Elite School Designation and House Prices: Quasi-Experimental Evidence from Beijing, China

Elite School Designation and House Prices: Quasi-experimental Evidence from Beijing, China

Bin Huanga, Xiaoyan Hea and Yu Zhub, * a: School of Public Administration, Nanjing University of Finance and Economics, China a: School of Business, University of Dundee, UK

Version 2.0 (June 18, 2018)

Abstract

We explore two recent comprehensive reforms which aim to equalize access to elite elementary schools in Beijing, to identify the causal effect of access to quality education on house prices. Whereas the multi-school dicing reform involves randomly assigning previously ineligible pupils to key elementary schools through lotteries, the reform of school federation led by elite schools consolidates low quality schools through alliance with elite schools. We allow for systemic differences between the treated and non-treated school attendance (catchment) zones using the Matching Difference-in-Differences (MDID) approach. Our estimates indicate that the causal effect on house prices of being eligible to enroll in a municipal-level key primary school is about 7.5-10.5%, while the premium for being eligible for a district-level key primary school is statistically insignificant. On the other hand, the price premium for access to a federation of schools led by an elite school is around 2.4-4.3% and statistically significant.

Keywords: quality school designation, house price premium, Matching DID, China.

JEL code: R21 (Urban/Regional Economics: Housing Demand); I28 (Education: Government Policy); H44 (Publicly Provided Goods: Mixed Market)

* Corresponding Author: Yu Zhu, School of Business, University of Dundee, Dundee, DD1 4HN, UK. E-mail: [email protected].

“In Beijing’s overheated housing market, where schools go, money follows.”

– Caixinglobal (2017)

1. Introduction

It has been almost half a century since Oates’ seminal paper on the capitalization of local property taxes on house values (Oates (1969)). Since then, a growing number of studies have contributed to the literature on school quality capitalization under different contexts in terms of country of study, school quality measures and methodological innovations, see Ross and Yinger (1999), Gibbons ad Machin (2008), Black and Machin (2011) and Nguyen-Hoang and Yinger (2011) for reviews.

The phenomenon of steeply priced “school district houses (xuequfang)”, i.e. properties giving access to prestigious publicly funded schools, has consistently been one of the hottest topics in the Chinese media in recent years. According to one estate agent, in 2013 house prices in Beijing's elite school districts were 30 percent higher than other districts on average (Xinhua 2016).

Using a panel data of residential quarters, or school attendance (catchment) zones, derived from comprehensive data on real estate transactions in Beijing in 2013-2106, we investigate how house prices react to the quality of education offered by neighbouring publicly-funded elementary schools. To overcome the endogeneity of education quality, we exploit two recent comprehensive reforms which aim to equalize access to quality educational resources in compulsory education, to identify the causal effect of access to quality school on house prices. Whereas the multi-school dicing reform involves randomly assigning previously ineligible pupils to key elementary schools through lotteries, the school federation led by elite schools reform consolidates low quality schools through alliance with elite schools.

We start by estimating the spillover effects of public education quality on house prices in Beijing, using the hedonic price model. The results indicate that, after controlling for housing and residential features, neighborhood and location characteristics, the mean house price in key primary school catchment areas is 9% higher than that for ordinary primary school catchment areas. Moreover, the average house price for district-level key primary school and municipal- level key primary school catchment areas are 5.5% and 18.6% higher than their ordinary primary school catchment area counterparts, respectively. Secondly, school attendance zone changes based on school district adjustment and multi-school dicing have increased the premium of key

1 primary school catchment areas.

Furthermore, we allow for systemic differences between the treated and non-treated school attendance (catchment) zones using Propensity Score Matching and account for the common trend in house price inflation using the Difference-in-Difference (DID) approach. Our Matching DID (MDID) estimates indicate that the causal effect on house prices of being eligible to enroll in a municipal-level key primary school is about 7.5-10.5%, while the premium for being eligible for a district-level key primary school is statistically insignificant. On the other hand, the price premium for access to a federation of schools led by an elite school is around 2.4-4.3% and statistically significant.

Moreover, we find that the number of private primary schools within ten kilometers, higher service charges and more local amenities all have a significant positive impact on the average house price of school attendance zones. In contrast, mean floor area ratio, mean number of floors, mean floor area per flat, and the distances to the city center, to the nearest top-grade hospital, and to the nearest subway station all have significant negative correlation with average house price of school attendance zones.

The remainder of the paper is structured as follows. Section 2 presents the background of the reforms in Beijing. Section 3 briefly reviews the relevant literature. Section 4 discusses the MDID methodology. Section 5 presents the data and the descriptive statistics. In Section 6, the empirical analyses are presented and discussed. Finally, Section 7 concludes.

2. Background

A private housing market was only introduced in China in the early 1990s. Before that, most urban residents lived in housing units built and owned by their employers. After the reform, employees no longer received allocated housing and had to buy from a private housing market which had grown from strength to strength (Sato (2006), and Zhang and Yi (2017)). According to Fang et al. (2015), the residential housing market as measured by residential house sales volume grew by about 15% per annum on average between 2002-2013.

Beijing offers an excellent case study on the education reform and housing market of China. As the capital since the founding of the People’s Republic in 1949 and nation’s political, cultural and educational centre, Beijing has not only the most developed housing market but also arguably the best resources of education, in particular higher education, in China. However, competition for access to the elite schools which traditionally has excellent track records of

2 graduate enrolment into the country’s best-known universities, is exceptionally fierce and starts well before the formal entry to the public education system.

The public schools dominate all stages of education in Beijing. In theory, access to 9- years of compulsory education is free and non-selective, and based on the principle of “attending nearby schools”, according to parental household registration (hukou) and house ownership (Feng and Lu (2013)). This implies that securing an address in the catchment of the school district is a necessary if not sufficient condition to enroll one’s kids into a so-called key school.

3. Literature

A large literature has been devoted to the effect of school quality on house prices, in general finding support to the Tiebout model which predicts residential sorting (Tiebout (1956)). Ross and Yinger (1999), Gibbons ad Machin (2008), Black and Machin (2011) and Nguyen- Hoang and Yinger (2011) offer excellent reviews. While earlier studies are largely descriptive, recent ones tend to use quasi-experimental framework in an attempt to uncover the causal relationship, which is extremely important for policy designs.

Traditional hedonic pricing model estimates of the school quality effect are likely to suffer from omitted variable bias or endogeneity problems. Black (1999) first applies the regression discontinuity design (RDD) using administrative boundaries, also known as the boundary discontinuity design (BDD) approach, in an attempt to remove time-invariant unobserved neighbourhood fixed-effects which are correlated with school quality. Fack and Grenet (2010) and Gibbons et al. (2013) further develop the RDD approach using matching. Compared to the OLS baselines, they all find a smaller capitalization effect, at below 4% for a one standard deviation increase in test scores.

To the best of our knowledge, Feng and Hu (2013) is the only causal study of the effect of school quality on house prices in China. Using a difference-in-difference approach, they find that the re-designation of a previously ordinary high school to a specific high-quality school status increases the house price in its residential area by 6.9% in Shanghai. However, to the extent that school designation policy by the municipal government is not entirely exogenous, e.g. due to concerns for equal access across geographical areas (districts), one cannot rule out the possibility of endogeneity bias in the DID estimates.

4. Methodology

This study employs a quasi-experimental research design to examine two recent educational policy reforms in Beijing which aim to widen access to quality education for all. Conventional multivariate regression analysis is unlikely to uncover the true causal effect of the treatment due to omitted variable bias and endogeneity or self-selection in the treatment (see e.g. Rubin (1974) and Blundell and Diaz (2009)).

To the extent that the treatment status is randomly assigned, a conventional Difference- in-difference (DID) would suffice to uncover the true causal effect with the help of a well-defined control group which is assumed to share the common trend. However, there are good reasons to believe that the assignment of the treatment status by policy makers is non-random in our case. In other words, the non-ignorable treatment assignment required for unbiased DID estimates is not satisfied.

To deal with this issue, we will use propensity score matching to achieve data balance such that DID can yield unbiased estimates on the post-matching data. In practice, we will use 4 alternative matching strategies to ensure that there are no systemic differences between the treatment and control groups (Guo and Fraser (2010)). The strategies are defined by propensity scores estimation using either logistic regressions method or Generalized Boosted Modelling method, with either Mahalanobis distance or nearest neighbour within caliper.

Nearest neighbor Mahalanobis Metric within caliper

Logistic Regression Strategy 1 Strategy 2

Generalized Boosted Modeling (GBM) Strategy 3 Strategy 4

5. Data

This paper is based on a balanced panel of residential complexes (xiaoqu) in the 12 urban districts in Beijing in 2013 and 2016.1 A residential complex is the urban equivalent of a village and serves as the most fundamental organization unit for the urban population in China. Each residential complex has its own neighbourhood or residents’ committee. In Chinese megacities like Beijing, a residential complex usually contains hundreds of condominiums in medium or

1 The remaining 4 districts where data is unavailable are all rural suburbs, and far away from the Central Business District (CBD).

4 high-rise buildings within well-defined boundaries and one or several designated publicly funded primary schools where the kids can enrol (Zhang and Yi (2017)).

Using the half million or so actual transaction records of second-hand properties from the two leading property websites Fang.com (http://www.fang.com/) and Lianjia.com (https://www.lianjia.com/),2 we derive the mean transaction prices and key characteristics for the 3,167 residential complexes for 2013 and 2016 respectively. Using Google Maps, we can also construct the distance of each SD to the city centre, the nearest subway station and the nearest top-grade hospital and the number of independent schools within a 10 kilometre radius. The designated schools are identified from the school’s admission policies available online for the relevant years. The grade of the school and the policy regime it belongs to are derived from the websites of the school itself and relevant District Education Authorities.

We also exclude residential complexes with too few transactions in either of the two years. To ensure our results are not driven by outliers in the outcome measure of mean price per square metre (in RMB yuan), we also drop the top and bottom 5% of the mean price distribution.

< Table 1 about here >

Table 1A presents the descriptive statistics for the overall sample before and after the policy change year. The house prices are converted to constant 2013 prices using the Consumer Price Index (CPI) for Beijing. The mean house price in Beijing grows from 38520 RMB yuan (USD 6105) in 2013, to 50917 yuan (USD 8069) in 2016, an increase of 32.2% in real terms over 3 years.3 The extent of house price appreciation is consistent with Zhang and Yi (2017), who show that prices of newly-built houses increase by 15–24% for different quantiles in Beijing between January 2013 and December 2013 alone. While no residential complex experienced a change in the School District (SD) in 2013, 9.8% did in 2016. Only 1.6% of residential complexes in 2013 are subject to multi-school dicing, meaning that children are randomly assigned to a consortium of schools rather than a single school. Three years later, this proportion was increased to 5.9%. On the other hand, the proportion of SDs that were part of a school federation increased from 2.4% to 14.2% over the sample period. While 35.9% of all residential complexes are in the SD of a Key primary school, the share of elite SDs grows to 45.7% in 2016, with increases in both the district-level and municipal-level key schools. All control variables except for years since

2 Jointly they cover virtually all “used (second-hand)” transactions in Beijing. 3 The year-end exchange rates between USD and CNY are 6.152, 6.158, 6.284 and 6.643 for 2013, 2014, 2015 and 2016 respectively. We use the mean of 6.31 over the period to derive the USD equivalents.

5 construction are time-invariant. The mean greening rate of 0.325 indicates that the green areas account for almost one-third of the land surface of the residential quarter. The floor area ratio is the ratio of total construction area to the land area. The average service charge is 1.704 RMB yuan (0.27 USD) per month/m2. The mean number of floors is 13, reflecting the fact that is Beijing is very densely populated metropolis. The mean floor area per flat is 83.5m2, while the average years since construction is 15.5 in 2013. The average number of amenities including stores, post-offices, banks and leisure facilities is 4. The straight-line distances to the city centre and the nearest top-grade hospital are 10.9 and 2.2 km’s respectively, while the distance to the nearest subway station is only 0.9 km.

Table 1B presents the descriptive statistics by the treatment status and year. The treatment group includes all residential complexes whose designated school(s) changed status between 2013 and 2016, from ordinary to either district-level or municipal level key schools, whereas the control group consists of residential complexes in the catchment of ordinary schools throughout the sample period. This implies that we exclude residential complexes which are already in the catchment of elite schools in 2013 from the main analysis. In 2013, the treatment group of residential complexes enjoyed a price advantage of 3590 yuan over the control group even before the treatment taking place, suggesting systematic difference between the two groups. After the treatment taking place, the gap widened to 5660 yuan. Whereas there was no significant difference in multi-school dicing or school federation between the treatment and the control groups in 2013, by 2016 the treatment group has an advantage of 11.6 and 13.2 percentage points, respectively. Three complexes of the SDs for the treated residential complexes were re-designated as district-level key primary schools with the remaining one quarter as the more prestigious municipal-level key primary schools. The treatment group is also surrounded by more independent (or private) schools, compared to the control group.

It turns out that the treatment and the control groups have statistically significantly different means in half of all the control variables, in the years since construction and the various distance measures. This highlights the need to control for these systematic differences in the formal analysis.

6. Empirical Results

6.1. Elite School Designation

Table 2 presents the OLS estimates as well as the corresponding DID estimate, without and with the breakdown of the elite schools into district or municipal-level. These will form the benchmark against which the MDID results are compared. We choose the semi-log specification:

ln price =  +  key_ sch +  X + it 0 1 i  i i it where lnpriceit is the logarithm of mean house price of residential complex i in year t, key_sch is the grade of the designated primary school, Xi’s are control variables, εit is the error term, and

β0, β1, and βi’s are coefficients. < Table 2 about here >

Using the pooled sample from both years which contains key school SDs in 2013, Column 1 shows that the regression adjusted of price premium of access to a key primary school is 9.0%. When we distinguish between district and municipal-level key primary schools in column 2, we find that the price premium for the more prestigious municipal-level key school is more than 3 times as high as its district-level counterpart, at 18.6%. All these estimates are statistically significant at the 1% level. Moreover, there is a modest but significant effect of school federation at around 3%. However, there is no significant effect of multi-school dicing per se. Columns 3 and 4 exclude the residential complexes with access to elite schools in the base year and only use the 2016 subsample. While the magnitude and the level of significance have changed, the overall pattern remains the same. The effect of the re-designation as an elite school is driven by the change to a municipal-level key school. On the other hand, the access to school federation is now significant with the same magnitude as that of a municipal-level key school.

The last two columns of Table 2 present the DID estimates. Again, the results are consistent with the OLS. The re-designation as an elite school is only significant for change to a municipal-level key school while the school federation is still significant.

Table 3 shows the post-matching balancing test results, for each of the 4 matching strategies employed. Due to the common support restriction, the matched sample is smaller than the unmatched sample used in Table 2. For the first 3 matching strategies, none of the variance ratios are statistically significant at the 5% level post-matching. For Strategy 4 (GBM using nearest neighbor within caliper) which has by far the largest sample size, there are some remaining differences in the number of amenities and the distance to subway station squared.

< Table 3 about here >

Figures 1-4 compares the kernel densities of propensity score before and after matching, for each of the 4 matching strategies used. They show that the matching has been successful, especially for strategies 2 and 1.

< Figures 1-4 about here >

Table 4 shows the MDID estimates. The single indicator of SD change is only significant at 10% level under Strategy 2 and at 1% level under Strategy 4, with a price premium of 2.4% and 5% respectively. When we distinguish between district and municipal-level key schools, only the latter is statistically at 1% consistently, with a price premium between 7.5% and 10.5%.

< Table 4 about here >

6.2. School Federation

The analysis so far is concerned with the effect of the re-designation of an ordinary primary to a key primary school on the mean house prices of the affected residential quarter. Over the same sample period, Beijing has undertaken an alternative reform which we term “school federation” as a shorthand. This usually takes the form of the designated primary school becoming part of a federation of schools by (another) existing elite school.

Table 5 presents the descriptive statistics by this alternatively defined treatment status and year. In 2013, the treatment group of residential complexes enjoyed a price advantage of 2906 yuan over the control group even before the treatment taking place, suggesting systematic difference between the two groups. After the treatment taking place, the gap widened to 5688 yuan. Whereas treatment group are more likely to be under the multi-school dicing regime, in 2013, this gap becomes statistically insignificant in 2016 due to the higher growth in the control group. On the other hand, the treatment group is 3.3 percentage points less likely to be in the SD of an elite school in 2013 compared to the control group, even though this gap is not significant at the conventional level. However, three years on, the residential complexes in school federations are 7.0 percentage points more likely to have access to elite schools (note that we do not distinguish between school federations led by district or municipal-level key primary schools).

While there appears to be no difference in the number of independent schools within 10km between the treatment and the control groups, the means of many of the control variables are significantly different.

< Table 5 about here >

In the interest of space, we will only focus on the post-matching balancing test results using logistic regressions method, with either Mahalanobis distance or nearest neighbour within caliper (i.e. Strategies 1 and 2, respectively) in Table 6. It is clear that no variance ratio is statistically significant at the 5% level post-matching,

< Table 6 about here >

Figures 5 and 6 compare the kernel densities of propensity score before and after matching, for matching strategies 1 and 2, respectively. They suggest that the matching has been very successful, especially for strategy 2.

< Figures 5-6 about here >

Finally, Table 7 shows the OLS, DID and MDID estimates using the two alternative matching strategies. While the key primary school on its own is significant at 9.3% for both OLS and DID, the coefficient on school federation is only marginally positive and statistically insignificant in both specifications. In contrast, school federation yields a price premium of 4.3% which is significant at 5% under Strategy 1, and a more modest 2.4% which is also only significant at 10% under Strategy 2.

< Table 7 about here >

6.3. Allowing for Interaction with Independent Schools

For both treatments, it turns that having more independent schools in the surrounding areas (with 10km radius) have a statistically significant positive effect. We are concerned that the effect might be endogenous, and importantly, could affect the estimates of the effect of the reforms. Therefore, we rerun the estimation, allowing for the interaction of number of independent schools with the key variables of interest. Our results in Tables A1 and A2 in the Appendix suggest that none of these interaction terms are statistically significant in OLS, DID and MDID specifications. This is reassuring.

< Tables A1-A2 about here >

7. Concluding Remarks

This paper examines the effect access to quality education on house prices, by exploring

9 two recent comprehensive educational reforms which aim to equalize access to elite elementary schools in Beijing, China. While the multi-school dicing reform involves randomly assigning previously ineligible pupils to key elementary schools through lotteries, the reform of school federation led by elite schools consolidates low quality schools through alliance with elite schools. Using the Matching Difference-in-Differences (MDID) approach, we identify the causal effect of being eligible to enroll in elite primary schools on house prices while allowing for underlying systemic differences between the treated and non-treated school districts. Our estimates suggest that the price premium of being eligible to enroll in a municipal-level key primary school is about 7.5-10.5%, while the premium for being eligible for a district-level key primary school is statistically insignificant. On the other hand, the price premium for access to a federation of schools led by an elite school is around 2.4-4.3% and statistically significant. Our findings are robust to the use of alternative matching strategies and to possible interaction effects of the reforms with the number of independent school in surrounding areas.

One limitation of our study is that we do not have measures of the probability of getting into a key school under multi-school dicing or the exact formation of the school federation led by an elite school. Having such variation would allow us to discriminate between treatments of various intensity. Therefore, our estimates should be interpreted as a lower bound effect.

Nevertheless, our findings have important policy implications. Although both reforms aim to equalize education opportunities for all, they are shown to have the unintended consequences of pushing up the house prices that are already out of reach for people on average earnings in this metropolis. Future educational policy changes would benefit from careful evaluations of similar programmes implemented in different contexts and possibly randomized controlled pilot studies.

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Appendix

Table A1: Effect of independent schools on price premium (OLS, DID) OLS DID

(1) (2) (1) (2) School characteristics School District (SD) change -0.028 - 0.011 - (0.039) (0.011) # independent schools (within 10km) 0.026*** 0.025*** 0.028*** 0.028*** (0.002) (0.002) (0.002) (0.002) SD change X # independent schools 0.006 - 0.0002 - (0.005) (0.004) SD change to district-level key school - -0.071* - -0.004 (0.037) (0.012) SD change to district-level key school - 0.009** - 0.002 X # independent schools (0.005) (0.004) SD change to municipal-level key - 0.327** - 0.063*** school (0.131) (0.019) SD change to municipal -level key - -0.026 - -0.021 school X # independent schools (0.016) (0.013) Federation and consolidation of SD 0.092*** 0.096*** 0.079*** 0.082*** (0.017) (0.016) (0.015) (0.015) Control Variables Greening rate 0.021 0.018 0.041 0.039 (0.091) (0.090) (0.085) (0.084) Mean floor area ratio -0.016*** -0.016*** -0.016*** -0.016*** (0.004) (0.004) (0.003) (0.003) Service charges 0.034*** 0.034*** 0.031*** 0.031*** (0.008) (0.008) (0.007) (0.007) # floors -0.003*** -0.003*** -0.003*** -0.003*** (0.001) (0.001) (0.001) (0.001) Mean floor area per flat -0.0002 -0.0002 -0.0003 -0.0002 (0.0002) (0.0003) (0.0003) (0.0002) Years since construction -0.002* -0.002* -0.001 -0.001 (0.001) (0.001) (0.001) (0.001) # Local amenities (Banks, stores etc.） 0.091*** 0.108*** 0.091*** 0.109*** (0.019) (0.177) (0.014) (0.015) Distance to City Centre -0.016*** -0.016*** -0.018*** -0.018*** (0.001) (0.001) (0.001) (0.001) Distance to nearest top-grade hospital -0.026*** -0.028*** -0.027*** -0.028*** (0.004) (0.004) (0.004) (0.004) Distance to nearest subway station -0.049*** -0.049*** -0.039*** -0.039*** (0.014) (0.014) (0.012) (0.012) Distance to nearest subway station 0.007*** 0.007*** 0.007*** 0.008*** squared (0.002) (0.002) (0.002) (0.002) F-stats 83.19*** 77.67*** 434.44*** 380.58*** R2 0.525 0.531 0.668 0.671 Observations 1275 1275 2550 2550 Note: Robust standard errors in parentheses. ***, ** and * indicate statistical significance at the 1%, 5% and 10% respectively.

Table A2: Effect of independent schools on price premium (MDID) Strategy 1 Strategy 2 Strategy 3 Strategy 4 (1) (2) (1) (2) (1) (2) (1) (2) School District (SD) change 0.027* - 0.024* - 0.021 - 0.043*** - (0.015) (0.014) (0.019) (0.014) # independent schools (within 0.041*** 0.041*** 0.033*** 0.033*** 0.041*** 0.041*** 0.025*** 0.025*** 10km) (0.005) (0.005) (0.004) (0.004) (0.006) (0.006) (0.005) (0.005) SD change X # independent schools -0.013* - -0.002 - -0.013 - 0.007 - (0.007) (0.005) (0.008) (0.007) SD change to district-level key - 0.008 - 0.008 - 0.009 - 0.026* school (0.016) (0.014) (0.020) (0.015) SD change to district-level key - -0.012* - -0.002 - -0.013* - 0.009 school X # independent schools (0.007) (0.005) (0.007) (0.006) SD change to municipal-level key - 0.089*** - 0.079*** - 0.075** - 0.097*** school (0.025) (0.020) (0.030) (0.021) SD change to municipal-level key - -0.027 - -0.008 - -0.029 - -0.009 school X # independent schools (0.024) (0.014) (0.042) (0.019) Federation and consolidation of SD -0.024 -0.018 (0.031) (0.030) F-stats 265.44*** 178.50*** 352.66*** 250.71*** 166.03*** 119.54*** 195.10*** 157.19*** R2 0.436 0.443 0.587 0.589 0.503 0.512 0.380 0.385 Observations 548 800 312 800 Note: Robust standard errors in parentheses. ***, ** and * indicate statistical significance at the 1%, 5% and 10% respectively.

Figures

Figure 1: Comparison of kernel density of propensity scores before and after matching, multi-school dicing, Strategy 1 (Logit & Mahalanobis Metric)

Figure 2: Comparison of kernel density of propensity scores before and after matching, multi-school dicing, Strategy 2 (Logit+Neighbour+DID)

Figure 3: Comparison of kernel density of propensity scores before and after matching, multi-school dicing, Strategy 3: Boost+Mahal+DID

Figure 4: Comparison of kernel density of propensity scores before and after matching, multi-school dicing, Strategy 4: Boost+Neighbour+DID

Figure 5: Comparison of kernel density of propensity scores before and after matching, Federation & and Consolidation of schools, Strategy 1 (Logit & Mahalanobis Metric)

Figure 6: Comparison of kernel density of propensity scores before and after matching, Federation & and Consolidation of schools, Strategy 2: Logit+Neighbour+DID

Tables

Table 1A: Descriptive Statistics, Overall Sample 2013 2016 Price per m2 (dependent variable) 38519.5 50917.2 School characteristics School District (SD) Change 0 0.098 Multi-school dicing 0.016 0.059 School federation 0.024 0.142 Key Primary School 0.359 0.457 District-level Key Primary School 0.266 0.327 Municipal-level Key Primary School 0.093 0.130 # independent schools (within 10km) 7.282 7.282 Control variables Greening rate 0.325 Mean floor area ratio 2.615 Service charges 1.704 # floors 12.415 Mean floor area per flat 83.453 Years since construction 15.453 18.453 # Local amenities (Banks, stores etc.） 3.989 Distance to City Centre 10.940 Distance to nearest top-grade hospital 2.196 Distance to nearest subway station 0.910 Observation 2249 2249 Note: Robust standard errors in parentheses. ***, ** and * indicate statistical significance at the 1%, 5% and 10% respectively

Table 1B: Descriptive Statistics and balancing tests Year 2013 Year 2016 Treatment Control Mean Variance Treatment Control Mean Difference Ratio Difference Price per m2 (dependent variable) 39037.5 35447.6 3589.9*** - 51754.1 46094.5 5659.6*** School characteristics School District (SD) Change 0 0 0 - 1 0 1 Multi-school dicing 0.004 0.007 -0.003 0.69* 0.157 0.041 0.116*** School federation 0.031 0.024 0.007 1.31* 0.260 0.128 0.132*** Key Primary School 0 0 0 - 1 0 1 District-level Key Primary School 0 0 0 - 0.753 0 0.753*** Municipal-level Key Primary School 0 0 0 - 0.247 0 0.247*** # independent schools (within 10km) 7.924 6.366 1.558*** 0.95 Control variables Greening rate 0.319 0.325 -0.006 0.80 Mean floor area ratio 2.658 2.541 0.117 0.88 Service charges 1.719 1.628 0.091 1.41* # floors 13.012 12.164 0.848* 1.04 Mean floor area per flat 81.338 83.008 -1.670 1.22 Years since construction 16.384 14.911 1.473** 0.93 # Local amenities (Banks, stores etc.） 3.973 3.990 -0.017 2.92* Distance to City Centre 9.672 11.584 -1.912*** 0.45* Distance to nearest top-grade hospital 2.060 2.457 -0.397*** 0.74* Distance to nearest subway station 0.723 1.029 -0.306*** 0.33* Observation 223 1219 - - Note: Robust standard errors in parentheses. ***, ** and * indicate statistical significance at the 1%, 5% and 10% respectively

Table 2: Effect of multi-school dicing on price premium (OLS, DID) OLS DID

(1) (2) (3) (4) (1) (2) School characteristics Key Primary School 0.090*** - - - - - (0.008) District-level Key 0.055*** - - - - - Primary School (0.009) Municipal-level Key 0.186*** - - - - - Primary School (0.014) SD Change (Multi- 0.022 0.011 - - - - school Dicing) (0.014) (0.011) SD Change to District- 0.0005 -0.004 - - - - level Key (0.015) (0.012) SD Change to 0.098*** 0.063*** - - - - Municipal-level Key (0.032) (0.019) School federation 0.033*** 0.039*** 0.090*** 0.090*** 0.079*** 0.079*** (0.012) (0.012) (0.017) (0.017) (0.015) (0.015) Multi-school Dicing 0.006 -0.001 - - - - (0.019) (0.018) # independent schools 0.026*** 0.026*** 0.027*** 0.026*** 0.028*** 0.027*** (within 10km) (0.001) (0.001) (0.002) (0.002) (0.002) (0.002) Control variables Greening rate 0.074 0.108* 0.018 0.016 0.041 0.040 (0.066) (0.064) (0.091) (0.090) (0.084) (0.084) Mean floor area ratio -0.010*** -0.010*** -0.016*** -0.015*** -0.016*** -0.016*** (0.003) (0.003) (0.004) (0.004) (0.003) (0.003) Service charges 0.030*** 0.029*** 0.035*** 0.034*** 0.031*** 0.031*** (0.005) (0.005) (0.008) (0.008) (0.007) (0.007) # floors -0.003*** -0.003*** -0.003*** -0.003*** -0.003*** -0.003*** (0.0008) (0.0008) (0.001) (0.001) (0.001) (0.001) Mean floor area per flat -0.0005** -0.0005** -0.0002 -0.0002 -0.0003 -0.0002 (0.0002) (0.0002) (0.0003) (0.0003) (0.0002) (0.0003) Years since construction -0.0001 -0.0004 -0.002* -0.002* -0.001 -0.001 (0.0007) (0.0007) (0.001) (0.001) (0.001) (0.001) # Local amenities 0.083*** 0.088*** 0.091*** 0.102*** 0.091*** 0.102*** (Banks, stores etc.） (0.023) (0.027) (0.019) (0.014) (0.014) (0.014) Distance to City Centre -0.023*** -0.022*** -0.016*** -0.018*** -0.018*** -0.018*** (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) Distance to nearest top- -0.019*** -0.020*** -0.027*** -0.027*** -0.027*** -0.027*** grade hospital (0.003) (0.003) (0.004) (0.004) (0.004) (0.004) Distance to nearest -0.018*** -0.019*** -0.049*** -0.039*** -0.039*** -0.039*** subway station (0.007) (0.007) (0.014) (0.012) (0.012) (0.012) Distance to nearest 0.004*** 0.004*** 0.007*** 0.007*** 0.007*** 0.007*** subway station squared (0.0004) (0.0003) (0.002) (0.002) (0.002) (0.002) F-stats 780.55*** 775.60*** 88.68*** 464.06*** 461.61*** 417.45*** R2 0.662 0.676 0.524 0.669 0.668 0.670 Observations 4006 4006 1275 1275 2550 2550 Note: Robust standard errors in parentheses. ***, ** and * indicate statistical significance at the 1%, 5% and 10% respectively.

Table 3: Post-matching balancing tests

Strategy 1 Strategy 2 Treatment Control Variance Treatment Control Variance Mean Mean Ratio Mean Mean Ratio Service charges 1.64 1.64 0.99 1.719 1.729 1.13 # Local amenities 4 4 - 3.98 3.98 0.99 Distance to City 8.84 8.79 0.95 9.61 9.50 0.76* Centre Distance to nearest 1.75 1.75 1.01 2.00 2.07 1.05 top-grade hospital Distance to nearest 0.60 0.61 1.04 0.72 0.72 1.18 subway station Distance to subway 0.43 0.44 0.92 0.80 0.76 1.07 station squared School Federation 0 0 - 0.04 0.03 1.04 Observations 548 800 Strategy 3 Strategy 4 Treatment Control Variance Treatment Control Variance Mean Mean Ratio Mean Mean Ratio Service charges 1.35 1.35 0.99 1.72 2.05 1.04 # Local amenities 4 4 - 3.98 3.99 2.56** Distance to City 7.91 7.92 0.95 9.62 9.63 1.14 Centre Distance to nearest 1.49 1.51 0.97 2.00 1.63 1.20 top-grade hospital Distance to nearest 0.58 0.58 0.97 0.72 0.61 1.30* subway station Distance to subway 0.39 0.39 0.94 0.80 0.50 3.05** station squared School Federation 0 0 - 0.04 0.02 1.64* Observations 312 800 Note: ***, ** and * indicate statistical significance at the 1%, 5% and 10% respectively.

Table 4: Matching Difference-in-differences (MDID) Estimates Strategy 1 Strategy 2 Strategy 3 Strategy 4 (1) (2) (1) (2) (1) (2) (1) (2) SD Change (Multi- 0.027 - 0.024* - 0.021 - 0.050*** - school Dicing) (0.015) (0.014) (0.019) (0.014) SD Change to District- - 0.008 - 0.008 - 0.009 - 0.033** level Key (0.016) (0.014) (0.020) (0.015) SD Change to - 0.089*** - 0.079*** - 0.075** - 0.105*** Municipal-level Key (0.025) (0.020) (0.029) (0.021) # Local amenities ------0.152*** 0.166*** (0.025) (0.026) Distance to City Centre - - -0.028*** -0.028*** - - - - (0.002) (0.002) Distance to nearest ------0.065 -0.061 subway station (0.057) (0.057) Distance to subway ------0.002 -0.005 station squared (0.017) (0.017) School Federation ------0.066** -0.063** (0.032) (0.032) F-stats 423.33*** 266.76*** 430.69*** 308.15*** 246.37*** 159.96*** 238.39*** 196.24*** R2 0.261 0.271 0.455 0.460 0.281 0.299 0.273 0.280 Observations 548 800 312 800 Note: ***, ** and * indicate statistical significance at the 1%, 5% and 10% respectively.

Table 5: Descriptive Statistics and balancing tests, School Federation Year 2013 Year 2016 Treatment Control Mean Variance ratio Treatment Control Mean Difference Difference Price per m2 (dependent variable) 40990.0 38084.0 2906.0*** - 55721.3 50032.8 5688.5*** School Characteristics Multi-school Dicing School District 0.041 0.013 0.028*** 2.99* 0.075 0.059 0.016 Key Primary School 0.331 0.364 -0.033 0.96 0.519 0.449 0.070** # independent schools (within 10km) 7.398 7.282 0.116 0.50* 7.398 7.282 0.116 Control variables Greening rate 0.319 0.326 -0.007* 0.89 Mean floor area ratio 2.834 2.579 0.255** 1.07 Service charges 2.089 1.658 0.431*** 2.75* # floors 13.410 12.275 1.135*** 1.09 Mean floor area per flat 85.238 83.308 1.930 1.40* Years since construction 16.932 15.261 1.671*** 0.95 19.932 18.261 1.671*** # Local amenities 3.996 3.990 0.006 0.20* Distance to City Centre 8.679 11.315 -2.636*** 0.62* Distance to nearest top-grade hospital 1.697 2.277 -0.580*** 0.42* Distance to nearest subway station 0.800 0.931 -0.131** 0.27* Distance to nearest subway station squared 0.906 1.840 -0.934 0.01* Observations 266 1930 - - Note: ***, ** and * indicate statistical significance at the 1%, 5% and 10% respectively.

Table 6: Post-matching balancing tests Strategy 1 Strategy 2 Treatme Treatme Variance Treatme Treatme Variance nt Mean nt Mean Ratio nt Mean nt Mean Ratio Service charges 1.476 1.442 1.15 2.089 2.008 1.37* Mean floor area per flat 75.376 75.037 1.07 88.793 86.2 1.32* # Local amenities 4 4 - 3.996 4 - Distance to City Centre 6.817 6.924 0.91 8.988 9.343 1.14 Distance to nearest top-grade hospital 1.440 1.449 0.99 1.756 1.643 1.14 Distance to nearest subway station 0.647 0.656 0.98 0.786 0.805 1.59* Distance to subway station squared 0.501 0.508 0.93 0.891 0.822 1.80* # independent schools (within 10km) 7.642 7.606 1.09 7.423 7.714 0.56* School Federation 0.009 0.009 1.00 0.030 0.051 0.65* Observations 364 936 Note: ***, ** and * indicate statistical significance at the 1%, 5% and 10% respectively.

Table 7: Matching Difference-in-differences (MDID) Estimates OLS DID PSM_DID Strategy 1 Strategy 2 School Federation 0.011 0.005 0.043** 0.024* (0.012) (0.010) (0.018) (0.013) Greening rate 0.078 0.078 - - (0.067) (0.067) Mean floor area ratio -0.010*** -0.010*** - - (0.003) (0.003) Service charges 0.030*** 0.030*** - 0.021*** (0.005) (0.005) (0.008) # floors -0.003*** -0.003*** - - (0.001) (0.001) Mean floor area per flat -0.0004* -0.0004* - -0.0007* (0.0002) (0.0002) (0.0004) Years since construction 0.0001 0.0001 - - (0.0007) (0.0007) # Local amenities 0.082*** 0.082*** - - (0.023) (0.023) Distance to City Centre -0.023*** -0.023*** - - (0.001) (0.001) Distance to nearest top-grade -0.019*** -0.019*** - - hospital (0.003) (0.003) Distance to nearest subway station -0.017** -0.017** - -0.122** (0.007) (0.007) (0.061) Distance to subway station squared 0.004*** 0.004*** - 0.008 (0.0004) (0.0004) (0.023) # independent schools (within 10km) 0.026*** 0.026*** - 0.034*** (0.001) (0.001) (0.004)

Key Primary School 0.093*** 0.093*** - - (0.009) (0.009) Multi-school dicing 0.007 0.007 - 0.108** (0.019) (0.019) (0.042) F-stats 772.48*** 730.66*** 380.24*** 249.51*** R2 0.661 0.661 0.318 0.408 Observations 3912 3912 364 936 Note: ***, ** and * indicate statistical significance at the 1%, 5% and 10% respectively.