condition is negative, probably be-
cause private car ownership has grown rapidly 
during the rapid economic development period in 
Hangzhou and has thus reduced the dependence 
on public transport such as buses. The presence of 
buses around the residential area inevitably brings 
about some negative effects, such as traffic conges-
tion, exhaust pollution, and noise pollution. Hence, 
bus lines are likely to have a negative effect on 
housing price. The results are substantially con-
sistent with the findings of Wu et al. (2008) and 
Wen et al. (2014b), Wen and Tao (2015).
The regression coefficient of the nearby sub-
way variable does not pass the significance level 
of 10%, which indicates that the subway has no 
significant influence on housing price in the tradi-
tional hedonic price model. However, from a theo-
retical point of view, subways should have a signif-
icant impact at least on the surrounding housing 
prices. As the traditional hedonic price model can 
estimate only the average implicit price, the re-
gression coefficient of the nearby subway variable 
ultimately fails to reach the 10% significance level. 
Similarly, the building age variable in the tradi-
tional hedonic price model is not significant. Fur-
thermore, the statistics of Moran’s I for the spatial 
autocorrelation test is 0.387, and the significance 
level is below 0.001. These results show the obvi-
ous spatial effect of housing price on the regional 
distribution in Hangzhou, indicating that OLS pa-
rameter estimates are inefficient and t-ratios are 
biased (Dubin 2003). Therefore, We use the spatial 
extension and GWR models for further analysis.
4.2. Spatial expansion model
With the interaction terms between the 13 vari-
ables and the coordinates of the sample points, two 
spatial expansion models are estimated by OLS. 
Table 2. Regression results of the traditional hedonic 
price model
Variables
Coefficients
t
Constant
10.188***
117.612
ln(building age)
−0.011
−0.734
Inner environment
0.013
1.221
External environment
0.008
0.809
Property management
0.042***
5.328
Sports facility
0.031***
3.925
Nearby university
0.046***
2.979
Living facility
0.018**
2.208
Education facility
0.033***
3.390
Nearby subway
0.020
1.162
Traffic condition
−0.002***
−3.023
ln(distance to Wulin Square)
−0.067***
−3.429
ln(distance to the West Lake)
−0.221***
−12.694
ln(distance to the Qianjiang 
New Center)
−0.059***
−4.018
AICc
−468.846
Adjusted R2
0.567
Note: ***,**, and * represent significance at the 1%, 5%, and 
10% levels, respectively.


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H. Wen et al.
22
The values of the variance inflation factor of all 
variables are less than 10, which show that the se-
rious collinearity is not present in the two expan-
sion models. We report only the coefficients that 
are at least significant at the 10% level.
The results for Model 2, the one-degree spatial 
expansion, are shown in the second and third col-
umns. The adjusted R2 is 0.671, which indicates 
that Model 2 can more effectively explain the vari-
ations of the dependent variable and demonstrate 
a more favorable goodness of fit compared with 
Model 1. Ten ‘‘base’’ housing characteristic vari-
ables have significant effects on housing prices, 
and five of these variables interact with location 
coordinates. Ten location–characteristic interac-
tion terms are significant at the 10% level, which 
indicates that spatial heterogeneity exists in the 
marginal prices of these housing characteristics. 
For example, the regression coefficients of Living 
facility is 0.032 which indicate that, in general, the 
value of Living facility increases by 1 unit and the 
housing prices will increase by 3.2%. The inter-
action term of U(living facility) is −0.007, which 
reveal that spatial heterogeneity exists in the hori-
zontal direction, and for the same quality of living 
facility, an additional 1 km from the Wulin Square 
(measured horizontally) will reduce an average 
community housing price by 0.7%.
Five variables, namely, building age, inner envi-
ronment, external environment, property manage-
ment, and sports facility, have significant effects 
on housing prices, but their interaction terms are 
not significant. This condition indicates that the 
marginal prices of these variables do not vary in 
the locational context. Furthermore, two variables, 
namely, nearby university and nearby subway, are 
not significant. However, their interaction terms 
are significant at the 10% and 5% significance lev-
els, respectively, indicating that the interaction 
terms still have space differences to some extent.
Table 3 also reports the results of Model 3, the 
quadratic spatial expansion model. The addition 
of the quadratic interaction terms in Model 3 re-
sults in an improvement in the explanatory power 
as the adjusted R2 increases from 0.671 to 0.704. 
A total of 15 out of the 65 interaction variables 
are significantly different from 0 at the 10% sig-
nificance level. The one-degree interaction terms 
of four variables and the quadratic interaction 
terms of seven variables have significant effects 
on the housing prices. This result provides strong 
evidence of implicit prices with complicated spatial 
distribution patterns.
Table 3. Regression results of spatial expansion models
Variables
One-degree term 
model
Quadratic term 
model
Coeffi-
cients
t
Coeffi-
cients
t
Constant
10.698 ***
91.871
10.699 *** 67.515
ln(building age)
−0.061 *** −3.765 −0.079 *** −3.247
Inner 
environment
0.022 *
1.649
0.029 ***
1.729
U(inner 
environment)
0.008 *
1.803
External 
environment
0.022 *
1.653
0.050 ***
2.616
U(external 
environment)
−0.015 **
−2.526
Property 
management
0.036 ***
3.490
0.033 **
2.267
V2(property 
management)
−0.001 *
−1.718
Sports facility
0.032 ***
4.034
0.055 ***
4.131
V2(sports 
facility)
−0.001 *
−1.877
V(nearby 
university)
0.007 *
1.792
Living facility
0.032 ***
3.043
U(living facility)
−0.007 **
−2.445 −0.010 **
−1.984
Education 
facility
0.050 **
2.461
U2(education 
facility)
−0.003 **
−2.471
Nearby subway
−0.209 *** −3.208
U(nearby 
subway)
0.053 ***
2.587
V(nearby 
subway)
0.018 **
2.387
0.081 ***
3.232
UV(nearby 
subway)
−0.013 **
−2.493
Traffic condition
−0.005 *** −3.585 −0.004 **
−2.037
U(traffic 
condition)
0.001 *
1.818
V(traffic 
condition)
0.001 ***
3.682
0.001 *
1.952
ln(distance 
to the Wulin 
Square)
−0.087 *
1.786
−0.168 **
−2.149
Uln(distance to 
Wulin Square)
0.033 **
2.212
0.128 ***
3.099
Vln(distance to 
Wulin Square)
0.019 *
1.898
U2ln(distance to 
Wulin Square)
−0.021 **
−2.547
ln(distance to 
the West Lake)
−0.269 *** −7.596 −0.336 *** −6.557
Vln(distance to 
the West Lake)
−0.022 **
−2.413
V2ln(distance to 
the West Lake)
−0.008 *
−1.648
ln(distance to 
the Qianjiang 
New Center)
−0.185 *** −4.028 −0.237 *** −3.061
Uln(Distance to 
the Qianjiang 
New Center)
−0.015 *
−1.716 −0.076 **
−2.505
U2ln(distance to 
the Qianjiang 
New Center)
0.017 ***
3.134
AICc
−605.089
−657.128
Adjusted R2
0.671
0.704
Note: ***,**, and * represent significance at the 1%, 5%, and 
10% levels, respectively.


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Spatial heterogeneity in implicit housing prices: evidence from Hangzhou, China
23
The results of the two spatial expansion mod-
els confirm that spatial heterogeneity exists in the 
implicit prices of the housing characteristics of the 
Hangzhou market. For example, the variables of 
inner environment, external environment, nearby 
subway, and building age are insignificant in the 
traditional hedonic price model, but their interac-
tion terms are significant in Models 2 and 3. This 
result indicates the influence of the four variables 
on housing price and their tendency to still change 
over space. No significant residual dependence on a 
0.01 level is detected by the Moran’s I, which indi-
cates spatial expansion models can capture the spa-
tial effect and be used to improving the misspecifi-
cation problem, which lead to inefficient parameter 
estimations in the traditional hedonic price model.
4.3. Geographically weighted regression 
model
With a Gaussian kernel, CV determines an opti-
mal adaptive bandwidth that includes 182 obser-
vations. Sensitivity analysis with alternative ker-
nels (i.e. bi-square kernel) shows no significant dif-
ferences. The values of VIF of all variables are less 
than 5, which do not suggest a problem of collin-
earity among the independent variables. Table 4 
shows the regression results of Model 4 (GWR). 
The adjusted R2 is 0.757, which is significantly 
better than that in the traditional hedonic price 
model and the two spatial expansion models. This 
improvement reflects that the GWR model can ef-
fectively explain the relationship between housing 
prices and the explanatory variables and provide 
strong evidence that spatial heterogeneity plays 
an important role in the Hangzhou housing mar-
ket. The GWR parameter estimates, which vary 
at each observation point, are described by their 
minimum, median, and maximum values, as well 
as by their interquartile range.
For example, the lower quartile of the regres-
sion coefficients of the distance to the West Lake 
is −0.421 and the upper quartile is −0.171. These 
values indicate that in a certain space location, the 
distance to the West Lake increases by 1% and the 
housing prices decline by 0.421%. Meanwhile, in 
another space location, the distance to the West 
Lake increases by 1% while the housing prices 
decline by 0.171%. The magnitude of change is 
0.25%. One advantage of GWR is that the spatial 
patterns of the parameter estimates can be eas-
ily mapped and visualized. Figure 1 reveals the 
spatial effect of the distance to the West Lake on 
housing price. Almost all samples reach the signifi-
cance level of 1% by P value. Hence, the distance 
to the West Lake has an important influence on 
the housing prices throughout the entire study 
area. As expected, the estimates are negative and 
exhibit localized spatial patterns. The highest es-
timates are found within North Hangzhou, where 
the housing prices are relatively lower than that 
in other areas, resulting in the rapid decrease 
of the price gradient of the distance to the West 
Lake. The estimates are the smallest and exhibit 
Table 4. Results of GWR model
Variables
Min
Lwr Quartile
Median
Upr Quartile
Max
Constant
5.373
9.804
10.520***
10.848
12.687
ln(building age)
−0.180
−0.107
−0.061**
−0.024
0.006
Inner environment
−0.034
0.029
0.043**
0.066
0.097
External environment
−0.042
−0.005
0.015*
0.028
0.103
Property management
−0.015
0.006
0.016***
0.026
0.051
Sports facility
−0.019
0.015
0.028***
0.043
0.076
Nearby university
−0.104
−0.015
0.015***
0.050
0.210
Living facility
−0.087
−0.017
0.012***
0.047
0.092
Education facility
−0.068
−0.015
0.010***
0.047
0.155
Nearby subway
−0.170
−0.004
0.021**
0.048
0.164
Traffic condition
−0.009
−0.004
−0.002***
0.000
0.005
ln(distance to Wulin Square)
−1.295
−0.151
−0.034***
0.124
1.159
ln(distance to the West Lake)
−1.224
−0.421
−0.280***
−0.171
0.083
ln(distance to the Qianjiang New Center)
−1.317
−0.272
−0.131***
0.082
2.775
AICc
−714.328
Adjusted R2
0.757
Note: ***,**, and * represent significance at the 1%, 5%, and 10% levels, respectively.


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H. Wen et al.
24
relatively smooth spatial trends within Central 
Hangzhou (the eastern region of the West Lake), 
which belongs to the traditional downtown area 
with convenient public facilities. The housing pric-
es in this area are relatively high. In other words, 
the GWR model shows that the implicit prices of 
13 housing characteristics are not entirely fixed in 
space but exist with spatial heterogeneity. These 
results verify that the global/average estimation by 
the traditional hedonic price model may be flawed.
Model 5 is the MGWR. Compared with the 
GWR model, the MGWR model divides independ-
ent variables into two types: global variables with 
fixed estimated coefficients (see Table 5) and lo-
cal variables that change over space (see Table 6). 
Following the test statistic of Leung et al. (2000a), 
we find that four independent variables in the 
study are global variables while the remaining 
nine variables are local variables. Again, applying 
a Gaussian kernel function, CV results in an opti-
Fig. 1. P value and regression coefficients for the distance to the West Lake variable
Table 5. Regression results for global variables
Variables
Coefficients
t value
Critical value 
(10%)
Critical value (5%)
Inner environment
0.048
4.176
1.648
1.965
Nearby university
0.040
2.635
Sports facility
0.021
3.246
Property management
0.012
1.722
Table 6. Regression results for local variables
Variables
Min
Lwr Quartile
Median
Upr Quartile
Max
Constant
3.401
9.887
10.354
10.879
13.094
ln(building age)
−0.214
−0.113
−0.079
−0.030
0.033
External environment
−0.055
−0.006
0.015
0.031
0.109
Living facility
−0.107
−0.016
0.011
0.051
0.105
Education facility
−0.094
−0.015
0.025
0.045
0.194
Nearby subway
−0.205
−0.013
0.007
0.042
0.254
Traffic condition
−0.011
−0.004
−0.002
0.000
0.005
ln(distance to Wulin Square)
−1.739
−0.160
−0.003
0.120
1.515
ln(distance to the West Lake)
−1.328
−0.403
−0.307
−0.142
0.142
ln(distance to Qianjiang New Center)
−1.594
−0.279
−0.069
0.072
3.862
AICc
−756.902
Adjusted R2
0.766