Tohoku University Research Center for Policy Design Discussion Paper

TUPD-2022-010

The Quantity Quality Trade-off of Children and Qualityof High School
Wataru Kureishi
National Institute of Population and Social Security Research
Graduate School of Economics and Management, Tohoku University

Midori Wakabayashi
Graduate School of Economics and Management, Tohoku University

Colin McKenzie
Faculty of Economics, Keio University

Kei Sakata
Australian Institute of Family Studies

June 2022

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The Quantity Quality Trade-off of Children and Qualityof High School∗
Wataru Kureishi†

Midori Wakabayashi‡

Colin McKenzie§

Kei Sakata¶

Abstract
Using data from the Longitudinal Survey of Newborns in the 21st Century, we
examine the effect of sibship size on high school standardized rank score in Japan.
Using twin births as a control variable, the causal effect of sibling size on high school
standardized hensachi scores is not found in the pooled sample across Japan, but
emerges only when we divide the sample into urban and rural areas. We also findthat when the number of children increases, parents and children in urban areas try
to mitigate the adverse effects on hensachi by increasing the inputs of study timeand conversations with parents. On the other hand, rural parents and their children
reinforce the adverse effects by reducing their inputs.

1 Introduction
The trade-off between quantity and quality of children, i.e., sibling size negatively affects
child outcomes, is one of the main economic theories of household fertility behavior (Becker∗
We thank seminar participants at Kansai Labor Workshop, Empirical Moral Science Workshop, theFamily Economics Workshop at Keio University for helpful comments. The data used in this paper comefrom the Japanese Ministry of Health, Labour and Welfare’s Longitudinal Survey of Newborns in the 21stCentury (21 seiki shusshoji judan chosa) and the Live Birth Form of Vital Statistics (Jinko dotai chosashusseihyo).
†
National Institute of Population and Social Security Research‡
Tohoku University§
Keio University¶
Australian Institute of Family Studies

1and Lewis (1973)), but previous studies that conduct empirical analysis using data fromdeveloped countries find that this theory does not necessarily hold. Using twin births as
an instrumental variable, for example, Black et al. (2005) used a large Norwegian data
set to measure the causal effect of an increase in the number of children and found that
controlling for birth order effects, the impact on educational attainment was negligible.
Similar conclusion is also reached in the Angrist et al. (2010) using Israeli data.1 The
prevailing view behind these studies is that schooling is publicly provided in many developed
countries, with parents bearing little cost. In addition, regulations on child labor have kept
the opportunity cost of children’s time low, allowing parents to send their children to school
even as the number of children increases (See Doepke (2015), Liu (2015) and Clarke (2018)
for detailed surveys).
Unlike previous studies, as a measure of child quality, this study focuses on enrollment
in selective high schools, where students are selected based on academic achievement andentrance examinations. We regard attending children in selective high schools because of
their high performance in getting into top universities as a parental investment in theirchildren to increase their children’s chances of acceptance into post-secondary institutions.
In the United States, given the intense competition for four-year colleges and universities,
students prepare better academically by taking more challenging courses and participatingin activities that are viewed favorably by admissions committees (Bound et al. (2009)) andwell-educated parents increased their childcare time as an optimal response to increased
competition for scarce university slots (Ramey and Ramey (2009).
In addition, East Asian countries, such as Japan, Korea, and China, students use private
cram schools (which is called ”shadow education”) in addition to public educational institutions to prepare for higher education facilities after the compulsory education is completed(Bray and Lykins (2012), Entrich (2017)).
Our focus is that parents’ motivations to provide their children with a higher quality
1

However, studies using data from developing countries such as India and China provide evidence insupport of the quantity-quality trade-off (Rosenzweig and Wolpin (1980), Rosenzweig and Zhang (2009)).

2

secondary education to prepare their children for the fierce competition of university entrance
examinations may be placing financial and time burdens on families in developed countries.
From this focus, we expect that, even in developed countries, there will be a trade-off between
quantity and quality of children, where the quality of the high school education that parents
provide for their children is adversely affected when the number of children/siblings increases.
Another focus is that the strength of this motivation differs between urban and rural
areas. In the U.S., competition for high school graduates’ college aspirations is most intensein the Northeast region and in California (Bound et al. (2009)), while in Japan, competition for entrance exams is more intense in the Tokyo metropolitan area and around Osaka(Tsuneyoshi (2013)). While 7.4% of all junior high school students attend private schools,
the highest percentage is in Tokyo, where one out of every four junior high school students
attends a private school. In urban prefectures such as Osaka, Kanagawa, and Kyoto, the percentages are higher than average, ranging from 10-13% (Japan Institute of Life Insurance2 ).
Therefore, when attempting to estimate the trade-off between the quantity of children andthe quality of secondary education, the sample needs to be divided between urban and rural
areas, taking into account the severity of exam competition in urban areas.
This paper examines how the number of siblings affects the quality of high schools attended by children. We utilize long-term panel data from the Longitudinal Study of the
Newborn in the 21st Century (NLS2001), which covers Japanese children born in 2001 andprovides important information related to children’s schooling, such as the name of the highschool the child attended. The advantage of using this information is that the responses
to the questions are convertible into the high school ranking score (hensachi score, see below). Since Japan’s high school enrollment rate is close to 100%, it is possible to compare
the quality of high schools for the majority of the children used in the analysis. Note thatregarding the quality of the universities attended, the university enrollment rate is about
60%, so it is impossible to observe children who do not go to universities by using hensachi
2

https://www.jili.or.jp/lifeplan/lifeevent/789.html

3

score. Furthermore, note that the information on years of education used in many studies
does not identify quality within the same number of years of schooling.
Another unique feature of this survey compared to other nationally representative household surveys is that it asks a wide range of questions about parental investment and expenditures: spending on children (e.g., extracurricular activities and cram schools), time parents
spend with their children, talking with their children, and children’s study time. Mothers
and fathers were asked about their employment status. These items can be considered inputs to the child’s production function. Cáceres-Delpiano (2006) says that focusing on inputs
rather than using outcomes is a more powerful test because inputs are one step closer toassessing the effect of family size in the causal chain. In addition, an increase in the numberof children can reveal whether parents attempt to mitigate or enhance the adverse effects onchild quality by reallocating these inputs.
Even though there is a rich variation in the hensachi score, there is an identification
problem because the quality and quantity of children are determined jointly. Therefore, theobserved correlations do not necessarily reflect causal relationships. One possibility is that,for example, unobserved factors may cause parents, especially mothers, to quit their jobs andjoin the household. This will lead to changes in household budgets and how they interact
with their children. The housewife may then choose to have a small family and raise her
children more generously. Another possibility is the bias from simultaneity. The high qualityof the youngest child may make them feel that they do not need to have another child (Blacket al. (2005) points out this possibility).
To address this identification problem, we adopt an instrumental variable method and use
twin births as a source of exogenous variation in family size following Rosenzweig and Wolpin(1980). In the baseline specification, we add twins at the second birth as an instrumental
variable to control the selection bias. In addition, given that indicators of maternal healthand health-related behaviors and exposures are systematically positively correlated withthe probability of twin births (Bhalotra and Clarke (2020)), we will control for child birth4

weight, gestational weeks, and maternal smoking. As an alternative specification, we also
try to estimate using twins at the third birth as the instrumental variable with first-bornand second-born sample and identify the effect of birth order (Black et al. (2005)).
The main empirical result is that the causal impacts of family size on the quality of highschool, measured by the standardized hensachi score of the high school the child attends is
not found in the pooled sample across Japan, but emerges only when we divide the sample
into urban and rural areas. We find that each additional child is associated with 3.4 points
decrease in hensachi score for first-born children with one or more siblings in the urban
area and 3.3 points for first- and second-born children with two or more siblings in ruralarea, respectively. Our uniquely rich data set also allows us to explore the mechanisms
behind the differences in trade-offs between urban and rural areas. We find contrasting
reallocation behaviors in urban and rural households concerning household resources. In
urban areas, households mitigate the adverse effects of having more children by substituting
fewer extracurricular activities, such as piano and swimming, for more study time outsideof school and more conversations with parents as the number of children increases. In
rural areas, by contrast, households instead reinforce the harmful effects of an additionalchild by reducing their input into children’s educational production, including spending on
extracurricular activities and cram school, study time outside of school, and conversations
with parents. The mitigating and reinforcing effects of the reallocation of resources within
the household may exaggerate the trade-off between the number of siblings and the qualityof the high school children attend, underestimating it (i.e., in the direction of no adverse
effects) in urban areas and overestimating it (i.e., in the direction of adverse effects) in rural
areas.
We conducte the estimation with several additional specifications. First, the sample isanalyzed separately by parental education level, household income, and child gender. The
results show a strong trade-off between the number of siblings and high school hensachi scorefor boys from highly educated households. We find that parents with higher socioeconomic

5status in urban areas are willing to invest in the education of their boys in high school. Our
results are unaffected by the specific choice of child output variables, such as acceptance rate
to a prominent university or the percentage of children who attend a middle or high school.
Furthermore, the rate of children entering high school in rural areas also increases. Finally,
the results were also robust when another instrumental variable, the combination of genderof the first and second child, was selected as the instrumental variable (Angrist and Evans(1998)).
The rest of this paper is organized as follows. In Section 2, we describe educational
background in Japan. Section 3 explain the data we use. We explains our empirical strategy
and then we show the descriptive statistics in Section 4. Section 5 reports the result. In
Section 6, we discuss the mechanism behind our main results. Section 7 checks the robustnessof our findings. Section 8 concludes the paper.

2

Education in Japan

This section outlines three aspects of Japanese education relevant to this study.
The first is the institutional background of education in Japan. The Fundamental Law of
Education and the School Education Law in 1947 stipulated that the period of compulsory
education is nine years, consisting of six years of elementary school and three years of juniorhigh school and recently most children attend high school after graduating from junior highschool. The percentage of students who go on to high school is now 98%. After graduatingfrom high school, students who wish to enter a university, especially a diﬀicult-to-enter
university, must pass entrance exams, which are paper tests taken only once a year. In 2020,
the university enrollment rate is 54.4 percent (according to the 2020 Basic School Survey).
The second is that how to measure the quality of schools in Japan. In Japan, a standardized score called the hensachi (deviation value, literally in Japanese) is often used tomeasure the quality of schools (Højlund Roesgaard (2006), Entrich (2017), p.133). Large6private cram schools, called juku, conduct mock exams on a national scale and derive therelative position of each test taker with a standardized score, where the mean is 50 and thestandard deviation is 10 (test taker’s hensachi score). Then, by comparing the hensachiscores of past test takers with the actual pass/fail results, high school hensachi is calculated
as a border or threshold value for the diﬀiculty of each high school entrance exam (Goodman
and Oka (2018)). It has been published as distribution tables by juku as an index of thediﬀiculty level of the entrance exam for each school. Thus, hensachi score is an important
indicator for junior high school students to determine the quality of high school. The relationship between school hensachi score and children’s academic performance was examined
by Kondo (2014), who indicated that the difference in school quality was reflected in thehensachi score of junior high schools.3
Third, we characterize Japan by a large education spending on their children. Japanesefamilies try to increase their chances of being accepted into the desired university by enrolling
their children in high schools with a high achievement rate in getting into diﬀicult-to-enter
universities. Japanese families also send their children to cram schools. According to theresults of the National Survey of Academic Performance and Learning (2017) conducted by
the Ministry of Education, Culture, Sports, Science and Technology, 46.3% of sixth-grade ofelementary school students and 61.2% of third-grade of junior high school students attended
cram school. Then, it is a considerable financial burden for parents to send their children tohigher quality schools because high quality schools are not only in the public sector but also
in the private sector. For example, according to the 2016 Household Survey on Educational
Expenditures per Student, there is a significant difference between public and private schools
in terms of cost. At the junior high school level, the cost of schooling is about 480,000 yen
for public schools and about 1,330,000 yen for private schools. At the high school level, thecost is 450,000 yen for public schools and 1,040,000 yen for private schools, which is about
3

Previous studies outside Japan that have examined whether going to a higher-ranked high school improves academic performance include Cullen et al. (2006), Clark (2010), and Pop-Eleches and Urquiola(2013).

7

2.3 to 2.8 times the cost of public schools. Note that whether a school is of good quality is
not necessarily positively correlated with tuition.

3

Data

We use data from the Longitudinal Survey of Newborns in the 21st Century (LSN2001), a
parent-child-level panel data set conducted by the Ministry of Health, Labour and Welfare(MHLW). LSN2001 has recorded all 53,575 babies (including multiple births) born in Japanon January 10-17 and July 10-17 in 2001. The first survey in 2001 collected 47,015 pairs ofparents and children (collection rate: 87.8%). Since then, the collection rate for each year
has been about 90%, and, when the children entered high school in the sixteenth survey
in 2017, 26,900 parent-child pairs remained.4 MHLW’s website provides a summary of thissurvey in English,5 and Sakata et al. (2015) provide a summary of this survey in Japanese.
This data set includes variables on schooling, household composition, education at home,monthly child-rearing expenses, parental employment status, and municipality-level residency. Using the information on sibling composition, we obtain the sibling size by counting
the number of children in the household. If a parent works away from home alone and isabsent for more than three months, he or she is not included in the same household, but if
he or she returns home at least once every three months, he or she is included in the same
household.
The dataset includes an identifier for whether the children surveyed are twins or not: 478(1.78%) of the 26,900 are twins. We do not use these twins because they are more likely
to be born prematurely, affecting their later life and biasing their scholarly output (Blacket al. (2007)). Nevertheless, we use birth weight and gestational week as control variables inour estimation. This restriction leaves us with a total of 26,422 non-twin children. For theirsiblings, twin identifiers are not provided, thus, we define two siblings of a surveyed child in
4

Since there was a change in the survey timing in the seventh survey, the survey was not conducted in2007.
5https://www.mhlw.go.jp/english/database/db-hw/vs03.html

8the same household as twins if they report being born in the same year and month.
Table 1 shows the distribution of sibship size for the 26,422 non-twin children includedin LSN2001 in 2017. More than half of them have only one sibling (that is, two children in
their household), and three or more siblings (four or more children) are quite rare. There
are approximately 11-15 % of only children. In terms of birth order, more than half of thechildren are first-born, and slightly more than one-third are second-born. Over 10 percent
are third and subsequent children.
Numberof
Siblings
0
1
2
3
4
5+
Total

Urban Areas
1st-born 2nd-born
3rd or
Total
Children Children later-bornChildren
1,576
1,576
(28.69)(14.74)
2,950
3,098
6,048
(53.69)(76.17)(56.58)
829
841
885
2,555
(15.09)(20.68)(78.46)(23.9)
111
105
184
400
(2.02)(2.58)(16.31)(3.74)
20
14
40
74(0.36)(0.34)(3.55)(0.69)
8919
36(0.15)(0.22)(1.68)(0.34)
5,494
4,067
1,128
10,689
(100)
(100)
(100)
(100)

1st-bornChildren
1,767(23.26)
4,094(53.89)1,469(19.34)226(2.97)
32(0.42)
9(0.12)
7,597(100)

Rural Areas
2nd-born
3rd or
Total
Children later-bornChildren
1,767(11.23)
4,063
8,157(70.99)(51.85)
1,405
1,797
4,671
(24.55)(74.47)(29.69)213
483
922(3.72)(20.02)(5.86)
27
94
153(0.47)(3.9)(0.97)
15
39
63(0.26)(1.62)(0.40)
5,723
2,413
15,733
(100)
(100)
(100)

Table 1: Distribution of Number of Siblings by Birth Order. In 2017, of the 26,900 remaining
children, 26,422 are non-twin.
One of the LSN2001 data advantages is that it asks children to name the high school theyattend, allowing us to match that information with the high school’s hensachi score, and, we
use hensachi as an indicator variable to measure the selectivity of the high schools that thechildren attend for the analysis. We obtained the 2017 hensachi information for each highschool from ReseMom6 , an educational information site that contains hensachi rankings foralmost all high schools in Japan. The site notes that the hensachi information is provided
6

https://resemom.jp/feature/hensachi/

9

by major cram schools. Out of the above 26,900 children, 26,625 are enrolled in higher
educational institutions. There are 19 who are employed and 256 who are other/unknown.
Since the hensachi score is not available for technical colleges, specialized training colleges,
and special needs schools, we can assign the high school hensachi score to 24,287 children’shigh schools. Figure 1 shows the histograms of the hensachi scores, divided into urban areas
and rural areas. The hensachi scores of the high schools the children attend are distributed
between 33 and 86. The mean and standard deviation are 56.5 and 9.9 in urban areas and52.9 and 9.3 in rural areas. The distributions are skewed to the right, with the degree being
greater in rural areas (Skewness is 0.12 for urban and 0.39 for rural).
Several studies have examined the reliability of the hensachi scores as an indicator ofschool selectivity. Abe (2002) used school-level panel data and found a cross-sectional relationship between university entrance exam hensachi scores and labor market performance.
Kondo (2014) found a strong correlation between the relationship between hensachi scoreat entrance to private girls’ junior high schools in Tokyo and Kanagawa prefectures anduniversity admission performance.

4 Empirical model
To identify the causal effect of the number of siblings on the quality of children, we consider
the following equation (1), which states:

yi = β0 + β1 size i + Xi β2 + Zi β3 + εi ,(1)where the variable yi on the left-hand side is the quality of the target child i, as measured
by the hensachi score of the high school they attend. The right-hand side variable size i isthe number of their siblings in the family. We focus on the coeﬀicient β1 , which reveals thetrade-off between quantity and quality. Xi is a vector of child characteristics, including thechild’s sex, the month of birth (representing birth in July) and birth order (if applicable). We
10

0

.01

Density
.02
.03

.04

.05

Figure 1: The Distributions of Hensachi Score. 9,694 children in urban areas and 17,203
children in rural areas whose hensachi scores for the high school they attend are known.

20

40

60
Hensachi Score
Urban Area

80

100

Rural Area.
add the child i’s birth weight and gestational week to control for future adverse outcomesof premature babies (Black et al. (2007)). Zi contains variables for parental attributes,
including age and age squared of mother and father, university degree of mother and father,years living with grandparents, city size of residence, employment status of mothers andfathers before childbirth. In addition, to control for maternal health and maternal healthrelated behaviors and exposures, we add maternal smoking. Bhalotra and Clarke (2020)states that if unobserved maternal health is positively selected for twin births and positively
correlated with children’s educational output, then the estimate of β1 with twins as IV tends
to have an upward bias (toward no trade-off). They argue that addressing the omission ofvariables related to maternal health can adjust for the upward bias that IV estimates have.
11

The coeﬀicients β1 estimated by ordinary least squares (OLS) suggest correlation, notcausation, as the number of siblings is likely endogenous. If unobserved aspects (e.g., unemployment or illness) result in fewer available resources, parents may seek to have larger
families and invest less in their children. When adverse shocks occur, they may try to pursue
economies of scale or receive child benefits by increasing family size and reducing spending
on children. In addition, the high preference for full-time homemakers among women may
lead parents to choose larger families and have more time to focus on their children’s education. There is also the possibility of reverse causality. The child’s outcome may influence
whether the parents will try to have one more child. For example, a newborn child’s low orhigh quality may influence parents to have additional children, either by complementing it
or by being satisfied that it is adequate. Black et al. (2005) state that the effect of the lastchild follows the rule of optimal stopping.
Therefore, following Rosenzweig and Wolpin (1980) and Black et al. (2005), we use twinbirths as an instrumental variable for the number of siblings. If twin births are determined
independently of parental characteristics, then we can use the births of twins as an instrumental variable for sibling size to remove bias arising from omitted variables and simultaneity.
Then, the first stage of the two-stage least squares (2SLS) method is given as follows:

size i = α0 + α1 twin i + Xi α2 + Zi α3 + νi ,(2)

where twin i is a binary variable that takes the value one if there are twins at the n-th birth(n = 2, 3) and 0 if there are not. In order for this method of using twins as the instrumental
variable to make sense, there must be a correlation between twin births and the number ofsiblings. In other words, the effect of twin births on the number of siblings, i.e., the firststage regression of the 2SLS model, must have explanatory power. As Table 2 shows, thebirth of twins at the second birth increases the number of siblings the firstborn children has
by about 0.90 in the full sample. For the sample of children living in the urban area, theeffect of twins is 0.92, which is higher than 0.87 in the rural area. The effect of twins at the12third birth shows almost the same pattern. Looking at the F statistics corresponding to thenull hypothesis that the coeﬀicient of the instrumental variable in the first-stage regression
is zero, they ranged from 24.8 to 174.4, well above the Staiger et al. (1997) guideline of
10, suggesting that there is no concern that the twin instrumental variable is weak. Thissuggests that there is no concern about the weak instrumental variable for twins.
Sibling size
Full Sample
Urban
(1)
(2)

Rural
(3)

(a) First-born Children with One or More Siblings
Twin at Second Birth0.898***
0.923***(0.0484)(0.0753)
Cragg-Donald Wald F statistic
174.389
99.19
Observations
8,565
3,461
R-squared
0.080
0.088

0.871***(0.0624)78.6255,104
0.076

VARIABLES

(4)

(5)

(6)

(b) First- and Second-born Children with Two or More Siblings
Twin at Third Birth0.892***
0.909*** 0.876***(0.0491)(0.0389) (0.0732)
First Born
-0.0549***-0.0551 -0.0512**(0.0196)(0.0366) (0.0224)
Cragg-Donald Wald F statistic
70.98
24.77645.092
Observations
4,630
1,701
2,929
R-squared
0.055
0.065
0.058
Table 2: First Stage Estimates of Sibling Size. Significance levels: *** p < 0.01, ** p < 0.05,* p < 0.1. Robust standard errors are reported in parentheses. The F-statistic corresponds
to the null hypothesis that the coeﬀicient on the instrument (twin births) is zero. The
sample consisted of non-twin children. We include child characteristics (sex, birth month),parental attributes (age and age squared of mother and father, university degree of motherand father, years living with grandparents, and city size of residence, employment status
of mothers and fathers before childbirth), maternal health (child’s birth weight, gestational
week, and maternal smoking), but we omit them in this Table.
Considering that the severity of competition in high school choice differs between metropolitan prefectures and other rural prefectures, the causal effect of family size will differ withthe household’s region of residence. Therefore, we conducted separate regressions for the13

two metropolitan areas (Tokyo and Saitama, Chiba, Kanagawa, Kyoto, Osaka, Hyogo) andthe other 40 prefectures.

4.1

Sample Selection

As noted in the Data section, there are 24,287 children attending high schools for which
hensachi information is available in 2017. We use the following two samples for our analysis.
The first one consists of firstborn children with at least one sibling and is analyzed withthe hensachi score of the first child as an output variable and twins at the second birth as
the instrumental variable. If we restrict to children with all the necessary information foranalysis, there remain 3,461 children in urban areas and 5,104 children in rural areas. The
second sample consists of the first- and second-born children with at least two siblings. Using
this sample, we analyze the hensachi scores of the first and second children with twins at
the third birth as the instrumental variable. In this second sample, there are 1,701 children
available in urban areas and 2,929 in rural areas.
Table 3 shows the descriptive statistics of the sample used in the analysis. The left twocolumns show the mean and standard deviation for the first-born children in families with
two or more children, and the right two columns show those of first and second children with
two or more siblings.
From these descriptive statistics, we note three things. First, the hensachi score for thehigh school attended by the first children with one or more siblings is statistically significantly
higher in urban areas than in rural areas (57.03 vs. 53.53 (Panel (a)). The same is true forfirst and second children with two or more siblings (55.03 vs. 52.05 (Panel (b)), which meansthat the hensachi score is higher with fewer siblings and in urban living. Second, the size ofsiblings for the first child with one or more siblings is 1.29 in urban areas and 1.35 in rural
areas, a statistically significant difference (Panel (a)), whereas that for the first and second
child with two or more siblings is 2.16 in urban areas and 2.18 in rural areas, which is not asignificant difference (Panel (b)). Third, compared to the rural areas, mothers and fathers
14are older and more educated in the urban areas. In addition, in rural areas, children livewith their grandparents for longer years, and more mothers work before the birth of theirchildren.

5

Main Results

We first present the correlation between the hensachi score of the high school attended andthe number of siblings in the raw data. Figure 2 plots the average hensachi score of thehigh school children attended against the number of siblings, separately for the sample offirstborn children with one or more siblings (Panel (a)) and the sample of first- and secondborn children with two or more siblings (Panel (b)). In both panels, all curves show adownward relationship. In other words, the more siblings a child has, the lower his or her
hensachi scores are in the high school he or she attends. In addition, the urban graph (blueline) is higher than the rural graph (red line), indicating that children living in urban areas
attend high schools with higher hensachi scores than children living in rural areas.
Table 4 is our main results showing the results for the full sample and for urban andrural samples separately. Panel (a) shows the results for the hensachi score of high school
attended by the first-born children with at least one sibling, while Panel (b) shows the results
for the first- and second-born children with at least two siblings. These estimations include
all the control variables listed in Section 4, but for space considerations, coeﬀicients otherthan the number of siblings are not shown (in Panel (b), a dummy variable for birth orderis shown.)
Similar to the pattern observed in Figure 2, the OLS estimates consistently show asignificant negative correlation between sibling size and the quality of the child’s high school,
regardless of regional separation or whether we include second-born children. In sum, the
OLS coeﬀicients suggest that, holding everything else constant, an additional sibling reduces
the hensachi score of the high school children attend by about 0.71 to 1.28 points. However,15

Variable

Mean

Urban
Std. dev.

(a) First-born Children with One or More Siblings
Hensachi Score
57.03
Sibling Size
1.29
Twin at Second Birth
0.01
Mother’s Age
44.84
Father’s Age
46.88
University Degree (Mother and Father)
0.18
University Degree (Only Mother)
0.04
University Degree (Only Father)
0.32
Living with Grandparents (Year)
1.96
Gestational Period (Week)
39.6
Birth Weight (kg)3.02
Mother’s Smoking (Amount Per Day)
1.03
Ordinance-designated Cities
0.41
Other Cities
0.56
Employment Before Birth (Mother)
0.73
Employment Before Birth (Father)
0.98
Annual Household Income Before Birth+ 648.7
Observations
3,461

9.65
0.56
0.099
3.46
4.56
0.38
0.20
0.47
4.22
1.38
0.39
3.58
0.49
0.50
0.44
0.14
418.08(b) First- and Second-born Children with Two or More Siblings
Hensachi Score
55.03
9.49
Sibling Size
2.16
0.49
First Born
0.50
0.50
Twin at Third Birth
0.004
0.064
Mother’s Age
44.83
3.56
Father’s Age
46.9
4.53
University Degree (Mother and Father)
0.16
0.36
University Degree (Only Mother)
0.04
0.20
University Degree (Only Father)
0.29
0.45
Living with Grandparents (Year)
2.17
4.38
Gestational Period (Week)
39.5
1.31
Birth Weight (kg)
3.08
0.38
Mother’s Smoking (Amount Per Day)
1.32
4.14
Ordinance-designated Cities
0.39
0.49
Other Cities
0.57
0.50
Employment Before Birth (Mother)
0.51
0.50
Employment Before Birth (Father)
0.98
0.15
Annual Household Income Before Birth+ 602.91 367.66
Observations
1,701

Mean

Rural
Std. dev.

53.53
1.35
0.007
44.1
45.91
0.11
0.04
0.24
3.69
39.57
3.01
1.08
0.16
0.72
0.8
0.98
559.715,104

9.31 ***
0.60 ***
0.084
3.61 ***
4.58 ***
0.31 ***
0.19
0.43 ***
5.48 ***
1.43
0.39
3.62
0.36 ***
0.45 ***
0.40 ***
0.14
254.2 ***

52.05
2.18
0.51
0.005
44.19
46.17
0.11
0.03
0.23
4.09
39.45
3.05
1.12
0.14
0.73
0.61
0.98
536.1
2,929

9.08 ***
0.51
0.50
0.071
3.63 ***
4.61 ***
0.31 ***
0.17 *
0.42 ***
5.69 ***
1.47
0.40 **
3.81 *
0.35 ***
0.44 ***
0.49 ***
0.12
279.51 ***Table 3: Descriptive Statistics for the Samples We Use. Significance levels for t tests on
the equality of means between urban and rural: *** p < 0.01, ** p < 0.05, * p < 0.1. +:Observations for Annual Household Income Before Birth is 3,298 for urban and 4,808 forrural in Panel (a) and 1,641 for urban and 2,763 for rural in Panel (b).

16Hensachi Score
50
40

40

45

45

Hensachi Score
50

55

55

60

(b) 1st- and 2nd-born Children with 2+ Siblings

60(a) 1st-born Children with 1+ Siblings

1

2

3
4
Number of Siblings

Urban Area

5

2

Rural Area

3
4
Number of Siblings
Urban Area

All

5
Rural Area

All

Figure 2: Hensachi Score across the Sibling Size. This figure plots the average hensachiscore of high school students against the number of siblings, divided into urban and rural
areas, and pooled for both regions. Panel (a) uses first-born children with one or moresiblings in urban areas (3,461 children) and in rural area (5,104) and Panel (b) uses firstand second-born children with two or more siblings in urban area (1,701) and in rural area
(2,929). Bars represent 95% confidence intervals. Number of siblings 5 indicates more thanor equal to five siblings.

17

these results do not take into account the endogeneity between the number of siblings andthe quality of children, and thus this shows only correlation, not causation.
When we conduct 2SLS estimations using twin instruments with the full sample of children, the coeﬀicient on the number of siblings is negative but not statistically significant(columns (2) in Panel (a) and column (8) in Panel (b)). In Panel (b), we can observe theeffect of birth order and find that the eldest children enter high school with a hensachi score
1.3 to 1.4 points higher than the second children.
We find that when the sample was pooled and analyzed, no trade-off was observed between quantity and quality for Japanese children, even when endogeneity is taken into account. Black et al. (2005), Angrist et al. (2010), and Doepke (2015) state that the trade-off
between quality and quantity is absent or small if it exists, due to the prevalence of inexpensive and universal public education in developed countries. Japan has a school attendance
obligation. The obligation to attend school places an obligation on parents to have their children receive six years of elementary school and three years of junior high school education.
In such circumstances, the school attendance rate for elementary and junior high school is100% and the tuition fee is free. In addition, the school environment in Japan is generally
uniform and better than in other countries. The OECD’s 2013 Teaching and Learning International Survey (TALIS) asked about discipline and learning atmosphere in elementary andjunior high schools, and in every question item, Japanese elementary and junior high schools
are more relaxed than in participating countries. The results of the survey suggest that thefor example, 8.1% of teachers in Japanese junior high schools said that “a lot of time is lost
because students interfere in class,” compared to the average of 27.1% in the participating
countries. Therefore, the result is that Japan also has no developed country-type trade-offs.
Next, we examine the results of splitting the sample into urban and rural areas, whichyields statistically significant negative coeﬀicients of sibling size. In columns (4) of Panel(a), we have the coeﬀicient of sibling size turns to be negative and statistically significant for
the first-born child with one or more siblings. This means that a one-child increase in the18number of siblings is associated with decreases in the high school hensachi score by 3.1 points,
but the coeﬀicient on sibling size is still not significant in the case of first- and second-born
children with two or more siblings (Panel (b)). In the rural area, the coeﬀicient of sibling
size is not significant for first-born children with one more siblings but becomes negative andsignificant in the case of first- and second-born children with two or more siblings. That is,a one-child increase in the number of siblings is associated with decreases in the high school
hensachi score by 3.3 points.
These estimates implicate the most important claim of this study that the tradeoff between the number of siblings and the quality of the high schools attended by their children
emerged only when urban and rural areas were analyzed separately. We interpret that thisis due to the difference between urban and rural areas in the behavior of parents who send
their children to high schools with high hensachi scores in order to take advantage of the
fierce competition for the future college entrance exams. To explore the difference in parental
behaviors, we need to identify potential mechanisms by which urban and rural households
reallocate family resources in response to exogenous increases in children in the backgroundof the tradeoff between the number of siblings and high school hensachi score.

6 Mechanisms
In this section, we explores how exogenous births due to twins affect spending on children,
time allocation, and mothers’ working patterns in urban and rural areas. These input variables in children’s educational attainment are more closely tied to parental decision-making
when the number of children increases, making them a more robust test than using educational attainment results when assessing the urban-rural difference in the effect of family
size (Cáceres-Delpiano (2006)).

19

VARIABLES

Full Sample
OLS
2SLS
(1)
(2)

Urban
OLS
2SLS
(3)
(4)

(a) First-born Children with One or More Siblings
Sibling Size
-0.936***-1.378-1.284*** -3.144**(0.155)(1.158)(0.256)(1.573)Observations
8,565
8,565
3,461
3,461
R-squared
0.245
0.244
0.250
0.239
(7)

(8)

(9)

(10)

Rural
OLS
(5)

2SLS
(6)

-0.711***(0.196)
5,104
0.202

0.530
(1.693)
5,104
0.196

(11)

(12)

(b) First-born and Second-born Children with Two or More Siblings
Sibling Size
-0.961***-2.773-1.131*** -1.473 -0.827*** -3.335*(0.228)(1.856)(0.372)(4.014)(0.289)(1.802)First Born
1.430*** 1.329*** 1.333*** 1.315** 1.496*** 1.359***(0.299)(0.319)(0.501)(0.544)(0.371)(0.389)Observations
4,630
4,630
1,701
1,701
2,929
2,929
R-squared
0.227
0.218
0.240
0.240
0.197
0.178
Table 4: Main Results: Sibling Size Effects on Hensachi Score. Significance levels: ***p < 0.01, ** p < 0.05, * p < 0.1. We use OLS and 2SLS estimations with high school
hensachi score as the dependent variable. We include child characteristics (sex, birth month),parental attributes (age and age squared of mother and father, university degree of motherand father, years living with grandparents, and city size of residence, prefecture dummies,
employment status of mothers and fathers before childbirth), maternal health (child’s birthweight, gestational week, and maternal smoking), but we omit them in this Table. Robust
standard errors are reported in parentheses.

20

6.1

Parental Investment on Children in Terms of Financial and
Time

6.1.1

Expenditure on Children

The first group of input variables come from information on financial expenditures on children. The LSN2001 survey forms explicitly ask parents to answer the amount of money
spent per month per surveyed child.
We would like to discuss by using the following three categories of expenditures: total
expenditures (for example, school, extracurricular activities, cram school, childcare, medicalcare, food, clothing, and so on)7 , expenditure on extracurricular activities (piano lessons,swimming school, and so on), and cram school expenses. Then, for each of these three
expenditure categories, we take the average for preschool (ages -5), elementary school (ages7-12), and junior high school (ages 13-15). Note that the question about cram school expense
has been asked since the seventh survey when the children entered elementary school.
Including these expenditures on the left-hand side of the equation (1), we perform thesame 2SLS estimation with twin IV. The results are shown in Table 5. First, we findcontrasts between urban and rural areas in the response of households to spending on cramschools when the number of siblings increases. The results of the 2SLS estimation showthat in urban areas, the coeﬀicient of the number of siblings on cram school expenditures is
not statistically significant. In rural areas, it is negative and significant. Rural households
reduce their cram school expenditures (per surveyed child) by 3,500 yen per month for juniorhigh school students and 2,900 yen per month for elementary school students by adding one
sibling. Descriptive statistics for these expenditure variables in Table 8 show that the average
cost of cram school is higher in urban areas and lower in rural areas. Urban households
spend about twice as much per child on cram school during the elementary school years as
rural households. In junior high school, the figure is about 1.5 times higher. Thus, urban
7

The items exemplified in the question on total expenditures vary by age.

21

households spend high amounts on cram school and do not try to reduce their spending when
the number of children increases exogenously. Rural households spend only a small amounton cram school and reduce their spending when they have more children exogenously.
Second, commonly in urban and rural areas, when the sibling size increases from one totwo (Panel (a)), we find negative and significant coeﬀicients for the sibling size in extracurricular activity expenditures (such as piano lessons and swimming clubs) in the preschooland elementary school years. When the number of children increases by one, both urban
and rural parents decrease their spending on extracurricular activities by 1,600 yen to 4,200
yen. Table 8 of the descriptive statistics shows that for extracurricular activities, there is nolarge difference between urban and rural areas, ranging from 7,700 yen to 10,700 yen in theelementary school period and from 5,700 yen to 6,500 yen in the junior high school periods.
Note we do not obtain significant coeﬀicients for the total expenditures per child surveyed
and, although not shown here, for the expenditures spent on school (educational materials,
school lunches, and tuition).
6.1.2

Parental Time Investment and Child’s Study Time.

The next group of variables relates to time inputs to a child’s educational attainment. In
fact, Guryan et al. (2008) shows, using data from 14 industrialized countries, that mothers
have spent more time on child care in recent years. It is suggested that the time spent onchildren have become increasingly important.
In what follows, we use information from the following three questions in the LSN2001.
The first variable is the time parents spend with their children. The LSN 2001 asks
how much time mothers and fathers spend together with their surveyed children, either bycaring for them or eating with them on weekdays and weekends, intermittently up to andincluding the fourth grade. LSN2001 instructed respondents to omit time when the children
were sleeping. We convert the time spent with the child into hours per day.
The second variable is the frequency of talks with parents. The survey asks children

22UrbanPreschool
E.S.
VARIABLES
(1)
(2)

Rural
E.S.
(5)

J.H.S.
(6)-2.263(2.799)-2.214***(0.827)1.564(1.864)10.15(9.391)
2.747(3.838)-3.454*(1.784)

(7)
(8)
(9)
(10)
(11)
(b) First-born and Second-born Children with Two or More Siblings
Total-0.505
3.604
4.888
25.15
-0.334(10.12)(6.925) (22.95)(30.35)(3.717)
Lesson7.530
1.864-2.560 -3.010***1.825(4.991)(2.157) (1.667)(0.927)(1.737)
Cram
0.453
6.375
-2.920***(3.360) (8.177)(0.868)(12)

J.H.S.
(3)

Preschool(4)(a) First-born Children with One or More Siblings
Total
0.622
-1.179-2.094-1.630(5.196)(4.004) (9.969)(5.494)
Lesson-4.177*** -1.599** -1.307 -2.248***(1.521)(0.724) (1.373)(0.860)Cram-1.669-2.259(1.785) (3.182)-1.943(7.165)
6.216(4.716)-3.691(2.546)

Table 5: Family Size Effects on Expenditure on Children (a thousand yen). We use 2SLS
estimations with expenditure on children (total expenditures (school expenses, lessons, childcare, medical expenses, food, clothing, etc.), the expenses for lessons and sports clubs, andthe expenses for cram schools as the dependent variable. Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1
whether they talk with their mothers and fathers about five different topics during theirjunior high school period, ranging from ”not at all” to ”often” on a four-point scale: school,
friends, future/career path, studies/achievements, and the social issues. The variables aretransformed to take values from 1 to 4 so that the more frequent the talks, the larger thevalue, and the average of the five topics is taken separately for mothers and fathers.
The third and final variable is the daily study time outside of school, which has been asked
since the beginning of elementary school. During the elementary school years, homework andcram school time are answered by parents, while for junior high school students, time spent
studying at home or at cram school, including preparation and review for regular classes andstudying for exams, is answered by the children themselves on weekdays and weekends. We
convert children’s study time into hours per day for each elementary and junior high school
23

period.
Similar to the earlier results on spending on children, there is a clear difference between
urban and rural areas in the response of time inputs to children’s educational attainment
when the number of children increases due to twin births. Table 6 shows that in rural areas,
the first children with one or more siblings spend less time with their fathers until children’s
fourth grade and talk less frequently with their mothers and fathers in junior high school
age when adding one sibling (column (2)). The first and second children with two or moresiblings spend less time studying during elementary school (0.177 hours = 11 minutes perday, column (4)). In urban areas, there are no negative and significant coeﬀicients; instead,households increase these inputs when there are more children exogenously. Study time injunior high school increases by 24 minutes per day (= 0.4 × 60) for the first child with one
or more siblings in urban areas, and talk with the mother and father increases for the firstand second children with two or more siblings. Note that the descriptive statistics in Table 8
do not show as large a difference in spending time with children and studying time between
urban and rural areas as in the previous expenditure on children.

6.2

Mother’s Working.

An increase in the number of exogenous siblings may lead to changes in mothers’ employment
status. A priori, it is ambiguous what effect an increase in the number of children has on
mothers’ labor force participation and full-time employment when such an increase harms
children’s scholarly output, and parents are concerned about this. This is because mothers
may have more money to spend or invest in their children by working (financial incentives),or they may be able to spend more time with their children by working fewer hours (timeincentives).
In Table 7, we report the results of the impact of an increase in the number of siblings
on mothers’ labor force participation, full-time employment, working hours (both mothers
and fathers), and mothers’ annual income as the dependent variables on the left-hand side of24

VARIABLES
Time with Mother(1)(2)(a) First-born Children
with One orMore Siblings
Urban
Rural

-0.146(0.184)
Time with Father-0.124(0.219)
Talk with Mother
0.117(0.108)
Talk with Father
0.120(0.126)
Study Time (E.S.)-0.004(0.104)
Study Time (J.H.S.) 0.397*(0.213)-0.0927(0.162)-0.459**(0.228)-0.225**(0.106)-0.336***(0.120)-0.122(0.0760)-0.195(0.161)(3)(4)(b) First- and Second-bornChildren with Two orMore Siblings
Urban
Rural
-0.0960(0.359)-0.0217(0.376)
0.635***(0.132)0.404**(0.182)-0.179(0.184)0.371(0.397)-0.281(0.284)-0.314(0.333)0.0481(0.148)0.0118(0.187)-0.177**(0.0873)-0.108(0.206)

Table 6: Family Size Effects on Parental Time Investment and Child’s Study Time. We use
2SLS estimations with time with mother and father (hours per day), talk with mother andfather (“not at all (1)” to “often (4)”, children’s study time (hours per day) as the dependent
variable. Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1
equation (1). Note that we average each of the variables for employment over the preschool,elementary school, and junior high school years.
Differences between urban and rural areas are also evident concerning mothers’ employment. Statistically significant coeﬀicients on the number of siblings are obtained mainly inthe estimations with full-time employment and the mother’s annual income as dependent
variables. And it is concerning the magnitude of the coeﬀicient that we find differences
between urban and rural areas. On the one hand, in rural areas, the percentage of mothers
working full-time declines by 12% to 24% points after one additional child is born. On theother hand, in urban areas, the percentage of mothers working full-time declines by 9% to
13% points drop, and it is not statistically significant for mothers of children with one ormore siblings (columns (1) to (3)). The small or insignificant absolute value of the coefficients for urban areas may be because more urban mothers in the LSN2001 sample are25

non-working or working part-time, if at all, than rural mothers. More mothers in urban
areas are likely to have a higher propensity to be housewives than those in rural areas. In
fact, in Table 8, the labor force participation rate and the percentage of mothers working
full-time are about ten percentage points higher in rural areas than in urban areas, withmothers working about 6 hours longer per week and earning about 250,000 more per year.
In addition, for urban households with more children (column (7) in Panel (B)), we find adivision of labor in which mothers work fewer hours and fathers work longer hours when
their children are in preschool. We conducted similar estimations for fathers but obtained
no significant results other than fathers’ working hours significantly getting longer.
Urban Area
Preschool
E.S.
J.H.S.
(1)(2)(3)(a) First-born Children with One or More Siblings
LFP-0.0551-0.0234
0.0313(0.0642)(0.0663)(0.0743)
Fulltime
0.00439-0.02310.0364(0.0583)(0.0552)(0.0672)
Work Hour (Mother)-2.686-1.347(1.652)(2.628)0.692
2.055Work Hour (Father)(2.092)(2.414)
Annual Salary (Mother)-12.83-26.39-17.62(21.69)(24.85)(26.65)Preschool(4)

Rural Area
E.S.
(5)

-0.0939(0.0663)-0.136***(0.0468)-3.687(2.381)1.014(1.808)-39.74***(12.91)

0.0968(0.0625)-0.175***(0.0433)-4.311(3.523)2.004(2.251)-42.33***(14.18)0.159***(0.0432)-0.122**(0.0546)

(11)

(12)

0.0863(0.111)-0.162***(0.0562)-3.947(3.928)-1.957(2.511)-29.66(28.43)-0.116(0.103)-0.238***(0.0640)

(7)
(8)
(9)
(10)
(b) First-born and Second-born Children with Two or More Siblings
LFP-0.0644-0.02810.0420-0.0552(0.108)(0.159)(0.162)(0.0971)
Fulltime-0.0119-0.0915** -0.126*** -0.120**(0.0591)(0.0406)(0.0383)(0.0598)
Work Hour (Mother)-4.629**-1.945-3.167(2.202)(2.465)(2.979)Work Hour (Father)8.028*
7.067
2.326(4.835)(5.617)(2.664)
Annual Salary (Mother)-21.21-50.88*-60.19**-28.34*(15.95)(26.48)(27.13)(15.16)J.H.S.
(6)-30.53*(16.32)-51.13(32.79)

Table 7: (a) Family Size Effects on Mother’s Working (Labor Market Participation). Robust
standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1

26

Finally, we summarize these results in this section and discuss how households respond to
an exogenous increase in the number of children due to twin births in the background of its
adverse effect on hensachi scores. The most apparent implication is that there are differencesin the responses in reallocating household resources between urban and rural parents when
they face a trade-off between the quantity and quality of their children. As the number ofchildren increases in urban areas, substitution occurs in the inputs to children’s educational
production, from fewer extracurricular activities such as piano and swimming to more study
time outside school and more conversations with parents. In the rural areas, however, as thenumber of children increases, parents reduce all of the inputs in their children’s educational
production: spending on cram school, study time outside of school, and conversations withparents, in addition to extracurricular activities as piano and swimming.
Our interpretation is that as the number of children increases in urban areas, parents
and children try to mitigate the negative impact on hensachi by increasing study time andparental conversational input. Despite these attempts at mitigation, urban households stillshow a detrimental effect on the hensachi score when the number of siblings increased fromtwo to three. Rural parents and children instead reinforce the adverse effects of additionalchildbearing by reducing their input into their children’s educational production, which may
have led to the observed negative effect on the hensachi score in the rural households when
the number of siblings increased three to four. The above discussion confirms our claim thatthe incentives to send children to higher-quality high schools are more substantial in urban
areas than in rural areas. This creates a trade-off between the quantity and quality of thechildren they attend, even in developed countries.

7

Robustness Checks

This section confirms the robustness of this study’s claim that concerning Japanese children,the trade-off between the number of siblings and the quality of the high school their chil-

27

S.D.

Obs

Rural
Mean
S.D.

(a) First-born Children with One or More Siblings(I) Expenditure on Children
Total (E.S.) +3,459 41.29
Total (J.H.S.) +3,451 78.76
Cram (E.S.) +3,398 8.52
Cram (J.H.S.) +3,456 27.44
Lesson (E.S.) +3,454 10.72
Lesson (J.H.S.) +3,459 6.48

22.4
63.88
11.83
28.95
7.19
16.50

5,099
5,095
4,887
5,102
5,102
5,104

34.46
61.25
4.34
18.25
8.44
5.71

15.89 ***
44.13 ***
6.73 ***
22.81 ***
6.35 ***
12.96 **(II) Parental Time Investment, Child’s Study TimeTime with Mother++
3,460 5.71
Time with Father++
3,457 3.14
Talk (Mother)
3,439 3.03
Talk (Father)
3,308 2.51
Study Time (E.S.)++3,461 1.10
Study Time (J.H.S.)++3,457 1.83

0.90
1.07
0.53
0.64
0.60
0.92

5,104
5,092
5,070
4,850
5,104
5,103

5.58
3.42
3.00
2.50
1.02
1.76

0.91 ***
1.14 ***
0.53 ***
0.63
0.46 ***
0.87 ***(III) Mother’s Working
LFP (E.S.)
LFP (J.H.S.)
Fulltime (E.S.)
Fulltime (J.H.S.)
Work Hour (Mother)++Work Hour (Father)++
Annual Salary (Mother, E.S.)+++
Annual Salary (Mother, J.H.S.)+++

0.4
0.4
0.31
0.35
15.4
12.67
159.3
191.08

5,104
5,104
5,104
5,104
5,095
4,985
5,081
5,079

0.65
0.81
0.22
0.27
21.06
55.38
109.87146.730.39 ***
0.35 ***
0.38 ***
0.42 ***
16.66 ***
12.11 ***
144.5 ***
159 ***(b) First- and Second-born Children with Two or More Siblings(I) Expenditure on Children
Total (E.S.) +1,701 36.95
20.64
Total (J.H.S.) +1,697 72.05
67.68
Cram (E.S.) +1,655 6.87
10.79
Cram (J.H.S.) +1,700 24.02
27.34
Lesson (E.S.) +1,694 9.28
6.13
Lesson (J.H.S.) +1,700 6.1
20.25

2,927
2,926
2,783
2,928
2,927
2,929

32.47
56.46
3.58
14.91
7.76
5.52

17.11 ***
47.03 ***
6.2 ***
16.85 ***
5.93 ***
10.85(II) Parental Time Investment, Child’s Study TimeTime with Mother++
1,701 5.60
Time with Father++
1,697 3.09
Talk (Mother)
1,688 2.96
Talk (Father)
1,623 2.41
Study Time (E.S.)++
1,701 0.98
Study Time (J.H.S.)++
1,700 1.65

0.95
1.10
0.53
0.64
0.54
0.93

2,929
2,926
2,904
2,806
2,929
2,929

5.47
3.38
2.94
2.43
0.96
1.62

9.97 ***
1.19 ***
0.54
0.63
0.43
0.85

(III) Mother’s Working
LFP (E.S.)
LFP (J.H.S.)
Fulltime (E.S.)
Fulltime (J.H.S.)
Work Hour (Mother)++Work Hour (Father)++
Annual Salary (Mother, E.S.)+++
Annual Salary (Mother, J.H.S.)+++

0.4
0.4
0.31
0.36
15.53
12.47
148.6
174.5

2,929
2,929
2,929
2,929
2,926
2,886
2,916
2,919

0.64
0.81
0.22
0.27
21.11
55.44
109.24147.970.39 ***
0.35 ***
0.38 ***
0.42 ***
16.74 ***
12.36 ***
144.57 ***163.23 ***

Obs

3,461
3,459
3,461
3,459
3,454
3,401
3,442
3,438

1,701
1,700
1,701
1,700
1,696
1,669
1,693
1,692

Urban
Mean

0.48
0.73
0.13
0.17
14.29
57.4
84.94
125.3

0.48
0.71
0.13
0.17
14.48
57.6
82.58
123.88

Table 8: Descriptive Statistics for Expenditure on Children, Parental Time Investment,Child’s Study Time and Mother’s Working. +: a thousand yen. ++: hours per day. +++:
10 thousand yen. Significance levels for t tests on the equality of means between urban andrural: *** p < 0.01, ** p < 0.05, * p < 0.1.

28

dren attend is driven by the motivation to provide children with a higher quality secondary
education to prepare children for fierce competition in university admissions.

7.1

Socioeconomic Status: Gender and Parental Education

We have already observed that this motivation is stronger among urban parents, but it may
be related to other socioeconomic attributes, such as child gender and parental educationlevel. Given a wage gap between men and women, and the male-female ratio of students
enrolled in universities is skewed toward boys (56.6% for boys and 50.7% for girls according
to the 2020 Basic School Survey), parents of boys may be more likely to put their children
through the exam competition than parents of girls. In addition, if the parents themselves
are highly educated, their children may be more likely to commit to an entrance exam competition because the parents have the know-how, and the children use the parents as rolemodels. Regardless of the number of children they have, only high-income households might
be financially able to afford to provide their children with a higher-quality secondary education to prepare them for the fierce competition of college entrance exams. Nevertheless, weinterpret parental education as a proxy variable for household income because of endogeneity
issues in household income.
The results of the 2SLS estimation testing these robustness expectations are presented
in Table 9. First, the coeﬀicient on family size is negative and significant, especially when
the children surveyed are boys (Panel (a)). The magnitude of the absolute values of thecoeﬀicients is larger than the estimates at baseline in Table 4. In contrast, the coeﬀicientsare insignificant or rather positive and significant for girls (Panel (b)). Second, we divide thesample by whether the mother or the father has a university degree. We find that the family
size variable is negative and statistically significant for households with highly educatedparents (Panel (c)) and insignificant for children with less-educated parents (Panel (d)).
We argue that these results, which show a similar trade-off pattern as in Section 5, suggesting that there is a stronger motivation among parents with boys and parents with higher
29education to provide their children with a higher quality secondary education to preparethem for the fierce competition of university entrance exams. And in those households, thehensachi score is adversely affected when the number of children increases exogenously.

7.2

Alternative Output Variables for Hensachi Score

We argue that the motivation to provide children with a higher quality secondary education
to prepare them for the fierce competition of the university entrance exam creates a trade-off
between the number of siblings and the hensachi score of the high school attended by thechildren in urban areas. We then test the robustness of this claim by using variables otherthan high school deviation as the left-hand side yi of equation (1).
The first output variable is the percentage of high school students who go to Tokyo andKyoto universities. This information is based on the annual report “2017 Complete Recordof All University Entrance Examinations: High School Proficiency” (2017 nendo ban daigaku
nyuushi zenkiroku: koukou no jitsuryoku, in Japanese). If the above claim is correct, parents
would want their children to attend high schools with a high admission rate to prestigious
universities. Table 10 shows the results of the 2SLS estimation. We find that the ratioof the number of students accepted to Tokyo and Kyoto Universities to graduates has anegative and significant impact from an increase in the size of siblings, in the estimations forboth small and large urban households and for large rural households. This strengthens theexistence of a trade-off between the number of children and the hensachi score, as negative
coeﬀicients are obtained for both small and large households in urban areas and only in thecase of large households in rural areas.
Next, we use a dummy variable that takes the value of 1 if the student attends high schooland 0 if the student does not attend high school. If the trade-off motivation is related tothe quality of the high school, having more children exogenously will not affect the aspect ofwhether or not a child simply attends high school. In fact, the estimation with this dummy
variable as the dependent variable does not yield a significant coeﬀicient on the number of30

VARIABLES(a) Boys
Family SizeFirst-born Children
with one ormore Siblings
Urban
Rural
(1)
(2)

First- and Second-bornChildren with Two orMore Siblings
Urban
Rural
(3)
(4)

-4.250**(2.123)

3.171(3.946)

1,723
0.256

2,514
0.169

-7.562*(4.377)0.777(0.740)909
0.175-4.840**(2.167)1.285**(0.540)
1,466
0.174

(5)

(6)

(7)

(8)

-1.703(2.000)-0.626(1.603)

1,738
0.237

2,590
0.202

8.142***(1.915)1.981**(0.851)792
0.104-1.893(2.807)1.645***(0.576)
1,463
0.205

(11)

(12)

-9.018(5.486)0.747(0.785)823
0.019-7.702***(2.680)1.300*(0.756)
1,069
0.035

(15)

(16)

2.759
(3.650)1.811**(0.765)
878
0.044

0.923
(2.184)
1.291***(0.447)
1,860
0.072

First Born
Observations
R-squared(b) Girls
Family SizeFirst Born
Observations
R-squared(9)(10)(c) High Education Parents
Family Size
-5.345**0.145(2.275)(2.349)First Born
Observations
R-squared

1,863
0.072

1,970
0.130

(13)
(14)
(d) Low Education Parents
Family Size
-0.7350.551(1.836)(2.220)First Born
Observations
R-squared

1,598
0.081

3,134
0.061

Table 9: Family Size Effects on Hensachi Score Separately for Socio-Economic Status (Child
Gender and Parental Education). We use 2SLS estimations with high school hensachi scoreas the dependent variable. The coeﬀicients of size are presented. Robust standard errors inparentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

31

siblings in urban areas. Rather, we find that the number of siblings has a positive impact on
the percentage of students who go on to high school for large households in rural areas. Qian
(2009) is one of the few studies to show that the number of children has a positive effect onschool enrollment, citing the economies of scale that the number of children possesses as thereason for this.
Finally, we turn our attention to integrated junior high school and high school, where
there is no entrance examination or a simple examination to advance to high school. Parents
and children choose integrated junior and senior high schools because many of them are
attracted by the advantages of completing six years of classes by the second year of highschool and preparing for college entrance exams in the third year of high school. According
to the ”Survey on Junior High School Choice” conducted by Benesse Education ResearchInstitute in 2007, 63.3% of respondents answered that they chose the junior high schools
because many of them were accepted into famous universities (multiple answers). Oshio
et al. (2009) states that since many students who attend national and private junior highschools go directly to attached high schools, the percentage of students who attend national
and private junior high schools can be used to roughly capture the weight of integrated
junior high and high schools. They state that 7.9% across Japan, and 14.9% and 10.0% in
the Tokyo metropolitan area and Osaka metropolitan area, respectively, with more children
attending integrated junior high and high schools in urban areas. We find that the variable
for integrated junior high and high schools have a negative and significant impact from anincrease in the size of siblings for small households in urban areas. Our finding of trade-offs
in urban areas in enrolling children in combined junior high and high schools is consistent
with the motivation to provide children with a higher quality education at the secondary
level to prepare them for the university entrance examinations.

32

VARIABLES
Entrance Exam to Tokyo/Kyoto U
High School Attendance
Combined J.H.S. and H.S.

First-born Children
with one ormore Siblings
Urban
Rural
(1)
(2)

First- and Second-bornChildren with Two orMore Siblings
Urban
Rural
(3)
(4)

-0.671*** 0.0528-0.521*(0.167)(0.340)(0.291)-0.0226-0.0202 0.000429(0.0297) (0.0277) (0.00582)-0.0898** 0.0505
0.0178(0.0456) (0.0672) (0.132)-0.497**(0.225)0.0117**(0.00520)-0.0473(0.0683)

Table 10: The Effects of size on Other Output Variables. Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

8Conclusion

Using data from the Longitudinal Survey of Newborns in the 21st Century, we examine
the effect of sibship size on high school hensachi score in Japan. We use twin births as an
instrumental variable and find that the causal impacts of family size on the standardized
hensachi score of the high school the child attends is not found in the pooled sample acrossJapan, but emerges only when we divide the sample into urban and rural areas.
We also find that there are differences in the responses in reallocating household resources
between urban and rural parents: As the number of children increases in urban areas, substitution occurs in the inputs to children’s educational production, from fewer extracurricular
activities such as piano and swimming to more study time outside school and more conversations with parents. In the rural areas, however, as the number of children increases,
parents reduce spending on cram school, study time outside of school, and conversations
with parents, in addition to extracurricular activities as piano and swimming. This implies
that parents and children in urban areas try to mitigate the adverse effects on hensachi byincreasing the inputs of study time and conversations with parents, while rural parents andtheir children reinforce the adverse effects by reducing their inputs.
Policy implications from this study include the following. Previous empirical findings33that the number of children does not affect educational attainment in developed countries
have led many to believe that policies aimed at increasing fertility are unlikely to impact
child quality negatively. However, the results of this study prompt a reconsideration of thisidea. The results suggest that policies that encourage couples to have more children, suchas tax breaks or subsidies for families with more children, are likely to hurt the access ofexisting children to a high-quality, high school education. They may be at a disadvantage inthe competition for their university entrance. As urban parents try to reallocate household
resources in anticipation of such disadvantages, government policies should help facilitatesuch reallocation.

34

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37

A

Appendix A: Alternative Instrument for Sibling SizeWe employ another identification strategy, using the mix of sibling gender as the instrumental
variable to estimate the 2SLS (Angrist et al. (2010)). Results in Panel (a) of Table 11 showthat the effect of sibship size is statistically significant when we use the first- and second-born
children with one or more siblings and using the gender combination of the first- and secondborn children as the instrumental variable, with a decrease in the hensachi score of 8.2 points
per additional child in urban areas, but insignificant in rural areas, which is consistent with
our main estimation results using twins as an instrumental variable. In Panel (b), estimations
using the first through third-born children with two or more siblings and using the gender
combination of the first through third-born children as the instrumental variable, did notyield statistically significant coeﬀicients for sibling size. The Hansen J statistic, which tests
for the exogeneity of the instrument, shows that the null hypothesis that the instrument isexogenous is not rejected, but that the Cragg-Donald Wald F statistic is quite small, ranging
from 1.6 to 2.7, so we need to be careful about the exogeneity of the gender combination as an
instrumental variable. In sum, in the analysis using gender combination as an instrumental
variable, our result that family size has a negative effect on the hensachi score of the highschool attended by the child is found in relatively small households with two or more children,

38

VARIABLES

Full Sample
First Stage
2SLS
(1)
(2)

Urban
First Stage
2SLS
(3)
(4)

(a) Gender Combination of First and Second Born Children
Family Size
-2.279-8.236**(2.354)(3.817)First Born
-0.106*** 1.452*** -0.0945***0.803*(0.0115)(0.298)(0.0183)(0.464)
BoyBoy0.0667***0.0834***(0.0127)(0.0193)
GirlGirl
0.0447***0.0248(0.0128)(0.0184)
Cragg-Donald
20.05
10.84
Wald F statistic
Hansen J statistic
0.459
0.000
Chi-sq(1) P-val
0.49810.9903Observations
16,181
16,181
6,627
6,627
R-squared
0.073
0.226
0.073
0.067

Rural
First Stage
2SLS
(5)
(6)

-0.113***(0.0147)
0.0561***(0.0168)
0.0575***(0.0174)
11.02
0.055
0.8148
9,554
0.072

(7)
(8)
(9)
(10)
(11)
(b) Gender Combination of First, Second, and Third Born Children
Family Size
-0.851
1.531(6.317)(8.637)First Born
-0.126*** 2.929*** -0.155***
2.826*-0.114***(0.0265)(0.878)(0.0481)(1.499)(0.0315)
Second Born
-0.118***1.224-0.104***1.707-0.128***(0.0166)(0.789)(0.0276)(1.046)(0.0209)
BoyBoyBoy
0.0458**0.0266
0.0538*(0.0224)(0.0363)(0.0287)
GirlGirlGirl
0.02780.06710.0126(0.0271)(0.0488)(0.0326)
Cragg-Donald
2.65
1.552
1.83
Wald F statistic
Hansen J statistic
1.72
1.294
0.745
Chi-sq(1) P-val
0.18970.2553
0.388
Observations
5,874
5,874
1,996
1,996
3,878
R-squared
0.061
0.224
0.062
0.204
0.063

1.974
(3.010)1.996***(0.398)

9,554
0.164
(12)
-0.738(7.192)
3.176***(0.933)1.068(0.965)

3,878
0.205

Table 11: Alternative Specifications for Family Size Effects on Hensachi Score. We use 2SLS
estimations with high school hensachi score as the dependent variable. Robust standard
errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1

39