Discussion Papers In Economics
And Business

The Effects of Student–Teacher Gender Matching on Students’ Performancein Junior High Schools in Japan

Hisanobu Kakizawa

Discussion Paper 17-29

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Effects of Student–Teacher Gender Matching on Students’ Performancein Junior High Schools in Japan

Hisanobu Kakizawa

Discussion Paper 17-29
September 2017

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Effects of Student–Teacher Gender Matching on Students’ Performance in JuniorHigh Schools in Japan*

Hisanobu Kakizawa†

September 28, 2017

ABSTRACTThis study analyzes the student–teacher gender matching effect on students’ academic
performance and questioning behavior. The results indicate as follows: 1. Positive effects ofsame gender teachers on students’ performance are observed, especially for girls. 2. The
gender-matching effect appears to be most significant in the study of English, followed bymath and science. 3. Gender matching has an effect on students’ questioning behavior. 4.
Changes in questioning behavior may partly explain the improvement in performance. 5.
Even when the effects of questioning behavior are controlled for, female teachers still have apositive effect on girls’ performance.

JEL classification: I20, I21
Keywords: Academic performance; Gender-matching effect; Questioning behavior* This research forms part of the results of the “Investigative Research Regarding the Effectsof Education”, a research project of the National Institute for Educational Policy Research(NIER). The author has received many excellent comments regarding the drafts of this paper
from members of the project. The author would like to thank for these contributions here. Anyremaining errors are the author's own.
† Center for Education in Liberal Arts and Sciences, Osaka University, 1-16 Machikaneyama,
Toyonaka, Osaka 560-0043, Japan; e-mail: hkakizawa@celas.osaka-u.ac.jp

I. Introduction
Much research has been conducted on the effects of gender matching between
students and teachers on the academic behavior and performance of students as well as theirlife choices. However, the results of previous research vary depending on subject and grade.
Some studies have found that same-gender teachers have a positive effect on student
academic performance, while other studies indicate a negative effect or no effect at all.
A prominent hypothesis that explains the mechanism by which gender has an effecton performance is the role model effect. According to this effect, the mere presence of ateacher serves as a role model for students, and functions to stimulate academic achievement.
If this hypothesis is correct, then, as same-gender teachers are typically easier for students to
identify with as role models, students taught by same-gender teachers should have increased
performance in comparison to students taught by teachers of a different gender. Anotheroft-cited hypothesis is stereotype threat. Stereotype threat considers the effects of various
social stereotypes that exist concerning gender and academic performance. Typically, thishypothesis deals with common ideas, like the notion that girls are good at the liberal arts andboys are good at science, technology, engineering, and math (STEM) subjects. Stereotypes
pose a threat of being internalized by students and of leading to behavior of teachers that
could affect students. Either way, if this hypothesis is correct, the behavior of students andteachers should tend to occur in a way that conforms to such stereotypes.
On the other hand, in the study of education, interactions between students andteachers in the classroom have been examined in detail. In particular, the questioning behaviorof students is regarded as an important factor that influences grades and other measures ofacademic performance. Several previous works have already pointed out that gender matching
between students and teachers has an effect on questioning behavior. Furthermore, it ispossible that gender matching affects academic performance by causing changes inquestioning behavior. This study attempts to analyze these points using micro data from alarge survey conducted by the National Institute for Educational Policy Research (NIER). The
subjects of this analysis are the three grades of Japanese middle school.
The structure of the rest of this paper is as follows. Previous research is detailed in
Section II. In Section III, a summary of the data used in this study is presented. In Section IV,
the effects of gender matching on test performance, which is a major component of academic
performance, is estimated. In Section V, an analysis that considers questioning behavior isconducted. Section VI presents the conclusion.
II. Literature Review
A. Relationship between Gender Matching and Performance
The effects of gender matching between students and teachers on students’ academic
performance have been analyzed at many stages of education. In particular, regarding higher
education at university level and beyond, there is a comparatively large body of research
indicating that a role model effect exists between female students and female teachers. Nixon

and Robinson (1989) discovered a higher rate of majoring in STEM fields in university forgirls who attended high schools with a large number of female STEM teachers, indicating thepossibility of a role model effect. Rothstein (1995) showed that the percentage of female
university students going on to graduate school increased with the ratio of female teachers
within the university. However, this had no effect on wages earned upon entering the labormarket later. Neumark and Gardecki (1998) analyzed the relationship between the number offemale teachers and performance of female students in doctoral courses in economics, andshowed that, although the presence of female teachers had no special effect on the rate at
which students successfully found employment in research positions, it did have the effect ofsomewhat shortening the amount of time it took female students to finish graduate school.
Hoffman and Orepoulos (2009) discovered that female teachers had a small effect on boostingfemale students’ performance in university-level education. Bettinger and Long (2005)
discovered a positive effect on the number of credits acquired by female students at university
level in some subjects, including math, and a negative effect for other subjects. Carrell et al.
(2010) discovered a matching effect between female students with a high level ofmathematical proficiency at the time of enrollment and female teachers, but observed no such
effect for male students. Conversely, Canes and Rosen (1995), after analyzing the relationshipbetween the ratio of female students choosing STEM subjects at a number of universities andthe ratio of female teachers for those subjects, concluded that no special relationship existed
between the two. Price (2010) showed that the number of female teachers had a negative
effect on the tendency of female university students to major in STEM subjects. Overall,although the relationship is not entirely clear, there is much research that indicates thatmatching between female students and female teachers at the level of university higher
education and beyond has a positive effect on academic performance and life choices.
By comparison, the results vary for research on primary and secondary education.
Dee (2007), who analyzed US middle schoolers, found that female teachers had a positiveeffect on the performance of girls in English and history. However, female teachers had anegative effect on both male and female students on performance in math. Muralidharan and
Sheth (2016) performed an analysis of Indian elementary school students using large-scale
panel data, and reported that female teachers had a positive effect only on the performance ofgirls. Parades (2014), in a study of middle school students in Chile, found that female teachers
had the same positive effect on girls’ performance, and concluded upon further analysis that
this was not due to stereotype threat but rather the role model effect. Conversely, Steele(1997) and Spencer et al. (1999) conducted an analysis that connected girls’ lower
performance in math to stereotype threat. Lavy (2008) analyzed the effects of stereotype
threat using data for Israeli high school students and, contrary to initial expectations, theresults indicated that male students faced negative bias from teachers.
However, there is also a great deal of research that argues that female teachers have anegative effect or no effect at all on performance. Ehrenberg et al. (1995) indicated that,1although white, female teachers have no improvement effect on the performance of white,female students in STEM fields, such teachers tend to evaluate such students relatively
positively when performing subjective evaluations. Beilcock et al. (2010) argued that, when
women with math anxiety became primary school teachers, they had a negative effect on girls’
performance in math. Furthermore, Antecol et al. (2015) discovered that, although female
teachers had a negative effect on average on girls’ test scores in math at the primary schoollevel, female teachers who majored in math as students actually had a positive effect. This
indicates the possibility that a lack of female teachers majoring in STEM fields produces anaverage negative effect. Holmlund and Sund (2008), who use data on Swedish high schoolers,and Cho (2012), who uses the Trends in International Mathematics and Science Study datafrom 15 countries, reported a negative result for the existence of a gender-matching effect.
B. Questioning Behavior
In this subsection, we shift our focus to previous research on the questioning
behavior of students. Much research has already been undertaken on this topic, primarily inthe field of pedagogy, which regards students’ questioning behavior as an important factor
that affects academic performance. Zoller (1987) argued that questioning behavior is an
essential skill for solving problems. Rosenshine et al. (1996) performed a meta-analysis ofreading comprehension using previous research, and calculated an average of 0.36 for theeffect of questions on performance in research using standardized tests and of 0.86 in researchusing independent tests. Concerning the effect of questioning behavior in STEM fields, anincrease in text comprehension in physics (Koch and Eckstein 1991) and the promotion ofdeeper autonomous thinking (King 1992) have been indicated. King and Rosenshine (1993)
reported that students who had received training to produce thought-provoking questions
performed better on average than students who did not receive training. Harper et al. (2003)
indicated that the content of questions, more than their quantity, contributed to increased
understanding of concepts in physics. Chin and Osborne (2010a, 2010b) argued thatquestioning behavior might raise the quality of group discussions in science classes. Chin andOsborne (2008) provided a survey of previous research regarding the effect of questioning
behavior on learning in STEM fields.
In addition, much previous research indicates that the gender of the student andteacher has an effect on the questioning behavior of students, or on the mutual exchange
between students and teachers, which includes questioning behavior. However, the various
conclusions from these studies do not necessarily coincide. Sternglanz and Lyberger-Ficek(1977), in a survey targeting university students, found that male students were more assertivein mutual exchanges with instructors that occurred through asking questions. Brooks (1982)
indicated that male university students were more assertive in asking questions when theirprofessors were female. Bowers (1986), in a survey conducted at Iowa University, determinedthat students were more comfortable when their teachers were female. Pearson and West2

(1991) discovered that, in universities, male students were more likely to ask questions in theclassroom, while having a female teacher led to a small increase in the rate at which female
students asked questions. Canada and Pringle (1995) analyzed cases in which women’s
universities transitioned to co-educational institutions, and discovered that not only did thegender of students and professors have an effect on the relationship between students andteachers, but so did the ratio of men and women within the class. Conversely, Good et al.
(1987) reported a tendency for boys to ask questions assertively in childhood, but thisdifference narrowed gradually as students grew older. Crawford and MacLeod (1990),
although observing a tendency for male university students to participate in class in an
assertive manner, determined that the gender of the teacher had no significant effect on thistendency. Keeling et al. (2009), in a survey performed for high-level molecular biology
courses in universities, concluded there was no difference between the two genders in thequality and number of questions asked. Blonder et al. (2015), concerning the number andcontent of questions asked in an inquiry chemistry laboratory, reported that either there wasno difference between the two genders or female students tended to ask more questions of ahigher quality than male students did. In other related research, Rocca (2010) offered a surveyof the literature.
III. Data
The NIER is a research institute established under the Ministry of Education, Sport,
Science, Education and Technology for the purpose of conducting investigative research
related to education policy. This study used micro data from the “Survey on the Course of
Study Implementation at Elementary Schools” conducted by the NIER. The subjects of thissurvey were students between elementary grade 5 and middle school grade 3 (aged 11-15
years) as well as the teachers that supervised these students. This national survey was
conducted between January and February 2004.
The sample for this survey was chosen as follows. First, all elementary and middle
schools in Japan were divided into four groups: Public schools in the 23 wards of Tokyo or ingovernment designated cities (public metropolitan); public schools in cities (public urban);public schools in towns and villages (public rural); and national and private schools(national/private). Next, subject schools were randomly selected from each group.
Furthermore, for each selected school, a subject class was randomly selected for each grade.
The sample for this survey comprised all students in this class, as well as the teachers
responsible for instructing this class in each subject. This study used data for the three middle
school grades from this survey. Approximately 240,000 students selected from over 2,500
schools comprise the total sample, which includes every subject for these three grades.
The classes in the sample participated in a test and a questionnaire on the learning
attitudes for five subjects: English, Japanese, math, science, and social studies. However, not
all classes were surveyed for all subjects. Instead, three of five possible subjects were3

assigned at random. In addition, for each subject, three types of problem booklets wereprepared. Each class was given one of these problem booklets, also assigned at random, as an
examination. These three types of problem booklets were produced so as to be of identicalscope and difficulty. A questionnaire was distributed to the teachers responsible for thesestudents in each subject, asking about fundamental personal attributes and teaching methods.
IV. Estimation of Gender-Matching Effects
First, the effect on students’ performance of having female teachers was estimated forboth girls and boys. A potential problem here is that correlation might exist between theunobservable individual effects for each student and the distribution of female teachers.
In compulsory education in Japan, students themselves do not determine their course
subjects and teachers. Classes are determined by schools. Normally, a class set up in April
does not change for at least a year. The teacher responsible for each subject visits theclassroom to present a lesson. In addition, the assignment of these teachers is determined by
the school. As a result, each teacher is assigned in a manner unrelated to the wishes of thestudents. This is similar to the case studies performed by Carrell and West (2010) and Carrel
et al. (2010) concerning the United States Air Force Academy (USAFA). Under such a system,
for matching between students and teachers, it is considered unlikely that self-selection by
students themselves occurs.
However, there is no uniform system for how to consider student ability andindividuality when determining classes, with such decisions being largely dependent on eachschool’s policy. If students were non-randomly sorted in the determination of classes, and if
the assignments of teachers to each class were biased based on gender, it would be possible
for correlation to occur. In addition, as many schools are included in the data used in thisstudy, it is possible that correlation exists between trends in student attributes and the
distribution of female teachers at the school level. For instance, there are cases in which areas
with strong average academic performance have a greater number of teachers of a particulargender. Accordingly, in this study, it is necessary to consider ways of dealing with suchcorrelations when proceeding with the analysis.
Antecol et al. (2015) avoided this problem by using data obtained from a randomized
experiment. Carrell and West (2010) used data on USAFA students from before they enrolled
in the academy to confirm by means of a permutation test that matching between students andteachers was random. Neither of these methods is possible for the cross-sectional survey data
used in this study. A further method to consider is first-difference estimation, used by Dee(2007) and Cho (2012). However, in this method, modeling that considers the endogeneity ofquestioning behavior becomes difficult. Therefore, in this study, we attempt to deal with thisproblem by using a correlated random-effects model.１

１

See Mundlak (1978) and Wooldridge (2010, p.332).
4

A. Empirical Strategy
The five subjects are represented by

1, ⋯ ,5. Each student takes tests in, withthree of these subjects. The three tests that student takes arewith∗focus on one subject, . To estimate the gender-matching effects in∗

1,2,3. Here, we, we consider thefollowing model.
γ

(1)
γ

∗

γ

γ

∗

γ
γ

∗

γ

∗

is the test score of student
in subject.
is the shared curriculum
exogeneity variable vector, that is, variables that express the individual attributes of studentthat are not the student’s gender, as well as the attributes of the class and the school to which
the student belongs.
denotes the attributes other than gender of the teacher who teaches
subject

to student .

value of 1 if∗∗

is a dummy variable that expresses subject, and otherwise 0.

∗

and takes a

is a female student dummy variable.

is afemale teacher dummy that takes a value of 1 if the teacher teaching subject
to student
is female, and 0 if the teacher is male.
is a vector composed of these three variables andtheir cross-terms.
is a random variable with mean 0 and variance. It expresses theunobservable individual effect for student on performance regardless of subject.
is anerror term that satisfies the standard assumptions.
Furthermore, we consider the possibility that correlation exists between the female
teacher dummy, the variables for other teacher attributes, and the student
individual effects variable . To express this correlation, the following linear relationship isassumed.
̅(2)̅

is a vector made up of the averages of teacher attributes for thethree subjects in which student took tests. Substituting equation 2 into 1, the following
model is obtained, which incorporates the correlation between these variables.２

To perform this estimation, it is necessary for teacher attributes
andto havevariance for each . In other words, each subject must have a different teacher. However, thiscondition is not satisfied, as in primary school, a single teacher typically teaches all subjects.
As a result, the subjects of the analysis in this study are limited to middle schools.

２

5

(3)
The versions of equation 3 for each subject for which student

took tests are as

follows:
(4)
E
E
,

,

,

,
=
, and
.
is a
three-element unit vector, andis a rank three identity matrix. Equation 4 is estimated foreach grade by changing the subject of focus, ∗ , in a sequential manner.
If male student takes a test in subject ∗ under the instruction of a female teacher,the values of the three dummy variables become∗

1,0, and

1. In thiscase, the test score is expressed as, , . Similarly, if this student is under the instructionof a male teacher, the test score is expressed as, , . With the independent variable fromequation 4 as the condition, if conditional independence is established between
and the female teacher dummy, then the conditional average
, , ,
, ,
treatment effect (CATE) produced by the assignment to female teachers can be written in thefollowing way using the estimates from equation 4.
:

, ,

, ,

γ

γ

In other words,
is a value obtained by adding the inherent female teacher effect∗to the average effect (γ on boys for female teachers in the four subjects(γ ) for subject∗
other than .
Similarly, the CATE of female teachers on girls who took a test in subject ∗ is asfollows.
:

, ,

, ,

γ

γ

γ

γ

Furthermore, the differences between the CATEs produced by boy and girl students
are as follows.
:γγ

I obtain all these values.
6B. Variables
The dependent variable in this estimation is the test scores. As described in section III,for the tests conducted in this study, three types of problem booklets of equal difficulty wereused for each subject. The problem booklets were randomly distributed to each middle school.
Therefore, the standardized scores for each test booklet is used as the dependent variable inthis study.
The sample size and means by gender for standardized scores in each subject are
shown in Table 1. Asterisks denote the results of t-tests performed on the differences in means.
This table shows that girls outperform boys in English and Japanese for all three grades. The
difference is particularly large in Japanese. However, boys perform better in science in all
three years. Girls perform better in math in both grades 2 and 3. In social studies, boys do
better in grade 1 and girls do better in grade 3, and thus, no consistent trend is observed.
Table 1
Sample Sizes and Means of Standardized Scores
Grade 1
Grade 2EnglishJapanese
Math
Science
Social studies

Grade 3

Girls

Boys

Girls

Boys

Girls

Boys

23990
0.143
24150
0.183
24129
-0.00824243-0.01024385-0.01025759-0.13325981-0.170
25641
0.007
25692
0.009
25782
0.010

23843
0.147
23888
0.192
23936
0.018
24067
-0.02524120-0.00725628-0.13725462-0.18025445-0.017
25413
0.024
25626
0.007

21731
0.122
21704
0.226
21722
0.012
17526
-0.017
21802
0.088

22998
-0.11523208-0.21123141-0.010
18332
0.017
23425
-0.082

***
***
*
**
**

***
***
***
***

***
***
**
***
***

Note: The upper rows show the sample sizes. The lower rows show the mean
standardized scores by gender. The asterisks indicate the results of t-tests of differencesin means. * p < .10, ** p < .05, *** p < .01.
However, the independent variable that is the focus of this analysis is the teacher’s
gender. A dummy variable is used for this; it takes a value of 1 for female teachers and 0 for
male teachers. The ratios of female teachers at every grade and in every subject are shown in
Table 2. While female teachers comprise the majority in English and Japanese for all 3 years,
male teachers make up around 80% of teachers in math and science, and the ratio of female
teachers in social studies is even lower than in math and science.
7

Table 2
Ratios of Female Teachers (in percentages)
EnglishJapanese

Math

Science

Socialstudies

Grade 1

59.83

61.88

27.21

23.14

15.36

Grade 2

61.94

59.09

27.58

21.09

15.96

Grade 3

56.18

59.67

20.77

19.30

16.48

Other independent variables are as follows. First, years of teaching experience isused as a non-gender teacher attribute. Next, the number of students and the ratio of female
students are used as class attributes, and school classification is used as a school attribute. The
number of students and the ratio of female students are both continuous variables. Schoolclassification indicates the division into the groups used when separating subject classes into
“public metropolitan,” “public urban,” “public rural,” and “national/private.” Here, dummy
variables created using “public metropolitan” as the reference category are used. Finally, a girldummy is created as a variable expressing individual student attributes. In addition, four
variables are used to express attitude towards life and study outside of school. These variables
represent hours of daily sleep, whether a student eats breakfast daily, whether items thestudent brings to school are checked, and whether a cram school or home tutor is used in any
subject. The descriptive statistics for these are shown in Table A1 in appendix.
C. Results
The CATEs obtained from the estimated values of equation 4 are compiled in Table 3
below. Asterisks in this table indicate the results of testing linear constraints with the null
hypothesis that each value from equation 4 is zero (for all estimation results, see appendix
Tables A2, A3, and A4).
First, to outline results by student gender, regarding girls, for three subjects in grade
1, all subjects in grade 2, and four subjects in grade 3, the estimated values ofaresignificantly positive. In other words, regarding performance in these subjects, female
teachers have a relatively positive effect in comparison to male teachers. Non-significant
estimated values for other subjects are also all positive. However, regarding boys, for English
in grade 1 and English and Japanese in grade 3, the estimated values ofare significantly
negative, meaning that male teachers had a relatively positive effect. The only case in whichteachers of the opposite gender were more effective than those of the same gender was forboys in grade 3 science.
Next, we consider the results by subject. The effect of same-gender teachers wasstrongest through all three grades in English. The effect of female teachers on girls, , issignificantly positive for all three grades. The average taken for all three grades is 0.0534, thewas negative for all threelargest of all five subjects. Conversely, the effect on boys
8

grades, and significant for grades 1 and 3. In other words, regarding boys’ performance inEnglish, male teachers tend to have a relatively positive effect. The average for all threegrades for boys is -0.0202. These results for English are similar to those of Dee (2007). The
estimates from that study showed an effect of 0.045 for girls and -0.047 for boys. By
comparison, the effect from the results in this study is rather large for girls, and the absolutevalue of the effect for boys is rather small. For all three grades, the difference between theeffects for male and female students,, is significant.
Table 3
Estimated CATEs of Female Teachers
EnglishJapanese

Math

Science

Socialstudies

Grade 1-0.0253 ***-0.0101-0.0103

0.0067-0.0191

0.0559 ***0.00750.0359 ***0.0257 **0.01700.0812 ***0.0176

0.0462 ***0.01900.0361 **-0.01410.00110.00740.01700.00530.0453 ***0.0273 ***0.0712 ***0.0359 ***0.0449 ***0.0594 ***0.0262 **0.0639 ***0.01900.0397 **-0.0214 **-0.0237 **-0.0050

0.0633 ***-0.00390.0589 ***0.00010.0457 ***0.0482 ***0.0317 ***0.0803 ***0.0238 *0.0508 ***-0.0151

0.0356 **-0.0202-0.0109-0.0026

0.0290-0.0059

0.05340.0116

0.05100.0366

0.03120.07360.02250.05360.0076

0.0371

Grade 2

Grade 3

Average

Note: The asterisks indicate the results of chi-square tests of linear constraints in equation 4.

*

p < .10, ** p < .05, *** p < .01.

In math, the effect on girls of having a female teacher was, as with English,
significantly positive for all three grades. The absolute value of the effect for grade 2 was
0.0712, the highest value for any grade or subject. The average over all three grades was
0.0510, slightly below the average for English. However, the effect on boys was not
significant for any of the three grades. In other words, unlike for girls, for boys, gendermatching between students and teachers did not have any particular effect on performance of
math. The difference in effect between male and female students was significant.
In science, as well as math and English, the effect on girls of having a female teacher
9was significantly positive for all three grades. However, the estimated values werecomparatively small, with an average over all three grades of 0.0366. As stated earlier in thissubsection, in grade 3 science class, female teachers had a significantly positive effect onboys. In grades 1 and 2 too, the effect was positive, although not at a significant level. As aresult, the difference between male and female students was judged to not be significant for
all three grades.
In social studies, for grades 2 and 3, the effect on girls of having a female teacher
was significantly positive. The estimated value averaged over all three grades was 0.0312.
However, as with math, there was no significant effect on boys for all three grades.
Although the difference between test scores for boys and girls was the largest inJapanese (Table 1), the effect of gender matching between students and teachers was notespecially clear. The effect of female teachers on girls was significantly positive for only
grade 2, and the effect on boys was significantly negative only for grade 3.
From the abovementioned effects, it is possible to observe that gender matching
between students and teachers has some effect on students’ performance in Japanese middle
schools. As the results for boys and girls differ, it is unlikely that the problem is a differencein average ability between male and female teachers. For both girls and boys, there aresubjects in which the instruction of a teacher of the same gender had a stronger effect on
performance than the instruction of a teacher of the opposite gender. This tendency wasparticularly remarkable for girls. Concerning education in STEM subjects, which has often
been the focus of previous research, this study confirms that, for all three grades in middle
school, female teachers had some positive effect on girls’ performance in both math andscience. This result is shared by Paredes (2014), Muralidharan and Sheth (2016), and Carrell
et al. (2010) with regard to university students, among others. Furthermore, it is clear that, inJapan, the gender-matching effect appears to be larger for English than for STEM subjects.
These results for English are similar to those from Dee (2007). However, for Japanese, whichis the native language of the sample in this study, although girls perform better than boys inall grades, having female teachers does not appear to have any clear effect.
V. Effects of Questioning Behavior
A. Empirical Strategy
Based on the analysis results presented in Section IV, we continue our analysis in thissection by considering students’ questioning behavior. The questionnaire distributed during
the survey asked students what behavior they engaged in for each subject when they did notunderstand something during class. The possible answers to this question were: (i) Ask theteacher on the spot, (ii) Ask the teacher after class, (iii) Ask a friend, (iv) Ask a family
member, (v) Ask a cram school teacher or home tutor, (vi) Investigate independently, and (vii)
Do nothing. Students were allowed to choose multiple answers. In this section, we makeestimates focusing in particular on answers (i) and (ii), which represent questions posed to10teachers responsible for instruction at the school.
As in Section IV, with regard to the test score of student
following model is considered.

in subject

, the

∗

(6)
(7)

1
0

∗
∗

0
0

Here,
is a dummy variable that takes a value of 1 if, of the choices listed above,(i), (ii), or both (i) and (ii) were selected, and 0 if neither of these was selected. In other words,
this variable indicates whether students directly queried the teacher responsible for theirinstruction about subject matters they did not understand, either during or after class.
. ,Henceforth, this is referred to as the question dummy. ∗ is the latent variable for,, andare defined as in equation 3.
in equation 6 is the individual effect for student
regarding questioning
behavior. In this equation, as in equation 3, a correlation between students’ individual effects
and teacher attributes is assumed with regard to questioning behavior. In other words, thetendency for a certain student to ask questions of a teacher in a certain subject should beshared and observed across subjects, as it is considered to be related to the student’s
personality or other individual characteristics. Furthermore, it is possible that a correlation
exists between those individual characteristics and the distribution of teachers. For thesereasons, vector, which is composed of the averages of teacher attributes, is included inequation 6.
andare error terms that satisfy the typical assumptions.
in equation
7 is a cross-term vector between the question dummy and the other dummy variables.
is a coefficient vector that corresponds to each element of.
ζ ,ζ ,⋯,ζfrom equation 6 should correlate with, but not with. This variable is discussed later inthis subsection.
This study deals with the effect of gender matching between students and teachers onquestioning behavior. Therefore, the endogenous variable
is used as a binary variable,
and estimates are performed using the following procedure. First, equation 6 is estimated as a
probit model, and the effect of the teacher’s gender on the probability that a student asks adirect question (the questioning probability) is checked. Next, from these estimation results,
the following predicted probability is obtained.
ΦΦ̂Here, Φ is the standard normal distribution function and ̂
11is the best linearunbiased estimator of individual effects. Finally, the instrumental variable estimation ofequation 7 is performed using Φ and Φ
as instrumental variables.３
Although this estimation procedure itself is possible without variable , to avoid
multiple collinearity between Φ and other variables, a variable that satisfies the conditions
mentioned earlier should be appended. For this purpose,is used; it is the answer to thequestion from the questionnaire targeting students that asks, “When you study, do yourparents praise you?” Students had to respond on a four-point scale, ranging from “I do notthink so” to “I think so.” Using the response “I do not think so” as a reference, three dummy
variables are created and added to the estimate in equation 6. In addition, the results of a testof over-identifying restrictions that considers
as a continuous variable are shown in
Tables A8–A10 in the appendix. J-statistics are sufficiently small in all grades and subjects,
and thus, exogeneity is not rejected. Furthermore, F-statistics regarding weak instrumental
variables show sufficient size for all five subjects in grade 3. However, F-statistics in grades 1
and 2 are rather small overall. In the data set for this study, no other variables with conditions
better than these exist.
B. Gender-matching Effect on Questioning Behavior
First, the partial effects of the female teacher dummy on the questioning probability
are calculated using the probit estimation of equation 6.
For simplicity of description, the linear combination of independent variables fromequation 6 is again expressed as.
is a row vector that contains theaverages of all independent variables except, andis a column vector made up of
corresponding coefficient estimates for each independent variable. Using this notation, thepartial effect due to female teachers, evaluated using the averages of independent variables
other than
, is written as the following equations 8 and 9. First, for a boy taking a test insome subject ∗ ,
(8)

:
∗

,

Φ γ

γ

γ

Φ γ

Here,
Φ γ
γ
γ
denotes the probability that the boy will
ask a female teacher a direct question, andΦ γdenotes the probability
that the boy will ask a male teacher a direct question. Similarly, for a girl taking a test in somesubject ∗ ,
(9)

≔
∗

３

,

See Wooldridge (2010, p.939).

Φ ∑

γ

Φ γ

12

γ

γ

Here,
Φ ∑γdenotes the probability that the girl will directly
ask a female teacher a question, andΦ γγγ
denotes theprobability that the girl will directly ask a male teacher a question. The difference between
equations 8 and 9 is:
The calculation results of these probabilities are compiled in Table 4. Asterisks in thistable indicate the results of a z test performed using standard errors determined by the delta
method (see appendix Tables A5, A6, and A7 for all estimation results from equation 6.
First, considering the effect that female teachers have on questioning probability (and), these values are all significantly positive regardless of the student’s gender.
Furthermore, the partial effects of female teachers (and) are all positive andsignificant, except boys in grade 1 English. Considering the average effect for all three grades,
the largest value is for girls in math (0.1295), followed by girls in science (0.0984), Japanese(0.0889), and English (0.0855). The next largest average effect is for boys in math, but at agrade-3 average of 0.0722, this value is almost the same as the smallest value for girls, insocial studies (0.0715). In addition, values of, which denotes the difference in effectbetween boys and girls, are all positive and significant, except grade 3 social studies andmath.
In summary, in every subject, if the teacher responsible for instruction were female,students were relatively more likely to ask questions. This result is not inconsistent withindications from previous research on university students (Brooks 1982; Bowers 1986;
Pearson and West 1991). In addition, this trend is more pronounced for girls than for boys.
and
with
and
, the difference between the former
However, comparing
tends to be smaller than the difference between the latter. In the data used in this study, theeffect appears to be primarily due to the fact that girls experience a large decline inquestioning probability if their teacher is male, rather than because having a female teacher
encourages students to ask questions.
C. CATE with Questioning Behavior Taken into Consideration
Next, the CATE for female teachers that considers questioning behavior is calculated
by conducting an independent variable estimation of equation 7 using the procedure describedin SubsectionV.A.
A male student who took a test in subject ∗ under the instruction of a female
teacher and who also asks direct questions of his teacher will have values for four dummy
variables as follows:

1,

∗

1,

0, and13

1. In this case, test scores areTable 4
Estimated Questioning Probabilities and Female Teachers' Partial Effects
EnglishJapanese

Math

Science

Socialstudies

Grade 10.20460.20250.00210.18410.11970.06440.0623

***
***
***
***
***
***

0.18290.13840.04440.13740.07470.06270.0183

***
***
***
***
***
***
**

0.30570.23850.06720.29980.18200.11770.0505

***
***
***
***
***
***
***

0.22140.18900.03240.15170.07990.07180.0394

***
***
***
***
***
***
***

0.18510.14450.04060.10690.04400.06290.0223

***
***
***
***
***
***
*

0.20340.18600.01740.20640.12160.08470.0674

***
***
**
***
***
***
***

0.19260.1291
0.06350.18030.09260.08770.0241

***
***
***
***
***
***
***

0.30280.26170.04110.35720.21200.14520.1041

***
***
***
***
***
***
***

0.25410.21950.0346
0.22210.1241
0.09800.0634

***
***
***
***
***
***
***

0.19020.13390.05630.12110.04590.07520.0189

***
***
***
***
***
***

0.22780.19290.03490.28620.17880.10730.0725

***
***
***
***
***
***
***

0.19700.12890.06810.24490.12860.11630.0482

***
***
***
***
***
***
***

0.39540.28710.10840.4671
0.34140.12570.0173

***
***
***
***
***
***

0.28920.25320.03600.33400.20860.12540.0894

***
***
***
***
***
***
***

0.18690.12610.06080.15140.07500.07650.0157

***
***
***
***
***
***

Grade 2

Grade 3

Average
0.21190.19080.33470.25490.18740.19380.1321
0.26240.22050.13480.0181
0.05870.07220.03430.05250.22550.18750.37470.23590.12650.1401
0.0986
0.24510.13750.05490.08550.08890.12950.09840.07150.06740.03020.05730.06410.0190Note: The asterisks indicate the results of z-tests based on delta-method standard errors.
* p < .10, ** p < .05, *** p < .01.

14

expressed as, , , . Similarly, when direct questions are not asked, test scores are writtenas, , , . Then, the expected value of the performance of the boy receiving instruction
from a female teacher, as the probability-weighted sum of these scores based on questioning
probability, is expressed as follows.
1

, , ,

, , ,

, , ,

, , ,

ζ

, , ,

ζ

, , ,

ζ

, , ,

Here
ζ
ζ
ζ is the marginal effect of the question dummy. In otherwords, it is the increment in marginal test score that the male student obtains by asking
questions of a female teacher.
Similarly, the performance of this student if he receives instruction from a maleteacher is expressed as
and
, , ,
, , , . Then, the expected value is
1

, , ,

, , ,

, , ,

, , ,

, , ,

ζ

, , ,
, , ,

ζ is the increment in marginal test score obtained by asking direct questionsof a male teacher. The CATE of having a female teacher for boys is expressed as thedifference between these:
10

:

, , ,

, , ,

, , ,

γ

, , ,

γ

Here
γ
γ expresses the difference in effects between male and female
teachers if questions are not asked. Likewise,
expresses thedifference in effects between male and female teachers if questions are asked. These are.
totaled to obtain the CATE for female teachers,
The CATE of female teachers for girls is denoted in a similar fashion:

11

:

ζ

, , ,

, , ,

γ

γ

ζ

, , ,

γ

ζ

, , ,

γ
15

ζ
ζ

ζ
ζ

ζ

γ

γ

γ

γ denotes the difference in effects between male and female∑
teachers if questions are not asked.
ζ and
ζ
ζ
ζ are theincrements in marginal test score obtained by asking direct questions of female and maleteachers, respectively.
is the difference between the expectedvalue of effects when questions are asked of male and female teachers.
D. Results
Of the elements in equations 10 and 11, questioning probability is examined in theprevious subsection. Next, we review the marginal increment in test scores obtained by asking
questions. In Table 5 below, each estimated value and difference between male and female
teachers, that is,and, is shown. Asterisks in thistable indicate the results of testing linear constraints with the null hypothesis that each value
from equation 7 is zero (see appendix Tables A8, A9, and A10 for a complete set of estimation
results from equation 7).
First, comparing male and female students, in general, increments in girls’ test scores
tend to be greater than increments in boys’ test scores. The question dummy used here
expresses whether a direct question is asked of the teacher when a student does notunderstand something. The specific frequency and content of the question or questions are notcontrolled. Several previous studies have pointed out the importance of frequency and content(King and Rosenshine, 1993; Harper et al., 2003). There might be differences in tendencies
between boys and girls when questioning behavior is considered from such a standpoint.
It is particularly important at this point to confirm the presence or absence of, which concerns boys,
difference due to the gender of the teacher. First, in reviewing
although values for grade 1 social studies and grade 3 English are significantly negative at the
10% level, no other values are significant. In reviewing, which concerns girls,
significant values at the 5% level are seen in grade 1 social studies, grade 2 English, andgrade 3 Japanese. All these values are negative, indicating that increments are larger whengirls have a male teacher. However, the other 12 values are not significant. Generally,
concerning the effect of questions on performance itself, it can be said that there is no clear
difference due to teacher gender.
Based on this, we confirm the CATE for female teachers taking questioning behavior
into consideration. Calculation results for equations 8 and 9 are compiled in Table 6 below.
Asterisks indicate the significance of each value. For
and, the results are fromtesting linear constraints with the null hypothesis that each value from equation 7 is zero. For
all other values, the results are from a z test using a standard error obtained through the delta
method.
First, we review the results for male and female students. The total effect on boys of16

Table 5
Estimated Marginal Increments of Scores by Questioning Behavior
SocialEnglishJapanese

Math

Science

0.1065 ***0.0365 **0.0928 ***0.0926 ***0.03790.0743 ***0.0390 **0.0868 ***0.0965 ***0.0939 ***0.0322-0.0025

0.0060-0.0039-0.0560 *0.1835 ***0.1486 ***0.1931 ***0.1671 ***0.1347 ***0.1927 ***0.1184 ***0.1734 ***0.1957 ***0.2139 ***-0.0092

0.03020.0197-0.0286-0.0792 **0.1366 ***0.0381 **0.1160 ***0.1045 ***0.0618 *0.1482 ***0.0614 ***0.1128 ***0.0996 ***0.1043 ***-0.0116-0.0233

0.00310.0049-0.04250.2558 ***0.1813 ***0.2373 ***0.2208 ***0.2558 ***0.3267 ***0.1914 ***0.2335 ***0.2552 ***0.2786 ***-0.0709 *** -0.0102

0.0038-0.0344-0.0228

0.1172 ***0.0565 ***0.1312 ***0.0543 *0.1431 ***0.1617 ***0.02800.1517 ***0.0838 ***0.1206 ***-0.0444 *0.0285-0.0204-0.0295

0.02240.3564 ***0.1963 ***0.3011 ***0.2272 ***0.3280 ***0.3699 ***0.2550 ***0.3355 ***0.2867 ***0.3031 ***-0.0135-0.0587 **-0.0343-0.0595 *0.02490.1201

0.04370.11330.08380.08090.12800.04280.1171

0.09330.1063-0.00790.0009-0.0038-0.0095-0.02530.26530.17540.24380.20500.23950.29640.18830.24740.24590.2652-0.0312-0.0129-0.0036-0.0408-0.0257

studies

Grade 1

Grade 2

Grade 3

Average

Note: The asterisks indicate the results of chi-square tests of linear constraints in equation (7).
* p < .10, ** p < .05, *** p < .01.

having a female teacher,, is significantly negative for grades 1 and 2 English and grade 3

Japanese. In other words, in these grades and subjects, having a male teacher has a relatively
positive effect. Most other values are not significant, with only grade 3 science being
17

Table 6
Estimated CATEs of Female Teachers Considering Questioning Behavior
EnglishJapanese

Math

Science

Socialstudies

Grade 1-0.0380 *** -0.0035-0.01700.00510.01000.00670.00130.00770.0023-0.0066-0.0312 *** -0.0022-0.00930.00740.00340.0491 *** -0.0038

0.01130.01960.01980.0107 ***0.0116 ***0.0263 ***0.0097 **0.00500.0598 ***0.00770.0376 ***0.0293 **0.0248 *-0.01700.00240.00180.01390.00690.0002-0.0006

0.00560.0047-0.0022-0.0168 *0.00180.00740.01860.00470.0459 ***0.01180.0450 ***0.0275 **0.0276 *0.0130 ***0.0149 ***0.0353 ***0.0174 ***0.0182 ***0.0590 ***0.0268 ***0.0803 ***0.0449 ***0.0458 ***-0.0112-0.0342 **-0.00120.0712 *** -0.0170-0.0045

0.00750.0084-0.0055-0.0157-0.0266 **0.0071

0.0657 *** -0.0055

0.0428 ***0.00040.0374 **0.0561 *** -0.0041

0.0358 ***0.0153 ***0.0261 **0.01610.0270 ***0.0786 ***0.01570.0636 ***0.0722 ***0.0229 *-0.0221-0.0118-0.0055

0.0301-0.0001

0.00080.00270.00720.00050.0009-0.0212-0.00900.00170.03060.00090.04590.00280.03130.03440.01440.01990.01390.02920.01440.01670.06580.01670.06050.04880.0311

Grade 2

Grade 30.0115 *Average

Note: The asterisks forandindicate the results of chi-square tests of linear

constraints in equation (7). The asterisks for other values indicate the results of z-tests basedon delta-method standard errors.

* p < .10, ** p < .05, *** p < .01.

significantly positive. This is largely similar to the results from Table 3. However, the total
effect of female teachers on girls,, is significantly positive for four subjects in grade 1, allsubjects in grade 2, and four subjects in grade 3. This, too, is similar to the results from Table18

3.
Next, we review the effects of questions. Here the difference between male andfemale students is striking. First, for boys,
is significant at the 10% level for only grade
3 social studies. All other values are not significant. In comparison, for girls,
issignificantly positive for four subjects in grade 1, all subjects in grade 2, and four subjects ingrade 3. In other words, while there is almost no difference in the size of the effect of asking
questions of the teacher arising from teacher gender for boys, there is a clear difference forgirls. As confirmed earlier in this subsection, in addition to having a comparatively large
marginal increment for girls’ questions, the questioning probability for girls shows a sharp
decline for male teachers. This is connected to the overall effect.
Next, we review effects when questions are not asked.
, which deals with boys,
has a significantly negative value for grade 1 English and grade 3 Japanese. On the contrary,
the value for grade 3 science is significantly positive. All other values are not significant. In
comparison, with regard to, which deals with girls, significantly positive values arepresent for grade 1 English and grades 2 and 3 English, math, and science. Furthermore, thevalue for grade 2 social studies is significantly positive at the 10% level. In other words, theeffect of having same-gender teachers in these grades and subjects is due in part to causes thatcannot be attributed to the presence or absence of questioning behavior.
Considering the effect of female teachers on girls by subject, the most clear effectappears in English. Through all three grades, the effects of female teachers on girls,,
and, are all significantly positive. In other words, an effect produced by asking
questions and a female teacher effect that cannot be attributed to questioning behavior areboth observed. Calculating the portion of the total effect made up by the question effect,⁄ , yields 17.9% for grade 1, 22.1% for grade 2, and 45.6% for grade 3.
In addition, in STEM subjects, a comparatively clear effect is obtained. For math,andare significantly positive for all grades, andis significantly positive in⁄
grades 2 and 3. Calculating
for grades 2 and 3 yields proportions of 43.9% and41.1%, respectively. For science,is significantly positive for all grades, whileissignificantly positive for grades 1 and 2, andis significantly positive for grades 2 and 3.
⁄
for grade 2, when all three values are significant, this yields a figure of
Calculating
38.8%.
Concerning Japanese and social studies, the question effectis significantly
positive for all cases, except grade 1 social studies. Although
is significantly positive atthe 10% level for grade 2 social studies, it is not significant for all other cases. In other words,
the CATE for female teachers in these two subjects is determined by the difference in ease ofasking questions between male and female teachers.
VI. Conclusion
In this research, for all grades in Japanese middle schools, the effect of gender19

matching between students and teachers on academic performance was empirically analyzed
using individual data from the “Survey on the Course of Study Implementation at Elementary
Schools.”
The main conclusions are as follows. First, gender matching between students andteachers has an effect on student performance. In subjects for both male and female students,
when taught by a same-gender teacher, some improvement in performance occurs. This isparticularly striking for girls. For boys, of all five subjects over all three grades, a positiveeffect was observed for three subjects due to a same-gender teacher. By contrast, the same
was for girls for 12 subjects.
Second, the effect of gender matching between students and teachers differs
depending on subject. The clearest trend was observed in English, in which matching between
female teachers for girls and male teachers for boys improved the respective performance ofeach gender. In addition, concerning STEM subjects, on which previous research has
frequently focused, although matching between girls and female teachers improved
performance in math and science through all grades, no effect was observed consistently formatching between boys and male teachers.
Third, gender matching between students and teachers had an effect on students’questioning behavior. The probability that students would ask questions was lower when theirteacher was male in comparison to when their teacher was female. This trend was observed
regardless of student gender. However, through all grades and subjects, the decrease in theprobability of asking a question under a male teacher was larger for girls than for boys.
However, because a trend of lower questioning probability was also observed for boys, thisresult should be considered an indication of a reaction to the teacher’s gender on the part ofthe students, rather than an indication of the existence of bias in the behavior of the teachers.
Fourth, a part of the positive effect that female teachers have on girls’ performancemight be caused by a difference in questioning behavior. This kind of question effect was
hardly seen for boys. This effect is due to the fact that the decrease in the probability of asking
a question for girls under the instruction of male teachers is comparatively large, and themarginal increment in girls’ performance from asking questions was greater than for boys.
This result indicates the importance of questioning behavior in learning for female students.
In particular, it is possible that male teachers improve the performance of female students byencouraging them to ask further questions.
Fifth, even controlling for the effect of questions, a positive effect of same-genderteachers that cannot be attributed to questioning behavior remains, particularly for girls in
English, math, and science. In other words, this effect is observed for both liberal arts and
STEM subjects. The percentage of the total effect made up by this non-questioning effect isaround 60% in math, science, and grade 3 English and around 80% in grades 1 and 2 English.
Conversely, in Japanese, in which girls outperform boys by the greatest margin, this effectwas not observed. In addition, this positive effect was hardly seen for boys, confirmed in only
20

grade 1 English and grade 3 Japanese. It is difficult to think of a stereotype that fits all theseresults. However, as there was a positive effect for same-gender teachers for both male andfemale students in almost all remaining subjects, excluding grade 3 science for boys, theresults obtained here are not inconsistent with the role model hypothesis. However, naturally,
the possibility of some separate, unconsidered effect cannot be excluded.
Finally, I touch on issues that the analysis presented herein did not address. The
analysis in this study pooled cross-sectional data from five subjects and performed estimatesthat controlled individual effects shared across subjects. However, it was not possible tocontrol individual effects inherent in each subject. For example, if these effects had been
controlled through the use of panel data, it is possible that different results would have beenobtained. Furthermore, in this study, questioning behavior was treated as an endogenous
variable, and individual effects common to subjects were addressed. However, as the question
dummy was included unilaterally in the estimates of test scores, it was not possible to deal
with the possibility that performance and questioning behavior were determined
simultaneously. Therefore, there is room for improvement on this point.

21

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24

Appendix Table A1
Descriptive Statistics of Independent Variables
N
Teacher attributes
Female teacher
Experience
Class attributes
Class size
Girl ratio
School attributes
Public urban
Public town
Private/national
Student attributes
Girl
Outside education

Amount of sleep
Breakfast
Belongings checked

Grade 1
Mean Std.Dev.

N

Grade 2
Mean Std.Dev.

N

Grade 3
Mean Std.Dev.

=1 if the teacher is a female, 0 otherwise
Years of teaching experience

2517 0.331
2493 16.390

0.471
9.074

2491 0.348
2473 16.323

0.477
8.725

2497 0.323
2487 17.295

0.468
8.148

Number of students in the class
Ratio of girls in the class

2463 34.199
2463 0.486

5.878
0.098

2411 34.704
2411 0.486

5.585
0.097

2466 34.534
2466 0.485

5.568
0.094

=1 if the school is a public school in an urban area, 0 otherwise=1 if the school is a public school in a rural area, 0 otherwise=1 if the school is a national school or a private school, 0

2557
2557
2557

0.539
0.248
0.057

0.499
0.432
0.233

2535
2535
2535

0.540
0.249
0.057

0.499
0.432
0.232

2530
2530
2530

0.543
0.249
0.049

0.498
0.433
0.217

=1 if the student is a girl, 0 otherwise=1 if a cram school or home tutor is used, 0 otherwise (English)=1 if a cram school or home tutor is used, 0 otherwise (Japanese)=1 if a cram school or home tutor is used, 0 otherwise (Math)=1 if a cram school or home tutor is used, 0 otherwise (Science)=1 if a cram school or home tutor is used, 0 otherwise (Social
Sleeping hours per day. 1: less than 6 hours, 2: 6–7 hours, 3: 7–8
hours, 4: 8–9 hours, 5: 9–10 hours, 6: 10 or more hours
Frequency of eating breakfast. 1: Never or almost never, 2: Often
do not eat breakfast, 3: Generally eat breakfast, 4: Always eat
Frequency with which items brought to school are checked the day
before or in the morning. 1: Almost never checked, 2: Often notchecked, 3: Generally checked, 4: Always checked

83477
49749
50131
49770
49935
50167
82677

0.484
0.518
0.314
0.484
0.284
0.270
3.010

0.500
0.500
0.464
0.500
0.451
0.444
1.169

82853
49471
49350
49381
49480
49746
82035

0.485
0.575
0.350
0.550
0.344
0.320
2.746

0.500
0.494
0.477
0.498
0.475
0.466
1.130

75404
44789
44986
44924
35926
45284
74387

0.485
0.686
0.499
0.679
0.528
0.501
2.340

0.500
0.464
0.500
0.467
0.499
0.500
1.086

82617

3.615

0.748 81968

3.580

0.790 74318

3.522

0.848

82819

3.160

0.925 82166

3.098

0.958 74475

3.108

0.946

Appendix Table A2
Estimated Results for Equation (4) (Grade 1)
EnglishCoef.

Japanese

Science

Social studies

Coef.

R.S.E

Coef.

Subject (γ1)-0.1406 *** 0.0070 -0.1625 *** 0.0075

0.00640.00520.0735 *** 0.0052

0.0803 *** 0.0050

Girl (γ2)-0.0051

0.0420 *** 0.0066

0.0453 *** 0.0065

0.0504 *** 0.0066

Female teacher (γ3)-0.0850 *** 0.0048 -0.0802 *** 0.0047 -0.1089 *** 0.0046 -0.0976 *** 0.0045 -0.0819 *** 0.0045

Subject×Girl (γ4)

0.2133 *** 0.0098

0.3441 *** 0.0105 -0.0912 *** 0.0073 -0.0983 *** 0.0072 -0.1043 *** 0.0070

Girl×Female teacher (γ5)

0.1782 *** 0.0065

0.1551 *** 0.0064

0.2060 *** 0.0062

0.1999 *** 0.0061

0.1796 *** 0.0061

Subject×Female teacher (γ6)

0.0597 *** 0.0100

0.0702 *** 0.0105

0.0986 *** 0.0105

0.1042 *** 0.0111

0.0628 *** 0.0130

Subject×Girl×Female teacher (γ7)-0.0970 *** 0.0139 -0.1376 *** 0.0145 -0.1598 *** 0.0145 -0.1809 *** 0.0156 -0.1435 *** 0.0180

Experience
Class size
Class size
Girl ratio

0.0064 -0.0177 *** 0.0064

0.0051 *** 0.0005
2

2

Coef.

Math
R.S.E

Experience

R.S.E

0.0051 *** 0.0005

0.0051 *** 0.0005

R.S.E

0.0054 *** 0.0005

Coef.

R.S.E

0.0052 *** 0.0005-0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000-0.0005

0.0012 -0.0006

0.0012 -0.0006

0.0012 -0.0007

0.0012 -0.0004

0.00120.0000 **0.00000.00000.00000.00000.00000.0000 **0.0000 **0.0000 **0.0000 **-0.3933 *** 0.0240 -0.3996 *** 0.0240 -0.3875 *** 0.0240 -0.3874 *** 0.0240 -0.3960 *** 0.0240

Public urban

0.0294 *** 0.0083

0.0296 *** 0.0083

0.0292 *** 0.0083

0.0294 *** 0.0083

Public town

0.00430.00450.00440.0045

Private/national

0.7686 *** 0.0120

0.7695 *** 0.0120

0.7667 *** 0.0120

0.7666 *** 0.0120

0.7665 *** 0.0120

Outside education

0.1822 *** 0.0041

0.1774 *** 0.0041

0.1831 *** 0.0041

0.1798 *** 0.0041

0.1801 *** 0.0041

Amount of sleep: 6–7h

0.0747 *** 0.0112

0.0747 *** 0.0112

0.0747 *** 0.0112

0.0746 *** 0.0112

0.0744 *** 0.0112

Amount of sleep: 7–8h

0.1141 *** 0.0110

0.1138 *** 0.0110

0.1144 *** 0.0110

0.1141 *** 0.0110

0.1137 *** 0.0110

Amount of sleep: 8–9h

-0.0239 **Amount of sleep: 9–10h-0.2323 *** 0.0148 -0.2323 *** 0.0148 -0.2318 *** 0.0148 -0.2321 *** 0.0148 -0.2326 *** 0.0148

Amount of sleep: >10h-0.5523 *** 0.0252 -0.5544 *** 0.0252 -0.5524 *** 0.0252 -0.5530 *** 0.0252 -0.5528 *** 0.0252

Breakfast: Often do not eat

0.0763 *** 0.0205

0.0766 *** 0.0205

0.0763 *** 0.0205

0.0765 *** 0.0205

Breakfast: Generally eat

0.2460 *** 0.0178

0.2467 *** 0.0178

0.2455 *** 0.0178

0.2460 *** 0.0178

0.2461 *** 0.0178

Breakfast: Always eat

0.5755 *** 0.0168

0.5757 *** 0.0168

0.5750 *** 0.0168

0.5754 *** 0.0168

0.5755 *** 0.0168

Belongings checked: Often not checked

0.1674 *** 0.0140

0.1666 *** 0.0140

0.1667 *** 0.0140

0.1669 *** 0.0140

0.1672 *** 0.0140

Belongings checked: Generally checked

0.3352 *** 0.0121

0.3349 *** 0.0121

0.3347 *** 0.0121

0.3349 *** 0.0121

0.3353 *** 0.0121

Belongings checked: Always checked

0.4876 *** 0.0120

0.4870 *** 0.0120

0.4868 *** 0.0120

0.4873 *** 0.0120

0.4871 *** 0.0120

Female teacher (Average)-0.0043

Experience (Average)

0.0073 *** 0.0017

20.00960.0117 -0.0245 **0.01130.00080.00960.0117 -0.0236 **0.01130.0072 *** 0.0017

0.00080.00960.0117 -0.0242 **0.0113 -0.0028

0.0072 *** 0.0017

0.00960.0294 *** 0.0083
0.00430.0117 -0.0245 **0.01170.0765 *** 0.0205

0.0112 -0.0052

0.0072 *** 0.0017

0.00960.01130.0072 *** 0.0017

Experience (Average)
Constant term

-0.0002 *** 0.0000 -0.0002 *** 0.0000 -0.0002 *** 0.0000 -0.0002 *** 0.0000 -0.0002 *** 0.0000

sigma_u0.73770.73780.73770.7375sigma_e0.55400.55220.55400.55400.5544rho

0.63940.64100.63930.63920.6390-0.8849 *** 0.0367 -0.8824 *** 0.0367 -0.9075 *** 0.0367 -0.9229 *** 0.0367 -0.9249 *** 0.0367
0.7376

No. of students

81944

81944

81944

81944

81944

No. of obs.

234575234575234575234575234575

R-sq: within

0.02440.03060.02410.02420.0230R-sq: between

0.16520.16600.16500.16540.1652

R-sq: overall

0.13610.13780.13580.13610.1357

Chi-sq(3) : H0 : m=0
Note: * p < .10, ** p < .05, *** p < .01.

18.5473

17.5400

17.310317.6888

18.2654

Appendix Table A3
Estimated Results for Equation (4) (Grade 2)
EnglishCoef.

Japanese
R.S.E

Coef.

Math
R.S.E

Coef.

Science

Social studies

R.S.E

Coef.

R.S.E

Coef.

0.00530.0971 *** 0.0052

0.0736 *** 0.0053

R.S.E

0.0290 *** 0.0066

0.0543 *** 0.0066

0.0460 *** 0.0066

Subject (γ1)-0.1385 *** 0.0072 -0.1675 *** 0.0074 -0.0105 **Girl (γ2)-0.0078

Female teacher (γ3)-0.0708 *** 0.0049 -0.0717 *** 0.0048 -0.1011 *** 0.0047 -0.0792 *** 0.0046 -0.0763 *** 0.0046

Subject×Girl (γ4)

0.2173 *** 0.0101

0.3492 *** 0.0099 -0.0506 *** 0.0074 -0.1420 *** 0.0072 -0.1084 *** 0.0072

Girl×Female teacher (γ5)

0.1827 *** 0.0066

0.1616 *** 0.0064

0.2081 *** 0.0062

0.1879 *** 0.0062

0.1829 *** 0.0061

Subject×Female teacher (γ6)

0.0567 *** 0.0101

0.0728 *** 0.0105

0.1085 *** 0.0106

0.0962 *** 0.0115

0.0816 *** 0.0134

Subject×Girl×Female teacher (γ7)-0.1233 *** 0.0140 -0.1354 *** 0.0141 -0.1442 *** 0.0145 -0.1689 *** 0.0157 -0.1432 *** 0.0180

Experience
Experience
Class size
Class size
Girl ratio

0.0065 -0.0246 *** 0.0065

0.0037 *** 0.0005
20.0038 *** 0.0005

0.0036 *** 0.0005

0.0037 *** 0.0005

0.0038 *** 0.0005-0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000-0.0037 *** 0.0010 -0.0030 *** 0.0010 -0.0028 *** 0.0010 -0.0031 *** 0.0010 -0.0031 *** 0.0010

20.0001 *** 0.0000

0.0001 *** 0.0000

0.0001 *** 0.0000

0.0001 *** 0.0000

0.0001 *** 0.0000-0.3824 *** 0.0250 -0.3857 *** 0.0251 -0.3770 *** 0.0251 -0.3758 *** 0.0251 -0.3817 *** 0.0250

Public urban

0.00980.0084

Public rural-0.00610.0096 -0.0065

0.01000.00840.0101

Private/national

0.6721 *** 0.0125

0.6748 *** 0.0125

0.6715 *** 0.0125

0.6738 *** 0.0125

0.6704 *** 0.0125

Outside education

0.1673 *** 0.0041

0.1621 *** 0.0040

0.1661 *** 0.0041

0.1630 *** 0.0040

0.1628 *** 0.0040

Amount of sleep: 6–7h

0.0732 *** 0.0097

0.0730 *** 0.0097

0.0731 *** 0.0097

0.0730 *** 0.0097

0.0731 *** 0.0097

Amount of sleep: 7–8h

0.0752 *** 0.0098

0.0749 *** 0.0097

0.0753 *** 0.0098

0.0748 *** 0.0097

0.0749 *** 0.0098

Amount of sleep: 8–9h

-0.0853 *** 0.0111 -0.0861 *** 0.0111 -0.0854 *** 0.0111 -0.0862 *** 0.0111 -0.0858 *** 0.0111

0.0096 -0.0058

0.00840.00980.0096 -0.0071

0.00840.00980.00840.0096 -0.0066

0.0096

Amount of sleep: 9–10h-0.3213 *** 0.0169 -0.3221 *** 0.0169 -0.3218 *** 0.0169 -0.3215 *** 0.0169 -0.3223 *** 0.0169

Amount of sleep: >10h-0.5768 *** 0.0288 -0.5770 *** 0.0288 -0.5757 *** 0.0288 -0.5762 *** 0.0288 -0.5774 *** 0.0288

Breakfast: Often do not eat

0.0410 **Breakfast: Generally eat

0.2307 *** 0.0164

0.2302 *** 0.0164

0.2306 *** 0.0164

0.2317 *** 0.0164

0.2306 *** 0.0164

Breakfast: Always eat

0.5547 *** 0.0153

0.5544 *** 0.0153

0.5548 *** 0.0153

0.5558 *** 0.0153

0.5548 *** 0.0153

Belongings checked: Often not checked

0.2163 *** 0.0134

0.2160 *** 0.0134

0.2161 *** 0.0134

0.2164 *** 0.0134

0.2157 *** 0.0134

Belongings checked: Generally checked

0.3718 *** 0.0115

0.3711 *** 0.0115

0.3714 *** 0.0115

0.3716 *** 0.0115

0.3714 *** 0.0115

Belongings checked: Always checked

0.5288 *** 0.0115

0.5286 *** 0.0115

0.5287 *** 0.0115

0.5289 *** 0.0115

0.5286 *** 0.0115

0.01930.0406 **0.01920.0413 **0.01930.0417 **0.01930.0411 **0.0193

Female teacher (Average)

0.0395 *** 0.0113

0.0442 *** 0.0113

0.0444 *** 0.0113

0.0414 *** 0.0113

0.0409 *** 0.0113

Experience (Average)

0.00170.00180.00160.00180.00200.00180.00200.00180.00180.001820.00000.00010.00000.00010.00000.00010.00000.00010.00000.0001

Experience (Average)
Constant term

-0.8000 *** 0.0338 -0.8019 *** 0.0337 -0.8303 *** 0.0338 -0.8516 *** 0.0337 -0.8440 *** 0.0338

sigma_u

0.74170.74190.74160.7417

sigma_e0.55170.5496

0.55230.55120.5520rho

0.64380.64560.64330.64420.64350.7416

No. of students

81416

81416

81416

81416

81416

No. of obs.

231821

231821

231821

231821

231821

R-sq: within

0.01980.02730.01780.02180.0188R-sq: between

0.16450.16510.16420.16460.1644R-sq: overall

0.13420.13620.13360.13470.1340Chi-sq(3) : H0 : m=0
Note: * p < .10, ** p < .05, *** p < .01.

29.4056

31.2405

31.0766

28.3025

28.4358

Appendix Table A4
Estimated Results for Equation (4) (Grade 3)
EnglishCoef.
Subject (γ1)

Japanese
R.S.E

Coef.

Math
R.S.E

Coef.

Science
R.S.E

Coef.

Social studies
R.S.E

Coef.

R.S.E

-0.0760 *** 0.0073 -0.1406 *** 0.0079

0.0398 *** 0.0054

0.1069 *** 0.0059 -0.0090 *Girl (γ2)

0.0333 *** 0.0068

0.0855 *** 0.0070

0.0876 *** 0.0069

Female teacher (γ3)-0.0733 *** 0.0053 -0.0415 *** 0.0053 -0.0740 *** 0.0050 -0.0704 *** 0.0049 -0.0806 *** 0.0050

Subject×Girl (γ4)

0.0977 *** 0.0103

0.3538 *** 0.0106 -0.1471 *** 0.0075 -0.1995 *** 0.0081

Girl×Female teacher (γ5)

0.1863 *** 0.0072

0.1081 *** 0.0072

0.1619 *** 0.0067

0.1608 *** 0.0066

0.1997 *** 0.0067

Subject×Female teacher (γ6)

0.0519 *** 0.0107

0.01780.0690 *** 0.0122

0.1338 *** 0.0133

0.0767 *** 0.0134

Subject×Girl×Female teacher (γ7)-0.1060 *** 0.0150 -0.0843 *** 0.0150 -0.1111 *** 0.0168 -0.1760 *** 0.0184 -0.1641 *** 0.0180

Experience
Experience
Class size
Class size
Girl ratio

0.0029 *** 0.0007
220.00580.00680.01110.0032 *** 0.0007

0.0030 *** 0.0007

0.0032 *** 0.0007

0.00530.0277 *** 0.0070
0.0680 *** 0.0073

0.0030 *** 0.0007-0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000
0.00110.00110.00090.00110.00110.00110.00130.00110.00130.00110.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000-0.2718 *** 0.0279 -0.2757 *** 0.0280 -0.2668 *** 0.0279 -0.2657 *** 0.0279 -0.2646 *** 0.0279

Public urban-0.0166 *Public rural-0.0709 *** 0.0103 -0.0705 *** 0.0103 -0.0704 *** 0.0103 -0.0714 *** 0.0103 -0.0709 *** 0.0103

0.0091 -0.0166 *Private/national

0.4103 *** 0.0139

0.4134 *** 0.0139

0.4119 *** 0.0139

0.4113 *** 0.0139

0.4090 *** 0.0139

Outside education

0.1854 *** 0.0046

0.1860 *** 0.0046

0.1880 *** 0.0047

0.1803 *** 0.0046

0.1838 *** 0.0046

Amount of sleep: 6–7h

0.0193 **0.0193 **0.0192 **0.0190 **0.0189 **Amount of sleep: 7–8h

-0.0313 *** 0.0088 -0.0311 *** 0.0088 -0.0312 *** 0.0088 -0.0319 *** 0.0088 -0.0319 *** 0.0088

Amount of sleep: 8–9h

-0.2470 *** 0.0124 -0.2466 *** 0.0124 -0.2469 *** 0.0124 -0.2482 *** 0.0124 -0.2475 *** 0.0124

0.00790.0091 -0.0163 *0.00790.0091 -0.0167 *0.00790.0091 -0.0167 *0.00790.00910.0079Amount of sleep: 9–10h-0.4661 *** 0.0232 -0.4653 *** 0.0232 -0.4652 *** 0.0232 -0.4676 *** 0.0232 -0.4669 *** 0.0232

Amount of sleep: >10h-0.6712 *** 0.0339 -0.6704 *** 0.0338 -0.6706 *** 0.0338 -0.6723 *** 0.0338 -0.6717 *** 0.0339

Breakfast: Often do not eat

0.0877 *** 0.0185

0.0875 *** 0.0185

0.0876 *** 0.0185

0.0870 *** 0.0185

Breakfast: Generally eat

0.2506 *** 0.0160

0.2506 *** 0.0159

0.2504 *** 0.0159

0.2502 *** 0.0160

0.2508 *** 0.0160

Breakfast: Always eat

0.5437 *** 0.0147

0.5436 *** 0.0147

0.5436 *** 0.0147

0.5433 *** 0.0147

0.5437 *** 0.0147

Belongings checked: Often not checked

0.1510 *** 0.0147

0.1513 *** 0.0147

0.1508 *** 0.0147

0.1512 *** 0.0147

0.1509 *** 0.0147

Belongings checked: Generally checked

0.2792 *** 0.0128

0.2793 *** 0.0128

0.2792 *** 0.0128

0.2795 *** 0.0128

0.2791 *** 0.0128

Belongings checked: Always checked

0.4241 *** 0.0128

0.4240 *** 0.0128

0.4241 *** 0.0128

0.4244 *** 0.0128

0.4241 *** 0.0128

Female teacher (Average)

0.0159Experience (Average)

0.0122 *** 0.0022

2

0.01180.0231 *0.01180.0119 *** 0.0022

0.0200 *0.01180.0121 *** 0.0022

0.01870.01180.0122 *** 0.0022

0.0880 *** 0.0185

0.01550.01180.0121 *** 0.0022

Experience (Average)
Constant term

-0.0003 *** 0.0001 -0.0003 *** 0.0001 -0.0003 *** 0.0001 -0.0003 *** 0.0001 -0.0003 *** 0.0001

sigma_u0.74900.74950.74920.7494sigma_e0.55300.54920.55180.55090.5530rho

0.64720.65070.64830.64920.6471-0.8750 *** 0.0370 -0.8698 *** 0.0369 -0.9034 *** 0.0370 -0.9130 *** 0.0369 -0.8907 *** 0.0370
0.7489No. of students

73905

73905

73905

73905

73905

No. of obs.

205339205339205339205339205339R-sq: within

0.00700.02010.01100.01420.0069R-sq: between

0.14460.14580.14510.14460.1446

R-sq: overall

0.11560.11930.11690.11710.1156

Chi-sq(3) : H0 : m=0
Note: * p < .10, ** p < .05, *** p < .01.

41.0368

40.9579

39.6665

40.6286

39.5446

Appendix Table A5
Estimated Results for Equation (6) (Grade 1)

Subject (γq1)
Girl (γq2)
Female teacher (γq3)
Subject×Girl (γq4)
Girl×Female teacher (γq5)
Subject×Female teacher (γq6)
Subject×Girl×Female teacher (γq7)
Experience2
Experience
Class size
2
Class size
Girl ratio
Public urban
Public rural
Private/national
Outside education
Amount of sleep: 6–7h
Amount of sleep: 7–8h
Amount of sleep: 8–9h
Amount of sleep: 9–10h
Amount of sleep: >10h
Breakfast: Often do not eat
Breakfast: Generally eat
Breakfast: Always eat
Belongings checked: Often not checked
Belongings checked: Generally checked
Belongings checked: Always checked
Female teacher (Average)
Experience (Average)
2
Experience (Average)
Praised by parents: Not praised more than praised
Praised by parents: Praised more than not praised
Praised by parents: Praised
Constant term
var_u
No. of students
No. of obs.
Log likelihood
Chi-sq(3) : H0 : m=0
Note: * p < .10, ** p < .05, *** p < .01.

EnglishCoef.
0.0789 ***-0.4326 ***0.1164 ***0.0888 ***0.2635 ***-0.1090 ***0.0058-0.0243 ***0.0004 ***-0.0191 ***0.0001 *0.2950 ***-0.0813 ***-0.02220.4085 ***0.1286 ***0.00180.04370.0589 **0.1649 ***0.2010 ***0.1427 ***0.1769 ***0.2774 ***0.1407 ***0.2635 ***0.4102 ***0.0357-0.00690.0001-0.03110.00260.0858 ***-0.8141 ***2.5886 ***72505
207623-106603.22
8.4813

R.S.E
0.02230.01760.01480.03320.02140.03120.04600.00180.00010.00350.00000.07160.02120.02430.03490.01250.02800.02760.02900.03640.05320.0506
0.04390.04150.03370.02880.02860.02960.00470.0001
0.02210.0201
0.02140.1006
0.0413

Japanese
Math
Coef.
R.S.E
Coef.
-0.2044 *** 0.0227
0.2708 ***-0.4326 *** 0.0175-0.5208 ***0.1349 *** 0.0151
0.1211 ***0.0782 ** 0.0348
0.3242 ***0.3182 *** 0.0216
0.3536 ***0.04800.03150.0819 **-0.1513 *** 0.0471-0.1740 ***-0.0226 *** 0.0018-0.0226 ***0.0004 *** 0.0001
0.0004 ***-0.0185 *** 0.0035-0.0189 ***0.00010.00000.0001 *0.2732 *** 0.0718
0.2919 ***-0.0803 *** 0.0212-0.0840 ***-0.0233
0.0243-0.0279
0.4118 *** 0.0350
0.4116 ***0.1217 *** 0.0123
0.0628 ***0.00180.02810.00200.04390.02770.04070.0579 ** 0.0291
0.0525 *0.1642 *** 0.0365
0.1615 ***0.1998 *** 0.0533
0.1990 ***0.1434 *** 0.0507
0.1442 ***0.1775 *** 0.0440
0.1807 ***0.2788 *** 0.0415
0.2842 ***0.1414 *** 0.0338
0.1437 ***0.2645 *** 0.0288
0.2685 ***0.4120 *** 0.0287
0.4176 ***-0.0005
0.02970.0024-0.0074
0.0047-0.00680.00010.00010.0001-0.0308
0.0221-0.03180.00350.02010.00500.0875 *** 0.0215
0.0931 ***-0.7773 *** 0.1007-0.8647 ***2.6050 *** 0.0416
2.7041 ***
72505
72505
207623207623-106498.57-105759.14
7.72945.8115

R.S.E
0.01750.01860.01450.02600.02090.03360.04930.00180.00010.00350.00000.07260.02140.02460.03540.01260.02840.02800.02940.03690.05390.05130.04450.04200.03410.02910.02900.03000.00470.0001
0.02240.02030.02170.10170.0437

Science
Social studies
Coef.
R.S.E
Coef.
R.S.E
0.02700.0170-0.2118 *** 0.0168-0.3870 *** 0.0181-0.3558 *** 0.0183
0.0988 *** 0.0142
0.0432 *** 0.0141-0.1370 *** 0.0256-0.2903 *** 0.0257
0.2662 *** 0.0203
0.2277 *** 0.0203
0.01540.03490.1211 *** 0.0406-0.0038
0.05110.07130.0601-0.0247 *** 0.0018-0.0232 *** 0.0018
0.0004 *** 0.0001
0.0004 *** 0.0001-0.0186 *** 0.0035-0.0206 *** 0.0035
0.0001 *0.00000.0001 **0.00000.2912 *** 0.0716
0.3085 *** 0.0720-0.0810 *** 0.0212-0.0824 *** 0.0213-0.02190.0243-0.02360.02450.4121 *** 0.0349
0.4063 *** 0.0351
0.1394 *** 0.0123
0.0960 *** 0.0124
0.00250.02800.00230.02820.04460.0276
0.04180.02780.0599 ** 0.0290
0.0562 *0.02920.1663 *** 0.0364
0.1620 *** 0.0367
0.2014 *** 0.0532
0.2011 *** 0.0536
0.1430 *** 0.0506
0.1449 *** 0.0510
0.1773 *** 0.0439
0.1802 *** 0.0442
0.2772 *** 0.0415
0.2821 *** 0.0418
0.1411 *** 0.0337
0.1413 *** 0.0339
0.2637 *** 0.0288
0.2651 *** 0.0290
0.4105 *** 0.0286
0.4126 *** 0.0288
0.02860.0296
0.0692 **0.0299-0.0066
0.0047-0.0068
0.00470.00010.00010.00010.0001-0.03170.0221-0.03170.02220.00210.02010.00360.02020.0847 *** 0.0214
0.0897 *** 0.0216-0.8156 *** 0.1007-0.7590 *** 0.1010
2.5886 *** 0.0413
2.6432 *** 0.0424
72505
72505
207623207623-106613.00-106165.08
7.343912.6119

Appendix Table A6
Estimated Results for Equation (6) (Grade 2)

Subject (γq1)
Girl (γq2)
Female teacher (γq3)
Subject×Girl (γq4)
Girl×Female teacher (γq5)
Subject×Female teacher (γq6)
Subject×Girl×Female teacher (γq7)
Experience2
Experience
Class size
2
Class size
Girl ratio
Public urban
Public rural
Private/national
Outside education
Amount of sleep: 6–7h
Amount of sleep: 7–8h
Amount of sleep: 8–9h
Amount of sleep: 9–10h
Amount of sleep: >10h
Breakfast: Often do not eat
Breakfast: Generally eat
Breakfast: Always eat
Belongings checked: Often not checked
Belongings checked: Generally checked
Belongings checked: Always checked
Female teacher (Average)
Experience (Average)
2
Experience (Average)
Praised by parents: Not praised more than praised
Praised by parents: Praised more than not praised
Praised by parents: Praised
Constant term
var_u
No. of students
No. of obs.
Log likelihood
Chi-sq(3) : H0 : m=0
Note: * p < .10, ** p < .05, *** p < .01.

EnglishCoef.
-0.0151-0.3339 ***0.1205 ***0.0599 *0.3053 ***-0.0574 *-0.0207-0.0321 ***0.0006 ***-0.00220.00000.4260 ***-0.02150.0186
0.3552 ***0.1495 ***0.00060.0291
0.02110.03420.1753 ***0.1949 ***0.1573 ***0.2944 ***0.1354 ***0.2560 ***0.3982 ***-0.0440-0.0173 ***0.0003 **-0.0007
0.02600.0936 ***-1.0946 ***2.3529 ***71998
205071-107618.75
36.6560

R.S.E
0.02240.01700.01490.03360.02130.03110.04580.00170.00000.00350.00010.07200.02070.0236
0.03470.01190.02360.02390.02680.03890.05960.04570.03920.0366
0.03110.0266
0.02670.02880.00480.0001
0.02110.01900.02100.09280.0362

Japanese
Math
Coef.
R.S.E
Coef.
-0.2809 *** 0.0226
0.3374 ***-0.3467 *** 0.0170-0.4056 ***0.1150 *** 0.0150
0.1477 ***0.1527 *** 0.0334
0.2440 ***0.3406 *** 0.0211
0.3509 ***0.1474 *** 0.0315-0.0259-0.1925 *** 0.0461-0.0390-0.0302 *** 0.0017-0.0273 ***0.0006 *** 0.0000
0.0005 ***-0.00240.0035-0.00410.00000.00010.00000.4176 *** 0.0722
0.4301 ***-0.02150.0208-0.0261
0.01660.02370.01050.3571 *** 0.0348
0.3410 ***0.1216 *** 0.0118
0.0530 ***0.00040.0237-0.0005
0.02720.02400.02320.01790.02690.01120.03080.03900.01980.1733 *** 0.0597
0.1700 ***0.1972 *** 0.0458
0.2048 ***0.1594 *** 0.0393
0.1696 ***0.2977 *** 0.0367
0.3100 ***0.1366 *** 0.0312
0.1380 ***0.2565 *** 0.0267
0.2584 ***0.3996 *** 0.0267
0.4035 ***-0.0657 ** 0.0289-0.0725 **-0.0185 *** 0.0048-0.0223 ***0.0003 ** 0.0001
0.0004 ***0.0001
0.02120.00220.02740.01910.0304
0.0965 *** 0.0210
0.1054 ***-1.0466 *** 0.0929-1.1208 ***2.3693 *** 0.0365
2.4585 ***
71998
71998
205071205071-107481.48-106679.01
46.043651.8036

R.S.E
0.01700.01810.01440.02530.0206
0.03340.04830.00180.00000.00350.00010.07320.02110.02400.03520.01200.02400.02430.02720.03950.06050.04640.03970.03710.03150.02700.02700.02920.00480.0001
0.02140.01930.0213
0.09370.0383

Science
Social studies
Coef.
R.S.E
Coef.
R.S.E
0.1445 *** 0.0165-0.3001 *** 0.0170-0.3072 *** 0.0177-0.2644 *** 0.0178
0.1215 *** 0.0141
0.0252 *0.0141-0.0735 *** 0.0245-0.3135 *** 0.0257
0.3041 *** 0.0201
0.2648 *** 0.0199-0.0092
0.03570.2057 *** 0.0403-0.0266
0.05110.02090.0588-0.0319 *** 0.0017-0.0301 *** 0.0018
0.0006 *** 0.0000
0.0006 *** 0.0000-0.00290.0035-0.0034
0.00350.00000.00010.00000.00010.4215 *** 0.0720
0.4519 *** 0.0727-0.01990.0208-0.0249
0.02100.01990.02370.01190.02390.3613 *** 0.0347
0.3439 *** 0.0350
0.1573 *** 0.0118
0.0831 *** 0.0119
0.00120.02360.00120.02390.03000.02390.02760.02420.0226
0.02680.01690.02710.03630.03900.02720.03940.1772 *** 0.0596
0.1775 *** 0.0602
0.1956 *** 0.0457
0.1992 *** 0.0462
0.1580 *** 0.0392
0.1631 *** 0.0396
0.2950 *** 0.0366
0.3017 *** 0.0370
0.1357 *** 0.0311
0.1380 *** 0.0314
0.2564 *** 0.0267
0.2591 *** 0.0269
0.3991 *** 0.0267
0.4034 *** 0.0270-0.0514 *0.0288-0.0084
0.0291-0.0173 *** 0.0048-0.0189 *** 0.0048
0.0003 ** 0.0001
0.0003 **0.0001-0.00070.02110.00160.02140.02600.01900.02910.0192
0.0931 *** 0.0210
0.1017 *** 0.0212-1.1232 *** 0.0929-1.0123 *** 0.0933
2.3572 *** 0.0363
2.4287 *** 0.0377
71998
71998
205071205071-107572.25-106865.81
37.4840
38.6027

Appendix Table A7
Estimated Results for Equation (6) (Grade 3)

Subject (γq1)
Girl (γq2)
Female teacher (γq3)
Subject×Girl (γq4)
Girl×Female teacher (γq5)
Subject×Female teacher (γq6)
Subject×Girl×Female teacher (γq7)
Experience2
Experience
Class size
2
Class size
Girl ratio
Public urban
Public rural
Private/national
Outside education
Amount of sleep: 6–7h
Amount of sleep: 7–8h
Amount of sleep: 8–9h
Amount of sleep: 9–10h
Amount of sleep: >10h
Breakfast: Often do not eat
Breakfast: Generally eat
Breakfast: Always eat
Belongings checked: Often not checked
Belongings checked: Generally checked
Belongings checked: Always checked
Female teacher (Average)
Experience (Average)
2
Experience (Average)
Praised by parents: Not praised more than praised
Praised by parents: Praised more than not praised
Praised by parents: Praised
Constant term
var_u
No. of students
No. of obs.
Log likelihood
Chi-sq(3) : H0 : m=0
Note: * p < .10, ** p < .05, *** p < .01.

EnglishCoef.
-0.0342-0.0623 ***0.1226 ***0.00980.1880 ***-0.00160.0461-0.0226 ***0.0004 ***-0.0227 ***0.0001 **0.2809 ***0.0486 **0.1133 ***0.4148 ***0.2224 ***-0.0248-0.0535 **-0.0509 *-0.0199
0.10900.04730.0991 ***0.2427 ***0.2501 ***0.3547 ***0.4547 ***0.0356-0.0251 ***0.0006 ***0.0266
0.0634 ***0.1553 ***-0.6750 ***2.2943 ***65569
182246-99581.94
28.8929

R.S.E
0.02210.01750.01610.0321
0.02250.03230.04630.00220.00010.00380.00010.07490.02170.02470.03700.01310.01950.02150.02890.05030.06870.04240.03700.03390.03320.02850.02850.02940.00560.00020.02120.01920.02200.0996
0.0361

Japanese
Coef.
R.S.E
-0.3259 *** 0.0234-0.0706 *** 0.0175
0.1618 *** 0.0163
0.0693 ** 0.0341
0.2039 *** 0.0227
0.1175 *** 0.0330-0.04070.0476-0.0211 *** 0.0022
0.0004 *** 0.0001-0.0203 *** 0.0039
0.0001 *0.00010.2692 *** 0.0755
0.0457 ** 0.0219
0.1098 *** 0.0248
0.4077 *** 0.0373
0.1861 *** 0.0130-0.0260
0.0196-0.0577 *** 0.0216-0.0580 ** 0.0291-0.02770.05060.10530.0691
0.04840.04260.1020 *** 0.0372
0.2476 *** 0.0341
0.2507 *** 0.0334
0.3557 *** 0.0286
0.4563 *** 0.0287
0.00130.0296-0.0259 *** 0.0056
0.0006 *** 0.0002
0.02760.02130.0657 *** 0.0194
0.1596 *** 0.0221-0.6685 *** 0.1004
2.3334 *** 0.0368
65569
182246-99353.19
30.0134Math
Coef.
0.4092 ***-0.1569 ***0.1746 ***0.3103 ***0.2946 ***0.1221 ***-0.2653 ***-0.0187 ***0.0003 ***-0.0221 ***0.0001 **0.2967 ***0.0404 *0.1024 ***0.3830 ***0.1159 ***-0.0291-0.0671 ***-0.0734 **-0.0401
0.10220.05100.1083 ***0.2590 ***0.2559 ***0.3619 ***0.4635 ***0.0005-0.0258 ***0.0006 ***0.02880.0676 ***0.1674 ***-0.8144 ***2.4746 ***65569
182246-98189.71
25.9763

R.S.E
0.01740.01890.01550.02530.02170.0381
0.05450.00220.00010.00390.00010.07690.02230.02530.03810.01330.02000.02210.02970.05160.07070.04350.03800.03480.03400.02910.02920.03020.00580.00020.02170.01980.02260.10240.0396

Science
Coef.
R.S.E
0.2224 *** 0.0180-0.0381 ** 0.0179
0.1475 *** 0.0149-0.1089 *** 0.0264
0.1853 *** 0.0208-0.03880.04100.08850.0587-0.0226 *** 0.0022
0.0004 *** 0.0001-0.0223 *** 0.0039
0.0001 ** 0.0001
0.2699 *** 0.0752
0.0490 ** 0.0218
0.1138 *** 0.0247
0.4197 *** 0.0371
0.2332 *** 0.0130-0.02410.0196-0.0518 ** 0.0216-0.0491 *0.0290-0.0173
0.05040.11000.06890.04670.04240.0991 *** 0.0370
0.2431 *** 0.0339
0.2512 *** 0.0333
0.3569 *** 0.0285
0.4574 *** 0.0286
0.02780.0295-0.0260 *** 0.0056
0.0006 *** 0.0002
0.02600.0212
0.0630 *** 0.0193
0.1553 *** 0.0220-0.7178 *** 0.0999
2.3096 *** 0.0364
65569
182246-99474.74
29.5093Social studies
Coef.
R.S.E
-0.4043 *** 0.0174
0.00500.01840.01640.0152-0.2997 *** 0.0258
0.1636 *** 0.0211
0.2392 *** 0.0415-0.0097
0.0599-0.0180 *** 0.0022
0.0003 *** 0.0001-0.0232 *** 0.0039
0.0001 **0.00010.2860 *** 0.0762
0.0410 *0.0221
0.0994 *** 0.0251
0.3807 *** 0.0377
0.1506 *** 0.0132-0.02810.0199-0.0610 *** 0.0219-0.0656 **0.0294-0.03100.05120.10670.07000.04800.04310.1043 *** 0.0376
0.2526 *** 0.0344
0.2554 *** 0.0337
0.3607 *** 0.0289
0.4619 *** 0.0290
0.0918 *** 0.0300-0.0290 *** 0.0057
0.0007 *** 0.0002
0.0291
0.02150.0661 *** 0.0196
0.1645 *** 0.0224-0.5647 *** 0.1009
2.4108 *** 0.0383
65569
182246-98493.40
44.3146

Appendix Table A8
Estimated Results for Equation (7) (Grade 1)

Subject (γ1)
Girl (γ2)
Female teacher (γ3)
Subject×Girl (γ4)
Girl×Female teacher (γ5)
Subject×Female teacher (γ6)
Subject×Girl×Female teacher (γ7)
Question×Subject (ζ1)
Question×Girl (ζ2)
Question×Female teacher (ζ3)
Question×Subject×Girl (ζ4)
Question×Girl×Female teacher (ζ5)
Question×Subject×Female teacher (ζ6)
Question×Subject×Girl×Female teacher (ζ7)
Experience
Experience2
Class size
Class size2
Girl ratio
Public urban
Public town
Private/national
Outside education
Amount of sleep: 6–7h
Amount of sleep: 7–8h
Amount of sleep: 8–9h
Amount of sleep: 9–10h
Amount of sleep: >10h
Breakfast: Often do not eat
Experience2 (Average)
Breakfast: Always eat
Belongings checked: Often not checked
Belongings checked: Generally checked
Belongings checked: Always checked
Female teacher (Average)
Experience (Average)
Experience2 (Average)
Constant term
sigma_usigma_erho
No. of students
No. of obs.
R-sq: within
R-sq: between
R-sq: overall
Chi-sq(3) : H0 : m=0
Hansen J statistic (P-value)
Kleibergen-Paap rk Wald F statistic
Note: * p < .10, ** p < .05, *** p < .01.

EnglishJapanese
Math
Science
Social studies
Coef.
R.S.E
Coef.
R.S.E
Coef.
R.S.E
Coef.
R.S.E
Coef.
R.S.E
-0.1663 *** 0.0097 -0.1770 *** 0.0100 -0.0195 *** 0.0072 0.0435 *** 0.0070 0.0511 *** 0.0065-0.0475 *** 0.0075 -0.0647 *** 0.0075 0.0044
0.0075 0.0007
0.0076 0.0059
0.0077-0.1035 *** 0.0065 -0.1096 *** 0.0065 -0.1330 *** 0.0061 -0.1244 *** 0.0061 -0.1129 *** 0.0060
0.2290 *** 0.0134 0.3760 *** 0.0138 -0.0772 *** 0.0102 -0.0653 *** 0.0096 -0.0686 *** 0.0090
0.1943 *** 0.0089 0.1708 *** 0.0089 0.2246 *** 0.0083 0.2213 *** 0.0084 0.2052 *** 0.0084
0.0655 *** 0.0140 0.1061 *** 0.0143 0.1160 *** 0.0151 0.1296 *** 0.0152 0.1229 *** 0.0176-0.1072 *** 0.0194 -0.1712 *** 0.0195 -0.1964 *** 0.0211 -0.2068 *** 0.0211 -0.1954 *** 0.0241
0.0743 *** 0.0179 0.0390 ** 0.0198 0.0868 *** 0.0127 0.0965 *** 0.0135 0.0939 *** 0.0135
0.1879 *** 0.0134 0.2027 *** 0.0133 0.1844 *** 0.0137 0.1895 *** 0.0133 0.1748 *** 0.0128
0.0669 *** 0.0117 0.0864 *** 0.0114 0.0830 *** 0.0109 0.0885 *** 0.0107 0.0942 *** 0.0106-0.0694 ** 0.0272 -0.1233 *** 0.0302 -0.0978 *** 0.0199 -0.0903 *** 0.0209 -0.0548 *** 0.0212-0.1039 *** 0.0177 -0.1033 *** 0.0172 -0.1161 *** 0.0170 -0.1140 *** 0.0164 -0.1080 *** 0.0161-0.0347
0.0258 -0.0889 *** 0.0275 -0.0770 *** 0.0262 -0.0924 *** 0.0289 -0.1503 *** 0.0343
0.0625 *0.0377 0.1359 *** 0.0406 0.1298 *** 0.0378 0.0893 ** 0.0428 0.0848 *
0.05120.0057 *** 0.0005 0.0057 *** 0.0005 0.0057 *** 0.0005 0.0060 *** 0.0005 0.0058 *** 0.0005-0.0002 *** 0.0000 -0.0002 *** 0.0000 -0.0002 *** 0.0000 -0.0002 *** 0.0000 -0.0002 *** 0.0000
0.00020.0013 0.0002
0.0013 0.0001
0.0013 0.0001
0.0013 0.0003
0.00130.0000 *0.0000 0.0000 *0.0000 0.0000 *0.0000 0.0000 *0.0000 0.0000 *0.0000-0.4010 *** 0.0254 -0.4088 *** 0.0254 -0.3946 *** 0.0255 -0.3960 *** 0.0254 -0.4034 *** 0.0254
0.0282 *** 0.0088 0.0285 *** 0.0088 0.0278 *** 0.0088 0.0285 *** 0.0088 0.0283 *** 0.0088-0.00360.0101 -0.0032
0.0101 -0.0037
0.0101 -0.0030
0.0101 -0.0035
0.01010.7490 *** 0.0127 0.7502 *** 0.0127 0.7476 *** 0.0127 0.7468 *** 0.0127 0.7471 *** 0.0127
0.1765 *** 0.0044 0.1708 *** 0.0043 0.1777 *** 0.0044 0.1729 *** 0.0043 0.1744 *** 0.0043
0.0772 *** 0.0119 0.0773 *** 0.0119 0.0774 *** 0.0119 0.0772 *** 0.0119 0.0771 *** 0.0119
0.1136 *** 0.0117 0.1133 *** 0.0117 0.1140 *** 0.0117 0.1133 *** 0.0117 0.1133 *** 0.0117-0.0229 *0.0124 -0.0236 *0.0124 -0.0226 *0.0124 -0.0237 *0.0124 -0.0235 *0.0124-0.2404 *** 0.0158 -0.2407 *** 0.0158 -0.2401 *** 0.0158 -0.2407 *** 0.0158 -0.2408 *** 0.0158-0.5430 *** 0.0269 -0.5450 *** 0.0268 -0.5432 *** 0.0268 -0.5442 *** 0.0268 -0.5439 *** 0.0268
0.0673 *** 0.0220 0.0678 *** 0.0220 0.0673 *** 0.0220 0.0674 *** 0.0219 0.0677 *** 0.0220
0.2411 *** 0.0190 0.2418 *** 0.0190 0.2406 *** 0.0190 0.2409 *** 0.0190 0.2413 *** 0.0190
0.5610 *** 0.0180 0.5612 *** 0.0180 0.5602 *** 0.0180 0.5605 *** 0.0180 0.5607 *** 0.0180
0.1515 *** 0.0150 0.1512 *** 0.0150 0.1507 *** 0.0150 0.1509 *** 0.0150 0.1513 *** 0.0150
0.3137 *** 0.0129 0.3139 *** 0.0129 0.3132 *** 0.0129 0.3131 *** 0.0129 0.3136 *** 0.0129
0.4618 *** 0.0128 0.4618 *** 0.0128 0.4610 *** 0.0128 0.4610 *** 0.0128 0.4610 *** 0.0128-0.0080
0.0120 -0.0017
0.0120 -0.0021
0.0119 -0.0063
0.0119 -0.0097
0.01190.0067 *** 0.0019 0.0066 *** 0.0019 0.0065 *** 0.0019 0.0065 *** 0.0019 0.0065 *** 0.0019-0.0002 *** 0.0001 -0.0002 *** 0.0001 -0.0002 *** 0.0001 -0.0002 *** 0.0001 -0.0002 *** 0.0001-0.8575 *** 0.0390 -0.8559 *** 0.0390 -0.8825 *** 0.0390 -0.8966 *** 0.0390 -0.8962 *** 0.0390
0.73370.73420.73400.73330.73370.5526
0.55130.55270.55290.5531
0.63810.6394
0.6382
0.6376
0.6377
72505
72505
72505
72505
72505
2076232076232076232076232076230.02240.02850.02300.02200.02090.13480.13630.13490.13530.13480.16420.16470.16420.16500.164614.2952
13.1774
13.0272
13.5001
14.2760
3.5260(0.1715) 3.4720(0.1762) 3.4890(0.1748) 3.7100(0.1565) 3.5520(0.1693)8.14108.40109.64707.85008.9030Appendix Table A9
Estimated Results for Equation (7) (Grade 2)

Subject (γ1)
Girl (γ2)
Female teacher (γ3)
Subject×Girl (γ4)
Girl×Female teacher (γ5)
Subject×Female teacher (γ6)
Subject×Girl×Female teacher (γ7)
Question×Subject (ζ1)
Question×Girl (ζ2)
Question×Female teacher (ζ3)
Question×Subject×Girl (ζ4)
Question×Girl×Female teacher (ζ5)
Question×Subject×Female teacher (ζ6)
Question×Subject×Girl×Female teacher (ζ7)
Experience
Experience2
Class size
Class size2
Girl ratio
Public urban
Public town
Private/national
Outside education
Amount of sleep: 6–7h
Amount of sleep: 7–8h
Amount of sleep: 8–9h
Amount of sleep: 9–10h
Amount of sleep: >10h
Breakfast: Often do not eat
Experience2 (Average)
Breakfast: Always eat
Belongings checked: Often not checked
Belongings checked: Generally checked
Belongings checked: Always checked
Female teacher (Average)
Experience (Average)
Experience2 (Average)
Constant term
sigma_usigma_erho
No. of students
No. of obs.
R-sq: within
R-sq: between
R-sq: overall
Chi-sq(3) : H0 : m=0
Hansen J statistic (P-value)
Kleibergen-Paap rk Wald F statistic
Note: * p < .10, ** p < .05, *** p < .01.

EnglishJapanese
Math
Science
Social studies
Coef.
R.S.E
Coef.
R.S.E
Coef.
R.S.E
Coef.
R.S.E
Coef.
R.S.E
-0.1823 *** 0.0098 -0.1839 *** 0.0098 -0.0512 *** 0.0074 0.0612 *** 0.0072 0.0458 *** 0.0068-0.0722 *** 0.0076 -0.0962 *** 0.0076 -0.0330 *** 0.0076 -0.0131 *0.0077 -0.0259 *** 0.0079-0.1009 *** 0.0068 -0.1136 *** 0.0066 -0.1382 *** 0.0062 -0.1183 *** 0.0062 -0.1161 *** 0.0062
0.2373 *** 0.0137 0.3892 *** 0.0132 -0.0290 *** 0.0105 -0.1100 *** 0.0098 -0.0585 *** 0.0094
0.2059 *** 0.0092 0.1844 *** 0.0090 0.2336 *** 0.0084 0.2154 *** 0.0085 0.2186 *** 0.0085
0.0839 *** 0.0139 0.1160 *** 0.0142 0.1399 *** 0.0156 0.1323 *** 0.0163 0.1230 *** 0.0179-0.1429 *** 0.0193 -0.1750 *** 0.0193 -0.1903 *** 0.0218 -0.2019 *** 0.0222 -0.1979 *** 0.0240
0.1482 *** 0.0188 0.0614 *** 0.0201 0.1128 *** 0.0129 0.0996 *** 0.0132 0.1043 *** 0.0142
0.2467 *** 0.0127 0.2712 *** 0.0127 0.2640 *** 0.0129 0.2582 *** 0.0129 0.2447 *** 0.0122
0.0816 *** 0.0121 0.1154 *** 0.0116 0.1049 *** 0.0111 0.1077 *** 0.0109 0.1119 *** 0.0107-0.0683 ** 0.0285 -0.1412 *** 0.0283 -0.1433 *** 0.0197 -0.1026 *** 0.0202 -0.0704 *** 0.0220-0.1315 *** 0.0178 -0.1346 *** 0.0171 -0.1520 *** 0.0167 -0.1448 *** 0.0164 -0.1462 *** 0.0159-0.0932 *** 0.0265 -0.1387 *** 0.0281 -0.1017 *** 0.0269 -0.1028 *** 0.0297 -0.1543 *** 0.0366
0.0722 *0.0386 0.1478 *** 0.0391 0.1526 *** 0.0378 0.1055 ** 0.0419 0.1658 *** 0.0522
0.0045 *** 0.0006 0.0047 *** 0.0005 0.0043 *** 0.0006 0.0046 *** 0.0005 0.0046 *** 0.0006-0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000-0.0041 *** 0.0011 -0.0035 *** 0.0011 -0.0032 *** 0.0011 -0.0036 *** 0.0011 -0.0036 *** 0.0011
0.0001 *** 0.0000 0.0001 *** 0.0000 0.0001 *** 0.0000 0.0001 *** 0.0000 0.0001 *** 0.0000-0.4029 *** 0.0263 -0.4104 *** 0.0264 -0.3987 *** 0.0264 -0.3983 *** 0.0263 -0.4044 *** 0.0263
0.00780.0089 0.0078
0.0089 0.0082
0.0089 0.0077
0.0089 0.0078
0.0089-0.01520.0101 -0.0157
0.0101 -0.0148
0.0101 -0.0163
0.0101 -0.0155
0.01010.6444 *** 0.0132 0.6482 *** 0.0132 0.6451 *** 0.0132 0.6463 *** 0.0132 0.6439 *** 0.0132
0.1579 *** 0.0043 0.1535 *** 0.0043 0.1607 *** 0.0043 0.1534 *** 0.0043 0.1563 *** 0.0043
0.0643 *** 0.0102 0.0642 *** 0.0102 0.0642 *** 0.0102 0.0643 *** 0.0102 0.0642 *** 0.0102
0.0627 *** 0.0103 0.0625 *** 0.0103 0.0631 *** 0.0103 0.0625 *** 0.0103 0.0625 *** 0.0103-0.0996 *** 0.0117 -0.1003 *** 0.0117 -0.0994 *** 0.0117 -0.1005 *** 0.0117 -0.0999 *** 0.0117-0.3447 *** 0.0178 -0.3451 *** 0.0178 -0.3448 *** 0.0178 -0.3446 *** 0.0178 -0.3457 *** 0.0178-0.5805 *** 0.0312 -0.5811 *** 0.0311 -0.5800 *** 0.0311 -0.5808 *** 0.0312 -0.5827 *** 0.0311
0.02350.0206 0.0240
0.0206 0.0240
0.0206 0.0245
0.0206 0.0240
0.02060.2098 *** 0.0174 0.2099 *** 0.0174 0.2096 *** 0.0174 0.2110 *** 0.0174 0.2100 *** 0.0174
0.5302 *** 0.0163 0.5304 *** 0.0163 0.5300 *** 0.0163 0.5312 *** 0.0163 0.5304 *** 0.0163
0.1907 *** 0.0143 0.1905 *** 0.0143 0.1906 *** 0.0143 0.1907 *** 0.0143 0.1905 *** 0.0143
0.3483 *** 0.0122 0.3478 *** 0.0122 0.3477 *** 0.0122 0.3479 *** 0.0122 0.3480 *** 0.0122
0.4984 *** 0.0122 0.4984 *** 0.0122 0.4980 *** 0.0122 0.4981 *** 0.0122 0.4982 *** 0.0122
0.0389 *** 0.0119 0.0443 *** 0.0119 0.0447 *** 0.0119 0.0412 *** 0.0119 0.0392 *** 0.0119
0.00200.0019 0.0018
0.0019 0.0023
0.0019 0.0022
0.0019 0.0021
0.00190.00000.0001 0.0000
0.0001 0.0000
0.0001 0.0000
0.0001 0.0000
0.0001-0.7236 *** 0.0355 -0.7214 *** 0.0354 -0.7551 *** 0.0355 -0.7709 *** 0.0355 -0.7657 *** 0.0355
0.73210.73240.73190.73130.73180.55000.54800.55040.54950.55040.63930.6411
0.63880.6391
0.6386
71998
71998
71998
71998
71998
2050712050712050712050712050710.01790.02490.01670.01940.01630.13540.13720.13540.13620.13540.16710.16740.16730.16770.167528.6958
30.052030.669327.2443
26.6762
0.8490(0.6541) 0.8210(0.6632) 0.7320(0.6935) 0.8650(0.6488) 0.7620(0.6832)
6.88007.47909.25106.64708.3580Appendix Table A10
Estimated Results for Equation (7) (Grade 3)

Subject (γ1)
Girl (γ2)
Female teacher (γ3)
Subject×Girl (γ4)
Girl×Female teacher (γ5)
Subject×Female teacher (γ6)
Subject×Girl×Female teacher (γ7)
Question×Subject (ζ1)
Question×Girl (ζ2)
Question×Female teacher (ζ3)
Question×Subject×Girl (ζ4)
Question×Girl×Female teacher (ζ5)
Question×Subject×Female teacher (ζ6)
Question×Subject×Girl×Female teacher (ζ7)
Experience
Experience2
Class size
Class size2
Girl ratio
Public urban
Public town
Private/national
Outside education
Amount of sleep: 6–7h
Amount of sleep: 7–8h
Amount of sleep: 8–9h
Amount of sleep: 9–10h
Amount of sleep: >10h
Breakfast: Often do not eat
Experience2 (Average)
Breakfast: Always eat
Belongings checked: Often not checked
Belongings checked: Generally checked
Belongings checked: Always checked
Female teacher (Average)
Experience (Average)
Experience2 (Average)
Constant term
sigma_usigma_erho
No. of students
No. of obs.
R-sq: within
R-sq: between
R-sq: overall
Chi-sq(3) : H0 : m=0
Hansen J statistic (P-value)
Kleibergen-Paap rk Wald F statistic
Note: * p < .10, ** p < .05, *** p < .01.

EnglishJapanese
Math
Science
Social studies
Coef.
R.S.E
Coef.
R.S.E
Coef.
R.S.E
Coef.
R.S.E
Coef.
R.S.E
-0.1266 *** 0.0098 -0.1496 *** 0.0105 -0.0183 ** 0.0077 0.0796 *** 0.0083 -0.0424 *** 0.0069-0.0623 *** 0.0083 -0.0982 *** 0.0083 0.0024
0.0082 -0.0108
0.0083 -0.0828 *** 0.0086-0.1074 *** 0.0074 -0.0788 *** 0.0073 -0.1134 *** 0.0067 -0.1082 *** 0.0066 -0.1202 *** 0.0068
0.1261 *** 0.0140 0.3945 *** 0.0144 -0.1478 *** 0.0111 -0.1676 *** 0.0114 0.1478 *** 0.0097
0.2301 *** 0.0102 0.1220 *** 0.0103 0.1900 *** 0.0093 0.1952 *** 0.0093 0.2528 *** 0.0096
0.0962 *** 0.0149 0.0446 *** 0.0152 0.1122 *** 0.0187 0.1794 *** 0.0191 0.1031 *** 0.0178-0.1762 *** 0.0212 -0.0875 *** 0.0210 -0.1513 *** 0.0265 -0.2102 *** 0.0271 -0.2398 *** 0.0241
0.1617 *** 0.0196 0.0280
0.0211 0.1517 *** 0.0129 0.0838 *** 0.0146 0.1206 *** 0.0143
0.3065 *** 0.0123 0.3269 *** 0.0124 0.3011 *** 0.0125 0.3197 *** 0.0125 0.3110 *** 0.0120
0.0979 *** 0.0132 0.1042 *** 0.0128 0.1147 *** 0.0120 0.1112 *** 0.0117 0.1120 *** 0.0117-0.0982 *** 0.0284 -0.0999 *** 0.0292 -0.1173 *** 0.0191 -0.1168 *** 0.0213 -0.1285 *** 0.0211-0.1805 *** 0.0186 -0.1046 *** 0.0186 -0.1560 *** 0.0175 -0.1593 *** 0.0170 -0.1700 *** 0.0170-0.1423 *** 0.0287 -0.0756 ** 0.0296 -0.1351 *** 0.0303 -0.1406 *** 0.0337 -0.0896 ** 0.0356
0.2115 *** 0.0406 0.0174
0.0408 0.1421 *** 0.0422 0.1292 *** 0.0476 0.1725 *** 0.0498
0.0040 *** 0.0007 0.0043 *** 0.0007 0.0039 *** 0.0007 0.0043 *** 0.0007 0.0039 *** 0.0007-0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000 -0.0001 *** 0.0000
0.0028 ** 0.0012 0.0025 ** 0.0012 0.0027 ** 0.0012 0.0028 ** 0.0012 0.0030 ** 0.0012
0.00000.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000-0.2912 *** 0.0295 -0.2979 *** 0.0296 -0.2878 *** 0.0295 -0.2864 *** 0.0295 -0.2835 *** 0.0294-0.0217 ** 0.0096 -0.0214 ** 0.0096 -0.0210 ** 0.0095 -0.0219 ** 0.0096 -0.0212 ** 0.0096-0.0774 *** 0.0108 -0.0767 *** 0.0108 -0.0767 *** 0.0108 -0.0781 *** 0.0108 -0.0767 *** 0.0108
0.3794 *** 0.0146 0.3829 *** 0.0146 0.3840 *** 0.0146 0.3802 *** 0.0146 0.3804 *** 0.0146
0.1765 *** 0.0049 0.1770 *** 0.0049 0.1842 *** 0.0050 0.1704 *** 0.0049 0.1773 *** 0.0049
0.0208 ** 0.0083 0.0208 ** 0.0083 0.0206 ** 0.0083 0.0204 ** 0.0083 0.0205 ** 0.0083-0.0273 *** 0.0093 -0.0272 *** 0.0093 -0.0269 *** 0.0093 -0.0281 *** 0.0093 -0.0279 *** 0.0093-0.2469 *** 0.0131 -0.2466 *** 0.0131 -0.2461 *** 0.0131 -0.2481 *** 0.0131 -0.2470 *** 0.0131-0.4606 *** 0.0246 -0.4600 *** 0.0246 -0.4595 *** 0.0246 -0.4628 *** 0.0246 -0.4616 *** 0.0246-0.6688 *** 0.0357 -0.6676 *** 0.0356 -0.6681 *** 0.0356 -0.6705 *** 0.0356 -0.6714 *** 0.0357
0.0778 *** 0.0197 0.0776 *** 0.0197 0.0771 *** 0.0197 0.0774 *** 0.0197 0.0780 *** 0.0197
0.2476 *** 0.0170 0.2475 *** 0.0170 0.2464 *** 0.0170 0.2474 *** 0.0170 0.2472 *** 0.0170
0.5347 *** 0.0157 0.5348 *** 0.0157 0.5332 *** 0.0157 0.5346 *** 0.0157 0.5340 *** 0.0157
0.1410 *** 0.0157 0.1419 *** 0.0157 0.1402 *** 0.0157 0.1410 *** 0.0157 0.1407 *** 0.0157
0.2611 *** 0.0136 0.2624 *** 0.0136 0.2606 *** 0.0136 0.2613 *** 0.0136 0.2608 *** 0.0136
0.3996 *** 0.0136 0.4007 *** 0.0136 0.3992 *** 0.0136 0.3999 *** 0.0136 0.3996 *** 0.0136
0.0206 *0.0124 0.0277 ** 0.0124 0.0254 ** 0.0124 0.0229 *0.0124 0.0174
0.01240.0132 *** 0.0023 0.0128 *** 0.0023 0.0129 *** 0.0023 0.0130 *** 0.0023 0.0131 *** 0.0023-0.0003 *** 0.0001 -0.0003 *** 0.0001 -0.0003 *** 0.0001 -0.0003 *** 0.0001 -0.0003 *** 0.0001-0.8766 *** 0.0394 -0.8665 *** 0.0393 -0.8995 *** 0.0394 -0.9096 *** 0.0393 -0.8897 *** 0.0394
0.73710.73880.73830.73740.7374
0.55370.54820.55040.55190.55180.63930.64500.64270.64090.6410
65569
65569
65569
65569
65569
1822461822461822461822461822460.00610.01640.01050.01110.00620.12080.12350.12340.12190.1216
0.15390.15380.15530.15350.154642.5284
42.1232
41.131541.5016
41.13770.2560(0.8798) 0.3260(0.8497) 0.3210(0.8517) 0.2720(0.8728) 0.2240(0.894)15.5630
16.8630
18.6950
15.3880
17.7480