TCER Working Paper Series

Wholesome Lunch to the Whole Classroom: Short- and Longer-Term Effects on Early
Teenagers
WeightShiko Maruyama
Sayaka Nakamura
April 2021
Working Paper E-160
https://www.tcer.or.jp/wp/pdf/e160.pdf

TOKYO CENTER FOR ECONOMIC RESEARCH
1-7-10-703 Iidabashi, Chiyoda-ku, Tokyo 102-0072, Japan©2021 by Shiko Maruyama and Sayaka Nakamura.
All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without
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Abstract
Previous studies on the effect of school lunch programs on child obesity have beenhampered by effect heterogeneity, self-selection, and stigma-induced underreporting, having produced mixed findings. Their potential long-lasting effect has
also been debated. We study the body-weight effect of a Japanese school lunch
program, which provides nutritional lunch to all students at participating municipal
junior highs. The lack of means testing and individual participation choice offers
easily interpretable causal estimates. By exploiting almost all school lunch
coverage for elementary school children nationwide, we construct a difference-indifferences (DID) framework to alleviate potential bias due to unobserved
differences across municipalities. Using the 1975 1994 National Nutrition Survey, anationally representative household survey with measured height and weight, we finda regressive benefit of school lunch: while no statistically significant effect isfound for the full sample, we find a significant obesity-reducing effect for the
subsamples of children with low socioeconomic backgrounds. The obesity-reducing
effect remains at least a few years after graduation, implying effect through not
only nutritional contents but also guiding healthy eating behavior. We find little
evidence that school lunch reduces underweight. Propensity score weighting, quantile
DID analysis, and various falsification tests confirm the robustness of ourestimates.

Shiko Maruyama
University of Technology Sydney
Economics Discipline GroupPO Box 123, Broadway, NSW 2007 Australia
shiko.maruyama@uts.edu.au

Sayaka Nakamura
TCER
andNagoya University
School of Economics
Furocho, Chikusa, Nagoya, 464
nakamuras@soec.nagoya-u.ac.jp8601 Japan

Wholesome Lunch to the Whole Classroom: Short- and Longer-Term
Effects on Early Teenagers’ Weight

Shiko Maruyama a,*, Sayaka Nakamura b*

Corresponding authoraEconomics Discipline Group, University of Technology Sydney, PO Box 123, Broadway, NSW

2007 Australia, Email: shiko.maruyama@uts.edu.aubSchool of Economics, Nagoya University, Furocho, Chikusa, Nagoya, 464–8601 Japan, Email:nakamuras@soec.nagoya-u.ac.jp

THIS VERSION: April 20, 2021

JEL codes: H51, I18, I28
Keywords: school lunch; school nutrition programs; difference-in-differences; child obesity;
heterogeneous treatment effect1

Wholesome Lunch to the Whole Classroom: Short- and Longer-Term
Effects on Early Teenagers’ Weight
Abstract (200 words)
Previous studies on the effect of school lunch programs on child obesity have been hampered byeffect heterogeneity, self-selection, and stigma-induced under-reporting, having produced mixed
findings. Their potential long-lasting effect has also been debated. We study the body-weight effectof a Japanese school lunch program, which provides nutritional lunch to all students at participating
municipal junior highs. The lack of means testing and individual participation choice offers easilyinterpretable causal estimates. By exploiting almost all school lunch coverage for elementary school
children nationwide, we construct a difference-in-differences (DID) framework to alleviate potential
bias due to unobserved differences across municipalities. Using the 1975–1994 National Nutrition
Survey, a nationally representative household survey with measured height and weight, we find aregressive benefit of school lunch: while no statistically significant effect is found for the fullsample, we find a significant obesity-reducing effect for the subsamples of children with low
socioeconomic backgrounds. The obesity-reducing effect remains at least a few years after
graduation, implying effect through not only nutritional contents but also guiding healthy eating
behavior. We find little evidence that school lunch reduces underweight. Propensity score weighting,quantile DID analysis, and various falsification tests confirm the robustness of our estimates. (199words)

Highlights


The Japanese school lunch program is non-means-tested and satisfies strict nutritional
requirements.



We study its effect on junior-high students’ weight using a DID framework.

No statistically significant effect is found for the full sample.
2



We find significant obesity-reducing effects for subsamples of low-SES children.

The obesity-reducing effect remains at least a few years after graduation.

3

1. Introduction
Child obesity is a serious public health concern that is rapidly growing around the world (Reilly and
Kelly, 2011; Ng et al., 2014), and school lunch reforms have recently been implemented to combat
this threat. For example, stricter nutritional standards were introduced in the UK and the US during
the 2000s and 2010s, respectively, concurrent with the continuing expansion of eligibility for freeschool lunches in the UK (Evans and Harper, 2009; Baidal and Taveras, 2014). These reforms,
however, are under heated debate due to their high costs and the lack of agreement on theeffectiveness (Tickle, 2014; Baidal and Taveras, 2014). von Hinke Kessler Scholder (2013) finds the
UK school lunch program has had no significant effect. For the US National School Lunch Program(NSLP), some studies find weight-increasing effects (Schanzenbach, 2009; Li and Hooker, 2010;
Millimet et al., 2010; Hernandez et al., 2011; Capogrossi and You, 2017), but others find no
significant effect (Hofferth and Cuntin, 2005; Gleason and Dodd, 2009; Mirtcheva and Powell, 2013)
or find weight-reduction effects (Gundersen et al., 2012). 1
Differences across programs have most likely contributed to the lack of consensus. Yet, mixed
findings, even for a single program, might suggest individual-level effect heterogeneity. In thecontext of school lunch programs, effect heterogeneity is plausible because the causal effect depends
on not only what students eat at school lunch but also what they would have eaten in the absence ofthe program. School lunch will increase the weight of students who eat little without school lunch
and decrease the weight of students who regularly have energy-dense diets such as French fries andsweetened beverages. Smith (2017) finds substantial heterogeneity in the effect of the National1

For the US School Breakfast Program (SBP), some studies find weight-reduction effects (Gleason

and Dodd, 2009; Millimet et al., 2010; Millimet and Tchernis, 2013), while others find no significant
effects (Hofferth and Cuntin, 2005; Sudharsanan et al., 2016).
4

School Lunch Program (NSLP) on the quality of children’s dietary intake, with positive impacts forbelow-median quantiles of nutritional quality distribution and negative effects for upper quantiles.
Another important debate is the long-lasting impact on obesity that school meal programs may
have by altering children’s food preferences and eating habits. The nutrition education andencouragement of good eating habits are the stated goal of school lunch programs in many countries,
including Italy, Sweden, and Finland (Andersen et al., 2017), Japan (NIEPR, 2013), and South Korea(Jo, 2014). A long-lasting effect, if it exists, that could drastically enhance the cost-effectiveness of aschool meal program, and hence it is of policy interest. However, studies on the long-term effect ofschool meals on weight are scarce and their findings are mixed: Peterson (2014) finds a significant,positive association between NSLP participation and adulthood obesity, though Hinrichs (2010)
finds no significant effect of NSLP on adulthood weight.
In this paper, we study the body-weight effect of a Japanese school lunch program for students
at municipal junior highs (public lower secondary schools for 12- to 15-year-olds). Unlike the school
meal programs previously studied, the Japanese program requires all students at participating schools
to eat school lunch. We use individual-level data drawn from the 1975–1994 National Nutrition
Survey (NNS) and estimate the effect of the school lunch program on measures of weight-for-height,
obesity, and underweight, including the body mass index (BMI, defined as [weight in kilograms] /[height in meters]2). This paper advances the literature in several ways. First, by conducting
subsample and quantile analysis, we examine heterogeneity in the effect of school lunch on weightby socioeconomic status (SES) for the first time in the literature. Knowledge of individual-level
effect heterogeneity aids policymakers in the design of effective and efficient school meal programs.
Second, we estimate not only the contemporaneous effect but also the lagged effect of school meal
programs for children who graduate from junior highs and then stop having school lunch.
The unique features of the Japanese program allow us to obtain credible and easilyinterpretable causal estimates. First, all children attending a participating school must eat the5

provided lunch. The lack of individual choice in school lunch participation, together withmunicipality-level variation in school lunch provision, enables us to estimate the population effect of
actual participation in the school lunch program and assess treatment heterogeneity by children’ssocioeconomic background. This is in contrast to the aforementioned existing studies that examine
school lunch programs in which participation is up to each family. To address the concern about
selection bias, existing studies use regression discontinuity design (RDD) based on the eligibility
cutoff for school lunch subsidies (Schanzenbach, 2009) and difference-in-differences (DID) analysis
based on policy changes resulting in the increased out-of-pocket cost of school lunch for households
in specific income brackets (von Hinke Kessler Scholder, 2013). Consequently, these estimates are alocal average treatment effect (LATE) for specific income/SES groups at the margin affected by thepolicy change or policy discontinuity. Moreover, these estimates are interpreted as the effect of“intention to treat” (ITT) rather than the actual participation effect because of voluntary participation.
While a LATE parameter is informative for a marginal policy change, the estimates of population
average effect are informative for the overall effect of the program.
The second advantage of studying the Japanese school lunch program is its strict national
nutritional standards, which minimize program heterogeneity within the country. The strict standards
also make our estimates topical and informative to policymakers in other countries where nutritional
requirements are currently debated or have recently been strengthened. Third, there are no otherlarge-scale food provision programs in Japan. In the US there are various means-tested foodassistance programs, including NSLP, School Breakfast Program (SBP), and the Food Stamp
Program (Hofferth and Cuntin, 2005), and this coexistence of multiple programs complicates theanalysis (Capogrossi and You, 2017). Fourth, the non-means-tested nature of the program implies nostigma-induced reporting bias in school lunch participation. This is in contrast to programs in manyother countries. Gundersen et al. (2012) show that participation in NSLP is significantly
underreported, which is overlooked in other studies.

6At the core of our identification strategy is a large variation in the availability of school lunch
across municipalities. This municipality-level variation is useful because the program participation
decision is up to each municipality rather than the policy agenda of the central government.
However, our causal estimate may be confounded if municipalities’ decisions reflect unobserved area
characteristics. To address this concern, we employ a novel DID framework, in which we exploit
elementary school children as pre-treatment data. Japanese compulsory education consists of six
years of elementary school for 6- to 12-year-olds and three years of junior high school for 12- to 15year-olds, where the majority attend municipal schools (Ministry of Education, 1994). In contrast toa large variation in municipal school lunch provision for junior highs, nearly all municipalities
provide school lunch for elementary schools (NIEPR, 2013). Exploiting this structure, we form a
DID framework in which we compare differences between junior-high students and older (9- to 12year-old) elementary students between municipalities with and without school lunch for junior highs.
Because similarity between the treatment and control municipalities provides further assurance forthe common trend assumption of the DID approach, we also undertake DID estimation combinedwith propensity-score trimming and inverse probability of treatment weighting (IPTW). We further
conduct the raw quantile DID (QDID) analysis, i.e., the raw DID using percentiles instead of themeans, to examine the effect of school lunch on the distribution of weight measures.
Our main findings are as follows. While we find no significant effect of school lunch on bodyweight for the entire sample, we find a significant obesity-reducing effect for the subsample ofchildren with low socioeconomic backgrounds. We find little evidence that school lunch reduces
underweight prevalence. Quantile DID analysis reveals that the weight-reduction effect isconcentrated among obese children. The weight-reduction effect for low-SES children persists
several years after they graduate from junior high, implying effect through not only nutritional
content but also guiding healthy eating behavior. Various sensitivity tests confirm the robustness of
our DID estimates.

7

2. Backgrounds
School meal programs vary considerably across countries. Historically, dating back to the charitableprovision of free lunch for poor and undernourished schoolchildren in the mid-19th century in the UK
and US, the original goal of school meal programs was to feed children in hunger. By the mid-20th
century, national-level school lunch programs existed in Finland, France, Italy, Ireland, Portugal,
Spain, and Sweden, with the major nutritional goal of increasing energy intake rather than reducing it(Evans and Harper, 2009; Rutledge, 2015). Nowadays there is a large variation across developed
countries in nutritional content, targeting, and policy goals of school meal programs (Harper et al.,2008). 2
The scene of school lunch in Japan differs from that in many Western countries. Students atmunicipal elementary and junior-high schools are divided into a class of about 40 students and spend
the entire school day with their classmates, mostly at an assigned seat in the homeroom; students eat
lunch with their classmates in the classroom. 3 If a municipality provides lunch, all students have thesame menu (Sanborn, 2017). 4 A typical menu consists of a dish of meat or fish, a dish of vegetable,rice or bread, fruit, and milk (Nozue, 2011). Figure 1 shows typical lunch scenes at junior highs. As
in Panel (a), students in charge serve the meal. They are instructed to distribute food evenly to allstudents, but when there are leftovers students can have another serving (Nozue, 2011). Students eat

2

In developing countries, school feeding programs still play an important role in increasing energy

intake and reducing underweight (Jomaa et al., 2011).
3

A similar setup can be found in Italy, where many elementary and lower-secondary schools ban

home-prepared lunches at school so that students will eat school lunch together with their classmates(Kingston, 2019).
4

Few municipalities offer a menu choice.
8

together as in Panel (b). The homeroom teacher eats the same school lunch with the students and is
supposed to encourage students to eat everything served to them (NIEPR, 2013).
The first government-subsidized school lunch program in Japan started in 1932 for the children
at elementary schools from low-income families, but the program was interrupted in 1944 due toWorld War II. It was then resumed in municipal elementary schools in Tokyo in 1946, when Japanwas under American occupation, to combat child malnutrition resulting from severe food shortage.
Thereafter the program was gradually expanded to become nationwide. The nutritional and sanitary
guidelines became the School Lunch Law (henceforth SLL) in 1954, which was then revised toinclude municipal junior highs in 1956 (NIEPR, 2013). The SLL obliges municipalities only to“make efforts” to provide lunch at municipal elementary and junior-high schools.
The school lunch coverage rate for municipal elementary school students has been above 98
percent since the late 1970s, but the coverage rate for municipal junior-high students has increased
more gradually from about 58 percent in 1978 to about 83 percent in 2015, as detailed in Appendix 1(Figure A1). Figure 2 shows the 1985 school lunch coverage rate among municipal junior-highstudents across prefectures, which is evenly distributed across Japan with moderate spatial
correlation.
The Ministry of Education 5 requires that all students eat the provided school lunch, and notbring their own food to school, if their school receives government funding for school lunch. The
only exception to this requirement is for students with special dietary needs such as a food allergy(Ono, 2007). Nevertheless, households’ ability to pay for school lunch is unlikely to hinder
children’s participation. This is because municipalities receive subsidies that cover the cost of
construction and maintenance of facilities and the labor costs involved in preparing the food, and the5

The Ministry of Education was consolidated into the Ministry of Education, Culture, Sports,

Science, and Technology (MEXT) in 2001.
9

children’s guardians only pay ingredient costs and energy bills (NIEPR, 2013). In 2013, for example,
the average junior-high lunch fee was about 4,800 yen per person per month (approximately US$43)(MEXT, 2015). Moreover, payments are exempted for households on public assistance, and almost
all municipalities provide school lunch to all students regardless of fee payment (Fujisawa, 2008).
These compulsory and non-means-tested aspects of the Japanese school lunch program provide a
unique opportunity to evaluate the population average treatment effect (ATE) rather than a LATE or
ITT effect. 6
The Ministry of Education has set nutritional standards for school lunch, including target
values for energy, protein, total fat, calcium, and vitamin since 1954 (Nozue, 2011), and during ourstudy period the standards have had only one minor revision (see Appendix 1). Japan’s standards are
significantly higher than their contemporary counterparts in the US and UK. The current US federal
requirements lack target values for protein, total fat, calcium, and vitamin, and there was only aminimum requirement for energy intake until 2012 (Baidal and Taveras, 2014). In the UK,
requirements for the amount of energy, protein, and fat for school lunch were introduced in 1966 but
were abolished in 1980, leaving no legally binding nutrition requirements until 2000 (Evans andHarper, 2009). A survey conducted by the Japanese Ministry of Education finds that the actual intake
from school lunch complies well with the nutritional standards (National School Health Center ofJapan, 1990, 1991).
The SLL also lists the educational goals of the school lunch program such as encouraging
good eating habits, imparting knowledge on nutrition, and fostering sociability. The school lunch
program has been a part of the curriculum since 1958, instructing teachers to guide table manners
and encourage healthy eating (NIEPR, 2013). Since 2005, the school lunch program has been

6

An increasing number of municipalities nowadays allow students to choose between school lunch

and home-prepared lunch, but such a choice was rare during our study period (see Appendix 1).
10embedded as a part of the national food and nutrition education program called shokuiku, which aims
to promote healthy eating and prevent obesity and underweight. 7
Despite the low average BMI of the Japanese, the prevalence of obesity-related diseases inJapan is close to that of other developed countries with higher average BMIs (Guariguata et al.,2014). Because the rise in obesity-related health risks starts at a lower BMI level among Asians thanamong Caucasians, the Japan Society for the Study of Obesity has advocated defining obesity as
BMI of 25 or over since 2000, as opposed to the WHO’s benchmark of BMI 30 (Kanazawa et al.,2002). BMI and obesity among Japanese children have significantly increased since the late 1970s(Yoshinaga et al., 2010; Maruyama and Nakamura, 2015), raising concerns about child obesity,
which is a major risk factor for adult obesity (Togashi et al., 2002).
Underweight is also a serious public health issue among Japanese women, and is associatedwith various morbidities (Kodama, 2010). Female BMI has consistently decreased in post-war Japan(Maruyama and Nakamura, 2015), and underweight prevalence has significantly increased among
young women since the 1970s (Takimoto, 2004). Currently, more than 20 percent of non-pregnant
women in their 20s are underweight (a BMI of 18.5 or lower) (MHLW (Ministry of Health, Labourand Welfare), 2016).
We know of only one study examining the effect of the Japanese school lunch program on
child weight. Applying a fixed-effects OLS model with a lagged dependent variable to 2006–2015
prefecture-level data, Miyawaki et al. (2019) find a significantly negative effect of junior high school
lunch coverage rate on overweight prevalence for boys but a nonsignificant effect for girls, and anonsignificant effect on underweight prevalence for both genders. However, not only the lack oftime-variant control variables in their model could induce bias but also this type of dynamic model

7

The Third Basic Program for Shokuiku Promotion: www.mhlw.go.jp/file/06-Seisakujouhou-

10900000-Kenkoukyoku/0000129496.pdf (In Japanese).
11

makes OLS estimates inconsistent (Nickell, 1981; Angrist and Pischke, 2009, pp. 243–246). OtherJapanese studies find a positive association between school lunch and the intake of vegetables anddairy products (Takahashi et al., 1983; Kawaraya and Mori, 2009; Nozue et al., 2010) and the poor
nutritional contents of weekday lunch among junior-high students who attend schools without school
lunch (National School Health Center of Japan, 1990).

3. Framework for Causal Analysis
3.1. Difference-in-differences (DID) analysis
We conduct DID analysis using data of elementary and junior-high students drawn from the 1975–1994 NNS. The repeated cross-sectional data in the NNS allow for neither tracking the samemunicipalities/students over time nor identifying the name of the municipality of students’ residence.
However, encrypted identifiers enable us to group residents by census district, a subarea of amunicipality (henceforth “district”), and to impute the school lunch provision status of themunicipality the district belongs to.
Without loss of generality, we regard having school lunch as the baseline case and assess theeffect of not having school lunch, for the ease of presentation. We start with the following linear
regression for a sample of junior-high students:
��� = ��� � + �� � + � ��� ����ℎ�������ℎ� + ��� ,(1)

where ��� denotes an outcome variable (e.g., BMI) of student i in district d, ��� is a vector of student
i’s characteristics, including a constant term, and �� is a vector of district d’s characteristics,

including dummies for survey years. Because we do not track the same district or student over time,
we suppress year subscripts in Eq. (1) for conciseness. ����ℎ�������ℎ� is an indicator for no
junior-high school lunch in district d. ��� is the error term, and � and � are parameters to be
estimated. The OLS estimator of the “no school lunch” effect, � ��� , could be biased due tosystematic differences in unobserved local obesogenic environments between districts with and12districts without school lunch, such as access to healthy and unhealthy food, urban sprawl, access toparks and sports facilities, and transportation systems (Lake and Townshend, 2006).
To account for potential confounders, we capitalize on a unique feature of the Japanese school
lunch program: nearly all municipal elementary schools provide school lunch. This allows us to forma DID framework in which we subtract the pre-treatment difference, i.e., the difference in outcome
measures of elementary students between districts with and districts without junior-high school
lunch, from the post-treatment difference, i.e., the same difference of junior-high students, in order toadjust for the pre-existing age-invariant difference between the treatment and control districts, as
illustrated in Figure 3. Under the age-grade system in Japan, a child’s school grade is determined
strictly by the child’s age on April 2nd. For elementary students, we limit our sample to 9- to 12year-olds (Grades 4–6) for a better comparison with junior-high students (Grades 7–9). We estimate
the following DID equation using the sample of elementary and junior-high students:
��� = ��� � + �����ℎ�������ℎ� + � �� ���������ℎ�� × ����ℎ�������ℎ� + �� + ��� , (2)where ���������ℎ�� is an indicator for junior-high students, �� denotes district fixed effects, and� �� is the DID estimator of the effect of not having school lunch. The JuniorHigh indicator appears

only in the interaction term and not in a separate term, because junior-high attendance is absorbed byage dummies in ��� . The model is identified under the standard parallel trend assumption for ���

over age between the treatment and control districts, conditional on ��� . 8 We use standard errors

clustered at the district level to allow for within-district correlation of the error term. Unlike priorquasi-experimental studies, we quantify the effect of actual participation rather than the “intention to8

We require parallel trends over age within a survey year, whereas standard DID models based on

individual- or municipality-level panel data require parallel trends over age for a certain birth cohortor parallel trends over year for a certain age group.
13treat” effect, because attending schools with school lunch and participating in the school lunch
program are equivalent in the Japanese setup.

3.2. Subsample analysis
We examine effect heterogeneity for low SES children, a group of particular policy interests for two
reasons. First, in many countries, including the UK, US, and Canada, the main target of school meal
programs is children in low-income families (Harper et al., 2008). Second, we expect larger effects
for lower SES children. Low parental SES is associated with children’s poor diet quality (Darmon
and Drewnowski, 2008), less healthy eating habits (Hazano et al., 2017), and obesity in childhood(Shrewsbury and Wardle, 2008), adolescence (Kachi et al., 2015), and adulthood (Lee, 2013). Smith(2017) finds a larger impact of the US school meal programs on children’s nutrition for children withpoorer diet quality.
We conduct a subsample analysis for two low-SES groups. Because our data contain no
information on parental education or income, we first use paternal occupations as proxies for SES.
We study a subsample of children whose fathers are in non-white-collar occupations or unemployed(“children with non-white-collar fathers,” henceforth). White-collar occupations refer to white-collar
employees and self-employed professionals, such as practicing clinicians, and non-white-collar
occupations refer to all the other occupational categories, including non-professional self-employedworkers, laborers, and workers in agriculture/fisheries/forestry. 9
The actual SES of these households, however, may change over time, affecting comparability
across children of different ages and hence causing bias in the estimated long-term effects. To
address this concern, we study another subsample: children in households whose per-member

9

We do not include children without fathers in this subsample because we cannot distinguish cases

where fathers temporarily live apart from the family for work.
14

expenditure is below the median (“children with low household expenditure,” henceforth). 10
Household expenditure is a reliable measure of SES, capturing material well-being for low-income
households (Meyer and Sullivan, 2003).

3.3. Inverse probability of treatment weighting (IPTW) and propensity-score trimming
As a robustness check, we use IPTW and propensity-score trimming in the DID analysis. Combining
DID analysis with propensity score methods has been found effective for eliminating potential
sources of temporally invariant bias (Smith and Todd, 2005), balancing baseline characteristics
between the treatment and control groups and hence making the common trend assumption moreplausible. IPTW gives each subject a weight equal to the inverse of the probability of treatment the1

subject received. Thus, for students in district d, the weight equals p if d is a treatment district and
1

1−p�

�

if d is a control district, where p� denotes the propensity score of a lack of school lunch in d.

Propensity-score trimming excludes observations based on the propensity scores to ensure sufficient
overlap in characteristics between the treatment and control districts. Further details are provided inAppendix 2.

4. Data
4.1. The National Nutritional Survey

10

The median is defined among children of the same two-year age group in the same survey year.

Because per-member household expenditure in the NNS is reported in intervals that vary by year, wecannot determine which children in the median interval are below the median. To address this, we
randomly split the median interval so that all children of the same age group in each year are split
into two groups of equal size.
15

We use a sample of 9- to 15-year-old children in elementary and junior-high schools drawn from the
1975–1994 NNS. The NNS is a nationally representative, cross-sectional survey annuallyadministered by the Ministry of Welfare. 11 Katanoda et al. (2005) confirm the representativeness of
the NNS. The response rate, though not reported for all years, appears to be high: among about 5,000
households requested to participate in the 2002 survey, 4,160 participated (MHLW, 2003). The
survey includes information on the body measurements, diet, and sociodemographic characteristics
of each household member. Height and weight are measured without shoes and with adjustment for
the weight of clothes by health professionals and thus are accurate and free from self-reporting bias
(Gorber et al., 2007). The elementary and junior-high students consist of 9- to 12-year-olds and 12to 15-year-olds, respectively. We use the birth month to determine whether 12-year-old children are
in an elementary or junior-high school. Children at age 12 in the 1975–1985 surveys are not usedbecause the birth month information is unavailable in these years. A small number of children
without a mother and those with missing data are also excluded. Further details of the sample
construction are provided in Appendix 3.

4.2. Municipal provision of school lunch
The NNS samples districts from all Japanese prefectures and requests all households in the sampled
districts to participate in the survey. Only an encrypted identifier of the district of residence and thename of the prefecture is provided in the publicly available NNS dataset, hence we impute the school
lunch provision status of each district using NNS information on whether school children eat school
lunch.

11

The NNS was renamed the National Health and Nutrition Survey in 2003. The Ministry of Welfare

was consolidated into the MHLW in 2001.
16

This procedure involves several measurement issues. The first issue is that school lunch isserved only on weekdays, whereas the NNS does not specify which day of the week the food diaryrecord refers to. We solve this problem by exploiting the unique feature of the 1975–1994 NNS, thateach participating household is requested to choose three consecutive days excluding Sundays andholidays and to report the details of all meals each member had in each day. This means that eachhousehold’s survey period covers at least two consecutive weekdays, and we decide that school
lunch is available to a child if school lunch is reported for at least one of the three days.
Individual reports might not accurately reflect the municipal school lunch status, even for
weekdays, for two reasons. First, some children might miss school lunch due to sickness or extracurricular activities such as excursions. Second, because the NNS does not contain information on
the school children attend, school lunch status can be mismeasured if children attend municipal
schools outside of the municipality of residence or choose to attend private or national schools, few
of which provide school lunch. We presume that the first type of measurement error is small because
we use the food diary of three consecutive days and because the NNS instructs households to choose
a survey period when the household members have a normal daily life without special events.
Measurement error due to children attending municipal schools outside of their municipality is also
expected to be small due to the strict Japanese school district system. To address the noise due tochildren attending non-municipal schools, we exclude prefectures where more than 5 percent ofjunior-high students attend non-municipal schools in 1994 (shown as shaded areas in Figure 2).
Our sample still exhibits occasional disagreement within a district, in which case we determine
the school lunch status based on the majority rule: whether a half or more of junior-high students
report having school lunch. To improve accuracy, we exclude districts with only one junior-highrespondent and districts with exactly two conflicting answers. School lunch provision at a municipal
elementary school is determined analogously. In addition, when the school lunch provision status is17

obvious from official statistics, we use that information instead of survey response. Details on theprocedure to determine the school lunch status are provided in Appendix 3.
To illustrate the accuracy of the imputed school lunch status Table 1 presents the district-level
distribution of the percentage of students who report having school lunch. In 2,213 districts (97.4%),
the majority of elementary student respondents report having school lunch, consistent with the nearly
100 percent school lunch coverage rate in official reports (Appendix 1). For junior-high students, thereported percentage equals 100% in 65.7 percent and 0% in 20.6 percent of districts, and withindistrict reporting discrepancy arises in only 13.7 percent districts. Moreover, in the vast majority of
districts with mixed reports, the percentage of positive reports is 50 or more, suggesting that the
major cause of reporting discrepancies is occasional nonattendance. In Appendix 3, we also confirm
that the derived school lunch status is highly consistent with the official statistics. Our final sample
consists of 8,477 junior-high students and 9,794 elementary students from 2,265 districts, of which
498 districts do not provide school lunch in their municipal junior highs.

4.3. Weight measures, control variables, and summary statistics
Our outcome variables include BMI, binary indicators for obesity and underweight, and anothermeasure of weight-for-height widely used in Japan called Percentage of overweight (POW). POW is
the proportion of weight deviation to the standard weight-for-height by age and gender, defined as( [weight] – [standard weight] ) / [standard weight]. We take standard weight-for-height for Japanesechildren from Murata and Ito (2003). We also examine height in some analysis. For BMI and height,
we use both the raw value and the z-score that is normalized by gender, age, and five-year cohort.
Defining obesity and underweight requires caution because the distribution of children’s BMI
varies substantially by age, gender, and race. We use the extended International Obesity Task Force(IOTF) definition (Cole and Lobstein, 2012) and the POW definition. The IOTF definition is the
BMI-based definition widely used to account for racial differences in growth patterns. The cutoff of18

being obese for each age-gender group is determined based on the percentage rank corresponding to
BMI 30.0 at age 17.5. We use BMI 25.0 for the obesity cutoff instead of the widely-used 30.0,
following the recommendation by the Japan Society for the Study of Obesity (Kanazawa et al.,2002). Underweight is defined analogously: the percentage rank corresponding to BMI 18.5 at age
17.5 is used to determine the underweight cutoff. These IOTF cutoffs minimize across-age variationin the prevalence of obesity and underweight and thus fit well in our DID framework. For Asian
children, the IOTF definition is preferred over the WHO reference, which is based on American
children’s BMI distribution (de Wilde et al., 2013). We use the gender- and age-specific BMI
distributions for Japanese children reported in Kato et al. (2011).
Under the POW definition, children whose weight exceeds their standard weight by 20% (i.e.,
POW>20%) are categorized as obese. Likewise, POW less than −20% is underweight. The POW
definition has an advantage over BMI-based measures as BMI increases with height for children in
puberty (Sugiura and Murata, 2011).
Table 2 shows the summary statistics of height and weight measures of elementary and juniorhigh students by treatment status for the full sample (Panel (a)) and the two low-SES subsamples(Panels (b) and (c)). Junior-high students have larger BMIs than elementary students, but the otherweight measures show no clear age trends, as expected. The two obesity measures are reasonably
consistent. The two underweight measures are different in level but similarly lack strong age trends.
Children in the two socioeconomically disadvantaged subsamples are consistently shorter thanchildren in the full sample, but the weight measures show no clear difference. In all three samples,comparison between the treatment and control groups among elementary students shows little
difference, except that BMI, POW, and obesity prevalence are smaller in the treatment districts thanin the control districts. In contrast, among junior high students they are all larger in the treatment
districts than in the control districts in all three samples, consistent with the formal DID results
below.

19

To make our DID estimator more credible, we account for differential age-trends specific toeach area, which cannot be addressed by district fixed effects, by including controls for various child,parental, and household characteristics. For child characteristics we use gender-specific age
dummies, with separate age dummies for 12-year-old elementary students and 12-year-old juniorhigh students. Parental characteristics include age, height, BMI, and occupation dummies of thefather and mother. 12 Household characteristics include the coresidence of father, grandfather, andgrandmother, the number of children in the household, and the percentage ranking of monthly
household expenditure per household member.
Table 3 reports the summary statistics of the control variables by treatment status with thenormalized difference between the two groups. 13 The table shows that junior-high school lunch ismore likely to be provided in districts where children live with their grandparents, parents work inagriculture/fisheries/forestry, and per-member expenditure is lower. The absolute normalized
differences in the control variables between the treatment and control groups are overall small andnever exceed the threshold value of 0.25, where values above 0.25 are considered problematic(Rubin, 2001). IPTW and propensity-score trimming make these differences even smaller, as shownin Appendix 2 (Table A1).

4.4. Determinants of school lunch provision12

Because the NNS does not record kinship among household members, we regard 27- to 59-year-

olds in a child’s household as parents and those 60 years old or older as grandparents. Mean values
are used in the rare case of multiple “fathers” or “mothers.”
13

Many DID studies conduct t-tests for differences in covariate means between treatment and control

groups. However, the normalized differences are more effective for assessing the difficulty ofadjusting for covariate differences between the groups than the t-statistics (Imbens, 2015).
20

Tables 2 and 3 indicate that junior-high lunch status is not purely random and that a mere comparisonof outcome variables between junior-high students with and without school lunch might be biased.
Even if we control for observable district characteristics, the unconfoundedness assumption might beviolated. Our DID estimation addresses this non-randomness and yields unbiased causal estimates
under the common trend assumption. Specifically, the assumption requires that the school lunch
provision be determined orthogonally to children’s growth in height and weight from age 9 to 15(after controlling for district characteristics that vary over age).
To assess this premise, it is useful to understand the determinants of school lunch provision atjunior highs. We first conduct a district-level Logit regression analysis in which we regress the
NoSchoolLunch dummy on mean height, mean BMI, the prevalence rates of obesity and underweight
among children 1- to 11-year-old, and other various district characteristics. We use districts with fiveor more respondents of age 1 to 11. To minimize the influence of age-composition among children,
we use mean z-scores of height and BMI that are normalized by gender, age, and five-year cohort,and use the IOTF definitions for obesity and underweight. We include residents’ characteristics
defined as aggregated NNS values: the number of NNS participants, age composition, medianpercentage ranking of per-member household expenditure, mean household size, occupational
composition among 23- to 54-year-old workers, and the proportion of working women. Also
included are prefectural population density obtained from Statistics Bureau, Ministry of Internal
Affairs and Communications (2012), dummies for municipal size, 47 prefecture specific effects or
six region block specific effects, and year dummies. Their summary statistics are provided inAppendix 4 (Table A3).
Table 4 reports the regression results. Model 1 controls for region block fixed effects andModel 2 controls for prefecture fixed effects. Junior-high school lunch is less common in larger
municipalities. The coefficient on the prefectural population density is significantly negative only inthe prefecture fixed-effect model, implying a higher likelihood of school lunch provision in21

prefectures with a growing population. Consistent with this, school lunch is less common in “older”
areas with a larger fraction of the elderly population. The estimated coefficients of year dummies(reported in Appendix 4, Table A4) indicate a significant increase in school lunch provision overtime, consistent with both the nationwide and sample trends.
On the other hand, none of the other variables, including those directly related to obesogenic
environments, are significant. Most importantly, in both specifications, mean height, mean BMI,
obesity rate, and underweight rate among elementary and preschool children are independently andjointly nonsignificant, which suggests that the municipal school lunch provision is unrelated to thestature, obesity, and underweight of children. The lack of significance of the expenditure level
implies that the municipal decision on school lunch is not driven by the economic deprivation ofresidents. Occupation is a major determinant of obesogenic environments (Maruyama andNakamura, 2018), but occupational composition variables are not significant. These findings suggest
the absence of a direct link between the school lunch provision and obesogenic environments aroundchildren, supporting our common trend assumption. 14 To further address concerns about the possible

14

We also conduct a substantial archival work, examining media coverages, research articles, andminutes of municipal assemblies, to understand the determinants of school lunch provision, but little
information has been identified. Recently the coverage rate of junior-high school lunch started to rise
(Figure A1), and one reason is the rising concerns and awareness over child nutrition (Mainichi,
2016). In the Third Basic Program for Shokuiku Promotion of 2016, the government introduced anagenda to increase school lunch provision at municipal junior highs to promote healthy eating.
Reverse causality from local obesity prevalence to municipal school lunch provision is of little
concern during our study period 1975–1994, however, because until the 2000s few were aware ofchild obesity issues in Japan even among health professionals (Yoshinaga, 2012). The lack ofsignificance of the variables on children’s weight is consistent with this view.
22violation of the common trend assumption, we conduct a number of robustness tests, as discussed in
the next section.

5. Results
5.1. Main results
Figure 4 plots year-adjusted means of height and BMI by gender in the full sample and the low-SES
subsamples over ages 9 to 15 for the treatment and control groups. The vertical red line indicates age
12, the threshold age between elementary and junior-high students. In this figure, 15-year-olds
include both current- and post-junior high students. For all three samples, the trends in mean height
are highly similar between the treatment and control groups for both genders, highlighting little
difference in growth patterns. The differences in BMI trends are also small in the full sample.
Among children with non-white-collar fathers, while elementary boys’ BMI is similar between thegroups, elementary girls’ BMI is lower for the treatment than the control groups, but BMI of thetreatment group exceeds that of the control group at ages 13 and 14 for both genders. Amongchildren with low household expenditure, fluctuations in BMI are large, but the overall trends are
similar to those for children with non-white-collar fathers.
Table 5 reports the estimated effects of no school lunch from (a) junior-high OLS, as specified
in Eq. (1), (b) DID regression, and (c) DID regression with IPTW and propensity-score trimming, inPanels (a)–(c) respectively. 15 Whereas we find no statistically significant effect on any outcome
measure across all three specifications for the full sample, the subsample results reveal fairly robust
evidence that school lunch reduces BMI, POW, and obesity for children from lower socioeconomic
backgrounds. In the subsample of children with fathers in non-white-collar occupations, theestimated effects are significantly positive on BMI, BMI z-score, POW, and both of the obesity

15

Full regression results are available from the authors upon request.
23

measures in all three specifications, at least at the 10 percent level. The estimates from the base DID
imply that the lack of school lunch increases BMI by 0.403 and increases obesity prevalence by
about 3 percent under both IOTF and POW definitions, the estimates from the DID with IPTW andtrimming being even larger. In the subsample of children with low household expenditure, while
none of the estimated effects from the OLS are significant except for the obesity status under POW
definition, those from the base DID and DID with IPTW and trimming are all significantly positiveon all outcomes except for the underweight measures. The base DID estimates imply that the lack ofschool lunch increases BMI by 0.418 and increases obesity prevalence by about 5 percent under bothdefinitions, with the estimates from the DID with IPTW and trimming being larger again. We find noevidence that school lunch affects underweight prevalence in any specification regardless of thesample used. 16

5.2. Quantile DID
To explore effect heterogeneity over the baseline distribution of height and weight, we conduct raw
quantile DID (QDID) analysis, in which DID estimates are obtained by taking the difference of two
differences for each of 19 equidistant intervals between the 5th and 95th percentiles of the dependent
variable. 17 Figure 5 shows the QDID estimates for height in z-score, BMI in z-score, and POW. For
all three samples, the estimates for height are close to zero across quantiles. In contrast, the estimates

16

We also conduct a subsample analysis of children whose per-member household expenditure is

above the median and children with fathers in white-collar occupations or without fathers, and noneof the estimated effects are significant.
17

We refrain from formal quantile regression analysis because the econometric theory for thequantile treatment effect in DID settings with control variables is under development and because
our data and setting are not ideal for such analysis.
24for BMI and POW are mostly positive and larger for higher quantiles for all three samples, implying
the variance-reduction effect of school lunch for weight. This pattern is particularly large for thehighest quantiles of the low-SES subsamples. Obese children are the driving force behind thesignificant weight-reduction effect of school lunch among the low-SES subsamples.

6. The Robustness of Results
6.1. Permutation test
To assess the potential underestimation of standard errors due to correlation of the error terms amongchildren close in age and location, we implement permutation tests in the spirit of Bertrand et al.
(2004) and Abadie et al. (2010). In this test, the treatment NoSchoolLunch is randomly assigned tocontrol districts holding the same frequency as in the original sample, and the base DID model isestimated based on the hypothetical treatment assignment. Repeating this procedure 1,000 times
yields the distribution of the estimated placebo treatment effect. As detailed in Appendix 5 (FigureA3), the implied statistical significance in this test is highly consistent with the corresponding resultsin Table 5, suggesting that the statistical significance of our estimated school lunch effects is not due
to the misspecification of correlation structure.

6.2. Falsification test: regression analysis of heightOur DID framework relies on the common trend assumption that the school lunch provision isdetermined orthogonally to children’s growth in height and weight from age 9 to 15 (after controllingfor covariates that vary over age). This assumption might be violated if there are systematicdifferences in the growth pattern between the treatment and control districts, especially in the timingof puberty onset. The use of POW, POW-based obesity/underweight definitions, IPTW, andpropensity-score trimming should mitigate potential bias. We further conduct a falsification test inwhich we use height instead of the weight measures as a regressand. Because height is determined25

primarily by genetic factors and early-life environment (Beard and Blaser, 2002), school lunch
should not have a strong, immediate effect on height. Thus, the coefficient of the interaction of
JuniorHigh dummy and NoSchoolLunch dummy would reflect differences in children’s predetermined growth pattern between the treatment and control districts. As shown in Table 6, none of
the DID estimates are significant for the full sample and the low-SES subsamples, providing
additional support for the common trend assumption.

6.3. Other robustness checks
Further robustness checks support the robustness of our results, as detailed in Appendix 5. Our
results might be confounded by the differential effects of attending a junior high by urbanicity andsurvey timing. While the school lunch status is significantly associated with the municipality size andsurvey year (Table 4), the transition from elementary to junior-high schools might involve lifestylealterations, such as an increase in time spent for studying or school sports club activities, whose
effect on weight might vary with urbanicity and change over time. To address this concern, we addinteractions of JuniorHigh dummy with five-year period dummies, prefectural population density,and municipality size variables to the DID regression model. Furthermore, we also test specifications
with triple interactions of the JuniorHigh dummy, year dummies, and prefecture dummies to the DID
regression model to allow for differential effects of attending junior high by prefecture-year. Our
results are robust to these modifications. 18

18

Another robustness test of the common trend assumption would be to include linear age trends

specific to each district in the DID analysis. However, this is not appropriate in our setting because
the growth curves of height and weight over age are highly nonlinear. Additionally, it is not feasible
because the number of children is too small in many districts, especially in the subsamples.
26

We implement a synthetic control method proposed by Abadie et al. (2010) to compare theoutcome trends of the treatment group with an artificial control group with more similar pretreatment trends than the original control group. The results confirm the robustness of our findings.
Further specification tests are conducted. First, we estimate the DID regression model using aless restrictive criterion for the selection of prefectures: we include in our sample prefectures with atleast 90 percent of junior-high students attending municipal schools as of 1994 instead of 95 percent,despite a potential concern about bias due to students attending non-municipal schools. This
modification does not change our findings substantially. Second, we estimate the same model
excluding 12- and 15-year-olds. Among 12-year-olds, some are elementary and others are juniorhigh students, depending on the birth month. Similarly, some of the 15-year-olds are current juniorhigh students and others have finished junior high. Hence, our results might be affected by potential
differential effects of the birth month on children’s height and weight between the treatment andcontrol groups. We confirm the robustness of our findings to this exclusion and also find highly
similar effects of the birth month on height for both groups.

6.4. Misclassification in school lunch status
The imputed school lunch provision status for junior-high schools might be subject to measurement
error, potentially causing estimated effects attenuated toward zero. This might be an explanation for
the insignificant effects of school lunch on underweight. If that is the case, however, the estimatedpositive effects of the lack of school lunch on BMI and obesity can be considered the lower bound of
the true effect.

7. Long-Term Effects
Does the weight reduction effect of school lunch for low-SES children last after they graduate fromjunior high and stop having school lunch? The long-term effect of school lunch is a parameter of27policy interest because it can drastically alter the cost-benefit of such programs. To estimate theaftereffect of school lunch, we add 15- to 17-year-old post-junior-high students in the sample andestimate the following model:��� = ��� � + �����ℎ�������ℎ� + � ��� ���������ℎ�� × ����ℎ�������ℎ�+� ��� �������� × ����ℎ�������ℎ� + �� + ��� ,(3)

where �������� is an indicator for post-junior-high students, and � ��� and � ��� denote the DID

estimators of short- and long-run effects of no school lunch, respectively. The 15- to 17-year-olds inthe control group are assumed to have had school lunch for the three years before graduation. This
would be a reasonable approximation given the slow expansion in the school lunch coverage during
our study period. 19
Table 7 reports the two estimated coefficients on the NoSchoolLunch dummy interacted withthe junior-high and post-junior-high dummies. As expected, the estimated effects for junior-highstudents (henceforth “ongoing effects”) are all positive and close to the corresponding results inTable 5. They are all nonsignificant for the full sample, and all significantly positive for the low-SES
subsamples, at least at the 10 percent level. The estimated effects of post-junior-high students(henceforth “post-effects”) are also all positive and fairly close to the ongoing effect in bothsignificance and magnitude. At the 10 percent significance level, whereas only two out of ten
estimates of the post-effects are significant for the full sample, six out of ten are significant forchildren with non-white-collar fathers, and seven out of ten are significant for children with low
household expenditure. For the low-SES subsamples the estimated post-effects are either close to or

19

Even when a non-negligible fraction of the 15- to 17-year-olds in the control group was exposed toschool lunch for less than three years, our estimate of the longer-term effect can be interpreted as alower bound of the true effect. We refrain from estimating longer-term effects because relocation ofindividuals is very common after the age of 18.
28

smaller than the ongoing effects, except for a few estimates from DID with IPTW and trimming,
which exceed the ongoing effects.
We repeat the QDID analysis, treating post-junior-high students, instead of current junior highstudents, as post-treatment observations. The results shown in Figure 6 are highly consistent withthose from the main analysis (Figure 5). Although the estimates are overall smaller, the estimates for
the BMI and POW in the low-SES subsamples are positive for the highest quantiles.
These findings provide suggestive evidence that the obesity-reducing effect of the school lunch
program for children with low socioeconomic backgrounds lasts at least several years after they
graduate, implying the role of school lunch in preference and habit formation for low SES children,
consistent with the Japanese government’s policy to promote healthy eating habits and foodknowledge through school lunch.

8. Conclusion and Discussion
We examine the causal effect of a Japanese school lunch program on the weight of junior-highstudents using data drawn from the 1975–1994 NNS. To account for possible endogeneity of themunicipal provision of school lunch, we employ a DID framework that compares differences
between elementary and junior-high students across districts with and without school lunch at juniorhigh schools. Although we find no significant effects when the full sample is used, we find that thelack of school lunch significantly increases the BMI and obesity rate of children from low
socioeconomic backgrounds. We find little evidence that school lunch affects underweight
prevalence, implying the variance-reduction effect of school lunch. The obesity-reducing effect ofschool lunch for low SES children appears to last at least several years after graduation, suggestingthat the school lunch effect involves not only direct changes in caloric and nutritional contents but
also changes in behavior. Our findings are robust to propensity score-based trimming and reweighting (IPTW), permutation tests, various falsification tests of the common trend assumption, and29

several specification tests. We also present that municipal school lunch provision for junior-highschools is unrelated to the growth pattern of elementary and preschool children in the area.
This study has the following policy implications. First, school lunch with strict nutritional
requirements could reduce obesity. This finding is consistent with the literature in that, while
previous findings on American NSLP and SBP are mixed, the majority of studies find obesity
reduction effects of SBP, which satisfy stricter nutritional requirements than NSLP (Gleason and
Dodd, 2009; Millimet et al., 2010; Millimet and Tchernis, 2013). Second, the compulsory nature of
the Japanese school lunch program, with its primary purpose of abolishing stigma, might play a keyrole in obesity reduction because children with a strong preference for fattening food might avoid
school lunch if a choice is allowed. Third, school lunch might have long-term obesity-reducing
effects via preference and habit formation, consistent with the educational goals of the Japanese
school lunch program of promoting good eating habits and food knowledge (NIEPR 2013). Fourth,the obesity reduction effects of school lunch for low-SES children might have contributed to theabsence of significant income gradient in child obesity among elementary-school students (Kachi etal., 2015) and the small income gradient in child health in Japan (Nakamura, 2014).
We find beneficial effects of school lunch only for low SES children. From the efficiency pointof view, this finding seems to justify means-testing. However, the compulsory nature of the Japanese
program helps to avoid inefficiency due to self-selection and social stigma. The setting where
everyone eats together also facilitates food education and potentially brings beneficial peer effects.
Means-testing and allowing for choice need to be evaluated in further research.
Data limitation prevents us from using more recent data for this study, and future studies would
require the accumulation of microdata of children, with accurate information on both bodymeasurements and school lunch participation. Additionally, previous studies find a positive impact ofschool lunch quality on academic performance in the UK (Belot and James, 2011) and US (Anderson30

et al., 2017), and future research includes examining the effect of school lunch on other outcomes inJapan, including cognitive ability, which is infeasible with our data.

Acknowledgments: The authors are grateful for a Grant-in-Aid for Young Scientists (B) No.
25780187 from the Japan Society for the Promotion of Science. We also wish to thank Mayu Fujii,
Daiji Kawaguchi, Ayako Kondo, Jui-fen Rachel Lu, Eiji Mangyo, Hideo Owan, Mike Shields, Ryuichi
Tanaka, and seminar participants at Hitotsubashi, Nagoya, Osaka, Tokyo, and Toyama Universities
for their helpful comments. Both authors declare that they have no conflicts of interest. Official
permission to utilize the National Nutrition Survey and the National Health and Nutrition Survey was
obtained from the Statistics and Information Department of the Ministry of Health, Labour and Welfare
on October 2, 2015 (Permission Number 1002-6) and November 20, 2015 (Permission Number 11201), respectively.

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38

Figure 1. School lunch scenes in Japana) Students serving school lunch

Source: “School Lunch at Oyodo Junior High, Osaka City,” March 8, 2017, retrieved from Asahi
Shimbun Photo Archive.
b) Students eating together

Source: “School Lunch at Aoyama Junior High, Beppu City,” January 24, 2007, retrieved from
Asahi Shimbun Photo Archive.

39

Figure 2. School lunch coverage rate for municipal junior-high students in 1985 by prefecture

Source: National School Health Center of Japan (1986)
Note: Shaded areas indicate the prefectures excluded from our sample.

40

Figure 3. Illustration of the DID framework
Pre-treatment data:
Post-treatment data: JuniorElementary students in the high students (12 to 15
fourth to sixth grades (9 to years old)
12 years old; all haveschool lunch)

Treatment group: Districts
without junior-high lunch

Treatment:
No school lunch

Control group: Districts
with junior-high lunch

School grade

Note: In the Japanese compulsory education system, first to sixth graders attend elementary schools
and seventh to ninth graders attend junior highs. A child’s school grade is strictly determined by thechild’s age on April 2nd. Because the NNS is conducted in November each year, fourth to sixth
graders in our sample are 9 to 12 years old, and the seventh to ninth graders are 12 to 15 years old.

41

Figure 4. Means of height and BMI across age

Note: The lines plot year-adjusted means. To adjust for time trends and over-time changes in surveyyear composition, each year’s value is adjusted by the deviation from the aggregate mean. The
vertical red line indicates age 12, the threshold age that divides elementary and junior-high students.
While the sample for the main DID analysis only covers elementary and junior-high students, thegraph includes 15-year-old post-junior-high students. Values for 12-year-olds are omitted because
our sample excludes them for 1975–1985 due to data limitations.
42

Figure 5. Quantile DID estimates of the effect of no school lunch

Note: The estimates are obtained by calculating the difference of differences with respect to each of
the 19 equidistant intervals between the 5th and 95th percentiles.

43Figure 6. Quantile DID estimates of the effect of no school lunch for post-junior-high students

Note: The estimates are obtained by calculating the difference of differences with respect to each of
the 19 equidistant intervals between the 5th and 95th percentiles. In this Figure, post-junior-highstudents, instead of current junior-high students, are treated as post-treatment observations.

44

Table 1. The proportion of students reporting school lunch by district% of students who reported having school
lunch at least once during the survey period
No student
more than 0% and less than 50%
50% or more and less than 100%
All students
Total number of districts

Elementary students

Junior-high students

36
23
461
1,752
2,272

468
60
252
1,492
2,272

(1.6%)(1.0%)(20.3%)(77.1%)(100%)(20.6%)(2.6%)(11.1%)(65.7%)(100%)

Note: The unit of observation is a district. The figures are based on the sample before we exclude
districts with exactly two conflicting reports and districts where 50% or less of elementary students
had school lunch (see Appendix 3). Districts with one or no reports are not included.

45

Table 2. Summary statistics: Outcome variables

Elementary students
Districts with noControl districts
junior-high lunch
Std.
Std.
Mean
Mean
Dev.
Dev.

Junior-high students
Districts with noControl districts
junior-high lunch
Std.
Std.
Mean
Mean
Dev.
Dev.

(a) Full sample
Height (cm)138.548.38

Height in z-score0.034 0.962
BMI
17.1702.400
BMI in z-score-0.0320.930
POW-0.602 12.797
Obese (IOTF)
0.069
0.254
Obese (POW)
0.069
0.254
Underweight (IOTF)
0.159
0.365
Underweight (POW)
0.019
0.137
2,081
Number of children
498
Number of districts(b) Children with non-white-collar fathers
Height (cm)137.948.29
Height in z-score-0.034 0.953
BMI
17.0922.370
BMI in z-score-0.0500.907
POW-0.571 12.948
Obese (IOTF)
0.067
0.251
Obese (POW)
0.071
0.258
Underweight (IOTF)
0.164
0.371
Underweight (POW)
0.019
0.135
1,023
Number of children
349
Number of districts(c) Children with low household expenditure
Height (cm)138.298.45
Height in z-score-0.049 0.990
BMI
17.055
2.222
BMI in z-score-0.1020.857
POW-0.994 11.862
Obese (IOTF)
0.053
0.225
Obese (POW)
0.056
0.229
Underweight (IOTF)
0.162
0.369
Underweight (POW)
0.016
0.125
826
Number of children
312
Number of districts

138.468.55-0.031

0.984

158.30

7.66

0.052

0.969

158.067.62-0.0180.982

17.3042.475-0.0080.957
0.285 13.151
0.077
0.267
0.079
0.270
0.152
0.359
0.020
0.139
7,713
1,767

19.657
2.744
0.028
1.004
-0.068 13.558
0.062
0.242
0.071
0.257
0.159
0.366
0.020
0.139
1,778
498

19.6292.646-0.0040.956-0.360 12.897
0.059
0.235
0.066
0.248
0.155
0.361
0.019
0.135
6,699
1,767

138.27-0.051157.820.017

157.64-0.070

8.53
0.990

7.42
0.945

7.63
0.999

17.354
2.532
0.021
0.987
0.743 13.481
0.083
0.275
0.084
0.278
0.146
0.354
0.021
0.142
3,901
1,308

19.793
2.801
0.090
1.028
0.693 13.879
0.072
0.258
0.080
0.271
0.148
0.356
0.022
0.147
863
349

19.629
2.684
0.001
0.972
-0.250 13.024
0.056
0.229
0.064
0.244
0.155
0.362
0.016
0.127
3,439
1,308

138.22-0.083157.94-0.018157.82-0.0528.62
0.977

17.2842.493-0.0170.969
0.375 13.182
0.078
0.268
0.078
0.269
0.154
0.361
0.020
0.139
3,636
1,230

46

7.62
0.966

19.819
2.988
0.084
1.086
0.687 14.769
0.079
0.271
0.090
0.287
0.156
0.363
0.015
0.122
730
312

7.66
0.999

19.666
2.680
0.012
0.963
-0.076 12.974
0.058
0.233
0.064
0.245
0.149
0.356
0.015
0.122
3,125
1,230

Table 3. Summary statistics: Control variables

Variable
Male
Age
Father's age
Father's height (z score by age, sex, and 5-year cohort)
Father's BMI (z score by age, sex, and 5-year cohort)
Father's height and BMI missing
Father: white-collar worker (the reference category)
Father: laborer
Father: self-employed
Father: agriculture/fisheries/forestry
Father: other occupation (not working)Without father in household
Mother's age
Mother's height (z score by age, sex, and 5-year cohort)
Mother's BMI (z score by age, sex, and 5-year cohort)
Mother's height and BMI missing
Mother: white-collar worker (the reference category)
Mother: laborer
Mother: self-employed
Mother: agriculture/fisheries/forestry
Mother: other occupation (not working)Grandfather in householdGrandmother in household# of children in household (below 18 years old)
Per-member household expenditure ranking (defined
between 0.0 and 1.0 where 0.0 means households withhighest expenditures in each survey year)
Number of children
Number of districts

Districts with noNormalized
Control districts
junior-high lunch
difference
Std.
Std.
Mean
Mean
Dev.
Dev.
0.522
0.500
0.515
0.500
0.014
11.764
1.998 11.814
2.010-0.02538.133 13.071 38.079 12.950
0.004
0.024
0.851 -0.037
0.844
0.072
-0.017
0.865
0.013
0.846
-0.035
0.256
0.436
0.252
0.434
0.009
0.356
0.478
0.343
0.474
0.027
0.296
0.455
0.292
0.453
0.011
0.191
0.393
0.185
0.387
0.016
0.053
0.223
0.078
0.267
-0.104
0.009
0.089
0.009
0.091
0.002
0.095
0.293
0.093
0.291
0.005
39.5534.319 39.558
4.404-0.001-0.0190.981 -0.073
0.974
0.056
0.000
0.926
0.093
0.997
-0.097
0.036
0.186
0.036
0.187
-0.001
0.170
0.372
0.161
0.365
0.024
0.237
0.421
0.245
0.427
-0.020
0.136
0.342
0.130
0.334
0.019
0.056
0.227
0.094
0.288
-0.150
0.402
0.485
0.369
0.478
0.067
0.165
0.371
0.204
0.403
-0.101
0.272
0.445
0.317
0.465
-0.099
2.276
0.813
2.310
0.777
-0.042
0.607

0.239

0.643

3,859
498

0.241

-0.147

14,412
1,767

Note: The last column shows the normalized difference between the treatment and control groups.
All statistics are based on non-missing observations. When body measurement data (height and BMI)
are missing, dummies for the missing values are used in the regression analysis. Because thehousehold expenditure is reported in intervals that vary by survey year, we construct the percentage
rank within all households in each survey year for comparability across years. The ranking isrecorded in descending order: a larger value implies a smaller expenditure.

47

Table 4. District-level Logit regression of NoSchoolLunch dummy
Explanatory variable
District: mean child height (z score)
District: mean child BMI (z score)
District: child obesity rate (IOTF BMI 25+)
District: child underweight rate (IOTF BMI 18.5-)
District: # of participants
District: proportion of ages 1–19
District: proportion of ages 40–59
District: proportion of ages 60+
District: median per-member household expenditure
District: mean household size
District: proportion of laborer
District: proportion of self-employedDistrict: proportion of agriculture
District: proportion of working women
Prefectural population density (1,000 person/km2)
Municipal size: 11 largest cities
Municipal size: cities with 150k+ population
Municipal size: cities with 50–150k population
Municipal size: cities with 50k- population
Region block dummies
Prefecture dummies
Year dummies
R2
Number of districts

Model 10.201
(0.160)-0.071(0.202)0.409(0.492)-0.279(0.623)-0.001(0.003)1.297(1.409)1.098(0.963)
1.932*(1.121)-0.641(0.405)-0.030(0.136)0.209(0.372)0.092(0.441)-0.296(0.615)0.587(0.389)0.091(0.159)2.927***(0.273)1.602***(0.192)
1.375***(0.200)1.090***(0.235)
Yes
No
Yes
0.153
2,117

Model 20.054
(0.181)-0.107(0.232)0.233(0.528)0.024(0.687)-0.001(0.003)
1.532(1.540)1.307(1.060)2.124*(1.266)-0.442(0.460)-0.124(0.158)0.090(0.401)0.235(0.487)-0.752(0.670)0.185(0.449)-3.898**(1.613)3.434***(0.328)1.685***(0.212)
1.402***(0.221)
1.109***(0.256)
No
Yes
Yes
0.268
2,075

Note: Standard errors are in parentheses. The constant term is included in the model but omitted fromthe table. The estimated coefficients for year dummies are presented in Appendix 4 (Table A4). The
reference category for the municipal size dummies is towns and villages, that for the age composition
variables is the proportion of ages 20 to 39, and that for the occupational composition variables is the
proportion of white-collar workers. Districts with less than five respondents of ages 1 to11 are
excluded from the sample. Model 2 shows fewer observations than Model 1 because prefectures
without variation in the NoSchoolLunch dummy are omitted. *, **, and *** indicate statisticalsignificance at the 10%, 5%, and 1% levels, respectively.

48

Table 5. Effects of no school lunch
Panel (a): Junior-high OLS
Sample# children# districts

Full sample

8,470

2,262

Children with non-white-collar
fathers
Children with low household
expenditure

4,299

1,654

3,853

1,540

# children# districts

Full sample

18,271

2,265

Children with non-white-collar
fathers
Children with low household
expenditure

9,226

1,657

8,317

1,542

BMI

BMI
z-score0.020(0.028)0.089**(0.042)0.059(0.048)

POW

BMI

BMI
z-score0.093(0.091)0.403***(0.135)0.418***(0.152)BMI

0.047(0.076)
0.234**(0.111)0.131(0.128)

Obesity(IOTF)
0.001(0.007)0.021**(0.010)0.017(0.012)

Obesity(POW)
0.003(0.008)0.020*(0.011)0.025**(0.012)

Underweight(IOTF)
0.003(0.011)-0.014(0.015)0.015(0.018)Underweight
(POW)
0.003
(0.004)0.006(0.006)-0.002(0.006)

POW

Obesity(IOTF)

Obesity(POW)

Underweight(IOTF)

Underweight
(POW)

0.032
(0.035)0.152***(0.052)0.167***(0.057)0.767(0.469)2.076***(0.707)2.266***(0.774)0.007(0.009)0.031**(0.013)0.051***(0.015)0.007(0.01)
0.026*(0.014)0.052***(0.015)0.002(0.014)-0.023(0.020)-0.004(0.021)

0.005(0.005)0.010(0.008)0.005(0.007)

BMI
z-score0.036(0.042)0.197***(0.066)0.223***(0.064)

POW

Obesity(IOTF)
0.004(0.011)0.038**(0.017)
0.061***(0.016)

Obesity(POW)
0.008(0.011)
0.042**(0.018)0.056***(0.017)

Underweight(IOTF)
0.002(0.017)-0.021(0.023)-0.016(0.025)

Underweight
(POW)
0.005
(0.005)0.013(0.008)0.012(0.007)0.170(0.387)1.004*(0.565)0.574(0.647)

Panel (b): Base DID
SamplePanel (c): DID with IPTW and propensity-score trimming
Sample# children# districts

Full sample

13,9091,728

Children with non-white-collar
fathers
Children with low household
expenditure

6,568

1,178

6,305

1,175

0.085
(0.111)0.515***(0.175)0.535***(0.168)0.763(0.562)2.673***(0.898)2.913***(0.846)

Note: Standard errors clustered at the district level are in parentheses. For the list of control variables in each regression, see Table 3. OLS in
Panel (a) also controls for NNS-based district characteristics listed in Table 4. The number of districts in Panel (a) is smaller than that in Panel(b) because of missing district characteristics. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.
49

Table 6. The falsification test: regression analysis of height
Panel (a): Base DID
Sample# children# districts

Full sample

18,271

2,265

Children with non-white-collar
fathers
Children with low household
expenditure

9,226

1,657

8,317

1,542

Height-0.002(0.215)0.412(0.289)0.199(0.344)Heightz-score0.002(0.033)0.065(0.045)0.018(0.053)

Panel (b): DID with IPTW and propensity-score trimming
Sample# children# districts

Full sample

13,9091,728

Children with non-white-collar
fathers
Children with low household
expenditure

6,568

1,178

6,305

1,175

Height-0.152(0.261)0.377(0.333)0.048(0.383)Heightz-score-0.022(0.040)0.056(0.053)-0.004(0.059)Note: Standard errors clustered at the district level are in parentheses. For the list of control variables
included in each regression, see Table 3. *, **, and *** indicate statistical significance at the 10%,5%, and 1% levels, respectively.

50

Table 7. Effects of no school lunch for current and post-junior-high students
Panel (a): Base DID
BMI
Full sample(23,472 children, 2,265 districts)

Children with non-white-collar fathers(11,744 children, 1,657 districts)

Children with low household
expenditure(10,534 children, 1,547 districts)

NoSchoolLunchx JuniorHigh
NoSchoolLunchx PostJH
NoSchoolLunchx JuniorHigh
NoSchoolLunchx PostJH
NoSchoolLunchx JuniorHigh
NoSchoolLunchx PostJH

BMI
POW
Obesityz-score(IOTF)
0.085
0.028
0.756
0.006
(0.089)(0.034)(0.461)(0.009)
0.023
0.001
0.489
0.006
(0.102)(0.04)(0.524)(0.011)0.380*** 0.143*** 2.002*** 0.031**(0.132)(0.05)(0.691)(0.013)0.262*
0.092
1.524** 0.031**(0.152)(0.058)(0.769)(0.016)
0.349** 0.136** 2.101*** 0.041***(0.153)(0.057)(0.783)(0.015)0.339** 0.139** 2.122**
0.022(0.166)(0.065)(0.832)(0.018)

Obesity(POW)
0.007(0.010)0.010(0.011)0.026*(0.014)0.025(0.016)
0.046***(0.015)0.027(0.018)Panel (b): DID with IPTW and propensity-score trimming
BMI
Full sample(17,987 children, 1,729 districts)

Children with non-white-collar fathers(8,105 children, 1,121 districts)

Children with low household
expenditure(7,571 children, 1,119 districts)

NoSchoolLunchx JuniorHigh
NoSchoolLunchx PostJH
NoSchoolLunchx JuniorHigh
NoSchoolLunchx PostJH
NoSchoolLunchx JuniorHigh
NoSchoolLunchx PostJH

0.038(0.110)0.141(0.131)0.513***(0.177)0.363*(0.200)0.451**(0.177)
0.661***(0.209)BMI
z-score0.020(0.042)0.060(0.051)0.202***(0.067)0.142*(0.076)
0.189***(0.066)0.260***(0.082)

POW

Obesity(IOTF)
0.573
0.000(0.563) (0.011)
1.185*
0.010(0.672) (0.013)
2.791*** 0.031*(0.908) (0.018)
2.139**
0.020(1.025) (0.019)
2.501*** 0.047**(0.904) (0.018)
3.467*** 0.032(1.068) (0.024)

Obesity(POW)
0.005(0.011)
0.022*(0.013)0.040**(0.019)0.028(0.019)0.052***(0.018)0.041*(0.022)

Note: Standard errors clustered at the district level are in parentheses. PostJH is a dummy variablefor 15- to 17-year-old students who are not junior-high students. Standard errors clustered at the
district level are in parentheses. For the list of control variables included in each regression, see
Table 3. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

51

Appendices
Appendix 1. Details of the Japanese School Lunch Program

Trends in school lunch provision
Official statistics on trends in school lunch provision are drawn from the School Lunch Data Book(SLDB) for 1978–2004 and the Current Status Survey on School Meals (CSSSM) for 2006–2015.
The SLDB is published by the National School Health Center of Japan, and the CSSSM is conductedby the Ministry of Education, Culture, Sports, Science, and Technology (MEXT). 1 We calculateannual nationwide school lunch coverage rates as the fraction of municipal school students withschool lunch in all municipal school students.
Municipalities provide either “complete school lunch,” “complementary school lunch,” or“milk-only school lunch.” “Complementary school lunch” provides dishes except for staple food,and students bring steamed rice or bread on their own. “Milk-only school lunch” only provides milk,
and students bring their food. We use the sum of “complete school lunch” and “complementary
school lunch” to calculate the school lunch coverage rate, though the latter has always been less than
one percent for both elementary and junior-high students.
Figure A1 shows trends in the national school lunch coverage rate for municipal junior-highstudents and in the coverage rate in our sample (as defined in Subsection 4.2). Both lines show
similar increasing trends, although the latter is always higher than the former. This difference can be
explained by low school lunch coverage rates in prefectures excluded from our sample, as detailed inAppendix 3. The school lunch coverage rate for municipal elementary school students (not shown in
the figure) has always been above 98 percent since 1978.

Revisions in nutritional standards

1

www.mext.go.jp/b_menu/toukei/chousa05/kyuushoku/1267027.htm
52

Nutritional standards in the Japanese school lunch program have been revised eight times since 1954.
During our study period (1975–1994), revision occurred only once in 1986. In the 1986 revision,
three-year age categories for elementary school children were replaced by two-year categories, target
values for fat (17g, 20g, and 24g for age groups 6–8, 9–11, and 12–14, respectively) were replacedwith the maximum percentage of energy intake from fat of 30 percent, and the target amounts wereslightly reduced for energy (e.g., from 850kcal to 820kcal for ages 12–14) and protein (e.g., from36g to 32g for ages 12–14) (Nozue, 2011). The revision did not cause significant changes in theenergy or fat contained in school lunch (Narusaka, 1996).

Optional school lunch programs
Since the 1990s, the Ministry of Education has allowed municipalities to make their school lunch
programs optional as a temporary measure for schools that have newly started school lunch programs(Asahi Shimbun, 1996). Under an optional lunch program, students have a choice between a school
lunch and a home-prepared lunch, which might hinder the estimation of causal effects of having school
lunch on child outcomes. During our study period 1975–1994, however, only a handful ofmunicipalities had optional programs, and we remove all children who could have optional school
lunch from our sample, as detailed in Appendix 3.

53Appendix 2. Details of Inverse Probability of Treatment Weighting (IPTW) and Propensity-Score

Trimming
As a robustness check, we use IPTW and propensity-score trimming in the DID analysis to balancemunicipal characteristics between the treatment and control groups in order to make the common
trend assumption more plausible. The propensity scores for IPTW and trimming are estimated using
a logistic regression model, in which NoSchoolLunch dummy is regressed on district characteristics.
The unit of observation is a child. The set of explanatory variables closely resembles those in the
district level regression described in Subsection 4.4 but, following Imbens (2015), we use numericalvariables instead of dummy variables when possible, omit insignificant variables, and add interaction
terms of significant variables to increase the fitness of the model. Specifically, we control prefectural
population density and a linear time trend. We also control for the logged median population size foreach municipal population size category obtained from Statistics Bureau, Ministry of Internal Affairs
and Communications (2012).
IPTW gives each subject a weight equal to the inverse of the probability of treatment the1

subject received. Thus, for students in district d the weight equals p if d is a treatment district and
1

1−p�

�

if d is a control district, where p� denotes the propensity score of a lack of school lunch in d.

Propensity-score trimming excludes observations based on the propensity scores to ensure sufficient
overlap in characteristics between the treatment and control districts. We define the common support
as the interval between the 1st and 99th percentiles of the estimated propensity scores and exclude
from both the treatment and control groups observations that are outside of the common support(Stuart, 2010). We also exclude observations whose estimated propensity score is smaller than 0.1 orlarger than 0.9 (Imbens, 2015).
In these procedures, we require the absolute normalized difference of all the explanatory
variables used in the DID analysis between the treatment and control districts to be less than 0.25, as54

values above 0.25 are considered problematic (Rubin, 2001). Table A1 compares normalized
differences of individual and district characteristics between the treatment and control groups before
and after IPTW and trimming for the full sample and the two low-SES subsamples. Normalized
differences of individual characteristics (i.e., control variables in DID analysis) are shown in Panel(a) and those of district characteristics are shown in Panel (b). Both panels indicate that IPTW andtrimming reduce the absolute normalized differences substantially. The absolute normalized
difference occasionally increases slightly after these procedures, but it is when the original value issmall. When the original absolute normalized difference is large, these procedures always reduce it.
The absolute normalized differences of individual characteristics are always below 0.25, both withand without IPTW and trimming for all three samples. Some of the raw absolute normalized
differences of district characteristics exceed 0.25 without IPTW and trimming, but IPTW andtrimming reduce all of them to below 0.25.

Appendix 3. Details of Data Construction and Sample Selection

Identifying elementary and junior-high students
The NNS questionnaire asks if children are in compulsory education but does not distinguishbetween elementary and junior-high schools. Because a child’s school grade in Japan is strictly
determined by the child’s age on April 2nd, we can use children’s age for this purpose and categorize
6- to 11-year-old and 13- to 15-year-old children in compulsory education as elementary and juniorhigh students, respectively. The school grade of 12-year-olds cannot be determined from theinformation available in the NNS, but for those who are 12 years old in 1986–1994 we can use thebirth month information available in the Comprehensive Survey of Living Conditions (CSLC). The
CSLC is an annual large-scale household survey, administered by the MHLW since 1986, and can bemerged to our NNS data because the NNS target population is subsampled from that of the CSLC.
Because the NNS is conducted in November, we categorize 12-year-olds at the time of survey as55elementary students if they are born between April and October, and those born between December
and March as junior-high students. We exclude 12-year-olds for 1975–1985 from the sample because
we cannot determine their school grade. November-born 12-year-old children in 1986–1994 surveys
are also excluded for the same reason.

Sample Exclusion criteria
Our sample consists of 9- to 15-year-old children in elementary and junior-high schools, excluding
all the 12-year-olds in the 1975–1985 NNS and the November-born 12-year-olds in the 1986–1994
NNS, as described above. From this sample, we exclude children in prefectures with a highproportion of junior-high students attending non-municipal schools and children in Nagoya city in
1993 and 1994, as detailed below. Next, we limit our sample to children with valid information onheight and weight, and exclude a small number of children whose height in z-score exceeds 4.0 in
absolute value; whose POW is −45 percent or lower (i.e., whose weight is 55 percent or less of thestandard weight-for-height); or whose POW is 100 percent or higher (i.e., whose weight is double ormore of the standard weight-for-height), as these values may reflect genetic growth disorders or datacoding error. These threshold values for POW follow medical guidelines indicating emergency
hospitalization for POW of −45 percent or lower (Suzuki, 2016) and metabolic surgery for POW of
100 percent or higher (Kawamura, 1995). A small number of children without a mother in thehousehold or without valid household expenditure data are also excluded. We further limit oursample to children in districts with at least one elementary student and one junior-high student, as
required for DID. Lastly, we exclude children in districts with unreliable school lunch information
due to conflicting or too few answers, and children in districts where less than half of the elementary
school children report having school lunch, as detailed below in this Appendix. Figure A2 presentschanges in the sample size after each step of these exclusion criteria.

56

Reasons for the time frame restriction
The individual-level data from the NNS is available for every year since 1975. We do not use the
NNS data collected after 1994 for two reasons. First, after 1994 the food diary in the NNS covers
only one day of each household’s choice from weekdays and Saturdays. Because our data do notcontain information on the day of the week and school lunch is not served on Saturdays, our imputed
school lunch status will be understated due to the families who chose Saturday for the food diary.
Second, the expansion of optional school lunch programs since the late 1990s obscures the causal
interpretation of our estimate, as detailed in Appendix 1 and in the next section.

Excluding municipalities with optional school lunch programs
As described in Appendix 1, municipalities that newly start school lunch programs after the 1990s
are allowed to make their school lunch program optional and give students a choice between school
lunch and home-prepared lunch (Asahi Shimbun, 1996). This is potentially a concern to our analysis
because optional programs may attenuate our treatment-effect estimate. Among municipalities
included in our data, the city of Nagoya started an optional program on trial at seven of its municipal
junior highs in 1993 (Asahi Shimbun, 1993). We identify children living in Nagoya in 1993 and1994 using prefecture and municipal population size information and exclude those children fromour final sample. Two cities in the Chiba prefecture, Funabashi and Matsudo, also started optional
school lunch programs before 1994 (Asahi Shimbun, 1993), but this is not a concern for our sample
because our sample does not include children in the Chiba prefecture due to its high proportion ofjunior-high students attending non-municipal schools, as explained below.

Municipal provision of school lunch
57

From the individual reports, we only know whether a child had school lunch on certain days, and thisinformation does not necessarily accurately reflect municipal school lunch provision for thefollowing reasons. First, some children might miss school lunch due to sickness or extra-curricular
activities such as excursions. Second, children might attend municipal schools outside of themunicipality. Third, a non-negligible number of junior-high students attend private and national
schools, and few of these schools provide school lunch. We presume that the first type ofmeasurement error is small because we use the food diary of three consecutive days and because the
NNS instructs households to choose a survey period that reflects the household’s usual diet and avoid
a period with a special event. The second type of measurement error is also expected to be small dueto the strict Japanese school district system. Attending municipal schools outside of the municipalityof residence is only permitted for special reasons such as geographic difficulties in commuting to thedesignated school (Nakamura, 2000). Some parents make a false resident registration so that theirchildren can attend municipal schools outside of the school district (e.g., Mainichi, 2015), but this is
illegal and uncommon. To address the third type of measurement error, we exclude prefectures
where the proportion of junior-high students attending non-municipal schools is high. Because
information on the school ownership type is not collected in the NNS, we identify prefectures with ahigh proportion of junior-high students attending non-municipal schools using the number of juniorhigh students by prefecture and ownership type from the School Basic Survey conducted by MEXT. 2
Considering that the proportion of junior-high students attending non-municipal schools has
increased over time, we exclude ten prefectures where the proportion is five percent or higher in
1994: Tokyo, Kochi, Nara, Kanagawa, Kyoto, Hyogo, Hiroshima, Osaka, Chiba, and Mie (listed in
the descending order of the proportion). This exclusion drops 35.4 percent of the observations.

2

http://www.mext.go.jp/b_menu/toukei/chousa01/kihon/1267995.htm
58

We argue that our imputed school lunch status data are reasonably accurate due to the
exclusion of these prefectures, the use of the majority rule, and the exclusion of districts withinsufficient information. Additionally, we complement our imputation with official statistics from the
School Lunch Data Book (SLDB). Specifically, we regard children in prefectures with 99 percent or
higher school lunch coverage, according to the SLDB, as having school lunch. For the years without
SLDB statistics, we apply the same imputation using linearly interpolated values.
Additionally, the comparison of the derived school lunch status with the official statistics
confirms the reliability of our method. As described in Appendix 1, municipalities’ school lunch
programs provide either “complete school lunch,” “complementary school lunch,” or “milk-onlyschool lunch.” According to SLDB, 57.6–66.9 percent of Japanese municipal junior-high students
had “complete school lunch,” 0.5–0.7 percent had “complementary school lunch,” and 18.9–26.5
percent had “milk only school lunch” during our study period. Different types of school lunch
contents obscure the causal interpretation of “having school lunch.” We use “complete school lunch”
and “complementary school lunch” as the definition of school lunch in our analysis, but not “milkonly school lunch” because of its limited scope. However, the NNS does not include information on
the type of school lunch, and hence whether a respondent’s report on school lunch in the NNS
complies with our conceptual notion of school lunch warrants further investigation. To examine
which type of school lunch is captured in our school lunch status imputed from the NNS, we conduct
a prefecture-year level regression analysis in which we regress the imputed school lunch status on theofficially reported participation rates of the three types of school lunch. The dependent variable is theprefecture-year proportion of junior-high students who report having school lunch in our sample. In
constructing this variable, we relax the last two exclusion criteria in Figure A2 and include districts
with too few and/or conflicting reports and districts where less than half of elementary students
report having school lunch. From SLDB, we draw data on the prefecture-year proportions ofmunicipal junior-high students who have “complete,” “complementary,” and “milk-only” school59

lunch. We then conduct a regression analysis in which we regress the variable constructed from oursample on the three SLDB variables.
The results are shown in Table A2. The coefficients on the proportions of students with“complete” and “complementary” school lunch are both significantly positive and close to one,
implying that the vast majority of these students report having school lunch. The coefficient of the
proportion of students with milk-only school lunch is not significant and is small in magnitude,
implying that few of these students report having school lunch. These findings indicate that theschool lunch information in the NNS data closely coincides with the sum of “complete school lunch”
and “complementary school lunch,” which is our definition of school lunch.

Appendix 4. Additional Tables

Summary statistics of the district-level data
Table A3 shows the summary statistics of the district-level data. Junior-high lunch is less common inlarge municipalities. About 28 percent of the districts with junior-high lunch are in cities with apopulation of 150,000 or more, whereas about 54 percent of the districts without junior-high lunch arein cities with a population of 150,000 or more.

Coefficients on year dummies in NoSchoolLunch Logit regression
Table A4 presents the estimated coefficients on year dummies of the NoSchoolLunch regression, which
are not reported in Table 4. Consistent with the overtime increase in school lunch coverage (FigureA1), the estimated coefficients are significantly negative for most years since 1983.

Appendix 5. Further Robustness Checks

60Permutation test
To address a concern in our DID analysis that correlation among children close in age and location
might lead to underestimation of standard errors, we implement non-parametric permutation tests inthe spirit of Bertrand et al. (2004) and Abadie et al. (2010). In this test, the treatment NoSchoolLunchis randomly assigned to control districts holding the same frequency as in the original sample, and thebase DID model is estimated based on the hypothetical treatment assignment. Repeating this procedure
many times yields the distribution of the estimated placebo treatment effect. The resulting placebo
distributions from 1,000 random draws are shown in Figure A3 for (a) the full sample, (b) the
subsample of children with non-white-collar fathers, and (c) the subsample of children with low
household expenditure in Panels (a) to (c), respectively. The vertical red lines indicate the actual
estimate, i.e., the estimated treatment effect in the original estimation. Numbers below each graphshow the actual estimate and the pseudo P-value, defined as the frequency ratio of placebo estimates
exceeding the actual estimate in absolute terms. The results are highly consistent with our main resultsfrom the base DID presented in panel (b) of Table 5. For BMI, BMI z-score, POW, and the two obesity
measures, the actual estimates in all three samples are always in the right tail of the distribution, andin both of the low-SES subsamples the pseudo P-values are all smaller than 0.05, with the exceptionof one value of 0.068, while the pseudo P-values in the full sample are all larger than 0.1. For both of
the underweight measures, the actual estimates are around the middle of the distribution, and thepseudo P-values are all larger than 0.1 in all three samples. These findings imply that the statisticalsignificance of our estimated school lunch effects is not due to the misspecification of correlation
structure.

Adding interaction terms with JuniorHigh dummy61

To address the potential violation of the common trend assumption, we test a model with the interaction
terms of the JuniorHigh dummy with five-year period dummies, municipal size dummies, andprefectural population density. These interaction terms are to account for the possibility that changes
in the growth patterns after entering junior highs due to lifestyle alterations, such as time spent on
studying and school sports club activities, differ by urbanicity and survey timing. Because theregression analysis of the NoSchoolLunch dummy reveals the significant effects of urbanicity andsurvey years on school lunch status (Table 4), our results might be confounded by the differential
effects of attending junior highs on body weight. The estimated effects for the base DID and DID with
IPTW and propensity-score trimming are shown in Panels (a) and (b) of Table A5, respectively. The
results are highly similar to those from the base models (Table 5), confirming that our results are robust
to this modification.
Similarly, we add the triple interactions of the JuniorHigh dummy, year dummies, and prefecturedummies to the DID regression model to allow for differential effects of attending junior high byprefecture-year. The estimated effects for the base DID and DID with IPTW and propensity-score
trimming are shown in Panels (a) and (b) of Table A6, respectively. Again, this modification causes
little change to the results, confirming the robustness of our results.

Synthetic control method
While the common trend assumption implies similar pre-treatment trends between the treatment andcontrol groups, mean BMI by age and gender presented in Figure 4 show small but noticeable
differences between groups in pre-treatment ages. To address this concern, we implement a synthetic
control method proposed by Abadie et al. (2010) in which we create an artificial control group whose
pre-treatment trends are more similar to the treatment group than the original control group. Using
aggregate panel data at the level of the treatment group and control subgroups, this method assigns

62weights to the control subgroups so as to minimize the differences in predictors between thetreatment group and the weighted average of the control subgroups prior to the treatment, wherepredictors could include pre-treatment outcome values and other covariates. Using this weight, an
artificial control group called the synthetic control group is constructed as the weighted average ofthe control subgroups. Based on the premise that the post-treatment path of this synthetic control
group approximates the counterfactual path of the treatment in the absence of the treatment, the posttreatment outcome trends are compared between the treatment and synthetic control groups. To
obtain statistical inference of treatment effect estimates, Abadie et al. (2010) also propose a placebo
test that treats each of the control subgroups as a placebo treatment group and applies the synthetic
control method that regards the actual treatment group and the rest of the control subgroups as
placebo control subgroups.
We implement the synthetic control method to estimate the effect of the lack of school lunch
on age-specific means of BMI, BMI z-score, and POW, as well as rates of obesity and underweightunder IOTF and POW definitions. Because this method requires control subgroups with asufficiently large number of observations, we group NoSchoolLunch districts by five periods (1975–
78, 79–82, 83–85, 86–89, and 90–94) and two regions (east Japan consisting of prefectures Nagano,Niigata, Shizuoka, Yamanashi, and those to the east of these, and west Japan consisting ofprefectures to the west of these) to create ten control subgroups. Using this grouping, we constructaggregate panel data at the level of the treatment group and control subgroups over the ages of 7 to
11, 13, and 14. We exclude 12-year-olds and 15-year-olds due to the small number of observations.
To ensure a sufficiently long pre-treatment period, we add 7- and 8-year-old elementary students. For
predictors, we use pre-treatment values of the outcome variable and maternal BMI; and for obesity
and underweight outcomes, we also use pre-treatment values of BMI z-score for IOTF-based
outcomes and those of POW for POW-based outcomes. Among predictors, the pre-treatment63

outcome values are averaged for ages 7–10 and age 11, and the other predictors are averaged overthe entire pre-treatment ages of 7 to 11.
Figure A4 presents (a) the results for the full sample, (b) the subsample of children with nonwhite-collar fathers, and (c) the subsample of children with low household expenditure in Panels (a)(c), respectively. In the graphs on the left, black lines plot the gap in the mean between the actual
treatment group and synthetic control group against age, and gray lines show gaps between the placebo
treatment group and the corresponding synthetic control group (henceforth, the trend graph). The
vertical red line indicates age 12, the threshold age that divides elementary and junior-high students.
The graphs on the right present the histogram of the ratio of post- to pre-treatment mean-squared
prediction error (MSPE) for the actual and placebo treatment groups, where bars with vertical red
dotted line indicate the actual value and other bars indicate the ten placebo values. Loosely speaking,if the actual value is larger than the ten placebo values, the null hypothesis of zero treatment effect canbe rejected at the 10 percent level. Overall, the results are consistent with the DID results shown in themain text. In the full sample, the trend graphs show relatively small changes in the actual gap, and thehistograms do not support significant post-treatment changes. An exception is the obesity rate under
POW, with its histogram indicating a significant post-treatment change and the trend graph showing amoderate increase after age 11. In the subsample of children with non-white-collar fathers, the trend
graphs show clear increases in the actual gap after age 11 for BMI, BMI z-score, POW, and the obesity
rates under both definitions. The histograms also indicate significant post-treatment changes for all ofthese outcomes with the exception of the BMI z-score, where one placebo value exceeded the actual
value. For the underweight rate under POW definition, the actual gap for the underweight rate under
IOTF definition decreases after age 11, and according to the histogram this post-treatment change isstatistically significant, whereas almost no changes in the actual gap are observed in the trend graphand the histogram does not support significant post-treatment changes. In the subsample of children
with low household expenditure, post-treatment increases are observed in the trend graphs for BMI,

64

BMI z-score, POW, and the obesity rates under both definitions, and the histograms indicate significant
post-treatment changes for all of these outcomes except for POW. For both of the underweightmeasures, the post-treatment changes in the actual gap appear small in the trend graphs and are notstatistically significant according to the histograms.

Relaxing the prefecture selection criterionChildren in prefectures with 5 percent or more of junior-high students attending non-municipal (i.e.,
private or national) schools as of 1994 are omitted from our main analysis. As a robustness check, we
relax this selection criterion to include prefectures where the proportion is between 5 and 10 percent.
The majority of the previously excluded prefectures meet this criterion (Chiba, Hiroshima, Hyogo,
Kanagawa, Kyoto, Mie, Nara, and Osaka), and the prefectures excluded under this new criterion are
only Kochi (15.6 percent) and Tokyo (22.9 percent). The estimated treatment effects from the DID
regression are shown in Table A7. The estimated effects are highly similar to those with ourpreferred selection criterion shown in Table 5.

Exclusion of 12- and 15-year-olds
Among 12-year-olds, some are elementary and others are junior-high students, depending on thebirth month. Similarly, among 15-year-olds, some are current and others are post-junior-highstudents. Hence, our results might be affected by potential differential effects of the birth month onchildren’s height and weight between the treatment and control groups. To address this concern, we
estimate the DID models excluding 12- and 15-year-olds. The estimated treatment effects from the
DID regression, shown in Table A8, are highly similar to those without this exclusion shown in
Table 5.

65

To assess the effects of the birth month on growth patterns, Figure A5 plots year-adjusted
means of height by gender over age in month for the treatment and control groups for the full sample
and the two low-SES subsamples, where the age is aggregated by quarter of year. Children surveyed
before 1986 and November-born children are excluded because we cannot determine their age inmonth. To adjust for differences in survey year composition by age, we subtract the gap between themean by year and the aggregate mean from each value, as we do for Figure 4. The vertical graydotted lines show the birth months during the second quarter, i.e., April through June. Because
children born on April 2nd are the eldest in class and those born on April 1st are the youngest, under
the Japanese age-grade system, if parents select the birth timing to exploit the relative age effect, theselection effect would likely lead to an increased difference in height between children born in thefirst and second quarters. For all three samples and for both genders, the influence of the birth timing
appears small, and little systematic difference in the birth month effects is observed between thetreatment and control groups.

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Lunch. Retrieved from Asahi Shimbun Kikuzo database (In Japanese).

66Bertrand M, Duflo E, Mullainathan S, 2004. How much should we trust differences-in-differences
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Attending a School out of School District within This Year. Retrieved from mainichi.jp (inJapanese).
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Narusaka M, 1996. Changes in fat supply in school lunch menus in Okayama City. Japanese Journalof Nutrition and Dietetics 54 (2): 121–128 (in Japanese).
Nozue M, 2011. The contribution of school lunch to dietary intakes in school children andapplication of dietary reference intakes: A case study of fifth-grade school children. Ph.D.
Thesis, Kagawa Nutrition University (in Japanese).
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67Figure A1. Trends in the school lunch coverage rate for municipal junior-high students

Note: The nationwide coverage rate is based on the School Lunch Data Book (SLDB) and defined as
the share of municipal junior-high students who have school lunch. The sample coverage rate is theshare of junior-high students in districts with school lunch in our sample. For the discussion on the
difference between the two coverage rates, see Appendix 1.

68Figure A2. Sample exclusion criteria and changes in the sample size
Initial sample: 9- to 15-year-old children in compulsory education,
excluding 12-year-olds in the 1975–1985 NNS and November-born 12year-olds in the 1986–1994 NNS

5,580 districts,
37,990 children

Exclude children in prefectures with a high proportion of junior-highstudents in non-municipal schools and children in the city of Nagoya in
1993 and 1994
3,280 districts,
24,530 children
Exclude children without valid information on height and weight
3,228 districts,
22,241 children
Exclude children with deviant height and weight
3,227 districts,
22,205 children
Exclude children without a mother in the household or without valid
household expenditure data
3,205 districts,
21,327 children
Exclude districts without elementary students and districts without
junior-high students
2,661 districts,
20,064children
Exclude districts with conflicting or too few answers on school lunch
2,311 districts,
18,669 children
Exclude districts without school lunch for elementary school children
2,265 districts,
18,271children

69

Figure A3. Permutation tests: empirical distributions of placebo estimates
Panel (a): Full sample

actual estimate=0.093,
pseudo P-value=0.296

actual estimate=0.032,
pseudo P-value=0.351

actual estimate=0.767,
pseudo P-value=0.109

actual estimate=0.007,
pseudo P-value=0.464

actual estimate=0.007,
pseudo P-value=0.5

actual estimate=0.002,
pseudo P-value=0.901

actual estimate=0.005,
pseudo P-value=0.334

Note: Each graph shows the kernel density estimate of the distribution of estimated placebo
treatment effects using Epanechnikov kernel. The vertical red line represents the actual estimate.
“Pseudo P-value” refers to the frequency ratio of placebo estimates exceeding the actual estimate inabsolute terms (in 1,000 random draws).

70

Figure A3 (cont.)
Panel (b): Children with non-white-collar fathers

actual estimate=0.403,
pseudo P-value=0.001

actual estimate=0.152,
pseudo P-value=0.002

actual estimate=2.076,
pseudo P-value=0.002

actual estimate=0.031,
pseudo P-value=0.032

actual estimate=0.026,
pseudo P-value=0.068

actual estimate=-0.023,
pseudo P-value=0.22

actual estimate=0.01,
pseudo P-value=0.164

Note: Each graph shows the kernel density estimate of the distribution of estimated placebo
treatment effects using Epanechnikov kernel. The vertical red line represents the actual estimate.
“Pseudo P-value” refers to the frequency ratio of placebo estimates exceeding the actual estimate inabsolute terms (in 1,000 random draws).

71

Figure A3 (cont.)
Panel (c): Children with low household expenditure

actual estimate=0.418,
pseudo P-value=0.004

actual estimate=0.167,
pseudo P-value=0.003

actual estimate=2.266,
pseudo P-value=0.001

actual estimate=0.051,
pseudo P-value=0

actual estimate=0.052,
pseudo P-value=0

actual estimate=-0.004,
pseudo P-value=0.821

actual estimate=0.005,
pseudo P-value=0.48

Note: Each graph shows the kernel density estimate of the distribution of estimated placebo
treatment effects using Epanechnikov kernel. The vertical red line represents the actual estimate.
“Pseudo P-value” refers to the frequency ratio of placebo estimates exceeding the actual estimate inabsolute terms (in 1,000 random draws).

72

Figure A4. Results from the synthetic control analysis
Panel (a): Full sample

Note: In the graphs on the left, black lines plot the gap in the mean between the actual treatmentgroup and synthetic control group against age, and gray lines show gaps between the placebo
treatment group and the corresponding synthetic control group. Vertical red lines indicate age 12, thethreshold age that divides elementary and junior-high students. The graphs on the right present thehistogram of the ratio of post- to pre-treatment MSPE (mean squared prediction error) for the actualand placebo treatment groups, where bars with a vertical red dotted line indicate the actual value andother bars indicate the ten placebo values.

73Figure A4. (cont.)
Panel (b): Children with non-white-collar fathers

Note: In the graphs on the left, black lines plot the gap in the mean between the actual treatmentgroup and synthetic control group against age, and gray lines show gaps between the placebo
treatment group and the corresponding synthetic control group. Vertical red lines indicate age 12, thethreshold age that divides elementary and junior-high students. The graphs on the right present thehistogram of the ratio of post- to pre-treatment MSPE for the actual and placebo treatment groups,
where bars with a vertical red dotted line indicate the actual value and other bars indicate the tenplacebo values.

74

Figure A4. (cont.)
Panel (c): Children with low household expenditure

Note: In the graphs on the left, black lines plot the gap in the mean between the actual treatmentgroup and synthetic control group against age, and gray lines show gaps between the placebo
treatment group and the corresponding synthetic control group. Vertical red lines indicate age 12, thethreshold age that divides elementary and junior-high students. The graphs on the right present thehistogram of the ratio of post- to pre-treatment MSPE for the actual and placebo treatment groups,
where bars with a vertical red dotted line indicate the actual value and other bars indicate the tenplacebo values.

75

Figure A5. Mean height over age in monthNote: The age is aggregated by quarter of year. Children surveyed before 1986 or born in November
are excluded for data reasons. To adjust for differences in survey year composition by age, we
subtract the gap between mean by year and aggregate mean from each value. The vertical gray dottedlines indicate the birth months during the second quarter.
76

Table A1. Normalized differences of individual and district characteristics
Panel (a): Individual characteristics (control variables in DID analysis)
Variable
Trimming and IPTW-weighting
Male
Age
Father's age
Father's height (z score by age,sex, and 5-year cohort)
Father's BMI (z score by age, sex,
and 5-year cohort)
Father's height and BMI missing
Father: white-collar worker (thereference category)
Father: laborer
Father: self-employed
Father:agriculture/fisheries/forestry
Father: other occupation (notworking)
Without father in household
Mother's age
Mother's height (z score by age,sex, and 5-year cohort)
Mother's BMI (z score by age,sex, and 5-year cohort)
Mother's height and BMI missing
Mother: white-collar worker (thereference category)
Mother: laborer
Mother: self-employed
Mother:agriculture/fisheries/forestry
Mother: other occupation (notworking)Grandfather in householdGrandmother in household# of children in household (below
18 years old)
Per-member household
expenditure (defined as 100% =families with lowest expendituresin each survey year)

No
0.014
-0.025
0.004
0.072

Yes
0.012
-0.024-0.026
0.030

Children with nonwhite-collar fathers
No
Yes
0.028
0.053
-0.045-0.0430.000-0.0520.041-0.003-0.035-0.006-0.031-0.035-0.028-0.022

0.009
0.027

-0.002-0.011-0.033-0.069

0.017
0.013

-0.023-0.0270.011
0.016-0.1040.004-0.019
0.022

0.060
0.028
-0.1310.018-0.059
0.063

0.025
0.023
-0.096-0.001
0.000
0.043

0.002

-0.021-0.002-0.0200.009-0.011

0.005-0.001
0.056

0.026
0.011
-0.008-0.0430.003-0.048-0.0380.007-0.0260.028-0.001-0.009-0.011-0.097-0.059-0.073-0.055-0.097-0.059-0.001
0.024

0.021
0.072

-0.007
0.059

0.029
0.072

-0.013
0.041

0.004
0.069

-0.0200.019-0.1500.045
0.004-0.042-0.0150.019-0.1670.058-0.001-0.0210.010
0.039-0.1680.045
0.055-0.0530.067-0.0740.076-0.0880.048-0.101-0.101-0.099-0.042

0.021
0.035
0.002

-0.123-0.080-0.0290.001
0.030-0.028-0.073-0.050-0.007

0.059
0.093
0.017

-0.1470.038-0.172-0.035-0.186-0.093Full sample

Children with low
household expenditure
No
Yes
0.013
-0.004
0.003
0.013
0.004
0.010
0.048
0.036

Note: None of the absolute normalized differences exceed 0.25. Occupational proportions refer to the
proportion of 23- to 54-year-old workers in each occupation.

77

Table A1. (cont.)
Panel (b): District characteristics
Variable

Full sample

Children with nonwhite-collar fathersNo
Yes-0.2460.003
0.082-0.071Children with low
household expenditureNo
Yes-0.1050.095
0.056-0.151

Trimming and IPTW-weighting
Year
Prefectural population density(1,000 person/km2)
Logged municipal population size
District: mean child height (zscore)
District: mean child BMI (z score)
District: child obesity rate (IOTF)
District: child underweight rate
(IOTF)
District: # of participants
District: mean age
District: median per-member
household expenditure
District: mean household size
District: proportion of white-collar
workerDistrict: proportion of laborer
District: proportion of selfemployedDistrict: proportion of agriculture
District: proportion of working
women

No
-0.222
0.063

Yes
0.061
-0.1260.729*
0.111-0.0480.124

0.794*
0.102-0.021
0.065

0.686*
0.124-0.0950.091-0.031-0.004
0.034

0.044
0.064
-0.028-0.0370.018
0.054-0.0020.046-0.0260.009-0.023-0.0200.051
0.001-0.043-0.145-0.080-0.328*-0.0750.170-0.041-0.106-0.100-0.346*-0.0930.116-0.097-0.112-0.044-0.353*-0.0390.238-0.093-0.2120.059-0.011-0.051-0.2070.008-0.025-0.131-0.1950.094

0.020-0.065

0.021
0.124

0.039
0.024

0.070
0.165

0.062
0.028

0.044
0.110

0.019
0.021

-0.214-0.143

0.000
0.190

-0.213-0.133

0.030
0.197

-0.215-0.115

0.028
0.239

Note: * indicates absolute normalized difference exceeding 0.25. Occupational proportions refer to the
proportion of 23- to 54-year-old workers in each occupation.

78

Table A2. Prefecture-year level regression of the proportion of junior-high students who had school
lunch
Variable
SLDB proportion of students with complete school lunch
SLDB proportion of students with complementary school lunch
SLDB proportion of students with milk only
ConstantN
Adjusted R2

Coefficients(0.092)0.893***(0.458)0.947**(0.107)0.031(8.863)
8.083
427
0.320

Note: Standard errors are in parentheses. The unit of observation is a prefecture-year. The proportion ofjunior-high students who had school lunch in our NNS sample is calculated at the prefecture-year level
and regressed on the proportions of those with the three types of school lunch in the official SLDB
statistics. Both the regressand and the regressors are in percentage terms. *, **, and *** indicate
statistical significance at the 10%, 5%, and 1% levels, respectively.

79

Table A3. Summary statistics of the district-level data

Variable
District: mean child height (z score)
District: mean child BMI (z score)
District: child obesity rate (IOTF BMI 25+)
District: child underweight rate (IOTF BMI 18.5-)
District: # of participants
District: proportion of age 1–19
District: proportion of age 20–39 (reference)
District: proportion of age 40–59
District: proportion of age 60+
District: median per-member household expenditure
District: mean household size
District: proportion of white-collar worker (reference)
District: proportion of laborer
District: proportion of self-employedDistrict: proportion of agriculture/fisheries/forestry
District: proportion of working women
Prefectural population density (1,000 person/km2)
Municipal size: 11 largest cities
Municipal size: cities with 150k+ population
Municipal size: cities with 50–150k population
Municipal size: cities with 50k- population
Municipal size: towns & villages (reference)
Region block: Hokkaido & Tohoku
Region block: Kanto
Region block: Chubu (reference)
Region block: Kinki
Region block: Chugoku & Shikoku
Region block: Kyushu & Okinawa
Year
Number of districts

Districts with nojunior-high lunch
Mean
Std. Dev

0.015
0.001
0.162
0.118
81.27
0.316
0.263
0.277
0.144
0.503
4.152
0.386
0.346
0.209
0.059
0.573
0.510
0.183
0.362
0.224
0.096
0.134
0.171
0.081
0.595
0.064
0.090
0.252
1982.7

0.360
0.395
0.142
0.115
27.49
0.067
0.075
0.071
0.079
0.184
0.582
0.207
0.192
0.152
0.141
0.188
0.433
0.387
0.481
0.417
0.295
0.341
0.377
0.273
0.491
0.245
0.286
0.434
5.6
469

Control districts
Mean

Std. Dev-0.010
0.010
0.159
0.113
85.4
0.309
0.260
0.275
0.156
0.571
4.291
0.370
0.345
0.187
0.098
0.608
0.462
0.031
0.248
0.217
0.103
0.402
0.184
0.190
0.485
0.018
0.123
0.194
1984.2
1,648

0.366
0.370
0.134
0.108
26.87
0.070
0.076
0.071
0.089
0.189
0.630
0.208
0.188
0.153
0.173
0.197
0.446
0.173
0.432
0.412
0.303
0.490
0.387
0.392
0.500
0.132
0.329
0.395
5.5

***
*

***
***
***

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

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

Note: Occupational proportions refer to the proportion of 23- to 54-year-olds in each occupation. The
number of districts is smaller than that in the full sample DID regression because 148 districts with lessthan five children of age 1 to 11 are removed from this sample. *, **, and *** indicate statisticallysignificant differences in means between the control and treatment districts at the 10%, 5%, and 1%
levels, respectively.

80Table A4. The estimated year effects from Logit regression of NoSchoolLunch
VariableYear 1976
Year 1977
Year 1978
Year 1979
Year 1980
Year 1981
Year 1982
Year 1983
Year 1984
Year 1985
Year 1986
Year 1987
Year 1988
Year 1989
Year 1990
Year 1991
Year 1992
Year 1993
Year 1994
Region block dummies
Prefecture dummies

Model1 (N=2,117)
0.056(0.299)0.089(0.319)-0.248(0.318)-0.252(0.334)-0.424(0.319)-0.318(0.336)-0.536(0.333)-1.135*** (0.384)-0.849**(0.346)-0.710**(0.345)-1.129*** (0.340)-1.002*** (0.357)-0.788**(0.338)-1.395*** (0.414)-0.958*** (0.368)-0.718**(0.356)-0.844**(0.371)-1.312*** (0.418)-1.203*** (0.448)
YesNo

Model2 (N=2,075)
0.089(0.335)0.200(0.377)-0.138(0.366)-0.179(0.364)-0.359(0.364)-0.335(0.385)-0.344(0.374)-1.127**(0.439)-0.746*(0.392)-0.642(0.401)-1.057***(0.391)-0.755*(0.409)-0.684*(0.398)-1.365***(0.466)-0.970**(0.440)-0.415(0.408)-0.729*(0.431)-1.153**(0.466)-1.048**(0.522)
No
Yes

Note: This table presents the year effects estimated in the NoSchoolLunch Logit regression, which are
not reported in Table 4. The reference year is 1975. Standard errors are in parentheses. *, **, and ***indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

81

Table A5. Effects of no school lunch: Interacting JuniorHigh with urbanicity variables and period dummies
Panel (a): DID + interaction terms
Sample# children# districts

Full sample

18,271

2,265

Children with non-white-collar
fathers
Children with low household
expenditure

9,226

1,657

8,317

1,542

BMI

BMI
z-scorePOW

Obesity(IOTF)

Obesity(POW)

Underweight(IOTF)

Underweight
(POW)

0.048
(0.094)0.402***(0.145)0.390**(0.155)0.020(0.036)
0.156***(0.056)0.158***(0.059)0.526(0.491)2.111***(0.760)2.023**(0.795)0.003(0.010)0.035**(0.015)0.053***(0.015)0.008(0.010)0.032**(0.015)0.054***(0.015)0.007(0.015)-0.017(0.021)
0.004(0.023)0.010*(0.006)0.016*(0.009)0.011(0.008)Panel (b): DID with IPTW and propensity-score trimming + interaction terms
Sample# children# districts

Full sample

13,9091,728

Children with non-white-collar
fathers
Children with low household
expenditure

6,568

1,178

6,305

1,175

BMI

BMI
z-scorePOW

Obesity(IOTF)

Obesity(POW)

Underweight(IOTF)

Underweight
(POW)

0.108
(0.105)0.546***(0.167)0.507***(0.168)0.043(0.040)0.211***(0.064)0.206***(0.064)0.873(0.540)2.873***(0.869)2.645***(0.851)0.004(0.011)0.039**(0.017)0.057***(0.016)-0.002(0.011)0.039**(0.017)
0.053***(0.017)0.002(0.015)-0.029(0.023)-0.009(0.023)0.003(0.006)0.010(0.009)0.007(0.008)

Note: Standard errors clustered at the district level are in parentheses. For the list of control variables included in each regression, see
Table 3. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

82

Table A6. Effects of no school lunch: Interacting JuniorHigh with state-year fixed effects
Panel (a): DID + interaction terms
Sample# children# districts

Full sample

18,271

2,265

Children with non-white-collar
fathers
Children with low household
expenditure

9,226

1,657

8,317

1,542

BMI

BMI
z-scorePOW

Obesity(IOTF)

Obesity(POW)

Underweight(IOTF)

Underweight
(POW)

0.074
(0.106)0.438***(0.168)0.502***(0.192)0.031(0.041)0.182***(0.065)0.217***(0.072)0.611(0.555)
1.943**(0.881)2.883***(0.986)0.004(0.011)0.029*(0.016)
0.055***(0.018)-0.002(0.011)0.017(0.017)0.044**(0.019)0.018(0.016)-0.027(0.026)-0.006(0.027)0.003(0.006)-0.002(0.010)0.005(0.010)Panel (b): DID with IPTW and propensity-score trimming + interaction terms
Sample# children# districts

Full sample

13,9091,728

Children with non-white-collar
fathers
Children with low household
expenditure

6,568

1,178

6,305

1,175

BMI

BMI
z-scorePOW

Obesity(IOTF)

Obesity(POW)

Underweight(IOTF)

Underweight
(POW)

0.093
(0.128)0.645***(0.204)0.670***(0.236)0.033(0.049)0.258***(0.080)0.294***(0.088)0.719(0.674)2.641**(1.086)3.766***(1.214)0.003(0.014)0.054***(0.020)0.071***(0.022)0.000(0.014)0.036*(0.021)0.047**(0.021)0.034*(0.019)-0.013(0.031)
0.007(0.033)0.001(0.007)0.002(0.013)0.001(0.011)

Note: Standard errors clustered at the district level are in parentheses. For the list of control variables included in each regression, see
Table 3. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

83

Table A7. Effects of no school lunch: Relaxing the prefecture selection criterion
Panel (a): DID
Sample# children# districts

Full sample

24,4603,148Children with non-white-collar
fathers
Children with low household
expenditure

11,723

2,179

11,076

2,086

BMI

BMI
z-scorePOW

Obesity(IOTF)

Obesity(POW)

Underweight(IOTF)

Underweight
(POW)

0.011
(0.067)0.255**(0.105)0.274**(0.111)

0.005(0.026)
0.092**(0.041)0.118***(0.042)0.307(0.351)1.426***(0.552)
1.557***(0.577)0.003(0.007)0.030***(0.011)0.036***(0.011)0.006(0.007)0.028***(0.011)
0.043***(0.011)0.001(0.011)-0.009(0.016)-0.015(0.017)0.006(0.004)0.012*(0.007)0.003(0.006)

BMI

BMI
z-scorePOW

Obesity(IOTF)

Obesity(POW)

Underweight(IOTF)

Underweight(POW)

0.323**(0.130)0.339**(0.139)0.128**(0.050)0.146***(0.053)

1.955***(0.682)2.046***(0.726)0.032**(0.014)0.043***(0.014)0.038***(0.014)0.056***(0.014)-0.002(0.019)-0.004(0.021)0.015*(0.008)0.006(0.007)

Panel (b): DID with IPTW and propensity-score trimming
SampleChildren with non-white-collar
fathers
Children with low household
expenditure# children# districts

9,274

1,686

9,695

1,770

Note: Standard errors clustered at the district level are in parentheses. For the list of control variables included in each regression, see
Table 3. In Panel (b), the results for the full sample are omitted because IPTW and propensity-score trimming failed to reduce thenormalized differences of individual and district characteristics between the treatment and control groups below the threshold value of
0.25. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

84

Table A8. Effects of no school lunch: Excluding 12-year-olds and 15-year-olds
Panel (a): DID
Sample# children# districts

Full sample

15,2452,168

Children with non-white-collar
fathers
Children with low household
expenditure

7,580

1,504

6,718

1,380

BMI

BMI
z-scorePOW

Obesity(IOTF)

Obesity(POW)

Underweight(IOTF)

Underweight
(POW)

0.152
(0.101)0.601***(0.154)0.504***(0.172)0.051(0.039)0.220***(0.059)0.199***(0.066)

1.065**(0.524)
3.104***(0.805)2.696***(0.886)0.013(0.010)0.042***(0.015)0.057***(0.017)0.013(0.011)0.036**(0.016)
0.056***(0.017)-0.008(0.015)-0.043**(0.022)-0.026(0.023)0.007(0.006)0.008(0.009)0.003(0.008)

BMI

BMI
z-scorePOW

Obesity(IOTF)

Obesity(POW)

Underweight(IOTF)

Underweight
(POW)

0.183
(0.120)0.683***(0.191)0.705***(0.189)0.073(0.046)0.256***(0.073)0.284***(0.072)

1.236**(0.613)3.530***(0.971)
3.691***(0.953)0.008(0.013)0.045**(0.019)0.068***(0.018)0.012(0.013)0.046**(0.020)0.068***(0.019)-0.019(0.018)-0.038(0.026)-0.032(0.026)0.003(0.005)0.008(0.009)0.010(0.008)Panel (b): DID with IPTW and propensity-score trimming
Sample# children# districts

Full sample

11,831

1,665

Children with non-white-collar
fathers
Children with low household
expenditure

5,471

1,069

5,422

1,104

Note: Standard errors clustered at the district level are in parentheses. For the list of control variables included in each regression, see
Table 3. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

85