# RECORD 58a9ab2513035056fdc6d56cafc04ae9d61a0955
# TITLE: Willing to pay more for high-quality schools?
# YEAR: 2018.0  VENUE: nan  DOI: 10.14246/irspsd.6.1_45
# AUTHORS: Lin-Chuan Yang; Bo Wang; Yunyi Zhang; Zi-Wei Ye; Yu-Zhuo Wang; Peng-Fei Li
# PAGES: 18  CANDIDATE TABLE PAGES (1-based): [9, 10, 12]
# ABSTRACT: : Principally, the enrolment of elementary school in China is solely based on residential location. Due to the scarcity of prestigious schools, the household registration (or hukou in Chinese) and the territorial-based school admission policy, a feasible approach for parents to provide the children with good education is to purchase the house in the attendance zone of a high-quality school (or xuequfang in Chinese). The supply-demand imbalance gives rise to the xuequfang phenomenon (much higher prices of xuequfang relative to non xuequfang) . Based on 1250 housing samples in 286 multi- or high-storey residential districts, this paper firstly develops two basic and four Box-Cox transformed hedonic price models to estimate the effect of high-quality schools on residential property prices. The consistency of six models greatly enhances the credibility of this study. Moreover, complementary, the propensity score matching technique is used to estimate the treatment effect. The two methods consistently suggest that residential property values are affected by top-tier schools. They reveal that xuequfang exhibit values that are between 9.3% and 12.1% higher than non- xuequfang , ceteris paribus . The negative influences of the xuequfang phenomenon and several countermeasures (gradually reforming household registration system , optimizing resource distribution to balance the quality of education, highlighting family education and children’s all-round development) are discussed.


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45 
International review for spatial planning and sustainable development, Vol.6 No.1 (2018), 45-62 
ISSN: 2187-3666 (online) 
DOI: http://dx.doi.org/10.14246/irspsd.6.1_45  
Copyright@SPSD Press from 2010, SPSD Press, Kanazawa 
 
Willing to pay more for high-quality schools?  
A hedonic pricing and propensity score matching approach 
Linchuan Yang¹, Bo Wang2*, Yunyi Zhang3, Ziwei Ye4, Yuzhuo Wang5, 
Pengfei Li6 
 
1 Faculty of Architecture, the University of Hong Kong 
2 Department of Geography, the University of Hong Kong 
3 Shanghai Digital Intelligence System Technology Co.Ltd 
4 Taubman College of Architecture and Urban Planning, University of Michigan 
5 China Academy of Urban Planning and Design 
6 School of Architecture and Civil Engineering, Xiamen University, Xiamen 
* Corresponding Author, Email: wangbo.nju@gmail.com 
Received: June 11, 2016; Accepted: June 23, 2017 
 
Keywords:     Box-Cox transformation; Hedonic price model, School attendance zone, 
Property price, Propensity score matching, Xuequfang 
Abstract:  
Principally, the enrolment of elementary school in China is solely based on 
residential location. Due to the scarcity of prestigious schools, the household 
registration (or hukou in Chinese) and the territorial-based school admission 
policy, a feasible approach for parents to provide the children with good 
education is to purchase the house in the attendance zone of a high-quality 
school (or xuequfang in Chinese). The supply-demand imbalance gives rise to 
the xuequfang phenomenon (much higher prices of xuequfang relative to non-
xuequfang). Based on 1250 housing samples in 286 multi- or high-storey 
residential districts, this paper firstly develops two basic and four Box-Cox 
transformed hedonic price models to estimate the effect of high-quality 
schools on residential property prices. The consistency of six models greatly 
enhances the credibility of this study. Moreover, complementary, the 
propensity score matching technique is used to estimate the treatment effect. 
The two methods consistently suggest that residential property values are 
affected by top-tier schools. They reveal that xuequfang exhibit values that are 
between 9.3% and 12.1% higher than non-xuequfang, ceteris paribus. The 
negative 
influences 
of 
the 
xuequfang 
phenomenon 
and 
several 
countermeasures (gradually reforming household registration system, 
optimizing resource distribution to balance the quality of education, 
highlighting family education and children’s all-round development) are 
discussed.  
1. 
INTRODUCTION 
Education, work and retirement, are three stages of our life. Education is 
the foundation of a nation and is closely related to the overall quality of 
citizens as well as the long-term development of a nation. The importance of 
education to individuals and a state has been universally recognized.  
“Residential property is a multidimensional commodity, characterized by 
durability and structural inflexibility as well as spatial fixity” ((So, Tse, & 
Ganesan, 1997), p.40). It is distinguished by a number of characteristics 


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Yang et al. 
53
 
Until 2015, there were eight provincial-level demonstration elementary 
schools in Xiamen Island (Fig.1). They are Yanwu Elementary School, 
Minli Elementary School, Experimental Elementary School, Second 
Experimental Elementary School, Datong Elementary School, Affiliated 
elementary school of Foreign Language School, Bindong Elementary School 
and Binlang Elementary School. It is noteworthy that all of them are situated 
in the west of Siming District, which reveals the apparent spatial variations 
and imbalance.  
3.3 
Variables 
Table 1 shows the definitions and descriptive statistics of twelve 
independent variables. Except for School, all other eleven independent 
variables are theoretically important variables that need to be statistically 
controlled for by being included in our regression models. It should be noted 
that a variable widely used in the western literature, number of bedrooms, 
was not included in our regression models, in the interest of model 
parsimony, because its effect would overlap with floor area, resulting in the 
presence of multi-collinearity (So, Tse, & Ganesan, 1997).  Moreover, job 
accessibility is not introduced due to the unavailability of data. 
Table 1. Variable Definitions and Descriptive Statistics 
Variable 
Description 
Expected 
sign1 
Mean 
SD 
Area 
Gross floor area (m2) 
+ 
105.69  43.02  
Age 
2015 minus the year of occupation permit 
(number of years) 
- 
12.13  
4.81  
Local 
environment 
Environment quality of residential 
complexes the property, rated on a 5-point 
Likert item from “very bad” (1) to “very 
good” (5)  
+ 
3.08  
0.93  
School 
Dummy variable, 1 if the property is 
xuequfang, 0 otherwise 
+ 
0.13  
0.33  
Kindergarten 
Dummy variable, 1 if there are at least one 
kindergarten within 500 meters, 0 otherwise 
+ 
0.83  
0.37  
Middle school 
Dummy variable, 1 if there are at least one 
middle school within 1000 meters, 0 
otherwise 
+ 
0.82  
0.38  
Xiamen 
University 
Dummy variable, 1 if Xiamen University is 
within 1000 meters, 0 otherwise 
+ 
0.02  
0.13  
BRT 
Dummy variable, 1 if there are at least one 
BRT (Bus Rapid Transit) station within 800 
meters, 0 otherwise 
+ 
0.23  
0.42  
Distance to 
hospital 
Euclidean distance to the nearest Class 2A or 
3A hospital (km) 
? 
0.81  
0.77  
Distance to 
cultural/sports 
center 
Euclidean distance to the nearest 
cultural/sports center (km) 
- 
1.11  
0.66  
Distance to 
city center 
Euclidean distance to Zhongshan Road, the 
city center of Xiamen Island (km) 
- 
6.84  
2.57  
Distance to 
lake 
Euclidean distance to the nearest lake (km) 
- 
1.08  
0.68  
Note: a + and − represent increasing and decreasing impacts on housing prices respectively; ? 
indicates a priori undetermined sign. 


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54 
IRSPSD International, Vol.6 No.1 (2018), 45-62
 
4. 
RESULTS 
4.1 
Initial hedonic price regression 
EVIEWS 9 is used to build a semi-log and a double-log model using the 
ordinary least squares (OLS) method. The dependent variable is modified by 
a natural log transformation in both models whereas independent variables 
are modified by a natural log transformation only in the double-log model. 
We do not transform five dummy variables as they are not definitely greater 
than 0. Table 2 provides the modeling results. The goodness-of-fit values of 
both models (0.801, 0.850) are higher than that based on the same data 
source in Yang et al. (2015) (0.789). This indicates that the two models were 
able to predict higher proportions of variability in their outcomes compared 
to the model in Yang et al. (2015). Moreover, with a higher model fit, the 
double-log model outperforms the semi-log model, which indicates that it 
captures more variations in housing prices. All but two variables are 
significant at the 5% level in both models. Kindergarten and Middle school 
are not significant at the 5% level, which implies that they are not associated 
with housing prices.  
Table 2. Regression results of semi-log and double-log models 
Variable 
Semi-log model 
Double-log model 
coefficient 
t-value 
coefficient 
t-value 
Constant 
4.579a 
88.67 
1.091a  
13.89 
Area 
0.010a 
59.16 
1.008a 
70.70  
Age 
-0.011a 
-7.65 
-0.153a  
-11.26  
Local environment 
0.068a 
8.36 
0.177a 
7.94  
School 
0.089a 
4.00 
0.108a  
5.45  
Kindergarten 
0.009c 
0.47 
-0.011c  
-0.68  
Middle school 
-0.001c 
-0.06 
0.032c 
1.91  
Xiamen University 
0.206a 
3.45 
0.144a 
3.04  
BRT 
0.077a 
4.72 
0.100a 
6.85  
Distance to hospital 
0.047a 
4.41 
0.018b 
2.13  
Distance to cultural/sports center 
-0.057a 
-5.04 
-0.049a 
-5.25  
Distance to city center 
-0.021a 
-6.04 
-0.077a 
-6.36  
Distance to lake 
-0.072a 
-6.06 
-0.051a 
-5.95  
Performance statistics 
Adjusted R2 
0.801 
0.850  
Log-likelihood 
66.00  
238.69  
AIC 
-0.09  
-0.37  
Note: a significant at the 1% level. b significant at the 5% level. c not significant at the 5% 
level. 
With no exception, the signs of all variables’ coefficients agree with a 
priori expectation. The coefficients associated with Area, Local 
environment, School, Xiamen University, BRT are positive. This implies 
that properties with larger size, having better local environment and BRT 
access, within attendance zone of a high-quality school and closer to Xiamen 
University, exhibit higher values. The coefficients of Age, Distance to 
cultural/sports center, Distance to city center, Distance to lake, have the 


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Yang et al. 
55
 
hypothesized negative signs. It indicates that houses at the younger age, with 
better accessibility to the city center, culture/sports center and lake, are more 
expensive, all else being fixed. 
The coefficient associated with Distance to hospital is positive, which 
indicates that proximity to Class 2A and 3A hospitals negatively affects 
housing prices. This indicates the nuisance effect of being located near 
hospitals, which seems somewhat surprising, but consistent with the findings 
in Li et al. (2013) and Peng, B. et al. (2015). There are two possible 
explanations. Firstly, different age cohorts have differing needs and 
preferences of services, for example health care services (Wong et al., 2018). 
Normally, young adults seldom go to hospital, so they may not consider 
proximity to hospitals when making residential location decisions, even tend 
to live far away from hospitals. Notwithstanding, the elderly are in general 
more likely to go to hospital (Yang, 2016; Szeto et al., 2017; Wong et al., 
2017) and may tend to live close to hospitals for better access due to higher 
visiting frequency (Li et al., 2013). In addition, it is crowded around high-
level comprehensive hospitals generally. There are a huge number of people 
and vehicles within these regions, generating noises and air pollution, 
thereby reducing nearby residents’ quality of life (Peng, B. et al., 2015).  
The coefficients of the double-log regression function correspond to 
average attribute elasticities. Gross floor area is found to be the dominating 
elemental attribute, which has the greatest influence on housing prices as 
hypothesized. In addition, being located in the attendant zone of a high-
quality school has nearly the same positive impact on housing prices as 
access to BRT (0.108 vs 0.100). Furthermore, among four location variables, 
Distance to city center exhibits the largest impact on housing prices, which is 
consistent with the bid-rent theory proposed by Alonso (1964). 
4.2 
Box-Cox transformation 
For further checking the robustness of variables, four Box-Cox functions 
are estimated. All functional forms represent relatively simple applications 
of the Box-Cox transformation: the simple left-hand-side Box-Cox model; 
the simple right-hand-side Box-Cox model; the simple both-side Box-Cox 
model; the separate both-side Box-Cox model. It should be noted that we do 
not transform five dummy independent variables as they are not definitely 
positive. 
Table 3 shows the results and reveals that the most flexible form, the 
separate both-side Box-Cox model, outperforms other three Box-Cox 
models. It has the lowest AIC (Akaike information criterion) value and the 
greatest adjusted R2 and Log-likelihood. 
The levels of statistical significance of all twelve independent variables 
are consistent in all six model specifications (two pre-specified and four 
Box-Cox transformed models). Kindergarten and Middle school are not 
associated with housing prices while other variables significantly affect 
housing prices (significant at the 5% level). This implies that our hedonic 
price models (both pre-specified and Box-Cox transformed) can explain 
price variations well and the variables included do affect housing prices. In 
addition, the signs of all coefficients are in line with expected. 
Table 3. Results of four Box-Cox transformed functional forms 
Variables 
Simple LHS 
Box-Cox 
model: 
Simple RHS 
Box-Cox 
model: 
Simple both-
side Box-Cox 
model: 
Separate both-
side Box-Cox 
model: 


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56 
IRSPSD International, Vol.6 No.1 (2018), 45-62
 
coefficient (t-
value) 
coefficient (t-
value) 
coefficient (t-
value) 
coefficient (t-
value) 
Constant 
9.784 (34.54)a  
58.907 (5.20)a 
1.137 (12.87)a 
1.618 (19.41)a 
Area 
0.055 (63.53)a  
1.429 (59.11)a 
1.035 (70.56)a 
0.833 (70.52)a 
Age 
-0.074 (-9.30)a 
-3.044 (-
10.17)a 
-0.169 (-
11.32)a 
-0.151 (-
11.20)a 
Local environment 
0.434 (9.36)a 
16.629 (8.05)a 
0.203 (8.00)a 
0.195 (8.01)a 
School 
0.616 (5.14)a 
36.359 (5.90)a 
0.128 (5.48)c 
0.129 (5.46)c 
Kindergarten 
-0.005 (-0.05)c 
-4.621 (-0.88)c 
-0.013 (-0.70)c 
-0.013 (-0.67)c 
Middle school 
0.029a (0.28)c 
4.011 (0.76)c 
0.036 (1.84)a 
0.033 (1.70)a 
Xiamen University 
0.990 (3.09)b 
42.604 (2.53)b 
0.170 (3.04)a 
0.172 (3.03)a 
BRT 
0.429 (4.93)a 
19.596 (4.38)a 
0.117 (6.81)a 
0.116 (6.72)a 
Distance to hospital 
0.252 (4.47)a 
11.195 (4.06)a 
0.022 (2.16)b 
0.023 (2.21)b 
Distance to 
cultural/sports center 
-0.294 (-4.71)a 
-12.988 (-
4.16)a 
-0.059 (-5.31)a 
-0.062 (-5.39)a 
Distance to city 
center 
-0.134 (-7.26)a 
-5.477 (-7.12)a 
-0.088 (-6.37)a 
-0.084 (-6.28)a 
Distance to lake 
-0.345 (-5.42)a 
-10.734 (-
3.32)a 
-0.061 (-5.99)a 
-0.063 (-5.99)a 
Left-hand side 
parameter 
0.317 (11.41)a 
- 
- 
0.032 (1.02)c 
Right-hand side 
parameter 
- 
1.128 (19.03)a  
- 
0.080 (1.45)c 
Both-hand side 
parameter 
- 
- 
0.030 (0.95)c 
- 
Performance statistics· 
Adjusted R2 
0.826  
0.806  
0.851  
0.851  
Log-likelihood 
-1999.85  
-6864.68  
39.83  
26.60  
AIC 
3.26  
11.15  
-0.04  
-0.02  
Note: a significant at the 1% level. b significant at the 5% level. c not significant at the 5% 
level. 
4.3 
Propensity score matching 
The “MatchIt” package in R constructs (Ho et al., 2011), is used for 
treatment effects estimation. The model employed to estimate propensity 
score, defined as the probability of receiving treatment, conditional on the 
covariates, is a binary logistic regression model. The explanatory variables 
used for logistics regression are the same as those used for the hedonic price 
function estimates. There are 158 treatment and 1092 control observations in 
our data set. The matching method we use is “optimal” matching, which 
seeks out the matched observations with the smallest total absolute distance 
within matched units. This method (i.e., “optimal” matching) is, in nature, 
strikingly different from “greedy” matching, which starts with some treated 
units and matches the closest control unit that has not yet been matched, 
without trying to minimize a global distance measure, so it efficiently avoids 
a problem of “greedy” matching, variant to the order in which units are 
matched (Ho et al., 2007).  
After matching, we compare the difference between the means for each 
explanatory variable in full samples and matched samples and find that 
matching does greatly enhance the balance of covariates. The estimation of 
the treatment effect reveals that the residential properties being located 
within high-quality school attendance zones (xuequfang) are 12.1% higher 
than the properties located outside of these areas (non-xuequfang), all else 
keeping fixed. 


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Yang et al. 
57
 
4.4 
High-quality school value premiums 
The following interpretation of the value premiums offered by high-
quality schools is based on the semi- and double-log hedonic price models 
developed and propensity score matching. The coefficient of School in the 
semi- and double-log model is 0.089 and 0.108, respectively. This indicates 
that residential properties being located within high-quality school 
attendance zones (xuequfang) exhibit values that are between 9.3% (=e0.089-
1) and 11.4% (=e0.108-1) higher than the properties located outside of these 
areas (non-xuequfang), ceteris paribus. The value premium estimation 
provided by propensity score matching (12.1%) is very consistent with the 
hedonic price regression results.  
The magnitude of the price premium offered by high-quality school of 
Xiamen Island is a little higher than that estimated in Beijing (8.1%) (Hu, 
Zheng, & Wang, 2014) and Shanghai (8.7%, 9.7%) (Shi & Wang, 2014; 
Peng, B. et al., 2015), but lower than that in Tianjin (l4.7%) (Wang, Z., Mei, 
& Wang, 2014) and Hong Kong (39.4%, 27.3%) (Jayantha & Lam, 2015). 
5. 
DISCUSSIONS 
According to the pedagogy theory, four factors - genetics, environment, 
school and subjective initiative - can affect the physical and mental 
development of people. Among them, only environment and school are 
space-relevant. The former involves loads of factors, with family 
environment accounting for a major proportion, while school is a very 
important factor which parents can do something for the physical and mental 
development of their children.  
The demarcation of school attendance zones is based on many factors 
such as school distribution, population distribution and natural boundary. It 
is, originally, to ensure the accessibility and security of school-age children. 
However, since elementary schools show exceptional heterogeneity (obvious 
disparities, tremendous diversity) in some aspects such as test performance 
and entering-school rate, parents’ expectation would deviate from the reality 
in terms of school choices. That is, assuming that a child with local hukou 
registered in the attendance zone of school A wants to attend school B, it is 
very difficult, if not impossible, according to strict policy of entrance from 
attendance zones alone, however. So, in most cases, parents need to buy a 
residence in the attendance zone of school B. As a result, the imbalance of 
inadequate supply and growing demand leads to the higher prices of 
xuequfang. For example, in Nanjing, the supply-demand ratio of xuequfang 
reaches 10 (Chen & Tang, 2009). Obviously, the advent of the xuequfang 
phenomenon is in stark contrast to original goals of school attendance zone 
demarcation. 
According to Chen and Tang (2009), there are a series of negative 
effects of the xuequfang phenomenon: (1) unfair educational resource 
allocation. Coupled with the advancement of the nation, education is no 
longer regarded as a privilege. Good educational resources are expected to 
be unfairly allocated and driven by the market mechanism. The introduction 
of territorial-based school admission policy which links educational 
resources with residential properties, distorts the market. As a result, the 
better the nearby educational resources are, the higher value the housing 
exhibits. This turns out that the rich can still obtain high-quality educational