Discussion Paper No.

996

MARGINAL RETURNSTO SCHOOLING AND
EDUCATION POLICY CHANGE
IN JAPAN

Nobuyoshi Kikuchi

March 2017
Revised October 2017

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Marginal Returns to Schoolingand Education Policy Change in Japan∗
Nobuyoshi Kikuchi†
ISER, Osaka University
October 24, 2017
Abstract
This paper examines the returns to university education in Japan, using tuition, availability of universities, and labor market conditions as instrumental variables. To measure
availability of universities, this paper uses total accredited capacity of all universities in
the prefecture of residence at the age of 15. This measure captures cross-time and crossprefecture variations, because birth cohort and prefecture dummies are also controlled. A
set of education policy-relevant instruments allows for estimation of the marginal effects forindividuals who are induced to enroll in university by policy changes. Using the estimatedmarginal treatment effect, this paper recovers the average treatment effect parameters. The
main empirical result shows that an additional year of university education increases hourly
wage by about 9% on the population average. This paper also finds heterogeneous effects by
subpopulation groups: the average effect of a year of university education for those enrolled
in university is about 17%, but less than 2% for those who did not enroll. Finally, this paper
investigates the average returns for those who are induced to enroll in university by a particular policy shift, such as free tuition or an increase in the capacity of local universities. The
results suggest that such policy changes bring about positive effects of university education.
JEL Classification: J24, J31, I23, I28
Keywords: Returns to education, education policies, marginal treatment effect, policyrelevant treatment effect∗ This paper is based on part of my dissertation at the University of Tokyo. I am grateful to my advisor, Hidehiko

Ichimura, for his guidance and support. I would also like to thank Takeshi Aida, Hideo Akabayashi, Yuji Genda,
Keisuke Hirano, Daiji Kawaguchi, Ayako Kondo, Jordan Matsudaira, Ryo Nakajima, Fumio Ohtake, Hideo Owan,
Shinpei Sano, Yasuyuki Sawada, Mari Tanaka, Shintaro Yamaguchi, Kengo Yasui, and seminar participants at Keio
University, Nihon University, Osaka University, the University of Tokyo, the Research Institute of Economy, Tradeand Industry, the 2011 HiStat/TCER/Tokyo Labor Economics Workshop Joint Conference on Early Formationof Human Capital, Kansai Labor Seminar (Kansai Rodo Kenkyukai), the 2011 Japanese Economic Association
Autumn Meeting, the Third Conference of Education Economics and Policy in Japan, the 4th Chulalongkorn
University and Osaka University Joint Workshop 2016, the 10th Trans-Pacific Labor Seminar, and the 2017 Annual
Conference of the International Association for Applied Econometrics for their helpful comments and suggestions
on earlier versions of this paper. Any remaining errors are my own. This research was supported by Grant-in-Aid
for Research Activity Start-up No. 16H06925 from the Japan Society for the Promotion of Science.
† Institute of Social and Economic Research, Osaka University; 6-1, Mihogaoka, Ibaraki, Osaka 567-0047,
Japan. E-mail: kikuchi@iser.osaka-u.ac.jp.

1

Introduction

Policy makers and scholars broadly agree about the importance of the government’s role inproviding equal opportunities for access to higher education. The trend of the university
enrollment rate in Japan suggests that this task is progressing satisfactorily: the enrollment rate
has risen from around 17% in 1970 to above 50% in 2010, according to the School Basic Surveyof the Ministry of Education, Culture, Sports, Science and Technology (MEXT). In contrast
to this absolute increase in enrollment rate, however, providing equal opportunities for accessto higher education still requires attention. University enrollment rates are still substantiallydifferent between regions, especially between rural and urban regions. Prefectural average
enrollment rates range from a low of about 30% in Kagoshima to a high of about 64% in Tokyoin 2015.1
Japan still has problems with accessibility and affordability of local universities. For example,
universities are highly concentrated in urban regions: more than half of universities are locatedin only 10 out of 47 prefectures.2 Sasaki (2006), Kobayashi (2009), Nakazawa (2011), andUeyama (2011, 2012) suggest that the high concentration of universities in urban regions partly
explains regional differences in prefectural average enrollment rates. If the number of local
universities is insufficient, public supply becomes a key factor in access to higher education.
Unfortunately, students also face the burden of high public tuition fees in Japan. OECD (2015)
notes that the average annual fee to attend a public tertiary institution in Japan during the 2014–2015 academic year was some of the highest among OECD countries. In addition, students havea limited opportunity for university tuition subsidies, because the Japanese government does notprovide national grants and scholarships until 2017. Less than 10% of university students arecovered by public or private tuition subsidies, and thus more than 40% of university students
depend only on national student loans in 2014 (JASSO, 2016).3 Consequently, it is important
to ask whether education policies address such inequality.
The purpose of this paper is quantifying the effects of a counterfactual policy intervention
1University enrollment rates for new upper secondary school graduates. The standard deviation is approximately
8%. All figures are from the author’s calculations based on the School Basic Survey.
2The author’s calculations based on the School Basic Survey in 2016.
3According to JASSO (2016), 52.5% of university students use some tuition subsidies or public students loans
in 2014 (excluding evening students). Among such students, 81.0% only use national student loans and 10.2% use
both national student loans and the other tuition subsidies, such as private, municipal, and university grants andscholarships.

1

to reduce inequality in the availability of local universities in Japan. For this purpose, I use
the program evaluation methods introduced by Heckman and Vytlacil (1999, 2001a, 2005) and
Carneiro, Heckman, and Vytlacil (2010, 2011), which apply the marginal treatment effect (MTE)
framework of Björklund and Moffitt (1987) and Heckman and Vytlacil (1999). First, I estimate
the probability of university enrollment using the capacity of universities, tuition fees in public
universities, and labor market conditions as instrumental variables (IVs). Second, I estimate
the MTE of university education on hourly wage, using the estimated probability of enrollment.
Finally, I recover the treatment effects parameters as weighted averages of the MTE. In addition
to the standard treatment effect parameters, I estimate the parameters related to average andmarginal returns to university for individuals induced to enroll in a university by a policy changeusing the policy-relevant treatment effect (PRTE) approach introduced by Heckman and Vytlacil(2001b). In the policy simulations, I examine three counterfactual policies: a capacity increasein prefectures with relatively smaller capacity, a tuition reduction in public universities, and atuition subsidy for economically disadvantaged students.
The main results show that the average effects of a year of university education in Japan are
significantly positive, but vary across population subgroups by treatment status. The results alsosuggest that policies increasing the probability of university enrollment, such as free tuition or an
increase in the local capacity of universities, bring about positive effects of university education.
However, counterfactual policy simulations of different levels of capacity increase and tuition
reduction show that larger interventions result in relatively smaller impacts, because individuals
with smaller benefits are more affected. An important implication of these results is that theheterogeneity in returns to schooling is key in evaluating an education policy. Impacts of policy
interventions depend on who is affected by such policies; thus effects of a policy that marginally
increases the probability of enrollment suggest potential room for policy interventions.
The policy simulations in this paper are directly related to actual two education policies considered by the Japanese government, and therefore provide important implications for ongoingpolicy discussions. First, the capacity policy is relevant to the government’s discussion about aregulation of new openings in Tokyo and facilitation of university relocation into rural regions to
reduce inequality in local university availability.4 The capacity policy simulations shed new lighton the effects of supply side policy interventions for expansion of higher education opportunity
4For example, see The Headquarters for Formulating Measures for Building-Up Towns and Jobs (2017).

2

in developed countries, which are investigated in the literature (e.g., Frenette, 2009; Oppedisano,
2011, 2014). Second, the government needs to progress a free tuition policy as an international
commitment. This is because Japan has withdrawn its reservation to subparagraphs (b) and (c)of paragraph 2 of article 13 of the International Covenant on Economic, Social and Cultural
Right, which includes the progressive introduction of free education in 2012. Therefore, thegovernment will start national scholarships from 2018 to partly reduce the burden of high tuition
fees (JASSO, 2017).
This paper relates to the literature on estimating average and marginal returns to higher
education using the MTE framework, such as Heckman and Li (2004), Wang et al. (2014) in
China, Chuang and Lai (2010) in Taiwan, Carneiro, Heckman, and Vytlacil (2011) in the UnitedStates, Belskaya, Sabirianova Peter, and Posso (2014), Kyui (2016) in Russia, and Nybom(2017) in Sweden. The paper most closely related to this paper is Belskaya, Sabirianova Peter,
and Posso (2014). They conduct policy simulations with an opening of a college campus inmunicipalities that did not have colleges before an expansion of the higher education system
in Russia. Their identification comes from an instrument of the number of campuses in local
municipality while controlling for federal districts dummies, and hence it might also depend on
permanent differences across municipalities that affect the college attendance decision.
One of the key identification sources of this paper is variation in capacity of local universities
as a supply quantity shifter, changing costs of access to universities. Because capacity is numeric,I can control birth cohort and prefecture dummy variables when estimating the effects of local
capacity on university enrollment decisions. Therefore, the identification of marginal impacts oflocal capacity is based only on changes within prefecture and year, not on permanent differences
between local residential regions over time. The local capacity is not only a good proxy for
local university accessibility, but also an important policy variable. In Japan, the total capacityof universities is regulated by the national government under the School Education Act (Gakko
kyoiku ho) and the Standards for Establishment of Universities (Daigaku setchi kijun). Alluniversities need to pass a one- or two-year screening process by the office of the MEXT tochange quotas for each department. To capture the exact variation in the availability of local
universities, I construct a unique data set that contains information on the opening/closing andincrease/decrease of all accredited capacities (quotas) for new students at the department level
for all Japanese universities.
3

Another key feature of this paper is that it simulates a tuition reduction policy for public
universities using the PRTE framework. There is a large literature on tuition fees and financial
aid policies in higher education using a program evaluation framework. However, the literature
mainly focuses on the effects on educational attainment and thus pays limited attention to theimpacts on future earnings.5 Using local college tuition as an instrument, Carneiro and Lee(2009) simulate the distributional impacts on earnings, and Carneiro, Heckman, and Vytlacil(2010, 2011) estimate the marginal version of PRTE (MPRTE) for individuals induced to enroll
by a policy shift, but they do not directly investigate policy simulations of tuition reduction.
Ichimura and Taber (2000, 2002) also estimate the effects of tuition subsidies applying analternative semiparametric approach.6 Most relevant to the present paper is Carneiro (2003).
He estimates the PRTE of different levels of tuition subsidies in U.S. and suggests that larger
tuition subsidy provides a smaller PRTE, although the effect of 500 USD subsidy and of 2000
USD subsidy are similar. This paper confirms the smaller impacts of larger interventions fromtuition reduction policies.
This paper also contributes to the literature on returns to schooling by assessing the causal
impacts of university education in Japan. Many previous studies also investigate returns toschooling in Japan. However, Oshio and Seno (2007) and Yasui and Sano (2009) point out
that a very limited studies estimate the causal effects of schooling.7 One exception to thislack is Nakamuro and Inui (2012). Using web-based twin-data, they find significant positive
returns to schooling in Japan. Unfortunately, their fixed-effects approach using twins controls fordifferences in family level only, and thus cannot control for unobserved individual heterogeneitythat affects schooling decisions. In this paper, the empirical models allow a general setting, inwhich students self-select into university attendance based on their individually heterogeneous
returns to schooling. To deal with the endogenous schooling decision, I compile original data
sets on direct and indirect costs of university enrollment for instruments, such as public tuition,
capacity of universities, and local labor market conditions.
5See Dynarski and Scott-Clayton (2013) and Page and Scott-Clayton (2016) for a survey.
6See also Heckman, Lochner, and Taber (1998) for an analysis using a general equilibrium model. See, forexample, Keane and Wolpin (2001) and Arcidiacono (2005) for simulations based on dynamic structural models.
Keane and Wolpin (2001) analyze the effects of financial aid on college attendance and subsequent earnings.
Arcidiacono (2005) investigates the effects of changes in the race-based admission and financial aid rules atcolleges on future earnings.
7Oshio and Seno (2007) comprehensively survey empirical studies on the economics of education in Japan.

4

The remainder of this paper is organized as follows. Section 2 explains the empiricalframework. Section 3 describes the data. Section 4 presents and discusses the results. Finally,
Section 5 concludes.

2

Empirical Framework

The empirical framework of this paper basically follows Heckman and Vytlacil (2005) and
Carneiro, Heckman, and Vytlacil (2010, 2011). They consider a standard model of potential
outcomes that is firstly applied to schooling by Willis and Rosen (1979).

2.1

Setup

Let consider a linear in the parameters model with two potential outcomes:

Y1 = X β1 + U1

(1)

Y0 = X β0 + U0,
where subscript 0 and 1 correspond to the untreated and treated states. Y1 is the potential log
wage if the individual enrolls in university, and Y0 is the potential log wage if the individual does
not enroll in university. X is a vector of observable characteristics and (U1, U0 ) are unobservablevariables. Let D = 1 denotes enroll in university; D = 0 denotes not enroll in university. The
measured outcome variable Y can be written in a potential outcomes framework:

Y = DY1 + (1 − D)Y0 .

(2)

This equation is related to a latent variable discrete choice model that represents an individual’s
decision to enroll in a university. I assume the following selection model:5D ∗ = µ D (Z ) − V,
D = 1 if D∗ ≥ 0,
= 0 otherwise,or D = 1[µ D (Z ) − V ≥ 0],
where V is an unobserved random variable. I assume that V is continuous with a strictlyincreasing distribution function FV . Z is a vector of observed random variables that includes
some part of X. Z also includes variables that determine the treatment decision but do not directly
affect the outcome (the exclusion restriction). I also assume that Z and X are independent of(V, U1, U0 ).
Let Pr (D = 1| Z ) denotes the probability of university enrollment conditional on Z. It is
innocuous to rewrite the the selection equation for convenience as follows:
D = 1[Fv (µ D (Z )) ≥ Fv (V )]= 1[P(Z ) ≥ UD ],
with
def

UD = Fv (V ) ∼ Uni f [0, 1],
def

P(Z ) = Fv (µ D (Z )) = Pr[D = 1 | Z].

Different values of UD correspond to different quantiles of V , and thus UD is the normalized
latent variable of the unobserved resistance to enroll in university.
Using equations 1 and 2, the observed outcome can be written as:
Y = X β0 + DX ( β1 − β0 ) + D(U1 − U0 ) + U0
= X β0 + DX β +  .

6(3)

This equation indicates that the effect of university enrollment varies across individuals fordifferences in their X and U1, U0 . If the enrollment decision depends on the unobservable gain
U1 − U0 , a dummy variable D is not independent of the disturbance . In this case, neither
ordinary least squares (OLS) nor simple linear IV estimates recover the standard average effectparameters, such as the average treatment effect (ATE): E(Y1 −Y0 ), the ATE on the treated (ATT):
E(Y1 − Y0 | D = 1), and the ATE on the untreated (ATUT): E(Y1 − Y0 | D = 0). Heckman and
Vytlacil (1999, 2001a, 2005) establish that these treatment effect parameters of interest can be
identified as weighted averages of the MTE of Björklund and Moffitt (1987) and Heckman and
Vytlacil (1999).8 The MTE is defined as:def

MT E(x, u D ) = E(Y1 − Y0 | X = x, UD = u D ).
The MTE indicates the effects of university enrollment for individuals with X = x who would
be indifferent between enrollment or not if they were exogenously assigned a value of Z such as
UD = u D .

2.2

Estimating Marginal Treatment Effect

Heckman and Vytlacil (1999, 2001a, 2005) show that the MTE can be identified by the local
instrumental variables. Using the equation 3, the conditional expectation of Y given X = x, andP(Z ) = p is
E[Y |X = x, P(Z ) = p] = x β0 + x( β1 − β0 )p + K (p)Z p= x β0 +MT E(x, u D )du D,
0

where,
K (p) = E(U1 − U0 | D = 1, P(Z ) = p)
Z ∞Z p=(u1 − u0 ) f (u1 − u0 | X = x, UD = u D )du D d(u1 − u0 ),−∞0

8Definitions of weights for the treatment effect parameters are in Appendix B.

7(4)

where f (u1 − u0 | X = x, UD = u D ) is the conditional density of U1 − U0 . Therefore, the MTE
is identified by differentiating the equation 4 with respect to p,∂
E[Y | X = x, P(Z ) = p] = E[Y1 − Y0 | X = x, UD = u D ].
∂p

(5)

The equation 4 can be estimated using the model of a semiparametric approach, such as thepartially linear model of Robinson (1988), and the equation 5 can be estimated in nonparametrically. One of the disadvantages of a semiparametric approach is that the MTE can only be
estimated over the empirical support of P(Z ), because the MTE is identified over the supportof P(Z ). If the empirical support does not cover full unit interval of P(Z ), it is impossible
to recover conventional treatment parameters. An alternative way of estimating the MTE is aparametric approach that assumes joint normal distribution of the unobservables (U0, U1, V ).
With this additional assumption, Heckman, Tobias, and Vytlacil (2001) show that the MTE canbe written as follows:

MT E(x, u D ) = x( β1 − β0 ) − (σ1V − σ0V )Φ−1 (u D ),(6)

where, σ jV = Cov(U j , V ), j = 0, 1, and Φ(·) is CDF of standard normal. This parametricapproach is a conventional way of estimating the equations and is related to switching regression
models (Björklund and Moffitt, 1987; Willis and Rosen, 1979).9 Following the literature, I estimate the outcome and selection equations together using the method of maximum likelihood.10
An advantage of specifying the normality assumption is that it helps to estimate the MTE overthe full unit interval of P(Z ) and to recover the treatment effect parameters of interest.

2.3

Policy-Relevant Treatment Effects

Once the MTE is estimated, the parameters that are directly relevant to the policy questions
can also be estimated as weighted averages of it. I compute PRTE introduced by Heckman and
Vytlacil (2001b) and MPRTE proposed by Carneiro, Heckman, and Vytlacil (2010). Let D∗ ,9See also Heckman, Tobias, and Vytlacil (2001) for further description.
10In the estimation, I normalize the variance of V to 1.

8

Y ∗ , and P∗ denote the treatment state, outcome, and probability of university enrollment after apolicy change. Heckman and Vytlacil (2005, 2007) define the PRTE when E(D∗ ) , E(D) as,E(Y ∗ ) − E(Y ) def=
E(D∗ ) − E(D)Z 1

MT E(u D )ω PRT E (u D )du D,

0

where,
ω PRT E (u D ) =Fp (u D ) − Fp∗ (u D ),EFp∗ (P) − EFp (P)where Fp∗ and Fp are the distribution of P∗ and P, respectively.11
The MPRTE is defined as the limit of PRTE with a sequence of alternative policies indexed
by a scalar variable α such that limα→0 Pα∗ (Z ) = P(Z ). I consider three policy sequences as
defined in Carneiro, Heckman, and Vytlacil (2010, 2011): (1) a policy intervention that has aneffect similar to a shift in one of the components of Z, say Z k , such that Zαk = Z k + α andjZα = Z j for j , k; (2) a policy that increases the probability of university enrollment by αso that Pα∗ = P + α; and (3) a policy that changes each individual’s probability of university
enrollment by the proportion (1 + α), so that Pα∗ = (1 + α)P.

3

Data

3.1

The Japanese General Social Survey

The main analysis data are the Japanese General Social Survey (JGSS).12 The JGSS is repeatedcross-section data for men and women aged 20–89, as of September 1 of each survey year. This
paper uses data from surveys conducted in 2000, 2001, 2002, 2005, 2006, 2008, and 2010, and11To simplify the notation, I suppress control variables.
12The Japanese General Social Surveys (JGSS) are designed and carried out by the JGSS Research Center at
Osaka University of Commerce (Joint Usage / Research Center for Japanese General Social Surveys accreditedby Minister of Education, Culture, Sports, Science and Technology), in collaboration with the Institute of Social
Science at the University of Tokyo. The data for this secondary analysis, the JGSS, the JGSS Research Center,
was provided by the Social Science Japan Data Archive, Center for Social Research and Data Archives, Institute ofSocial Science, The University of Tokyo.

9

pools male respondents from all waves.
From the pooled original data, I exclude observations in the following four steps. First, I limit
the sample by age. I exclude individuals who were younger than 28 years old in the survey year,
because they might not have completed their academic schooling. Second, I drop individuals
who answered that either of their parents was absent at the age of 15, because their single-parent
structure might substantially differ from a family with two parents, and thus, unobservableeffects cannot be controlled. Third, I only use individuals who had reached their first university
enrollment decision after the 1972 academic year due to the availability of tuition data. Finally,
I use individuals whose observational characteristics match the comparison information on the
instruments and covariates for the estimation explained below. The remaining sample after
restrictions contains male workers were born between 1953 and 1979 who were 28 to 54 years
old at the date of the survey.
The JGSS has the advantage of including information about workers’ annual earned income
and working hours per week. For the outcome variable, I calculate the worker’s individual
hourly wage as the worker’s annual income from his main job divided by annual working
hours.13 Unfortunately, the JGSS measures income in terms of 19 categories. Following Oshio
and Kobayashi (2009) and Sano and Yasui (2009), I assign the median value of each category
and evaluate it in 2005 consumer prices, transforming it into a logarithm.14
One of the disadvantages of the JGSS is that the data set contains limited information on
residence at the time of the university enrollment decision. I use information on the prefecture
where individuals resided at the age of 15 and assume that in the year of university enrollment,
their residence (at least their parental residence) was still in that prefecture. The control variablesfrom the JGSS are parents’ education level (and their squares), the number of siblings (and its
square), age at the survey date (and its square), urban residence dummy and rural (farm or fishingvillage) residence dummy at the age of 15, a set of dummies for prefecture resided in at the ageof 15, cohort dummies, and survey year dummies. I do not control for experience, which iscommonly included in the literature, because experience is endogenous and thus captures a partof the returns to schooling. For the educational attainment of respondents and their parents, I
13Annual working hours are defined as reported working hours per week × 52.
14For the lowest category (less than 700,000 Japanese Yen [JPY]), I assign 700,000. For the highest category(over 23,000,000 JPY), I assign 23,000,000. When I exclude the people in the lowest and the highest categories,
the estimated results are basically same.

10

use the last school attended and assign the standard years of schooling in Japan.
I also control for long-term trends in the active job openings to applications ratio (yuko kyujin
bairitsu) from the reports of the Employment Service Agency (Shokugyou Antei Gyoumu Toukei)
and the annual average monthly total cash earnings of the Monthly Labor Survey (Maigetsu Kinro
Tokei Chosa), and estimated population size at ages 15–19 from the Population Census (and its
square) for the prefecture where individuals resided when they were 15 years old.
In the analysis, I consider the binary treatment decision for university enrollment at thecompletion of upper secondary education. Therefore, I separate individuals into two groups:(1) individuals who graduated from high school or completed upper secondary education, and(2) individuals who had at least some university education.15

3.2

Instrumental Variables

This paper uses four IVs that capture differential changes in direct and opportunity costs ofuniversity attendance across prefectures and cohorts, while controlling for both permanent differences and aggregate trends. The IVs are local university availability measures covering all
universities, average tuition at a public university in the fresh-man year, and local labor market
conditions in the high school years, in the prefecture where the individual resided when he was
15 years old.16

3.2.1

Capacity of Universities

Local college availability measures are first used by Card (1993) and Kane and Rouse (1993) asa proxy for direct costs of college attendance, and are subsequently widely used in the literature.
Kane and Rouse (1993) use a distance to college measure as an instrument for schooling, andfollowed by Carneiro et al. (2011), Doyle and Skinner (2016), and Nybom (2017) in recent
years. An indicator of presence of college in the county of residence is used by Card (1993)
15For respondents, completion of their last level of schooling is available. When I construct the variable ofyears of schooling, I reduce the number by one year from the standard years for those who dropped out before
finishing their last school. However, I am unable to know whether technical college dropouts completed their
upper secondary education. In the analysis, I assume that they have completed their upper secondary education andinclude them in the analysis sample. If I exclude them from the analysis sample, the results are similar.
16The construction of these data is amply described in Appendix A.

11as a substitute for distance to college, and is commonly used in the literature, for example,
by Kling (2001), Cameron and Taber (2004), Carneiro and Lee (2009), Carneiro, Heckman,
and Vytlacil (2010, 2011), Carneiro, Meghir, and Parey (2013), and Doyle and Skinner (2016).
Unfortunately, the JGSS only has information on the prefecture of residence at the age of 15,
and because during the analyzed years, all prefectures in Japan contain at least one university, I
am unable to use this local presence measure.
Currie and Moretti (2003) use the number of two- and four-year colleges and Belskaya,
Sabirianova Peter, and Posso (2014) use the number of campuses as instruments for college
attendance. These measures are superior to the indicator definition because their continuous
variations across residential areas and years allow the researcher to control for permanentdifferences across residential areas. Although the number of colleges or campuses measuretakes into account quantitative differences in college availability across residential areas to adegree, it is too rough to precisely capture differences in local opportunities for college education.
Because colleges differ in size, each college has different effects on local availability of colleges.
The number of admitted students (e.g., Kyui, 2016) and the number of enrollments are also
widely used as a substitute for capacity of colleges.17 However, as Currie and Moretti (2003)
point out, not only the supply of college places but also the demand for these places determines
these variables, and thus the number of admitted students or enrollment might not be a valid
instrument in this case.
In this paper, I construct a unique data set that contains information on all accredited
capacity (quotas) for new university students by the national government in Japan. I collectthe information at the department level and total up new student quotas of national, prefectural,municipal, and private co-ed universities by prefecture in each year. This measure is merged with
the individual data based on the high school graduate’s standard college examination year andthe residence at the age of 15.18 I assume that this measure of local availability of universities
is a proxy of easy access to a local university; i.e., costs of geographical moving or costs of
not living at home with parents. This measure also reflects the potential costs of preparation
for taking examinations and the probability of acceptance.19 I also control cohort dummies and
17For example, Sasaki (2006), Kobayashi (2009) use the number of enrollment as a proxy of the potential
capacity of a prefecture. Doyle and Skinner (2016) also use distance-weighted enrollment for an instrument toanalyze postsecondary education in the United States.
18When I merge the year at age of 18, the acquired results are basically same.
19Although I integrate the capacity of all universities into one measure, changes in capacities might have12

prefecture dummies when I estimate the effect of capacity on university enrollment. Therefore,
the identification relies on unexpected changes of capacity within local prefecture and year of
the university enrollment decision, but not on permanent differences.
One potential problem with this capacity measure is that changes in cohort size are likely tohave an impact on the availability of universities given any fixed amount of capacity (Card andLemieux, 2001; Currie and Moretti, 2003). To avoid this problem, I control for local cohort size
at ages 15–19 when the individual was aged 18, in both selection and outcome equations.
Another concern regarding the use of this measure is that it is affected by new institution
openings or by increase in size of a university reflecting an expected increase in local demand
for university education.20 Although I am unable to completely rule out these possibilities, theJapanese centralized educational system to some degree mitigates this concern: The School
Education Act (Gakko kyoiku ho), prior to the revision in 2003, prescribed that all openings
and closings of university departments are required to be approved in advance by the national
government. Private universities also need approval in advance for changes in capacity at the
department level.21 To increase capacity, a university needs to pass a one or two years screening
and investigative process including a preliminary interview by the office of the MEXT based on
the Standards for Establishment of Universities (Daigaku setchi kijun). Therefore, no university
can freely control its capacity in response to the expected local demand for university education.
3.2.2

Average Tuition at Public Universities

The tuition measure is created as accredited capacity weighted averages over all public co-ed
universities in a prefecture, or at the regional level if there is no public university in the prefecture.
Kane and Rouse (1993), Cameron and Heckman (1998, 2001), Carneiro, Heckman, and Vytlacil(2010, 2011), Carneiro, Meghir, and Parey (2013), and Doyle and Skinner (2016) use tuition as
an instrument to predict college attendance.
heterogeneous effects on college attendance by student’s major field of study. In this paper, because the available
data set has no information on the major field of study, I cannot analyze the impacts of college major choice indetail, which I leave to future research.
20Currie and Moretti (2003) point out this concern in the case of the number of colleges.
21Public universities need to notice their changes in capacity in advance. Before 1974, private universities areallowed to increase their capacity with a notification to the government in advance, therefore capacity of private
universities might not be a valid instrument in these periods. For a robustness check, I exclude individuals who
were born before 1955 and re-estimate the analysis. The results are almost similar but more imprecise for thesmaller sample size.

13

One concern regarding this approach is that the tuition variable is highly correlated with
the quality of the university (Cameron and Heckman, 2001). If the measure captures both costof college attendance and college quality, it directly affects wage differences. To mitigate thisconcern, I only include entrance and course fees at prefectural and municipal universities inthe tuition measure.22 These are specified by local governments based on the fees set by thenational government for national universities, and individual universities are not permitted tochange the amount charged.23 Therefore, the public tuition measure relies on fees determinedat local government level, and basically reflects a variation at the prefecture level. I do notinclude other fees in public tuition, because each university is allowed to determine the amountof such fees at the department level. The same thing applies to tuition at private universities. It
varies from university to university, and thus might reflect the quality of the university. I exclude
tuition of national universities from the public tuition measure because it was unified across thecountry until 2003. The differences in tuition at national universities are captured by the cohort
dummies.
Using the local tuition at prefecture level, I presume that the variable influences schoolingchoice of the individual. One could argue that individuals might move to a different prefecture
for their university education to avoid high tuition costs at local public universities (Carneiro,
Meghir, and Parey, 2013). However, it appears reasonable to consider that prefectural variation
matters in Japan. Because prefectural and municipal universities usually set a lower tuition for
intra-regional students, movers are not only prevented from the option of living at home, butalso disadvantaged by paying higher tuition fees as extra-regional students.
3.2.3

Local Labor Market Conditions

Labor market conditions in the high school years are used as instruments to assess university
enrollment decisions. In Japan, previous studies find that temporary shocks in the labor market
significantly affect schooling decisions, by using aggregate data.24 I use the active job openings
to applications ratio and the annual average monthly total cash earnings in the prefecture of
22In Japan, new university enrollments require the payment f entrance fees, course fees, and other fees for school
expenses. Other fees inclued, for example, training fees, fees for facilities and equipment.
23Before 2003, entrance and course fees at national universities were specified by the national government. In
2004, national universities were incorporated by the the National University Corporation Act (Kokuritsu Daigaku
Hojin Ho).
24For example, see Yano and Hamanaka (2006), Ueyama (2011), and Ogawa (2015).

14

residence at age 15. Local labor market conditions are used as instruments by Cameron andHeckman (1998), and followed by Cameron and Taber (2004), Arkes (2010), Carneiro, Heckman,
and Vytlacil (2010, 2011), and Carneiro, Meghir, and Parey (2013) among others.
I construct these measures as a three-year average over the high school period and merge
them with the individual data for the year the individual was 18. I presume that local earnings
capture temporary shocks to family income. Local job openings reflect the speed of job transition
or of finding a job if unemployed, and thus they also are related to temporary variation in family
resources. In addition, local earnings might capture foregone earnings as opportunity costsof additional schooling. A potential problem of using local labor market conditions is that
long-run trends of labor market conditions might affect both these measures and residential
choice at age 15. If local active job openings to applications ratio and local earnings in highschool are correlated with the unobservables in the outcome equations, these would not bevalid instruments. To avoid this concern, I include trends in local labor market conditions
at ages 13–18 averaged over 6 years in both selection and outcome equations to control forresidential choice at age 15 and long-run differences in labor market conditions in the prefectureof residence during adolescent years. Additionally, I control for a set of dummy variables of theprefecture of residence at age 15, allowing for permanent or aggregate differences in prefecture
characteristics.
Table 1 shows summary statistics for the instruments, with outcomes and covariates. It
shows that individuals with some university education have, on average, higher wages than those
without university education. The difference between the two groups is about 3.81 years ofschooling. Using this figure, all estimates of treatment effects reported below are annualized.
Individuals with some university education have more-educated parents, fewer siblings, andhave lived in prefectures with better labor market conditions in both adolescence and the survey
year. Their residence at the age of 15 was more likely to be in an urban area and in a prefecturewith a larger number of adolescents. They are less likely to come from rural areas than those
without university education. Regarding the instruments, individuals with some university lived
in prefectures where with greater university capacity and better labor market conditions when
they were in high school or upper secondary education. However, these individuals also lived in
prefectures where the average tuition of public universities was higher than among those without
university education.
15

4

Results

4.1

University Enrollment Decision

Table 2 presents the estimates of the selection model of university enrollment. I estimate
the probit model where the dependent variable is a dummy variable that equals one if theindividual has ever attended university, and I report the marginal effects at the mean value
for each variable.25 All controls reported in the table perform well, and estimates show the
expected signs reported in previous studies except for the father’s years of schooling. For
example, individuals who have a mother with more years of schooling are more likely to enroll
in university than those whose mother has lower levels of education. The instruments are jointly
strong predictors of university enrollment, although local active job openings to applications
ratio (local job openings) is not individually significant. Local capacity of universities is an
important determinant of university enrollment. If local capacities increase by 1,000 places, theprobability of university enrollment increases by about 1%. Local tuition in public universities
also has a statistically significant effect on university enrollment. If local tuition rises by
10,000 JPY, it decreases university enrollment by about 0.7%. Local earnings play the roleof an opportunity cost variable for university enrollment. If local earnings averaged over highschool years increase by 1%, university enrollment decreases by about 2.5%. Finally, a better
local active job openings to applications ratio at university enrollment increases probability ofuniversity enrollment. Specifically, a 0.1 point improvement in local active job openings toapplications ratio in high school period increases probability of university enrollment by about
1.3%, but this in not a statistically significant effect.
Using the estimates of the selection model, Figure 1 shows the distributions of predictedprobability of university enrollment, P(Z ), for those with university and for those without
university. This figure indicates the empirical common support of P(Z ) over which the MTE
can be identified in the semiparametric model.26 Although the overlapping support of predicted
P(Z ) for these two distributions covers a wide range of unit interval, it lacks top and bottom
25The coefficients are reported in Table 8 in Appendix.
26Following the literature, I define common support as the intersection of empirical support of these distributions.

16

tails.27 Therefore, it is necessary to estimate the model with joint normal assumptions to recover
the treatment effects that need full support.

4.2

OLS and IV

In Table 3, I present standard OLS and IV estimates, and compare them with the estimatesin previous studies using these methods. The OLS estimate shows that annualized returns touniversity education are about 5.49%. The magnitude of the OLS estimate in this paper ismuch smaller than the estimates derived in previous studies using Japanese micro-data. Thesestudies report around 7–11% of OLS estimates of returns to schooling (e.g., Tachibanaki, 1988;
Trostel, Walker, and Woolley, 2002; Ono, 2004; Sano and Yasui, 2009; Yasui and Sano, 2009;
Nakamuro and Inui, 2012). The differences in the magnitudes of the literature and this paper’s
estimates might be explained by the differences in sample restriction and in model specification.
There are three main differences. First, I only use male observations. Trostel, Walker, and
Woolley (2002), Sano and Yasui (2009), and Yasui and Sano (2009) suggest a larger magnitudeof the returns for females. I exclude females from the analysis to avoid selection bias from labormarket participation decisions, as including female observations may provide larger estimatesof returns to schooling. Second, I consider binary treatment of university enrollment, thus
excluding individuals with less than upper secondary education. It is possible to consider amodel with multiple levels of treatment or with continuous treatment of schooling, but more
restrictions and additional instruments would be needed to identify the treatment parametersof interest.28 Finally, I specify the model with observational heterogeneity by interacting thetreatment and control variables. Such interaction terms are not included in previous studies.
Controlling for this observable heterogeneities might weaken the magnitude of the coefficientof university enrollment.
Table 3 shows that the IV estimate of returns to university education is 11.63%. In line withthe literature, the IV is larger than the OLS estimate. Card (2001) suggests that such a finding
indicates returns to schooling are heterogeneous and higher for individuals who are induced
to enroll in university by changes in the instruments than for those who have average returns.
27The empirical common support is 0.06951 ≤ P(Z ) ≤ 0.94474. I restrict the empirical estimates to thecommon support when estimating the model with semiparametric assumptions.
28See, for example, Heckman, Urzua, and Vytlacil (2006), Heckman and Vytlacil (2007), and Florens et al.
(2008).

17

This interpretation is related to the local average treatment effect (LATE) parameter of Imbens
and Angrist (1994). However, the IV estimates do not necessarily reflect the original LATE
parameter if instruments are multiple and the model includes a set of controls, as is the case inthis paper.29 Interpreting an IV estimate is not always straightforward. Even fort LATE, thisindicates the policy effect of interest only if the variation of the instrument corresponds exactly
to the policy variation (Heckman, Urzua, and Vytlacil, 2006; Carneiro, Heckman, and Vytlacil,
2011).

4.3

Marginal Treatment EffectHere, I estimate the MTE with both parametric and semiparametric approaches. In Figure 2,
I estimate the MTE assuming joint normality of (U1 , U0 , V ) and plot it with 90% confidence
interval bands. To depict the MTE depending only on UD , I evaluate it at the mean values ofcontrol variables. When the UD is particularly low, for individuals who are more likely to enroll
in university, the marginal effects are high at around 40%, but for those who have low valuesof UD , unwilling to enroll in university, the effects are substantially lower around −20%. These
individuals incur negative gains from attending university. The MTE monotonically declines as
UD increases, suggesting substantial heterogeneity of marginal effects of university education.
A simple test of selection on unobserved heterogeneity is a test of whether the slope of the MTE
is zero. For the normal selection model this is equivalent to a test of whether σ1v − σ0v = 0
in the equation 6. I estimate that σ1v − σ0v = −0.3064 with a standard error of 0.1192. This
supports that the effects are heterogeneous and students decide to enroll or not with at least
partial knowledge of their idiosyncratic gains. Carneiro, Heckman, and Vytlacil (2011) notethat these results imply individuals self-select university enrollment based on their comparativeadvantage with respect to their gains.
Figure 3 shows the semiparametrically estimated MTE with 90% confidence interval bands
computed from the bootstrap.30 The semiparametric estimates produce the same pattern as the
29See Angrist and Imbens (1995) and Heckman and Urzua (2010) for their discussion on the identification andinterpretation of IV estimates.
30Following Carneiro, Heckman, and Vytlacil (2011), I use Robinson (1988)’s method for estimating the MTE.
I run the Nadayara-Watson kernel regressions of Y and X on P using a Gaussian kernel and a bandwidth of 0.04,
and estimate the linear term using a linear regression with 1.5% trimming. Then, I run a local quadratic regression
to estimate K (P) using a Gaussian kernel and a bandwidth of 0.35. The results are robust to choices of both larger
and smaller bandwidths.

18

parametric estimates, implying that estimates of the MTE are free from parametric assumption.
Figure 3 suggests that unobservable heterogeneity has an important role in the effects of university
education. From the value of more than 40% for those with low UD , the MTE monotonicallydecreases to less than 0% for those with high UD . Unfortunately, the confidence intervals on thesemiparametrically estimated MTE are too wide, and thus include negative effects for low UD
and positive effects for high UD .

4.4

Average and Policy-Relevant Treatment Effects

The IV and MTE estimates show that university education has substantial and heterogeneous
effects on future pecuniary outcome. However, it is not clear how large the average impacts arefor different subpopulations, or how these effects are related to educational policies. To examine
these issues, I show the treatment effect parameters in Table 3, which are constructed from theMTE using the weights presented in Heckman and Vytlacil (2005) and Carneiro, Heckman, andVytlacil (2010, 2011).
Average effects are substantially different by subpopulation group. The ATE shows that anadditional year of university education increases hourly wages by 8.89%. The ATT is larger
than the ATE, and suggests that the return to one year of university education is 17.43% for
those who enrolled in university. The ATUT is much smaller than the ATE and the ATT, andshows that the effect is 1.67% for those who did not enroll in university, that is, the gain if they
had enrolled.
Conventional average treatment effects parameters are important by themselves, but theseparameters only answer policy questions in extreme cases. For example, the ATUT indicatesthe effects of a policy forcing an entire population to receive university education. In contrast,
the MPRTE parameter of Carneiro, Heckman, and Vytlacil (2010, 2011) answers questions
about marginal gains from specific policies in a more general case. Table 3 presents estimatesof different definitions of the MPRTE, where the policy is considered as a marginal change
in the probability of university enrollment. The MPRTE of a policy intervention that has aneffect similar to a shift in one of the components of Z, is 9.46%. The MPRTE with a policythat increases the probability of university enrollment by an amount α, is 9.39%. A policythat changes the probability of university enrollment by the proportion (1 + α) provides slightly

19smaller effects. The MPRTE of such a policy is 6.64%, but standard errors are large.
I also calculate the average returns for those induced to enroll in university by a particularpolicy shift as a counterfactual policy simulation. Table 3 reports the PRTE of two counterfactual
policies: (1) a policy of free tuition in public universities and, (2) a policy that increases university
capacity by 500 places if the number of places in the prefecture is less than the sample medianvalue of places. The PRTE of free public tuition has an effect of 8.17%, which is similar to themagnitude of the ATE. The PRTE of increasing capacity suggests a larger impact, 10.73%. A
free public tuition policy is a large intervention, but it provides relatively smaller effects thanthat of the capacity intervention. This is because it heavily weights on those with smaller MTE.
Figure 4 shows the weights on MTE for the PRTE parameters, all evaluated at the mean ofX. The capacity policy weights mainly the middle section of the MTE. The free public tuition
policy over-weights individuals with high values of UD because its effect on enrollment is larger
for those with already high levels of P. These results suggest that the magnitude of the PRTE isrelated to how a population is targeted.
Finally, I semiparametrically estimate the treatment effect parameters to examine the robustness of the estimates with the parametric assumptions. These parameters cannot be identified
semiparametrically because the empirical support of P(Z ) lacks the full unit interval. However,these parameters can be estimated over the empirical support when I restrict the weights tointegrate to one in the support. In Table 3, the semiparamteric estimates suggest substantial heterogeneity in the treatment effects of university education. The ATE is 9.18%, which is similar
to the magnitude of the parametric estimate. The ATT is 28.60%, which is much larger than theparametric estimate. The ATUT now shows a large negative effect, -8.26%. The MPRTE thathas an effect similar to a shift in one of the components of Z, is 9.47%. The MPRTE with apolicy that increases the probability of university enrollment by an amount α, is 9.69%. Theseestimates are very similar to the parametric estimates. These results validate the advantage of
MPRTE: the identification does not require a large support condition of P(Z ). The MPRTE
with a policy that changes the probability of university enrollment by the proportion (1 + α)
has a much smaller effect than the parametric estimate. The effect of such a policy is negative,-2.47%. The PRTE of two counterfacutual policies are also examined. The semiparametricestimates of PRTE are slightly larger than the parametric estimates. The PRTE of free public
tuition is 10.04%. The PRTE of increasing capacity is 12.72%. In general, the semiparametric20

estimates produce the same pattern as the parametric estimates. This suggests that the parametricestimates are basically free from the assumptions, although the semiparametrically estimatedstandard errors are too large to draw a confident conclusion.

4.5

Policy Simulations

In this section, I simulate several counterfactual policies to further investigate how PRTE varies
with different levels of policy intervention. First, I estimate the effects of different capacityincreasing policies. Second, I evaluate the intervention of tuition reduction policies. Finally, I
examine tuition subsidies for individuals from economically disadvantaged families.
Table 4 reports the results of policy simulations that increase the capacity of local universities
by a different number of places if the number of places in the prefecture is less than the sample
median value of places. A policy increasing capacity by 100 places changes the probabilityof university enrollment rate to 47.13%. This is 0.05% increase of the probability from thebaseline probability, 47.08%.31 The average returns to university education for those induced
to enroll in university by this policy change are 10.88%. Table 4 also shows that the magnitudeof PRTE is very similar across different increasing levels. If a policy increases the capacity by1000 places, the PRTE is 10.68%. This magnitude is similar to that of a policy increasing fewer
places, because this large intervention increases the average university enrollment rate by only
0.53%. These results suggest that the university capacity-increasing policies affect individuals
with relatively high returns to schooling, but weakly encourage them to enroll in university.
Therefore, a stronger intervention on university capacity does not imply a substantial change in
the PRTE.
Table 5 presents the estimates of policies reducing tuition fees of public universities. A
10% reduction in tuition fees increases the probability of university enrollment to 48.58% andprovides 9.70% of the PRTE for those induced to enroll in university by this policy shift. A
further tuition reduction shows a larger impact on university enrollment. For example, raising
the reduction rate to 50%, the probability of university enrollment increases to 54.53%, which is
7.45% increase from the baseline probability. This higher university enrollment rate implies asmaller PRTE because individuals with high UD are more induced to enroll in university by the
31Standard deviations of the baseline propensity score are 23.92%. Minimum value is 0.13%. Maximum valueis 99.17%.

21

policy change. The PRTE of 50% reduction policy is 8.98%. A 100% reduction, namely freetuition policy increases the probability of university enrollment to 61.47%, and the magnitudeof PRTE decreases to 8.17%, although the differences are not statistically significant. Thesesimulations indicate that the tuition reduction policies strongly encourage individuals to enroll
in university, and thus the large tuition reduction provides small average returns to university
education.
Finally, I simulate tuition subsidies for students from economically disadvantaged families
to examine the effects of national scholarships that will start from the academic year 2018. The
scholarships aim to support students from low-income families go to university or other higher
education institutions. Students are eligible to apply for the scholarships if they satisfy one ofthese conditions: they are from low-income families with residential tax-exempt status, they arefrom families receiving public assistance, and they live in children’s homes or youth treatment
centers at age 18 (JASSO, 2017). Unfortunately, the data set has no information about family
income at the time of university admission. Therefore, I use low parental education as a proxyfor economically disadvantaged families in the simulation.
Table 6 shows the simulation results of tuition subsidy policies. I simulate annual tuition
subsidies offered only to individuals whose parents do not finish high school or other upper
secondary education. About 29.68% of observations in the sample are eligible for the subsidies,
which is a relatively high share of low educated parents because the analysis data contain older
cohorts. A tuition subsidy of 100,000 JPY raises the probability of university enrollment to
48.81%. The PRTE for those induced to enroll in university by the subsidy is 12.82%. These are
greater impacts than that of the 10% tuition reduction policy. The distributional change in thepropensity score shows that the policy mainly affects individuals with lower baseline probability,
compared to the tuition reduction policies. These imply that the policy affects students who areat the margin of university enrollment due to the tuition burden.
I also simulate 500,000 JPY annual tuition subsidy. This amount of subsidy is roughly
equivalent to the maximum total amount of the new national scholarships, which is 40,000 JPY
per month (JASSO, 2017). The subsidy increases the average propensity score to 56.54%. Thischange is greater than that of the 60% tuition reduction. The PRTE of this policy is 10.26%. The
effect is smaller than that of 100,000 JPY subsidy because individuals with lower benefits are
more induced to enroll in university, but still is substantial compared to that of tuition reduction22policies. These results suggest that tuition subsidies for students from low-income families
might be an effective policy to reduce the inequality in an opportunity of university education.

4.6

Sensitivity Analysis

In Table 7, I examine the robustness of the main results, presented in Section 4.4. First, I
investigate whether an alternative choice of the sample changes the results. In this paper,I exclude high school dropouts from the sample to consider binary choice at the university
enrollment. Column 2 presents estimates of the model including high school dropouts. The
estimates show similar patterns as those of the baseline in column 1, although the magnitudes
are slightly smaller.
Second, I examine that the results are robust to the inclusion of additional controls for
current local labor market conditions. Column 3 presents estimates from the model including
unemployment rates and prefectural average earnings at the current residence as additional
controls. The patterns of the estimates are the same as in the baseline, while marginally larger.
Finally, I show that the results are insensitive to the choice of instruments for the policy
simulations. One concern in this paper is that the tuition variable is correlated with the university
quality. Following Carneiro, Heckman, and Vytlacil (2011), I re-estimate the model excluding
the tuition variable from the set of instruments. Column 4 shows that the results are consistent
with the baseline estimates. Another concern is whether the local university capacity is a valid
instrument. In column 5, I exclude the capacity variable from the set of instruments. The
magnitudes are larger, but the patterns of the estimates resemble that of the baseline model.
These results suggest that the main results are insensitive to the choice of instruments.

5

Conclusion

This paper investigates the efficacy of a counterfactual policy intervention that reduces inequality
in availability for local universities in Japan. For this objective, I estimate the MTE using
instruments that reflect the direct costs of college attendance: total accredited capacity of all
universities and tuition of public universities in the prefecture of residence at age 15. These
measures capture cross-time and cross-prefecture variation, because I also control for a set of23

birth cohorts and prefecture dummies. I use an empirical framework that allows students’ selfselection based on their heterogeneous returns, and I recover the average and marginal returns
to university education as weighted average of MTE. Specifically, I analyze the impacts of a setof counterfactual simulations as the PRTE, which show the effects of university education for
those induced to enroll in university due to a counterfactual policy change.
The main results of this paper are as follows. First, MTE varies across individuals. Thisimplies substantial heterogeneity of the marginal effects of university education. The test ofwhether the slope of the MTE is zero for the normal selection model shows that σ1v − σ0v =−0.3064. This figure suggests that heterogeneity in Japan is larger than in the US (Carneiro,
Heckman, and Vytlacil, 2011) or Sweden (Nybom, 2017), but smaller than in Russia (Belskaya,
Sabirianova Peter, and Posso, 2014).
Second, the estimates of a conventional ATE parameters show that additional university
schooling increases hourly wages. The ATE is 8.89%, which indicates the effects for the
population. Additionally, this paper finds heterogeneous average effects by subpopulation group.
The average effect for those enrolled in university, ATT, is 17.43%, but for the ATUT, the effectis 1.67% for those who did not enroll.
Finally, I find that counterfactual policy interventions increasing the probability of university
enrollment provide significant positive effects of university education. The MPRTE regarding
a general policy that marginally increases enrollment probability show the positive effects ofuniversity education, but the effects are substantially different by affected population. The PRTE
estimates of tuition subsidies suggest that financial aid policies for students from economicallydisadvantaged families might be useful in reducing inequality. However, the results of the PRTE
of different levels of capacity increase and tuition reduction show that larger interventions result
in relatively smaller benefits, because individuals with smaller the MTE are more affected.
These results appear to show that an equal expansion of opportunity to go to university might
be inefficient. In conclusion, there is potential room for policy interventions in university
enrollment opportunities, as individual benefits of university education induced by such policy
interventions are unstable due to the heterogeneity in returns to schooling.
I acknowledge that there are several limitations of the present paper. First, the program
evaluation framework rules out general equilibrium effects or peer effects. For example, if there
is a large increase in capacity of university by a policy change, then there is a large increase24

in the supply of skilled labor. This lowers the relative price of skilled labor, and thus violates
the assumption of identification. As such, the distribution of potential outcomes is changed bya policy intervention. Therefore, the results of the PRTE might overstate the impacts of policy
interventions. The estimates of the MPRTE are relatively robust to this violation, because
the MPRTE evaluates marginal gains corresponding to a marginal change in the probability ofuniversity enrollment by a policy shift.
Second, I paid less attention to the quality or heterogeneity of university due to data limitations.32 The estimation model implicitly assumes that the marginal impact of local capacity
is homogeneous across the individuals, conditional on the control variables. This is an invalid
assumption if marginal impacts of local university increases are heterogeneous across students’abilities. This paper is unable to control for the respondent’s ability measures or skill measuresrelating to cognitive and noncognitive skills, and thus the estimates might include the so-called
ability bias. However, in Japan, before the national achievement test held in 2007, there was nouniform criteria-based national academic indicator for students under the secondary educational
level. In addition, students had no obligation to take an IQ test or tests for personal traits.
Therefore, it is difficult to analyze the role of ability in detail. Nybom (2017) shows the returns
to schooling substantially vary with respect to abilities in Sweden. The heterogeneous effects ofpolicy intervention in local college availability by degree of students’ ability may be a fruitful
topic for future research.

32For effects of college quality on earnings, see, for example, Dale and Krueger (2002, 2014) and Andrews, Li,
and Lovenheim (2016).

25

References
Andrews, Rodney J., Jing Li, and Michael F. Lovenheim. 2016. “Quantile Treatment Effects ofCollege Quality on Earnings.” Journal of Human Resources 51 (1):200–238.
Angrist, Joshua D. and Guido W. Imbens. 1995. “Two-Stage Least Squares Estimation of
Average Causal Effects in Models with Variable Treatment Intensity.” Journal of the American
Statistical Association 90 (430):431–442.
Arcidiacono, Peter. 2005. “Affirmative Action in Higher Education: How Do Admission and
Financial Aid Rules Affect Future Earnings?” Econometrica 73 (5):1477–1524.
Arkes, Jeremy. 2010. “Using Unemployment Rates as Instruments to Estimate Returns to
Schooling.” Southern Economic Journal 76 (3):711–722.
Belskaya, Olga, Klara Sabirianova Peter, and Christian Posso. 2014. “College Expansion and
the Marginal Returns to Education: Evidence from Russia.” IZA Discussion Paper 8735,
Institute for the Study of Labor (IZA).
Björklund, Anders and Robert Moffitt. 1987. “The Estimation of Wage Gains and Welfare Gains
in Self-Selection Models.” Review of Economics and Statistics 69 (1):42–49.
Cameron, Stephen V. and James J. Heckman. 1998. “Life Cycle Schooling and Dynamic
Selection Bias: Models and Evidence for Five Cohorts of American Males.” Journal of
Political Economy 106 (2):262–333.
———. 2001. “The Dynamics of Educational Attainment for Black, Hispanic, and White
Males.” Journal of Political Economy 109 (3):455–499.
Cameron, Stephen V. and Christopher Taber. 2004. “Estimation of Educational Borrowing
Constraints Using Returns to Schooling.” Journal of Political Economy 112 (1):132–182.
Card, David. 1993. “Using Geographic Variation in College Proximity to Estimate the Returnto Schooling.” Working Paper 4483, National Bureau of Economic Research.
———. 2001. “Estimating the Return to Schooling: Progress on Some Persistent Econometric
Problems.” Econometrica 69 (5):1127–1160.
Card, David and Thomas Lemieux. 2001. “Can Falling Supply Explain the Rising Return toCollege for Younger Men? A Cohort-Based Analysis.” Quarterly Journal of Economics
116 (2):705–746.
Carneiro, Pedro. 2003. Heterogeneity in the Returns to Schooling: Implications for Policy
Evaluation. Ph.D. thesis, Chicago University.
Carneiro, Pedro, James J. Heckman, and Edward Vytlacil. 2010. “Evaluating Marginal Policy
Changes and the Average Effect of Treatment for Individuals at the Margin.” Econometrica
78 (1):377–394.
———. 2011. “Estimating Marginal Returns to Education.” The American Economic Review
101 (6):2754–2781.
26Carneiro, Pedro and Sokbae Lee. 2009. “Estimating Distributions of Potential Outcomes Using
Local Instrumental Variables with an Application to Changes in College Enrollment and Wage
Inequality.” Journal of Econometrics 149 (2):191–208.
Carneiro, Pedro, Michael Lokshin, Cristobal Ridao-Cano, and Nithin Umapathi. 2011. “Averageand Marginal Returns to Upper Secondary Schooling in Indonesia.” IZA Discussion Papers
6162, Institute for the Study of Labor (IZA).
Carneiro, Pedro, Costas Meghir, and Matthias Parey. 2013. “Maternal Wducation, Home
Environments, and the Development of Children and Adolescents.” Journal of the European
Economic Association 11 (s1):123–160.
Chuang, Yih-chyi and Wei-wen Lai. 2010. “Heterogeneity, Comparative Advantage, and Returnto Education: The Case of Taiwan.” Economics of Education Review 29 (5):804–812.
Currie, Janet and Enrico Moretti. 2003. “Mother’s Education and the Intergenerational Transmission of Human Capital: Evidence from College Openings.” Quarterly Journal of Economics
118 (4):1495–1532.
Dale, Stacy B. and Alan B. Krueger. 2014. “Estimating the Effects of College Characteristics Over the Career Using Administrative Earnings Data.” Journal of Human Resources
49 (2):323–358.
Dale, Stacy Berg and Alan B. Krueger. 2002. “Estimating the Payoff to Attending a More
Selective College: An Application of Selection on Observables and Unobservables.” The
Quarterly Journal of Economics 117 (4):1491–1527.
Doyle, William R. and Benjamin T. Skinner. 2016. “Estimating the Education-Earnings Equation
Using Geographic Variation.” Economics of Education Review 53:254–267.
Dynarski, Susan and Judith Scott-Clayton. 2013. “Financial Aid Policy: Lessons from Research.” The Future of Children 23 (1):67–91.
Florens, Jean-Pierre, James J. Heckman, Costas Meghir, and Edward Vytlacil. 2008. “Identification of Treatment Effects Using Control Functions in Models with Continuous, Endogenous
Treatment and Heterogeneous Effects.” Econometrica 76 (5):1191–1206.
Frenette, Marc. 2009. “Do Universities Benefit Local Youth? Evidence from the Creation of
New Universities.” Economics of Education Review 28 (3):318–328.
Heckman, James J. and Xuesong Li. 2004. “Selection Bias, Comparative Advantage andHeterogeneous Returns to Education: Evidence from China in 2000.” Pacific Economic
Review 9 (3):155–171.
Heckman, James J., Lance Lochner, and Christopher Taber. 1998. “General-Equilibrium Treatment Effects: A Study of Tuition Policy.” The American Economic Review 88 (2):381–386.
Heckman, James J., Justin L. Tobias, and Edward Vytlacil. 2001. “Four Parameters of Interestin the Evaluation of Social Programs.” Southern Economic Journal 68 (2):210–223.

27

Heckman, James J. and Sergio Urzua. 2010. “Comparing IV with Structural Models: What
Simple IV Can and Cannot Identify.” Journal of Econometrics 156 (1):27–37.
Heckman, James J., Sergio Urzua, and Edward Vytlacil. 2006. “Understanding Instrumental
Variables in Models with Essential Heterogeneity.” Review of Economics and Statistics
88 (3):389–432.
Heckman, James J. and Edward Vytlacil. 1999. “Local Instrumental Variables and Latent
Variable Models for Identifying and Bounding Treatment Effects.” Proceedings of the National
Academy of Sciences 96 (8):4730–4734.
———. 2001a. “Local Instrumental Variables.” In Nonlinear Statistical Modeling: Proceedingsof the Thirteenth International Symposium in Economic Theory and Econometrics: Essays in
Honor of Takeshi Amemiya, edited by Cheng Hsiao, Kimio Morimune, and James L Powell.
New York: Cambridge University Press, 1–46.
———. 2001b. “Policy-Relevant Treatment Effects.”
91 (2):107–111.

The American Economic Review———. 2005. “Structural Equations, Treatment Effects, and Econometric Policy Evaluation.”
Econometrica 73 (3):669–738.
———. 2007. “Econometric Evaluation of Social Programs, Part II: Using the Marginal Treatment Effect to Organize Alternative Econometric Estimators to Evaluate Social Programs,
and to Forecast Their Effects in New Environments.” In Handbook of Econometrics, vol. 6,
Part B, chap. 71. Amsterdam: Elsevier, 4875–5143.
Ichimura, Hidehiko and Christopher Taber. 2000. “Direct Estimation of Policy Impacts.” Working Paper 254, National Bureau of Economic Research.
———. 2002. “Semiparametric Reduced-Form Estimation of Tuition Subsidies.” The American
Economic Review 92 (2):286–292.
Imbens, Guido W. and Joshua D. Angrist. 1994. “Identification and Estimation of Local Average
Treatment Effects.” Econometrica 62:467–475.
Japan Student Services Organization (JASSO). 2016.
“Heisei 26-nendo Gakusei Seikatsu Chosa Kekka (Report on Students’ Life Survey in FY2014).”
URL http://www.jasso.go.jp/about/statistics/gakusei_chosa/__icsFiles/
afieldfile/2017/06/16/data14_all.pdf. (In Japanese).
———. 2017. Heisei 30-nendo Shingaku Yoteisha-yo Kyufu Shogakukin Annai (Guidebook of
Benefit Scholarship for People Planning to Enroll in an Institution of Higher Education in
FY2018). Kanagawa, Japan. (In Japanese).
Kane, Thomas J. and Cecilia E. Rouse. 1993. “Labor Market Returns to Two-and Four-Year
Colleges: Is a Credit a Credit and Do Degrees Matter?” Working Paper 4268, National
Bureau of Economic Research.
Keane, Michael P. and Kenneth I. Wolpin. 2001. “The Effect of Parental Transfers and Borrowing
Constraints on Educational Attainment.” International Economic Review 42 (4):1051–1103.
28

Kling, Jeffrey R. 2001. “Interpreting Instrumental Variables Estimates of the Returns to Schooling.” Journal of Business & Economic Statistics 19 (3):358–364.
Kobayashi, Masayuki. 2009. Daigaku Shingaku no Kikai (An Opportunity of University Enrollment). Tokyo, Japan: the University of Tokyo Press. (In Japanese).
Kyui, Natalia. 2016. “Expansion of Higher Education, Employment and Wages: Evidence fromthe Russian Transition.” Labour Economics 39:68–87.
Nakamuro, Makiko and Tomohiko Inui. 2012. “Estimating the Returns to Education Using the
Sample of Twins: The Case of Japan.” Discussion Paper 12-E-076, RIETI Discussion Paper
Series.
Nakazawa, Wataru. 2011. “Shussin Chiiki ni yoru Kosotsugo Shingaku Kikai no Hubyodo(Inequality of Opportunity for the Progression to Higher Education on the Basis of Residential
Areas).” Discussion Paper 43, Panel Survey Project Discussion Paper Series, Institute of Social
Science, the University of Tokyo. (In Japanese).
Nybom, Martin. 2017. “The Distribution of Lifetime Earnings Returns to College.” Journal ofLabor Economics 35 (4):903–952.
Ogawa, Kazuo. 2015. “Shitsugyo to Gakko Kyoiku niokeru Jinteki Shihon Keisei: Todofukenbetsu Panel Data niyoru Keiryo Bunseki (Unemployment and Human Capital Formation in
School Education: An Econometric Analysis of Prefectural Panel Data).” The Japanese
Journal of Labour Studies 656:37–53. (In Japanese).
Ono, Hiroshi. 2004. “College Quality and Earnings in the Japanese Labor Market.” Industrial
Relations: A Journal of Economy and Society 43 (3):595–617.
Oppedisano, Veruska. 2011. “The (Adverse) Effects of Expanding Higher Education: Evidence
from Italy.” Economics of Education Review 30 (5):997–1008.
———. 2014. “Higher Education Expansion and Unskilled Labour Market Outcomes.” Economics of Education Review 40:205–220.
Organisation for Economic Co-operation and Development (OECD). 2015. Education at a
Glance 2015: OECD Indicators 2015 – Country note for Japan. Paris: OECD Publishing.
Oshio, Takashi and Miki Kobayashi. 2009. “Happiness, Self-Rated Health, and Income Inequality: Evidence from Nationwide Surveys in Japan.” PIE/CIS Discussion Paper 451, Center forIntergenerational Studies, Institute of Economic Research, Hitotsubashi University.
Oshio, Takashi and Wataru Seno. 2007. “The Economics of Education in Japan: A Survey of
Empirical Studies and Unresolved Issues.” Japanese Economy 34 (1):46–81.
Page, Lindsay C. and Judith Scott-Clayton. 2016. “Improving College Access in the UnitedStates: Barriers and Policy Responses.” Economics of Education Review 51:4–22.
Robinson, Peter M. 1988. “Root-N-Consistent Semiparametric Regression.” Econometrica
56 (4):931–954.
29

Sano, Shinpei and Kengo Yasui. 2009. “Nihon ni okeru Kyoiku no Return no Suikei (Estimating
the Returns to Education in Japan).” Kokumin Keizai Zassi 200 (5):71–86. (In Japanese).
Sasaki, Yosei. 2006. “Kyoiku Kikaino Chiikikan Kakusa (Regional Gaps in Educational Opportunities).” The Journal of Educational Sociology 78:303–320. (In Japanese).
Tachibanaki, Toshiaki. 1988. “Education, Occupation, Hierarchy and Earnings.” Economics of
Education Review 7 (2):221–229.
The Headquarters for Formulating Measures for Building-Up Towns, People and Jobs.
2017. “Chiho Sousei ni Shisuru Daigaku Kaikaku ni Muketa Chuukan Houkoku (Interim
Report on University Reform that Contributes to Regional Revitalization).” URL http://www.kantei.go.jp/jp/singi/sousei/meeting/daigaku_yuushikishakaigi/
h29-05-22_daigaku_chuukanhoukoku.pdf. (In Japanese).
Trostel, Philip, Ian Walker, and Paul Woolley. 2002. “Estimates of the Economic Return to
Schooling for 28 Countries.” Labour Economics 9 (1):1–16.
Ueyama, Kojiro. 2011. “Daigaku Shingakuritsu no Todofukenkan Kakusa no Youin to Sono
Henyo: Taboshudan Path Kaiseki ni yoru 4jiten Hikaku (Factor Structure of the PrefecturalGap in College Entrance Rate and its Transformation: A Four Time Point Comparison Using
Multi-population Path Analysis).” The Journal of Educational Sociology 88:207–227. (InJapanese).
———. 2012. “Koto Kyoiku Shingakuritsu ni okeru Chikikan Kakusa no Saikensho (Reverification of Regional Disparities in Higher Education Enrollment Rate).” Gendai
Shakaigaku Kenkyu 25:21–36. (In Japanese).
Wang, Xiaojun, Belton M. Fleisher, Haizheng Li, and Shi Li. 2014. “Access to College andHeterogeneous Returns to Education in China.” Economics of Education Review 42:78–92.
Willis, Robert J. and Sherwin Rosen. 1979. “Education and Self-Selection.” Journal of Political
Economy 87 (5, Part 2):S7–S36.
Yano, Masakazu and Junko Hamanaka. 2006. “Naze, Daigaku ni Shingaku Shinainoka: Kenzaiteki Juyo to Senzaiteki Juyo no Kettei Yoin (Why Don’t High School Students Go to
University?: Determinants of the Demand for Higher Education).” The Journal of Educational Sociology 79:85–104. (In Japanese).
Yasui, Kengo and Shinpei Sano. 2009. “Kyoiku ga Chingin ni Motarasu Ingateki na Koka ni
tsuite (Causal Effects of Education on Wages).” The Japanese Journal of Labour Studies
588:16–33. (In Japanese).

30

Table 1: Summary Statistics
Variables
High school(D = 0)Years of schooling12.3299(0.7384)
Log hourly wage
7.4813(0.5436)
Control Variables
Mother’s years of schooling10.0539(2.2403)
Father’s years of schooling10.1556(2.5825)
Number of siblings
1.6836(1.0304)
Age at the survey date
39.7728(7.2197)
Urban residence at age 15
0.0871(0.2822)
Rural residence at age 15
0.4346(0.4960)
Local population of ages 15–19
28.5065(in 10,000)(22.3170)
Local log earnings at ages 13–18
12.5964(0.2311)
Local job openings at ages 13–18
1.0370(0.7304)
Instrumental Variables
Capacity of universities
11.0961(in 1,000)(18.4653)
Tuition in public universities
25.0574(in 10,000)(18.3435)
Local log earnings in high school
12.6435(0.1996)
Local job openings in high school
1.0296(0.7328)
Number of observations
964

University(D = 1)
16.1439(0.6304)
7.7428(0.5369)
11.4722(2.2391)
12.2285(3.0751)
1.3527(0.8185)
39.5835(7.0449)
0.1937(0.3955)
0.2575(0.4375)
34.4926(25.8994)
12.6493(0.2265)
1.0819(0.7093)17.3315(26.8027)
25.9429(17.7490)
12.6926(0.1971)
1.0402(0.7067)
862

Notes: This table reports summary statistics of the analysis data. Local job openings indicate the active
job openings to applications ratio. Standard deviations are in parentheses.

31

Table 2: University Enrollment Decision
Dependent variable: University Enrollment
Control Variables
Father’s years of schooling-0.0643(0.0424)
Mother’s years of schooling
0.0568(0.0560)
Number of siblings-0.1174(0.0342)
Age at the survey date
0.0325(0.0411)
Urban residence at age 15
0.1159(0.0523)
Rural residence at age 15-0.0978(0.0309)
Local population of ages 15–19-0.0250(in 10,000)(0.0099)
Local log earnings at ages 13–18
2.0878(1.0344)
Local job openings at ages 13–18-0.1479(0.0774)
Instrumental Variables
Capacity of universities
0.0114(in 1,000)(0.0046)
Tuition in public universities-0.0069(in 10,000)(0.0023)
Local log earnings in high school-2.4672(0.9247)
Local job openings in high school
0.1299(0.0731)
Test for joint significance of IVs
Chi-square
20.64
p-value
0.0004
Notes: This table reports the marginal effects evaluated at the mean value of each variable from the probit
model of university enrollment (a dummy variable that is equal to one if an individual has ever attended
university, and equal to zero if he has never attended university but has completed upper secondary
education). Local job openings indicate the active job openings to applications ratio. Survey year
dummies, cohort dummies, and a set of dummies for prefecture of residence at the age of 15 are also
controlled in the model but not reported. Robust standard errors are in parentheses, clustered by birthyear cohort and prefecture of residence at the age of 15. Chi-square and p-values indicate the results ofthe test of joint significance of coefficients on the instrumental variables.

32

Table 3: Estimates of Returns to a Year of University Education
Parameters
OLS
0.0549(0.0056)IV
0.1163(0.0510)
Parametric Semiparametric
ATE
0.08890.0918(0.0339)(0.2047)
ATT
0.17430.2860(0.0519)(0.2581)ATUT
0.0167-0.0826(0.0452)(0.2548)
MPRTE
Zαk = Z k + α
0.0946
0.0947(0.0343)(0.2036)
Pα = P + α
0.09390.0969(0.0349)(0.2041)Pα = (1 + α)P
0.0664-0.0247(0.0358)(0.2405)
PRTE
Free tuition
0.08170.1004(0.0333)(0.2033)
Increase in
0.10730.1272
capacities of universities (0.0349)(0.2102)
Notes: This table reports estimates of returns to university education: average treatment effect (ATE),
average treatment on the treated (ATT), average treatment on the untreated (ATUT), marginal policyrelevant treatment effect (MPRTE), and policy-relevant treatment effect (PRTE). The PRTE corresponds
to the two counterfactual policies: (1) free tuition: a policy of free tuition in public universities, (2)increase in capacities of universities: a policy that increases capacities of universities by 500 places
if the prefecture has less than median value of places. The IV estimate uses P(Z ) as the instrument(probit model for first stage with all instruments). Parametric column indicates the estimates for thenormal selection model. Semiparametric column indicates the estimates for the semiparametric model.
Standard errors (in parentheses) are obtained by the bootstrap method (250 replications). All estimates
are annualized (divided by 3.81 years).

33

Table 4: Simulations of Policies Increasing University Capacity
Increased Places
PRTE
Propensity Score
Mean
S. D.
Min
Max
100
0.1088 0.4713 0.2391 0.0013 0.9917(0.0350)200
0.1077 0.4718 0.2390 0.0013 0.9917(0.0350)300
0.1076 0.4724 0.2389 0.0013 0.9917(0.0350)400
0.1074 0.4729 0.2388 0.0013 0.9917(0.0349)500
0.1073 0.4734 0.2388 0.0013 0.9917(0.0349)600
0.1072 0.4740 0.2387 0.0013 0.9917(0.0349)700
0.1071 0.4745 0.2386 0.0014 0.9917(0.0349)800
0.1070 0.4750 0.2385 0.0014 0.9917(0.0349)900
0.1069 0.4756 0.2384 0.0014 0.9917(0.0349)1000
0.1068 0.4761 0.2383 0.0014 0.9917(0.0349)
Notes: This table reports estimates of policy-relevant treatment effect (PRTE) of a counterfactual policythat increases some places of university capacity if the prefecture has less than median value of places.
Standard errors (in parentheses) are obtained by the bootstrap method (250 replications). All estimates
are annualized (divided by 3.81 years). Increased places shows the number of places increased by
the counterfactual policy. Propensity score indicates the probability of university enrollment after thecounterfactual policy change. S. D. indicates standard deviations.

34

Table 5: Simulations of Policies Reducing Tuition Fees
Reduction Rate
PRTE
Propensity Score
Mean
S. D.
Min
Max
10%
0.0970 0.4858 0.2396 0.0019 0.9923(0.0345)20%0.0952 0.5008 0.2400 0.0029 0.9929(0.0343)30%
0.0934 0.5157 0.2405 0.0044 0.9934(0.0341)40%
0.0916 0.5306 0.2410 0.0064 0.9939(0.0339)50%
0.0898 0.5453 0.2415 0.0070 0.9946(0.0337)60%
0.0881 0.5598 0.2421 0.0073 0.9959(0.0336)70%
0.0864 0.5740 0.2427 0.0076 0.9968(0.0335)80%
0.0848 0.5879 0.2432 0.0080 0.9977(0.0334)90%
0.0832 0.6015 0.2438 0.0083 0.9984(0.0334)100%
0.0817 0.6147 0.2443 0.0087 0.9989(0.0333)
Notes: This table reports estimates of policy-relevant treatment effect (PRTE) of a counterfactual policythat reduces tuition fees of public universities. Standard errors (in parentheses) are obtained by thebootstrap method (250 replications). All estimates are annualized (divided by 3.81 years). Reduction rate
shows the tuition reduction rate by the counterfactual policy. Propensity score indicates the probabilityof university enrollment after the counterfactual policy change. S. D. indicates standard deviations.

35

Table 6: Simulations of Tuition Subsidies
Amount of Subsidy
PRTE
Propensity Score(in JPY)
Mean
S. D.
Min
Max
100,000
0.1282 0.4881 0.2283 0.0023 0.9917(0.0385)
500,000
0.1026 0.5654 0.2079 0.0031 0.9917(0.0353)
Notes: This table reports estimates of policy-relevant treatment effect (PRTE) of a counterfactual policyof tuition subsidies for individuals whose parents do not complete high school or other upper secondary
education. Standard errors (in parentheses) are obtained by the bootstrap method (250 replications). All
estimates are annualized (divided by 3.81 years). Propensity score indicates the probability of university
enrollment after the counterfactual policy change. S. D. indicates standard deviations.

36

37
0.0817(0.0333)
0.1073(0.0349)

0.0946(0.0343)
0.0939(0.0349)
0.0664(0.0358)

0.0889(0.0339)0.1743(0.0519)0.0167(0.0452)

0.0784(0.0561)
0.1021(0.0689)0.0905(0.0625)
0.0910(0.0653)0.0646(0.0527)0.0838(0.0304)
0.1084(0.0362)

0.0959(0.0330)
0.0957(0.0347)0.0691(0.0301)

0.1016(0.0477)0.0901(0.0437)0.0895(0.0452)
0.0655(0.0390)0.0898(0.0483)

0.0973(0.0504)
0.0971(0.0519)0.0792(0.0479)

0.0936(0.0472)0.1486(0.0907)0.0473(0.0576)

Without Capacity

Notes: This table reports estimates of returns to university education for various samples and specifications: average treatment effect (ATE), averagetreatment on the treated (ATT), average treatment on the untreated (ATUT), marginal policy-relevant treatment effect (MPRTE), and policy-relevant
treatment effect (PRTE). The PRTE corresponds to the two counterfactual policies: (1) free tuition: a policy of free tuition in public universities, (2)increase in capacities of universities: a policy that increases capacities of universities by 500 places if the prefecture has less than median value of places.
Column 1 reproduces the main results for easy reference. In column 2, high school dropouts are included in the sample. In column 3, unemployment rates
and prefectural average earnings at the current residence are included as additional control variables. In column 4, local tuition in public universities is
excluded from the set of instruments. In column 5, local capacity of universities is excluded from the set of instruments. Standard errors (in parentheses)
are obtained by the bootstrap method (250 replications). All estimates are annualized (divided by 3.81 years, by 3.86 years in column 2).

Increase incapacity of universities

PRTE
Free tuition

Pα = (1 + α)P

Pα = P + α

MPRTEZαk = Z k + α

ATU

ATT

ATE

Baseline

Table 7: Sensitivity Analysis
IncludingControlling
Without Tuition
High School Dropouts Current Variables
0.08380.09050.0850(0.0574)(0.0308)(0.0407)0.16560.17070.1608(0.1263)(0.0643)(0.0803)
0.01710.02320.0210(0.0516)(0.0386)(0.0452)

2
1.5
f(P)
1
.5
0
0

.2

.4

P(Z)

D=0

.6

.8

1

D=1

Note: Kernel Density Estimate (Epanechnikov kernel)

Figure 1: Support of P(Z ) for D = 1 and D = 0
Notes: This figure shows the support of P(Z ) for those who enroll in university (D = 1) and for those
who do not (D = 0). P(Z ) is predicted using the estimates from a probit model of university enrollment(a dummy variable that is equal to one if an individual has ever attended university, and equal to zero if
he has never attended university but has completed upper secondary education) on mother’s and father’s
years of schooling, the number of siblings, age at the survey date, dummy variables of survey years,
dummy variables of urban and of rural residence at the age of 15, local population of age 15–19, local
log earnings at age 13–18, local job openings at age 13–18, capacity of local universities, tuition in local
public universities, local log earnings in high school, the active job openings to applications ratio in highschool, cohort dummies, and a set of dummies for prefecture of residence at the age of 15 (see Table 2).

38

39

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0

0.1

0.2

0.4

UD

0.5

0.6

Figure 2: Marginal Treatment Effect

0.3

0.7

0.8

0.9

1

Notes: This figure depicts the marginal treatment effect (MTE) with assumptions on normally distributed unobservables. The solid line indicates theestimated effect. Dashed lines indicate 90% confidence intervals.

MTE

40

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0

0.1

0.2

0.4

UD

0.5

0.6

Figure 3: Marginal Treatment Effect

0.3

0.7

0.8

0.9

1

Notes: This figure depicts the marginal treatment effect (MTE) with a semiparametric model. The solid line indicates the estimated effect. Dashed lines
indicate 90% confidence intervals obtained by the bootstrap method (250 replications).

MTE

41

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0

0.1

0.2

0.4

UD

0.5

0.6

Figure 4: Weights for the PRTE

0.3

MTE
Free Tuition
Increase in Capa

0.7

0.8

0.9

1

Notes: This figure depicts weights for the policy-relevant treatment effect (PRTE) of two conterfactual policies: (1) a policy of free tuition in public
universities and, (2) a policy that increases university capacity by 500 places if the prefecture has less than the median value of places. The scale of thevertical axis is the scale of the marginal treatment effect (MTE), not the scale of the weights, which are scaled to fit the picture.

MTE, Weights

A

Data Construction

This appendix describes the construction of the instrumental variables. The data source forcapacity of universities is Zenkoku Daigaku Ichiran. This book is published with a list of all
accredited national, prefectural, municipal and private universities in each academic year by the
Bunkyo Kyokai. It contains the detailed information on the accredited capacity, the location,and the date of opening and closing by the department of the university. I collected the total
quota for new students offered in each prefecture of an academic year in the department level.
If the department is located in more than one prefecture, I take the prefecture where studentsof the department stay in longer. If general education courses are collectively offered in theother prefecture, I assign each department to the prefecture where they offer an upper-levelor a specialized course. I exclude the universities that offer only in correspondence, Internet
learning and a graduate school. I also exclude following categories of departments: art, music,
religious, home economics, and physical education. An important problem is the conversion of
female to co-ed universities. Zenkoku Daigaku Ichiran provides the information on conversionof single-sex to co-ed in university or college level, but not in department level. I search thehistory of the university in the official web cite or in an official report published by the university,and I identify the department started to offer courses to male. If I am unable to identify which
department was changed to co-ed, I assume that all departments offer co-ed courses based on
the information of Zenkoku Daigaku Ichiran.
Tuition data are based on Keisetsu Jidai for 1972-2000, published by Obunsha. I define
tuition is sum of entrance fees and course fees. Some prefectural and municipal universities
have price discrimination by residential area of students. I assign minimum price of tuition for
intra-regional students if prefectural or municipal universities are available and assign maximum
price of tuition for extra-regional students if there is no prefectural or municipal universities in theprefecture of residence at the age of 15. I construct the measure as accredited capacities weighted
averages over prefectural and municipal universities in a prefecture, or at the regional level if
prefectural and municipal universities are not available. The region is based on the definitionof region code of the Labor Force Survey (Rodo-Ryoku Chosa) of the Statistics Bureau of the
Ministry of Internal Affairs and Communications.
The active job openings to applications ratio (yuko kyujin bairitsu) is based on the report on

42

employment service (shokugyou antei gyoumu toukei) of the Bureau of Employment Security of
the Ministry of Health, Labour and Welfare. It is defined as the number of active job openings per
the number of active applications. I use the ratio that excludes new graduates and part-timers. I
construct average local earnings in high school years from the annual average monthly total cash
earnings (establishments with 30 employees or more) of the Monthly Labor Survey (Maigetsu
Kinro Tokei Chosa). Local earning is evaluated at the 2005 consumer prices and transform it inlogarithm.

43

B

Definitions of Weights for the Treatment Effect Parameters

The treatment effect parameter ( j) is weighted averages of the MTE with a weight (ω j ) conditional on X = x that can be estimated as,
Z 1

MT E(x, UD )ω j (x, u D )du D,

0

where j = {ATE, ATT, ATUT, PRTE, MPRTE}.
Heckman and Vytlacil (2005) and Carneiro, Heckman, and Vytlacil (2010, 2011) provide
the weights:

ω AT E (u D ) = 1

R1
ω ATT (u D ) =uD

f (p)dp

E(P)R uD

f (p)dp

ω ATUT (u D ) =0ω PRT E (u D ) =FP (u D ) − FP∗ (u D )EFP∗ (P) − EFP (P)E(1 − P)f P (u D ) f V FV−1 (u D )for Zαk = Z k + α
ω M PRT E (u D ) =E f V µ D (Z )

ω M PRT E (u D ) = f P (u D ) for Pα = P + α

ω M PRT E (u D ) =u D f P (u D )for Pα = (1 + α)P,E(P)where f is the desity of P(Z ) and conditional on X = x is implicit.

44

Table 8: Coefficients Estimates in University Enrollment Decision Model
Dependent variable: University Enrollment
Control Variables
Father’s years of schooling-0.1617(0.1065 )Father’s years of schooling squared
0.0115(0.0044)
Mother’s years of schooling
0.1429(0.1407)
Mother’s years of schooling squared-0.0012(0.0065)
Number of siblings-0.2953(0.0859)
Number of siblings squared
0.0198(0.0183)
Age at the survey date
0.0818(0.1034)
Age at the survey date squared
0.0002(0.0009)
Urban residence at age 15
0.2913(0.1316)
Rural residence at age 15-0.2459(0.0776)
Local population of ages 15–19-0.0628(in 10,000)(0.0248)
Local population of ages 15–19 squared
0.0005(in 10,000)(0.0002)
Local log earnings at ages 13–18
5.2492(2.6017)
Local job openings at ages 13–18-0.3719(0.1946)
Instrumental Variables
Capacity of universities
0.0288(in 1,000)(0.0117)
Tuition in public universities-0.0173(in 10,000)(0.0057)
Local log earnings in high school-6.2036(2.3256)
Local job openings in high school
0.3267(0.1839)
Notes: This table reports the coefficients from the probit model of university enrollment (a dummy
variable that is equal to one if an individual has ever attended university, and equal to zero if he has neverattended university but has completed upper secondary education). Local job openings indicate the active
job openings to applications ratio. Survey year dummies, cohort dummies, and a set of dummies forprefecture of residence at the age of 15 are also controlled in the model but not reported. Robust standard
errors are in parentheses, clustered by birth year cohort and prefecture of residence at the age of 15.

45