Discussion Paper No. 68

The Effect of School Quality on Housing Rent:
Evidence from Matsue city in Japan

Yuta Kuroda

April, 2017

Data Science and Service Research
Discussion Paper

Center for Data Science and Service Research
Graduate School of Economic and Management
Tohoku University27-1 Kawauchi, Aobaku
Sendai 980-8576, JAPANThe Effect of School Quality on Housing Rent:
Evidence from Matsue city in Japan１
Yuta Kuroda ２

Abstract
This study investigates the effect of public school quality on the housing rent within
its school district by using Japanese data. I estimate the causal effect of school quality
as measured by average test score on housing rent by using regression discontinuity
design to control for unobserved characteristics of neighborhoods. Specifically, I focus onapartment buildings located on school attendance district boundaries. I find that school
quality has significantly positive effect on housing rent of apartment for families, where
school quality does not have significant effect on housing rent of houses for single
person. This results show that parents are willing to pay more to send their child tobetter school.

Keywords: Housing rent, School quality, School District, Regression discontinuity

designJEL classifications: R31, R21, I20
I would like to thank my advisor Kentaro Nakajima. I am also grateful to Koichi
Ushijima, Jenn-Jou Chen, and participants at the 2016 Japanese Economic Association
Spring Meeting, the 30th Annual Meeting of the Applied Regional Science Conference(Kobe University) and workshop at National Chengchi University for helpful comments.
All remaining errors are my own.
２ Graduate School of Economics and Management, Tohoku University, Sendai
980-8576, Japan. Email: kuroda@student.econ.tohoku.ac.jp
１1

1. Introduction
How much do parents pay for the education of their children? Because education isinvestment not only for children but also for parents, many parents spend much fortheir children to make them enroll to good school and take high education. It is very
important to analyze the concrete parents' behavior concerning investments in
education of their children from the perspectives of equality in the public educational
system. However it is difficult to observe the parent's willingness to pay because
primary education is free and compulsory in Japan.
We cannot directly observe the parent's willingness to pay of the public school,
however can indirectly observe it from land price or housing rent under the school
district system. When parents having a child purchase a house or rents apartment, they
consider the characteristic of the local public school. In other words, the value of
education that parents consider might be capitalized as land price or housing rent.
Actuality, the real estate agency advertises high quality of the school in the district, thequality of the school may be made capital to land price or housing rent.
However, estimation of school quality from housing rent have difficulty fromendogeneity.

Because the test score of the child is influenced by parents characteristics

such as educational background or income level, good test score does not mean a highquality education provided at the school. Contrary to this, better schools tend to belocated in better neighborhoods. Furthermore, it is impossible to observe the parents
characteristics to influence their children's test score in many cases, and it may cause
bias for an estimate result.
To avoid these problems, Black (1999) uses the regression discontinuity design
focusing on houses located on opposite sides of school attendance district boundaries-thegeographic lines that determine which school a child attends within a school district. By
limiting the sample to those houses that are very close to the attendance district
boundaries, she can control for unobserved characteristics.
Following to Black (1999)’s methodology, I focus on the apartments located on the
public school boundary using the data from Matsue city ３ which is a local capital city inJapan. I estimate the causal effect of school quality on housing rent by using test score
to proxy for school quality. Results show that the quality of the school has significantly
positive effect on housing rent of apartment intended for families. This means that theparents who have a child have a willingness to pay of living the better school district
contrary to single person.
Matsue city is the capital city of Shimane Prefecture, in Southwest Japan.

３2

Furthermore, I find that the effect of test score on the apartment is strong in
proportion to number of rooms and occupied area. It means that the more theapartment intended for a family, the more apartment is affected by school quality. I also
estimate the effect of the junior high school test score by the same equation. In contrast
to the result of elementary school, junior high school test score has insignificant effecton housing rent.
The structure of the paper is as follows: Section 2 reviews the previous literature
analyzing the effect of school quality on housing rent. Section 3 describes my empiricalstrategies. Section 4 discusses data. Section 5 discusses some results. In Section 6 I
conclude.

2. Literature review
There are a lot of studies considering the effects of school quality on housing rent
around the world. Figlio and Lucas (2004) and Clapp, Nanda and Loss (2008) estimate
the effects of school quality on house price by a fixed effect model using the panel data tocontrol the unobserved neighborhood characteristics. Bogart and Cromwell (2000)
analyze using the data which there are some school districts in the same local
government to separate the quality of the public school and local characteristics. With
the case which there is one public school in one local government, we cannot distinguishwhether the difference of land prices is produced by a characteristic of the local
governments such as the tax system or community facilities or by the quality of theschool, because the border of the school district is the same as the border of the local
government. However, when there are some school districts in the same local
government, we can think the difference of the house price to be caused by a differenceof the quality of the public school under the other factors controlled, because thecharacteristics of the local government is unchangeable through a school district. In thisway, they show that the difference of a substantial house price exists between school
districts and conclude that the difference is caused by a difference of the quality of the
public school.
In Japan, Yoshida, Chou and Ushijima (2008) analyzed the effect of the quality of theschool on land prices and the change of it by the introduction of the school choice systemusing the achievement test score and the ratio of enrollment in private junior highschool for the proxy of the quality of the school. As a result, they conclude that thequality of the elementary school had an influence on the land prices in the school3

district, but the effect become smaller by the introduction of school choice system.
Ushijima and Yoshida (2009), estimate the effect of the school quality on land priceusing the panel data of land prices in special wards of Tokyo Prefecture from 2001
through 2007 assuming that the ratio of enrollment in private and national junior highschool for the proxy of the quality of the school. They control for unobserved
neighborhood characteristics by individual fixed effect approach. They find that thequality of the school influenced land prices only in the districts which have the highquality school, and the influence is not so big. However, there is still room for argument
about the validity of using the ratio of enrollment for the proxy of the quality of theschool because the ratio of enrollment in private and national junior high school
strongly correlated with educational achievement of elementary school, but the parents
consider about various factors such as budget or distance when they think about
entrance of their children. In addition, authors themselves point out the possibility thatthe relationship between the quality of the school and the land prices were weakened by
the influence of a school choice system introduced into the many special wards during
an analysis period.
On the other hand Black (1999) designed the highest reliability approach under thesituation that panel data is not available. She uses regression discontinuity design andestimates the effect of test score on the house price with controlling to the unobserved
neighborhood characteristics by focusing on the houses which differ only by theelementary school the child attends. As a result, she finds that parents are willing to
pay to enter their children to better school test.
Following to Black’s (1999) regression discontinuity design approach, I estimate theeffect of the quality of the school on housing rent. This paper’s contributions are as
follows. First, I can use the detailed information of the apartment because I use thehousing price instead of land price used by previous studies in Japan. In the land pricedata, we cannot identify whether the land is actually used for family residence or not.
On the other hand, I can estimate and interpret the effect of test score on the housing
rent more clearly because apartment data has indices as to whether the property is forfamily or for a single person. Because I can identify whether the apartment is intended
for families or single, I can estimate the impact on people who care about the quality ofelementary school appropriately. Furthermore I can analyze the difference between theapartment that can be affected by the school quality and the apartment that cannot beaffected by school quality.
Second, I estimate the effect of public school clearly by focusing on Japanese local city,
Matsue. Because the school choice system is introduced in Tokyo that is targeted in4

previous literature, the effect of public school may be underestimated. On the other
hand, school choice system is not introduced and a clear school district exists in Matsue
city. In addition, there is few of private elementary and junior high schools in Matsue.
In areas where there are a lot of private schools, like Tokyo, the relationship between
the quality of the public school and housing rent in the school district may weaken
because the private school does not restricted by school district. Furthermore, because
the child having rich parents is easy to go to the private school, the result will be biased.
These problems are solved by using my data that does contain little private school. Dueto the above reasons, I cancleanly estimate the effect of public school quality on

housing rent under the school district system.

3. Empirical strategies
As mentioned above, I estimate the effect of the quality of the school on housing rent
using hedonic regression. I regress the test score on housing rent with some control
variables. The basic relationship is as follows:
ln 𝑃𝑖𝑎𝑗 = 𝛼 + 𝛽𝑋𝑖𝑎𝑗 + 𝛿𝑍𝑗 + 𝛾𝑡𝑒𝑠𝑡𝑎 + 𝜀𝑖𝑗

where 𝑃𝑖𝑎𝑗 is the rent of the apartment i in attendance district a in school district j.

The vector X includes characteristics of apartment such as number of rooms and age ofbuilding, Z is a vector of neighborhood and school district characteristics. 𝑡𝑒𝑠𝑡𝑎 is theaverage test score of the public school.

However, it is difficult to observe all the socioeconomic characteristics such as accessto public facilities or average income in the district, the result without including thosevariables may have bias. To address this problem, I estimate using Regression
discontinuity design. I replace the vector of observed characteristics with the boundary
dummies that indicate apartment building that share an attendance district boundary.
ln 𝑃𝑖𝑎𝑏 = 𝛼 + 𝛽𝑋𝑖𝑎𝑏 + Φ𝐾𝑏 + 𝛾𝑡𝑒𝑠𝑡𝑎 + 𝜀𝑖𝑎𝑏

where 𝐾 is a boundary dummy if the apartment building located in the boundary b

takes one and it controls for any unobserved characteristics of shared by apartmentbuildings on either side of the boundary. It is considered that apartment buildings in thesame boundary resemble it in a characteristic such as accessibility to public facility or5average income in district.
Therefore I analyze using the data which I limited to the sample which there is toconstant distance from the boundary after having added the boundary dummy to an
equation. I become able to compare the apartment building which resembled closely of
the geographical information directly, and it is thought that the prices of apartment
difference are caused by the right to be able to go to the different public school.
In my estimation, in addition to the analysis using full sample, I make the subset of
an apartment located within less than 500m, 350m and 200m from the boundary of theschool district and analyze it for each sub sample.
Because the control variables such as the education expenditure per student or tax
rate are not different across schools in Matsue, unlike previous study, it is not necessary
to consider those variables.

4. Data and summary statistics
4.1 About Matsue city
Matsue is the one of the regional city in Southwest Japan and faces the Sea of Japan.
The population of the city is approximately 200,000 people in 2015.
There are several reasons that I focus on Matsue. Primarily, in Matsue, there is very
little number of private elementary and junior high schools. In area where there are a
lot of private schools, the relationship between the quality of the public school andhousing rent in the school district may weaken because the private school does not comeclose to the school district to live in, and anyone can go to school freely. However, I canidentify the effect of the quality of the public school on housing rent more clearlybecause there is little way to receive an elementary education other than public schoolin Matsue with a few private schools.
Furthermore, Matsue is the city which a school choice system is not introduced and aclear school district exists, and has the population scale that is enough for analysis. Of
course, if the school is very far from the house, or if parents change their address during
school year, they can send their child to school that is located outside their own school
district. But that kind of situations is very rare.
Figure 1 presents the map and the school district of Matsue that I used for analysis.
The bold black line represents the boundary line of the school district, and only one
public school exists each in all school districts. There are 35 public schools in Matsue,
6but the number of public schools which I used in this analysis is 23 of 35, because I
cannot use the data of the school in the non-city area where there is almost none of theapartment in the district or the branch school where test score is not shown because
there is only a few students. Furthermore, when I estimate using the boundary dummyof the school district, I omit the boundary divided by large object such as the big river orsite of castle from my dataset because I concern that neighborhood characteristic on
opposite sides of an attendance district boundary.

～

Attendance Districts

・Elementary School

Figure1. Elementary School Districts of Matsue City7

4.2 Data
Table 1 shows summary statistics. The full sample consists of 2,686 apartment data I
use apartment information placed in three kinds of rental information sites: HOME
MATE, CHINTAI and SUUMO. Each apartment includes data of housing rent, numberof the rooms, layout (have living room or dining room), occupied area (㎡), number offloors, age of building, building structure and address information. For a family dummy
equals to one if the apartment has two or more rooms. Here, the apartment intended fora family is defined as it has two or more than rooms. This definition is generally used byreal estate agent in Japan. Using address information and Google Maps, I calculate thedistance from house to nearest attendance boundary, nearest station, Matsue Stationand Shimane University. Furthermore, these websites provide the more detailed
information about the house, and I have used it to make some dummy variables. Living
dummy and Dining dummy is the dummy variable which equal to one if the apartment
has living or dining room. In addition, I set different dummy variables for eachconstruction method such as reinforced concrete and steel frame.
I obtained the statistics data about Matsue and the information of the school districtin the city from the website of Matsue. I used the students per teacher as acharacteristic of the schools, and I used the age group of less than 15 years, those of 65
or older, sex ratio, the average household size in the district as a variable to control a
local characteristic.
The test score as a proxy variable of the quality of the school are two kinds of test: 6th
grade elementary school student take NAAA, 4th and 5th grade elementary school
student take Shimane Academic Ability Survey (SAAS) . I use the sum of the math andlanguage test scores, averaged over the three years as the test score of the school. NAAA
is the scholastic ability investigation examination that MEXT carries out once a year
from 2007 and applies to a sixth grader and a ninth grader. SAAS is the scholastic
ability investigation that Shimane prefecture carried originally and 4th, 5th and 6th
grader of the public school and the student of the public junior high school take it. In
Matsue, however, it was carried out only for the 4th, 5th, 7th, and 8th grade school
student (because the 6th grader and the 9th grader exchanged NAAA with this).

8Table1. SUMMARY STATISTICS

Housing rent (YEN)
School characteristics

Elementary school test score
Junior high school test score

Mean
56724

Full Sample
S.D.
Min
12376 17000

Max
135000

Mean
56577

500m
S.D.
Min
13154 23000

Max
135000

67.35
63.83

2.77
2.06

61.58
59.75

72.75
66.80

67.92
64.03

2.89
1.88

61.58
59.75

72.75
66.80

1.67
0.39
0.73
0.55
44.30
2.60
14.26
0.33
0.20
0.13
0.00
1.78
3.18
3.78
0.82
1.29

0.69
0.49
0.45
0.50
14.43
1.55
9.60
0.47
0.40
0.34
0.05
1.05
2.25
2.56
0.50
0.59

1
0
0
0
12.15
1
0
0
0
0
0
0.03
0.10
0.12
0.10
0.09

4
1
1
1
157.86
14
68
1
1
1
1
5.90
17.06
17.89
3.96
3.73

1.65
0.38
0.70
0.52
43.28
2.72
15.67
0.31
0.22
0.17
0
1.70
2.63
3.65
0.87
1.27

0.72
0.48
0.46
0.50
14.79
1.67
10.36
0.46
0.42
0.38
0
0.94
1.72
2.40
0.53
0.61

1
0
0
0
15.60
1
0
0
0
0
0
0.03
0.10
0.12
0.10
0.09

4
1
1
1
106.06
14
49
1
1
1
0
4.81
9.15
10.64
3.96
3.24

17.30
0.15
0.24
0.48
2.25

2.88
0.04
0.07
0.02
0.28

6.17
0.01
0.00
0.41
1.47

21.56
0.36
0.55
0.56
3.28

17.07
0.15
0.23
0.48
2.20

2.71
0.04
0.08
0.02
0.29

9.00
0.01
0.04
0.41
1.48

21.56
0.36
0.55
0.53
3.18

House characteristics

Number of Rooms
Living Dummy
Dining Dummy
For a family Dummy
Occupied area (㎡)Number of Floors
Age of building
Steel Frame Dummy
Lightweight Steel Dummy
Reinforced Concrete Dummy
Earthquake‐Resistant SteelDistance from nearest station(km)Distance from Matsue station(km)Distance from Shimane University(km)Distance from Elementary school(km)Distance from Junior high school(km)Neighborhood characteristics

Pupil/teacher ratio
Percent 0-15 years old
Percent 65+ years old
Parcent mele
Average Number of Household

2686

N

Housing rent (YEN)
School characteristics

Elementary school test score
Junior high school test score

1423

Mean
56671

350m
S.D.
Min
13353 23000

Max
135000

Mean
55450

200m
S.D.
Min
12373 23000

Max
110000

67.87
64.16

2.81
1.81

61.58
59.75

72.75
66.80

67.55
64.14

2.77
1.82

61.58
59.75

72.75
66.80

1.65
0.39
0.71
0.51
43.28
2.79
15.68
0.29
0.23
0.19
0
1.67
2.65
3.62
0.91
1.28

0.73
0.49
0.46
0.50
14.74
1.76
10.74
0.45
0.42
0.39
0
0.95
1.81
2.37
0.52
0.63

1
0
0
0
15.60
1
0
0
0
0
0
0.03
0.10
0.12
0.10
0.09

4
1
1
1
106.06
14
49
1
1
1
0
4.81
9.15
10.64
3.96
3.24

1.60
0.37
0.70
0.48
42.35
2.73
15.17
0.25
0.20
0.19
0
1.7079
2.81
3.56
0.98
1.35

0.72
0.48
0.46
0.50
14.50
1.64
11.09
0.43
0.40
0.39
0
1.0489
2.05
2.31
0.51
0.65

1
0
0
0
15.60
1
0
0
0
0
0
0.219
0.23
0.12
0.10
0.09

4
1
1
1
106.06
14
46
1
1
1
0
4.807
9.15
10.64
3.96
3.24

16.97
0.15
0.23
0.48
2.19

2.68
0.05
0.08
0.02
0.30

9.00
0.01
0.04
0.41
1.48

21.56
0.36
0.55
0.53
3.18

16.86
0.15
0.23
0.48
2.20

2.61
0.05
0.08
0.02
0.31

9.00
0.02
0.04
0.42
1.48

21.56
0.36
0.55
0.53
3.18

House characteristics

Number of Rooms
Living Dummy
Dining Dummy
For a family Dummy
Occupied area (㎡)Number of Floors
Age of building
Steel Frame Dummy
Lightweight Steel Dummy
Reinforced Concrete Dummy
Earthquake‐Resistant SteelDistance from nearest station(km)Distance from Matsue station(km)Distance from Shimane University(km)Distance from Elementary school(km)Distance from Junior high school(km)Neighborhood characteristics

Pupil/teacher ratio
Percent 0-15 years old
Percent 65+ years old
Parcent mele
Average Number of Household

1088

N

9

718

5. Results and discussion
5.1 Baseline Results
Table 2 shows the baseline result. Column (1) shows the results which using fullsample and not including boundary fixed effect. It shows that the elementary school testscore has positive significant effect on housing rent just like Black’s (1999) result.
Furthermore, other major variables can also represent similar tendency. However, theseresults still have the problem of unobserved neighborhood characteristics.
Then, I restrict sample by the distance from boundary to control for unobserved
neighborhood heterogeneity. Column (2) shows the results restricting sample toapartment building located within 500 meters from boundary using the boundary
dummy instead of census variables. Column (3) and (4) also shows the results
restricting sample to apartment building located within 350 and 200 meters fromboundary. Unlike previous studies, these results show that the test score does not havepositive significant effect on housing rent. To indicate that the result does not come fromthe decreeing of sample size, I estimate the same equation of column (1) for the sample
located within 200 meters from the boundary as shown in column (5). Column (5) showsthat the similar trend to column (1) except for the significant level of the test scorecoefficient.
The result of Table 2 indicates that the public elementary school test score does noteffect on housing rent of apartment within its attendance district. One of the reasons
why these result is obtained is the difference of the dependent variables from previous
studies. In previous studies, the dependent variable is land price or house price.
However in this study I use the hosing rent of apartments or condominiums and about
half of those is only one room apartment which designed for a single person. Naturally,
someone who cares about the quality of school when renting a room is a family which
has or will have children. Therefore, the quality of the school may only effect on the
housing rent of the apartment which intended for a family.
To analyze this issue in detail, I set “for a family dummy” and added the interaction
term of the test score and the dummy into the equation. The results are represented inTable 3.

10

Table2. Baseline Estimation(1)
All houses.0029 **(.0008)(2)500m-0.0033(.0021)-.0065 **(.0024)(4)200m-0.0055(.0028)(5)200m
0.0025(.0017).0793 ***(.0126).0852 ***(.0151).1049 ***(.0131).1138 ***(.0125).1016 ***(.0114)

Living Dummy.0359 ***(.0081).0467 ***(.0111).0681 ***(.0110).0732 ***(.0144).0739 ***(.0122)Dining Dummy.0501 ***(.0091).0513 ***(.0103).0436 ***(.0109).0363 **(.0134).0293 *(.0128)

Occupied area (㎡).0073 ***(.0008).0078 ***(.0009).0067 ***(.0008).0062 ***(.0008).0067 ***(.0007)

Number of Floors.0216 ***(.0022).0152 ***(.0026).0150 ***(.0028).0121 **(.0044).0121 **(.0044)Age of building-.0126 ***(.0005)-.0126 ***(.0005)-.0125 ***(.0004)-.0129 ***(.0005)-.0122 ***(.0005)

Steel Frame Dummy.0228 ***(.0110).0438 ***(.0074).0488 ***(.0091).0478 ***(.0118).0293 **(.0097)

Lightweight Steel Dummy.0654 ***(.0065).0670 ***(.0078).0747 ***(.0094).0686 ***(.0116).0719 ***(.0095)

Reinforced Concrete Dummy.0240 *(.0091).0573 ***(.0108).0688 ***(.0120).0601 ***(.0147).0446 **(.0157)

Earthquake‐Resistant Steel.1291 ***(.0174)

Distance from nearest station (km)-.0239 **(.0091).0033(.0019)-.0396(.0271).0075(.0052).0057(.0037)-.0033(.0025).0079 *(.0039)-.0010 *(.0004)-.0345 *(.0161).0037(.0041)-.0311(.0259).0003(.0075)
YES
NO
1369
33
0.8641-.0549(.0290)-.0747(.0475).0126(.0067).0630(.0354)-.0420 *(.0204)

Elementary school test score
House characteristics
Number of Rooms

Distance from nearest station squared
Distance from Matsue station (km)-.0304 ***(.0037)Distance from Matsue station squared.0009 ***(.0002).0039(.0020)-.0003(.0002)-.0095(.0102).0041(.0026)-.0032 ***(.0134).0048(.0041)
NO
YES
2642
N/A
0.8442

Distance from Shimane University (km)Distance from Shimane University squared
Distance from Elementary school (km)Distance from Elementary school squared
Distance from Junior high school (km)Distance from Junior high school squared
Boundary fixed effects
Census variables
N
Number of boundaries
Adjusted R2

(3)
350m

-.0106 *(.0048)-.0045(.0230).0030(.0028)-.0086 *(.0043)-.0011 **(.0004)-.0247(.0201).0003(.0049)-.0116 ***(.0313).0039(.0090)
YES
NO
1035
32
0.8758※*, ** and *** indicate statistical significance at 5%, 1%, 0.1%, respectively.
※Culstered standard erroer at the attendance district level are in parentheses

11-.0114 **(.0041).0124 *(.0052)-.0014 *(.0006)-.0216(.0266).0006(.0066)-.0007(.0378)-.0114(.0093)
YES
NO
668
29
0.8741-.0075 *(.0034)-.0204(.0151)-.0003(.0015).0072(.0051)-.0011(.0006)-.00365(.0234)-.0124 *(.0058)-.0429(.0281).0064(.0085)
NO
YES
692
N/A
0.852

In short, table 3 shows the results that the test score has strongly positive significant
effect on the apartment intended for a family and negative significant effect on theapartment intended for a single person. The samples used in each column of table 3 aresimilar to those in table 2, and the results of columns (2) - (4), which are the key results,
will be explained below. The coefficient of the test score shows a negative and significant,indicating that the higher the score of the test, the lower the housing rent. For a family
dummy also showed negative and significant and it means that family-oriented
apartment showed lower rent for apartment which intended for single person. However,
the interaction term of the test score and the dummy has positive and significant effect,
and for families, the housing rent increases as the test score rises. Furthermore all thethree coefficients of test score, for a family dummy and the interaction term will be large
in inverse proportion to distance from boundary. It could mean that only family cares
about the quality of school, on the other hand single person does not care about it.
When I considered the monetary value, the coefficient of the regression where theapartment buildings are only 200 meters from the boundary (column (4)) suggests thata 10 percent increase in test score leads to approximately 1.7 percent increase in
housing rent. In other words, parents are willing to pay 921 Japanese yen in monthly
hosing rent more for a 6.7 point increase in test score (the mean of housing rent isapproximately 55,000 yen and the mean of test score is approximately 67).
It is difficult to compare with previous study because both proxy of school quality andindependent variable are different, I compare below as reference. Yoshida, Chou andUshijima (2008) revealed that the land price will increase by 2.6% (about 23,000 yen) if
the private school admission rate increases by 10% points. In addition, if themathematics test score increases by 10 points, it shows that the land price will rise by
0.09%, but the coefficient of the test score is not significant. In my result, if the testscore rises by 10 points, the housing rent will rise by about 2.5% (about 1400 yen). Thisdifference in the effect of test score may be caused by the educational environment suchas presence or absence of a private school.

12

Table 3 . Family vs. Sin gle

Elementary school test score
For a family Dummy
Test score × For a family
House characteristics
Boundary fixed effects
Census variables
N
Number of boundaries
Adjusted R2(1)
All houses

(2)
500m

(3)
350m

(4)
200m

(5)
200m

-.0043 **(.0014)-.8408 ***(.1547).0126 ***(.0016)
YES
NO
YES
2640
N/A
0.8494-.0087 ***(.0025)-.7608 ***(.1311).0118 ***(.0019)
YES
YES
NO
1367
33
0.8683-.0122 ***(.0027)-.8535 ***(.1400).0135 ***(.0021)
YES
YES
NO
1033
32
0.8820-.0122 ***(.0032)-.9333 ***(.1729).0147 ***(.0025)
YES
YES
NO
666
29
0.8815-.0051 *(.0021)-1.0302 ***(.1666).0160 ***(.0025)
YES
NO
YES
690
N/A
0.8607※*, ** and *** indicate statistical significance at 5%, 1%, 0.1%, respectively.
※Culstered standard erroer at the attendance district level are in parentheses

5.2 Robustness
5.2.1 Definition of “For a Family”
In this section, I check the robustness of the definition of for a family. In the analysis
of Table 3, I define that the apartment which has more than two rooms as theapartment intended for a family based on the definition by websites. However, in
actually, the more rooms and the larger occupied area the more the house is suitable forthe family. Therefore, I estimate whether the effect received from the test score becomesstronger as the degree for families is larger.
Then, table 4 shows that the result which using the interaction term of the test score
and the apartment characteristics which may have effect on the tendency to be intended
for a family. Column (1) and (2) show the result that using the interaction term of thetest score and the number of rooms. Column (1) shows the results which using fullsample and not including boundary fixed effect. Column (2) shows the results
restricting sample to apartment building located within 200 meters from boundary
using the boundary dummy. The interaction term of the test score and the number ofrooms has positive and significant effect, and it means that the effect of test score on theapartment will be strong in proportion to number of rooms. Column (3) and (4) show theresult that using the interaction term of the test score and the occupied area. The
samples used in each column (3) and column (4) are similar to column (1) and column (2).
The interaction term of the test score and the occupied area has positive and significant
13effect, and it represents that the larger occupied area is the stronger the effect of testscore is. These results also indicate that the apartment intended for a family tend to be
more effected by the test score than that intended for a single person.

Table 4 . Robu stn e ss of for familiy
Number of Rooms(1)(2)
All houses
200m

Occupied area
(3)
(4)
All houses
200m

Elementary school test score-.0140 ***(.0023)-.0206 ***(.0042)-.0183 ***(.0033)-.0198 **(.0062)

Test score × Number of Rooms.0097 ***(.0011).0091 ***(.0019).0005 ***(.0001).0004 **(.0001)

Test score × Occupied area
Test score × Distance from school
Number of Rooms-.5772 ***(.0798)-.5059 ***(.1282).0753 ***(.0129).1086 ***(.0128)

Occupied area

.0071 ***(.0021)-.0124(.0101)
YES
NO
YES
2641
N/A
0.8504.0061 ***(.0008)-.0265(.0064)
YES
YES
NO
667
29
0.8782-.0247 ***(.0044)-.0113(.0101)
YES
NO
YES
2641
N/A
0.8508-.0192 *(.0085)-.0277(.0262)
YES
YES
NO
667
29
0.8765Distance from Elementary school (km)Other house characteristics
Boundary fixed effects
Census variables
N
Number of boundaries
Adjusted R2※*, ** and *** indicate statistical significance at 5%, 1%, 0.1%, respectively.
※Culstered standard erroer at the attendance district level are in parentheses

5.2.2 Other Concerns
In this section, I conduct further robustness checks to address other potential
concerns.
First, the parents who are interested in school quality strongly may be more likely to
be interested in apartment quality. Because the apartment quality strongly correlateswith the housing rent, if there is a positive correlation between the quality of the school
14and the quality of the apartment, our findings may just represent the housing quality
effects instead school quality effects. To address this concern, I regress the apartment
quality such as number of rooms and occupied area on the test score as shown in Table 5,column (1) and column (2). Column (1) shows that the quality of the school does notaffect the number of rooms, and column (2) also shows that school quality does not affectthe occupied area. These results show that there is no positive correlation between thequality of the school and the quality of the apartment.
Another concern is that the test score used in this study may be accidental. Because
the test score used in this paper is of a single year, using different test score in otheryears may produce different results. Therefore I estimate the same equation of previous
estimation using the other year test score as shown in column (3) and column (4).
Column (3) shows the results which using full sample, column (4) shows the results
restricting sample to apartment building located within 200 meters from boundary
using the boundary dummy and for a family dummy. The result of either column issomewhat different in magnitude but positive and negative direction is the same as themain result. Thus I can emphasize the validity of using these test score as a proxy of theschool quality.

Table 5 . Se n itivity Te sts

Elementary school test score

House quality
(1)
(2)
Rooms
Occupied-.0014-.1820(.0106)(.1464)

Other test score
(3)
(4)
Rent
Rent
-.0023-.0052(.0035)(.0034)For a family Dummy-.5331 ***(.1258)

Test score × For a family Dummy.0096 ***(.0020)
YES
YES
NO
668
29
0.8793

Other house characteristics
Boundary fixed effects
Census variables
N
Number of boundaries
Adjusted R2

YES
YES
NO
669
29
0.8640

YES
YES
NO
669
29
0.8842※*, ** and *** indicate statistical significance at 5%, 1%, 0.1%, respectively.
※Culstered standard erroer at the attendance district level are in parentheses

15

YES
YES
NO
668
29
0.8734

5.2.3 Junior high school
The above result shows that there is a significant positive correlation between theelementary school test score and the housing rent. However, In Matsue City, theelementary school district is completely included in the junior high school district (seeFigure 2), so parents may consider the quality of junior high school rather thanelementary school. Therefore, in this section, I analyze not only the elementary school
test score but also the test score of junior high school.
Table 6 shows the results of estimating the equation using the junior high school testscore and the junior high school district boundary. Column (1) - (3) show the result thatusing only junior high school test score. Column (1) shows the results which using fullsample, column (2) shows the results restricting sample to apartment building locatedwithin 200 meters from boundary using the boundary dummy and column (3) shows theresults restricting sample to apartment building located within 200 meters fromboundary using the boundary dummy and for a family dummy. These results show thatthe junior high school test score has positive and significant effect on housing rent ofapartment for families and show the same tendency as the result of the estimation byusing the elementary school test score. Of course, in this analysis, it is not possible todistinguish between the effect of elementary school and the effect of junior high school.
Next, I estimated the equation that contained both the elementary school test score
and the junior high school test score as shown in column (4) - (6). The samples used ineach column (4) - (6) are similar to column (1) - (3). Looking at the results of column (6),the effect of elementary school test score remains positive and significant, but it turns
out that the effect of the junior high school test score is insignificant. These results
indicate that only elementary school test score has positive significant effect on housing
rent, however, junior high school test score has insignificant effect on housing rent ofapartment intended for a family.
Possible reasons for these results are as follows. First, the variation of junior highschool test score is small in comparison with elementary school test score because thenumber of junior high school is smaller and the number of students per school is larger
by contrast with elementary school. Second, elementary school and junior high school
are may considered as a continuously integrated process and the parents makedecisions of residential area only when their children enter elementary school. In
Matsue city, attendance district of junior high school is a combination of elementary
school attendance district, therefore, schoolmates from elementary school isschoolmates of junior high school. Thus parents and children may be refused to change
16their attendance school when entering junior high school. Third, parents who havejunior high school children may tend to have their own house in comparison to who haveelementary school children because they are older and their income and social status ishigher. Unfortunately I cannot test it because there is no information about detachedhouse in my data.
Table 6 . Usin g Ju n ior High Sc h ool Data
Only junior high school
(1)
(2)
(3)
All houses
200m
200m
Elementary school test score
Junior high school test score-.0005(.0012)-.0131 **(.0047)

For a family Dummy-.0221 ***(.0049)-.6955 *(.2774)

Elementary & junior high school
(4)
(5)
(6)
All houses
200m
200m
.0037 ***(.0010)-.0027 *(.0013)-.0076 **(.0028)-.0016 **(.0060)

YES
NO
YES
2641
N/A
0.8445

YES
YES
NO
671
25
0.8722Elementary test score × For a family
Junior high test score × For a family
Other house characteristics
Boundary fixed effects
Census variables
N
Number of boundaries
Adjusted R2

YES
NO
YES
2659
N/A
0.8431

YES
YES
NO
363
15
0.9051※*, ** and *** indicate statistical significance at 5%, 1%, 0.1%, respectively.
※Culstered standard erroer at the attendance district level are in parentheses

17.0128 **(.0043)
YES
YES
NO
361
15
0.9137-.0145 ***(.0032)-.0199 **(.0061)-1.0218 ***(.2985).0149 ***(.0027).0012(.0049)
YES
YES
NO
668
25
0.8800～Attendance Districts▪

Junior High School

Figure2. Junior High School Districts of Matsue City

6. Conclusion
In this paper, I estimate the effect of the elementary school quality on housing rent
using regression discontinuity design. As the result, I find that school quality has
significantly positive effect on housing rent of apartment intended for families. This
result shows that parents are willing to pay more to send their child to a better school.
Specifically, 10 percent increase in the test score leads to approximately 1.7 percent
increase in housing rent.
In contrast, test score has negative or insignificant effect on housing rent ofapartment for single person. This result indicate that the relative demand of single
room decreased in the district which has better school because university student andthe single person thought to be the main consumers of the single room do not consider
the school quality.
The test score has a strong positive effect compared with the previous study in Japan,
18and this result may be due to the absence of private elementary school. In areas withmany private elementary schools, school selection behavior of parents differ greatly, so
it is necessary to pay attention to the possibility that the result of this paper is unique toMatsue city.

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