Effects of Subsidized Childcare on Mothers’
Labor Supply Under a Rationing Mechanism

ISS Discussion Paper Series F-186
University of Tokyo
Shintaro Yamaguchi, Yukiko Asai and Ryo Kambayashi

April 2017

Effects of Subsidized Childcare on Mothers’
Labor Supply Under a Rationing Mechanism*
Shintaro Yamaguchi†

Yukiko Asai‡

Ryo Kambayashi§

April 18, 2017

Abstract
We estimate the marginal treatment effect of childcare use on mothers’
labor market outcomes by exploiting a staggered childcare expansion acrossregions in Japan. The estimates show that the treatment effect is negatively
associated with propensity to use childcare, which implies that mothers who
increase their labor supply more are less likely to use childcare. Negative
selection into treatment arises, because the childcare rationing rule gives preferential treatment to mothers working full-time before childcare application.
These mothers are strongly attached to the labor market and likely to work
regardless of the availability of subsidized childcare.
* The authors would like to thank seminar participants at the University of California, Berkeley,
the University of Toronto, and the University of British Columbia for their helpful comments. Allremaining errors are our own. Financial supports from the Murata Science Foundation and JSPS
KAKENHI Grant Numbers 15K17071, 16H02020, 16K21743 are gratefully acknowledged. The
data in the Longitudinal Survey of Newborns in the 21st Century were generously provided by theJapanese Ministry of Health, Labour and Welfare.
† Department of Economics, McMaster University, 1280 Main St. W., Hamilton, ON. Canada
L8S 4M4. Email: yamtaro@mcmaster.ca.
‡ Institute of Social Science, the University of Tokyo. Hongo 7-3-1, Bunkyo, Tokyo, Japan.
Email: y_asai@iss.u-tokyo.ac.jp.
§ Institute of Economic Research, Hitotsubashi University. Naka 2-1, Kunitachi, Tokyo, Japan.
Email: kambayas@ier.hit-u.ac.jp.

11Introduction

Many developed countries provide subsidized childcare to young families. Oneof the objectives of this policy is to increase mothers’ labor supply by resolving
the conflict between raising a family and pursuing a career. However, the existing evidence for the effectiveness of childcare reforms on mothers’ labor supply is
mixed across time and countries. Indeed, many papers find that the effect of childcare on maternal labor supply is small and/or statistically insignificant (see Lundin,Mörk, and Öckert (2008), Cascio (2009), Goux and Maurin (2010), Fitzpatrick(2010, 2012), Havnes and Mogstad (2011) and Asai, Kambayashi, and Yamaguchi(2015)).
One of the explanations for the insignificant effects of childcare reform is crowding out. Namely, subsidized formal childcare substitutes for informal childcare arrangements such as care by grandparents, and hence, mothers’ labor supply does
not increase. The availability and affordability of informal childcare arrangements
vary across families, which means the treatment effect of childcare use is heterogeneous across families. When the supply of childcare is not large enough to take careof all children in the country, the rationing rule for childcare determines the subpopulation treated by a childcare reform. Some countries allocate childcare randomly
by lottery, but other countries prioritize certain families by child’s age, householdincome, parents’ occupation, etc. Depending on the rationing rule, a childcare slot
may not be given to mothers who would increase their labor supply. If this is thecase, the average effect of a childcare reform may be small, even though there is a
subpopulation that would be strongly affected by childcare availability. This may
explain why many previous papers find no effect of childcare reforms.
The objective of this paper is to estimate the heterogeneous treatment effects
of childcare on mothers’ labor market outcomes including participation, hours ofwork, earnings, and job type. We allow treatment effects to vary by unobserved
propensity for childcare use by applying the marginal treatment effect (MTE) framework developed by Björklund and Moffitt (1987) and Heckman and Vytlacil (2005).
Unlike the standard instrumental variable (IV) regression adopted by previous papers in the literature, the MTE framework enables us to determine which mothers2are likely to change their labor supply the most and how likely they are to use childcare services, which is useful for designing an effective childcare policy.
We identify the causal effects by analyzing the childcare reform that occurredin the early 2000s in Japan. The national government legislated policies to support
young families, including the expansion of subsidized childcare, in order to increase
female labor supply and the fertility rate. While the national government committed to increase the supply of childcare across the country, local governments are
responsible for the implementation of the policy. Because local governments differ
in their policy priorities, financial status, local institutions, etc., the timing of the
program rollout varies by region, which is used for identification. Because our estimation method controls for time-constant differences across regions and nationwidechanges in economic conditions and policies, this identification strategy is similar
to the difference-in-differences approach.
Throughout the period of analysis (and to the present day), the demand for subsidized childcare is greater than the supply in most large cities. If excess demand
exists, local governments assess each family’s need for childcare. While singleparent families and families on welfare receive preferential treatment, most families
are ranked according to parents’ working hours at the time of childcare application.
This rationing rule favors full-time workers over part-time workers and job seekers.
The rationale is that parents working longer hours are more in need of childcare,but the rationing rule may undermine the efficacy of the childcare reform. This isbecause parents working full-time at the time of childcare application are likely to
use informal childcare and to work even if a subsidized slot is not provided, which
implies that the rationing rule is likely to cause crowding out.
Our estimates indicate that the MTEs of childcare use on market participation,
hours of work, and earnings are positive for most mothers, but they are significantly
heterogeneous across mothers. We find that the MTE is inversely related to theunobserved propensity for childcare use. That is, mothers with strong treatment
effects are less likely to use childcare, while mothers with weak treatment effects are
more likely to use childcare. Given the rationing rule that favors full-time workers,
the unobserved propensity for childcare use is likely to represent an unobserved
preference for work. We consider that mothers with a strong labor force attachment
3are willing to exert extra effort to find an informal childcare arrangement that allows
them to work and raise children, even if a subsidized slot is not provided, which
implies that their treatment effect is weak. By contrast, mothers with weak labor
force attachment may be unable to work without a subsidized slot, which implies
that their treatment effect is strong. We also find that this main result is robust toa number of issues including endogenous fertility, selective migration to the regionin which childcare is more available, and functional form assumptions.
We then examine the consequences of the negative association between thetreatment effect and the propensity for treatment in two ways. First, we calculate
the average treatment effect on the treated (TT) and the average treatment effect on
the untreated (TUT) by taking weighted averages of the MTE. The result indicatesthat TT is greater than TUT, which implies that the policy effects may improveby changing the rationing rule so that the government provides a childcare slot tomothers who do not have access to one currently. Second, we evaluate the effect of afurther expansion in the childcare program by counterfactual simulations under thecurrent rationing rule. The results indicate that the policy effects become increasingly stronger as the childcare program expansion occurs. This is because thosewith strong treatment effects use childcare at a later stage of the childcare expansion. Overall, our analysis suggests that the current rationing rule favors motherswith stronger labor market attachment, and hence, the policy effect is underminedby crowding out.
There are two more findings worth mentioning. First, the positive effects onparticipation, hours of work, and earnings are brought about mainly by increasing regular employment, while nonregular employment and self-employment are
not affected significantly. This result implies that not only the amount of work but
also the job quality is raised by childcare enrollment. Second, the treatment effect is strongest for mothers of an infant and decreases with the child’s age. This
seems reasonable because informal childcare arrangements and other options suchas kindergarten are available for older children.
The rest of the paper is structured as follows. Section 2 reviews the related literature. Section 3 describes the institutional background. Section 4 explains theMTE framework. Section 5 outlines the data structure and shows summary statis4

tics. Section 6 presents our estimates of the treatment effects. Section 7 discusses
the robustness of the results and shows counterfactual policy simulations. We conclude in Section 8.

2

Related Literature

Recent studies on childcare and maternal labor supply attempt to identify the causal
effects using plausible exogenous variations. One of the first such papers is that by
Gelbach (2002), who estimates the causal effects using the quarter of birth of fiveyear-old children as a source of exogenous variation. Using the 1980 US Census,
Gelbach (2002) identifies the effects of the eligibility for kindergarten on maternal
employment by comparing those who are barely eligible and those who are not because they were born shortly after the cutoff date to be eligible for kindergarten. He
finds that the enrollment for kindergarten increased mothers’ labor supply significantly. Fitzpatrick (2010) estimates the effect of childcare subsidies by applying
regression discontinuity design techniques similar to those used in Gelbach (2002)
to a newer cohort using the 2000 US Census and finds no subsidy effects except
for single mothers. Fitzpatrick (2010, 2012) argues that childcare subsidies becameless effective because the labor supply elasticity of US women has declined from1980 to 2000.
The evidence is mixed not only across time but also across countries. Evidence from Argentina (Berlinski and Galiani (2007)), Quebec (Lefebvre and Merrigan (2008)), Spain (Nollenberger and Rodriguez-Planas (2015)), and Germany(Bauernschuster and Schlotter (2015)) shows that childcare reforms increased maternal labor supply, while evidence from Sweden (Lundin et al. (2008)), France(Goux and Maurin (2010)), Norway (Havnes and Mogstad (2011)) shows that theeffect is negligibly small. Although the estimates are not directly comparable, theeffect of childcare tends to be small in countries where female labor supply was
already high prior to childcare reform. In those countries, the provision of formalchildcare only crowds out informal childcare arrangements without affecting maternal labor supply. By contrast, in countries where the female labor force participation
rate was low, a childcare reform tends to increase maternal labor supply.
5

The effect of childcare also varies within countries. Even in countries where theaverage policy effect was zero, childcare reform increased the labor supply of single
mothers (see Cascio (2009), Fitzpatrick (2010), and Goux and Maurin (2010), forexample). Andresen and Havnes (2016) find that Norwegian childcare reform from2002 increased the labor supply of mothers of children aged 0−2 years, which isa younger age group than that studied in previous papers. Because many single
mothers cannot afford to use other childcare arrangements and childcare for toddlers
is less available than that for older children, the provision of subsidized childcare
can increase the labor supply of single mothers and mothers of toddlers.
Using aggregate data at the province level in Japan from 1990 to 2010, Asaiet al. (2015) estimate the intention-to-treat (ITT) effect on mothers’ employment
and find it to be insignificant. The current paper differs from this previous study inthree important ways. First, the current paper estimates heterogeneous treatment effects using the MTE framework, while the previous paper estimates the average ITT
effect only. Second, the current paper estimates the effect of childcare use by child’sage, while the previous paper estimates the effect averaged over children aged 0−5
years. Given the findings by Andresen and Havnes (2016), a stronger effect is expected for younger children. Third, the current paper uses microdata after 2002,
which is more recent data than that used in the previous paper. Three-generation
households are common in Japan, and grandparents in the same household often
take care of children while a young mother works. However, the share of threegeneration households decreased from 29 percent in 1990 to 13 percent in 2010.
This implies that informal childcare by grandparents has become less available, andhence, childcare is expected to have a stronger effect in more recent years.1
1 Asai, Kambayashi, and Yamaguchi (2016) is a follow-up paper of their 2015 paper and estimate

the ITT effect on maternal employment for the periods of 1990-2000 and 2000-2010 separately.
They find insignificant effects for the 1990-2000 period and a small, but positive significant effect forthe 2000-2010 period. Very recently, Nishitateno and Shikata (2017) obtain a very similar estimate
for the 2000-2010 period using municipality-level data, instead of province-level data.

6

3

Institutional Background

3.1

Center-Based ChildcareChildcare centers in Japan are strictly regulated for quality control and are heavily
subsidized. According to the Comprehensive Survey of Living Conditions, 94% ofchildcare centers satisfy the national quality standard set by the Child Welfare Act
and are accredited by the governor of the province. Accredited childcare centers
are subsidized by municipal, provincial, and national governments so that averageusers pay about 40% of the cost.2 The average monthly fee per child is low at about
28,408 Yen (≈ 284 USD), although it depends on age, region, household income,and the number of siblings.3
The remaining 6% are nonaccredited childcare centers. Some of them areowned by large employers and/or are accredited by, and receive subsidies from,local governments but not from the national government.4 Because the vast majority of childcare centers are accredited and our main data set LSN21 does notdistinguish them, we sometimes refer to accredited childcare centers as “childcare
centers” for shorthand in the following.

3.2

Rationing Rule

To be eligible to use accredited childcare, parents and other extended family members under the age of 65 years and living in the same household must be unable toundertake childcare. The legitimate reasons for using an accredited childcare center
include working during the day, childbearing, disability, caregiving for sick peopleor people with disabilities, schooling, and job search. In practice, 94.2% of parents
using childcare centers satisfy the eligibility condition because they work during
the day.5
2 Parents of children aged 0 pay 20% of the cost, those of children aged 1 pay 30%, and those ofolder children pay 60%. See page 26 of Ministry of Health, Labour and Wealth (2008).
3 See Table 7 of Ministry of Health, Labour and Wealth (2009).
4 The fee for a child aged 0 is 46,330 JPY (about 460 USD), and that for child aged 5 is 34,161
JPY (about 340 USD). See Table 12 on page 14 of Ministry of Health, Labour and Wealth (2009).
5 See Table 3 of Ministry of Health, Labour and Wealth (2009).

7

Because accredited childcare is heavily subsidized and of high quality, many
parents would like to use it. When there are more applications than available slots
in a childcare center, the municipal government assesses the necessity of childcare
use and ranks applications following the guidelines set by the Ministry of Health,Labour, and Welfare. Although details may vary across local governments, therationing rule is largely uniform across the country.6
To be concrete, we describe the rationing rule for childcare using an example
from the city of Yokohama. Yokohama is the largest city in Japan, with a populationof 3.8 million. As is the case in major cities, there is excess demand for subsidized
childcare in Yokohama. The municipality ranks applications for childcare fromA (highest) to G (lowest) in the first round. Fathers and mothers are individuallyranked, and the lower rank is applied to the family.
Table 1 summarizes how applications are ranked in the first round. Most parents
use childcare because they usually work during the day. If a parent works outsideof the home for 20 or more days per month and 8 or more hours per day, he/she isranked highest at A. The rank is lowered if a parent works less, and a rank of C isgiven if he/she works 16 or more days per month but works 4−7 hours per day. A
parent who is currently not working but has a job offer is ranked lower than thosecurrently working, and a rank of D is given if he/she works for 16 or more days permonth and 7 hours per day. A parent working for fewer than 16 days per month or
4 hours per day is not considered to have a legitimate reason to use childcare. The
days and hours of work are assessed 1 month before the childcare application andmust be verified by a document signed by the employer. Those who are on parental
leave can report their days and hours of work before they took leave.
Although a parent can use accredited childcare if he/she is searching for a job,he/she is given the lowest rank of G. This is problematic for some job seekers. Some
employers may be unwilling to hire a young mother who does not find a childcarearrangement, because she may not be able to work without childcare. Employment
is required for childcare use, but childcare use may also be essential for finding
6 We confirm that the rationing rules are very similar among the largest cities, where rationing typically takes place. These cities include Yokohama, Osaka, Nagoya, Sapporo, Kobe, Kyoto, Fukuoka,
Kawasaki, Saitama, Hiroshima, and Sendai.

8

employment.
Lone parents and parents with disabilities are given the highest priority, andhence, a rank of A. The rank is raised by one unit if the family is on welfare, themain earner lost his/her job, etc.; however, household income has little influence onchildcare allocation otherwise.
If many applications are ranked equally at the cutoff level, the municipal government further ranks these applications in the second and third rounds. For example,
if older siblings are already enrolled in the same childcare center, extra points are
given to the application in the second round.
Table 1: Necessity Assessment in the First Round (Yokohama, 2010)
Reason
Note
Rank
Work
≥ 20 days/month and ≥ 8 hours/dayA≥ 16 days/month and ≥ 7 hours/day
B≥ 16 days/month and 4-7 hours/dayC≥ 16 days/month and ≥ 7 hours/day (Job Offer)D≥ 16 days/month and 4-7 hours/day (Job Offer)
E(Rank is lowered by one unit if work at/from home.)
Job Search
Up to 3 months
G
Single Parent If engaged with work, training, or job searchA
Disability
Class 1 or 2
A
Childbearing 8 weeks before and afterD
SchoolD..
..
.
.
Source: Page 12 of Aoba Ward, City of Yokohama (2009).
Note: If the family is on welfare, the rank is raised by one unit. If many households
are in the same rank at the threshold level for childcare allocation, the application
is further ranked for tie-break in the second and third rounds.

3.3

Childcare Expansion

The national government recognized the shortage of accredited childcare centersin the early 1990s. It launched the Angel Plan (1994−1998) and the New Angel
Plan (1999−2003), which included an expansion of childcare capacity, extension ofchildcare service hours to include weekends and holidays, and subsidies to promote

9the take-up of parental leave and shorter working hours. Unfortunately, these twoplans were too small and failed to increase the supply of accredited childcare. In
2003, the national government enacted the Basic Act for Measures to Cope withSociety with Declining Birthrate and committed to taking legal and financial measures to increase the supply of childcare. This policy reform increased the numberof accredited childcare slots by 12% from 2000 to 2010.
While the national government covers half of the cost, the provincial and municipal governments are responsible for the rollout of the childcare reform. Dependingon the financial status and policy priorities, the pace of the program rollout varied
by region. This variation in the pace of childcare expansion across regions is exploited for the identification of causal effects. We will discuss this identification
strategy extensively in Section 4.2 after we describe the MTE framework.

4

Analytical Framework and Empirical Strategy

4.1

Marginal Treatment Effect

4.1.1

Setup

Using the MTE framework developed by Björklund and Moffitt (1987) and Heckman and Vytlacil (2005),7 we estimate heterogeneous treatment effects varying byobserved and unobserved characteristics of mothers.
Define j ∈ {0, 1} as an index for treatment status such that j = 1 implies being
treated and j = 0 implies being untreated. A potential outcome Y j for treatment
status j is given by
Y j = Xβ j +U j
E(U j |X) = 0,

(1)
(2)

where X is a vector of control variables. Following Brinch, Mogstad, and Wiswall(forthcoming), we assume a zero conditional mean of errors U j instead of indepen7 Cornelissen, Dustmann, Raute, and Schönberg (2016) is an excellent introduction to the MTE

framework for applied researchers.

10dence.
Treatment status is determined by the following selection equation
D = 1{Xγ + δ Z −V > 0},(3)where D is a dummy variable for treatment, 1{·} is an indicator function that takes
a value of one if the condition in the curly brackets is satisfied and zero otherwise,
Z is a vector of instrumental variables excluded from the outcome equation (1),and V is a scalar of unobserved characteristics. Our instrument Z is the childcare
coverage rate, which is defined as childcare slots per child in a given region. The
validity of the instrument is discussed extensively in Section 4.2. We also include
the interactions of the coverage rate and a subset of exogenous variables X in the
instruments. Because a larger value of V keeps more mothers from treatment, werefer to it as a resistance to treatment.
The selection equation (3) can be rewritten as
D = 1{Xγ + δ Z > V }(4)= 1{FV (Xγ + δ Z) > FV (V )}(5)= 1{P(Xγ + δ Z) > UD },(6)

where FV is a cumulative distribution function for V , P(·) is a propensity score,and UD is a quantile of the unobserved resistance V . We assume that (U j ,UD ) is
independent of Z given X.
The MTE is defined as
MT E(X = x, UD = uD ) = E(Y1 −Y0 |X = x, UD = uD ).

(7)

It is interpreted as the gain from treatment for a mother whose observed characteristics are X = x and the quantile of the unobserved resistance to treatment is UD = u.
Policy relevant parameters such as the average treatment effect (ATE), the treatment
effect on the treated (TT), the treatment effect on the untreated (TUT), and the local
average treatment can be derived as weighted averages of the MTE.
What is the economic interpretation of uD in the context of this research? Recall
11how the local governments select successful applications. The rationing rule sorts
families by how much parents work. Because most fathers in the sample work fulltime, mothers’ working hours are the key determinant of the probability of childcareuse. Mothers’ unobserved preference for work and their skills are likely to be themain components of the unobserved resistance for work. Specifically, a low uD implies strong labor market attachment, while a high uD implies weak labor market
attachment.
4.1.2

Local Instrumental Variable Estimator

Heckman, Urzua, and Vytlacil (2006) show that the MTE can be identified by the
local IV estimator. We assume that the MTE is additively separable into an observed
and an unobserved component,
MT E(X = x, UD = uD ) = x(β1 − β0 ) + E(U1 −U0 |UD = uD ).

(8)

The conditional mean outcome given the observed characteristics and the propensity score isE(Y |X = x, P(X, Z) = p) = xβ0 + x(β1 − β0 )p + K(p),(9)

where K(p) is a nonlinear function of the propensity score. The MTE for the motherwith X = x and UD = p is given by the derivative of Equation (9) with respect to thepropensity score,∂ E(Y |X = x, P(X, Z) = p)∂p
∂ K(p)= x(β1 − β0 ) +.
∂p

MT E(X = x, UD = p) =

(10)
(11)

How does the local IV estimator identify the MTE defined by unobserved characteristics uD ? We ignore observed characteristics X to simplify the argument forthe moment. The selection equation (6) implies that those with the unobserved
characteristics uD < p are selected into treatment and that those with uD = p are indifferent. If we increase the propensity score by a small amount, those with uD = p
12

are newly induced into the treatment. Note that the average outcome as expressed in
Equation (9) changes in response to the change in the propensity score p. The MTE
is given by the change in the average outcome divided by the fraction of individuals
newly selected into treatment.

4.2

Threat to Identification

Our instrument is the childcare coverage rate, which is defined as childcare slots
per child in a given region. Because our control variables include year and region dummies, time-invariant regional characteristics and nationwide changes inthe social and economic conditions are accounted for. The variation exploited for
identification is the growth of the childcare coverage rate in a given region, whichis equivalent to the difference-in-differences approach.
One of the identifying assumptions is that the growth of the coverage rate isexogenous. To see whether this assumption is valid, we examine the potential determinants of the growth of the coverage rate. According to Cabinet Office (2010),
there are three obstacles preventing childcare expansion. First, the regulations arestrict and uniform across the country, even though some (e.g., area per child andrequirement for a kitchen) are unnecessary or unrealistic for urban areas. Second,
the local governments do not have a permanent budget for childcare operations,although the national government transfers some additional funds to the local governments temporarily. Third, some municipal governments cannot acquire the landto build new childcare centers, because the rents and land prices are prohibitively
high in urban areas.
We assess how these factors and other regional characteristics affect the paceof childcare expansion. We regress the change of the coverage rate from 2000 to2010 on several prereform regional characteristics including the female labor force
participation rate, the total fertility rate, the financial capability index of the local
government, the land price, and the average female wage in 2000.
Table 2 reports the regression results. The female labor force participation ratein the prereform period is positively and significantly correlated with the growth ofthe childcare coverage rate. The demand for childcare is considered to be high in

13

Table 2: Determinants of the Growth of Childcare Coverage Rate
Change inCoverage Rate
Female Labor Force Participation Rate
0.186
(0.089)Total Fertility Rate
−0.001(0.050)Financial Capability Index−0.062(0.035)
Log Land Price
0.009(0.015)
Log Average Female Wage
−0.060(0.099)Num. obs.
80
Sources: All explanatory variables are measured in 2000. Labor force participation rate for women
aged 20-64 is from the Census. The total fertility rate is from Vital Statistics. The financial capability index is from Table for Financial Capability Indices of Prefectures constructed by Ministryof Internal Affairs and Communications. The land price is the average land price per square meterin residential areas, which is taken from Survey on Land Price of Prefectures by Ministry of Land,
Infrastructure, Transport and Tourism. The mean female wage is calculated by dividing scheduled
cash earnings by scheduled hours of work, which are from Basic Survey of Wage Structure 2001.
For data consistency, I omitted City of Yokosuka and non-major cities in Province of Kanagawa,
although they are included in the main analysis.

14the region where the female labor force participation is high. The estimate suggeststhat the supply of accredited childcare increased to meet the high demand in such a
region. The total fertility rate in the prereform period has no effect on the growth ofthe coverage rate. Despite the argument by the Cabinet Office (2010), the financial
status of the provincial government, the land price, and the female wage rate in theprereform period do not affect the growth of the coverage rate significantly.
This result indicates that the growth of the coverage rate is not completely random, and hence, accounting for potential policy endogeneity is necessary for unbiased estimates. To address this issue, we include interactions of the prereform
regional characteristics and year dummies in our control variables.
Another threat to identification is selective migration. A popular narrative saysthat obtaining a slot in an accredited childcare center is extremely difficult in Tokyoand that some people even move to other districts for childcare. Using the Employment Structure Survey8 2012, we take a sample of mothers of children under age 6
and examine their reasons for the most recent move and where they moved from.
We find that “for childrearing and education,” 9.5% moved within the same city,
4.6% moved from another city in the same province, and 1.4% moved from anotherprovince. Because a region in this study is defined by the combination of city andprovince, at most 4.6% moved between regions for childcare. As we will show in
Section 7.1, selective migration seems to have little effect on the estimates.
There was another major policy reform that may have affected female labor
supply during the period of analysis. In 2005, nonregular workers became eligible
for a paid one-year parental leave. In addition, the replacement rate of cash benefits
was raised gradually from 25% to 50% from 2000 to 2007.9 We do not believe that
this policy reform biases our estimates, because it is uniformly legislated across thecountry and its effect on mothers’ labor supply is accounted for by the year dummy.
We are not aware of any major policy changes that may affect female labor supply
at the region level.
Other issues that might affect our estimates include endogenous fertility, presence of siblings, and functional form assumptions. These issues are discussed ex8 It is conducted by the Statistics Bureau every three years and covers about 1% of the population.
9 See Asai (2015) and Yamaguchi (2016) for evaluation of these policy changes.

15tensively in Section 7.1, but our main results are largely unaffected.

4.3

Empirical Implementation

We implement the local IV estimator as follows. In the first step, we estimate thepropensity score using a flexible probit model. The covariates include the coveragerate up to the third-order term, parents’ age and education, and year and region
dummies. To allow for heterogeneous responses to the coverage rate, we interact thecoverage rate and parents’ characteristics. In addition, we include the interactions ofyear dummies and prereform regional characteristics to address policy endogeneity.
In the second step, we estimate the outcomes equation (9) using a linear regression with the assumption that K(p) is a quadratic function. We allow for higherorder terms of the propensity score in the robustness checks. To allow for heterogeneous treatment effects by parents’ age and education, we interact them withthe propensity score. Standard errors are bootstrapped with 100 replications andclustered at the region level. Note that one replication in our bootstrap procedureincludes both the first and second steps so that uncertainty in the estimates in thefirst step is taken into account.

5

Data

5.1

Data Sources

Our main data source is LSN21, which is a census of children who were born January 10−17, 2001, July 10−17, 2001, and May 10−24, 2010. The first survey isconducted when the child is 6 months old. Subsequent questionnaires are completed every year about 6 months after their birthdays. The response rates are highat 93.5 and 88.1 percent in the first survey years for cohorts born in 2001 and 2010,
respectively. About 83 percent of respondents in the first survey remain in thesurvey 3 years later at age 3.5. These response rates for the LSN21 are higher
than those for the National Longitudinal Survey of Children and Youth,10 which
10 In the National Longitudinal Survey of Children and Youth in Canada, the response rate in thefirst cycle conducted in 1994/1995 was 86.5%, and 67.8% of the children in the original cohort

16

provides Canadian longitudinal data used by Baker, Gruber, and Milligan (2008),
among others.
We draw data on accredited childcare centers from the annual Report on Social
Welfare Administration and Services, which covers all provinces and major cities
with a population of over 200,000. We define region by a combination of cityand province: a region is a major city or a set of all municipalities in a province
except for the major cities. We include 82 regions that are included in the datain both 2002 and 2011, which consists of 45 provinces and 37 major cities. The
provinces of Fukushima and Miyagi were omitted because of missing data, as they
were severely affected by the Great East Japan Earthquakes and Tsunami in 2011.
Child population is taken from the quinquennial Census. For the years when
the Census is not conducted, we estimate child population by linear interpolation.
Other regional characteristics in 2000 are drawn from various sources. See the noteon Table 2 for details.

5.2

Descriptive Statistics

Table 3 shows the summary statistics of the sample. The childcare enrollment rate
is low at 3.6% when the child is 0.5 years old, but it increases to 23.4% 1 year later.
As children grow older, the enrollment rate increases to 36.8% when the child is 3.5
years old.
The coverage rate, defined as the number of slots per child, is about 0.3 andincreases gradually with the child’s age, which reflects the progress of the childcare
reform. The average coverage rate is higher for the treated than for the untreated,
implying that the coverage rate is positively associated with the childcare enrollment rate.
Parents’ ages are evaluated when the child is 0.5 years old. The average ageof mothers is 30.405, and fathers are about 2 years older on average than mothers.
Parents’ education is measured when the child is 1.5 years old. About 5% of parents
are less-than-high-school educated and about one-third of parents are high school
educated. Two-year college is the most common education level for mothers, andresponded in cycle 3 conducted in 1998/1999.

17

about 20% of mothers went to university. In contrast, four-year university is themost common education level for fathers, and about 17% of fathers went to twoyear college. We do not find large systematic differences in mothers’ characteristics
between the treated and untreated when other characteristics are not controlled for.
In contrast, father’s characteristics are substantially different between the treatedand untreated. The treated fathers are younger and less educated than the untreatedfathers.
The fraction of working mothers is 13.3% when the child is 0.5 years old. Notethat many mothers are entitled to 1 year of paid maternity leave until their childreaches the age of 1 year. Many mothers return to the labor market after their paid
leave period, and 33.7% of mothers work when the child is 1.5 years old. The
fraction of working mothers increases with child’s age, and 42.8% of mothers workwhen the child is 3.5 years old. There is a strong association between the use ofcenter-based childcare and mothers’ labor market participation. The labor market
participation rate of childcare users is high at 83−91%, but that of nonusers is only
10−20%.
Note that the fraction of working mothers is higher than the enrollment rate at
the same age, implying that many mothers work without using formal childcare.
The labor market participation rate among mothers not using childcare increases
with child’s age, suggesting more availability of informal childcare for older children.
The mean number of working hours increases with child’s age, although they are
not observed at age 1.5 years. The mean number of working hours among childcareusers is stable at about 30 hours per week, while that among nonusers is about 2−5hours per week. Mean earnings are not monotonically increasing with child’s age.
The mean earnings of childcare users are higher than those of nonusers. Earnings
are not observed at age 2.5 years.
Market work is categorized into either regular work, nonregular work, or selfemployment. Regular employment is typically under a permanent contract and afull-time job, while nonregular employment is typically under a limited-term contract and a part-time job. They also differ in hourly wages, nonwage benefits,
employer-sponsored training, and eligibility for the mandated PL (see Kambayashi
18Table 3: Summary Statistics
All

Childcare Enrollment
Age 0.5
Age 1.5
Age 2.5
Age 3.5
Coverage Rate
Age 0.5
Age 1.5
Age 2.5
Age 3.5
Mother’s Characteristics
Age
Less Than High School
High School
2-Yr College
4-Yr University or Higher
Father’s Characteristics
Age
Less Than High School
High School
2-Yr College
4-Yr University or Higher
Market WorkAge 0.5
Age 1.5
Age 2.5
Age 3.5
Hours Per Week Worked
Age 0.5
Age 2.5
Age 3.5
Earnings (mil. JPY)
Age 0.5
Age 1.5
Age 3.5
Regular WorkAge 0.5
Age 1.5
Non-Regular WorkAge 0.5
Age 1.5
Self-EmployedAge 0.5
Age 1.5

Comparison by Treatment
p-value forTreated
Untreated
Difference

Nobs.

Mean

S.D.

72475
72477
67929
65242

0.036
0.234
0.314
0.368

0.188
0.423
0.464
0.482

1.000
1.000
1.000
1.000

0.000
0.000
0.000
0.000

72475
72477
67929
65242

0.305
0.313
0.321
0.331

0.111
0.113
0.116
0.118

0.328
0.336
0.348
0.360

0.304
0.306
0.309
0.313

0.000
0.000
0.000
0.000

72475
72475
72475
72475
72475

30.405
0.046
0.334
0.419
0.200

4.516
0.210
0.472
0.493
0.400

30.663
0.057
0.343
0.431
0.169

30.395
0.046
0.334
0.419
0.201

0.003
0.012
0.314
0.233
0.000

72475
72475
72475
72475
72475

32.402
0.073
0.354
0.169
0.404

5.524
0.261
0.478
0.375
0.491

32.565
0.109
0.439
0.176
0.276

32.396
0.072
0.350
0.168
0.409

0.146
0.000
0.000
0.307
0.000

71817
72046
67338
64215

0.133
0.337
0.374
0.428

0.339
0.473
0.484
0.495

0.878
0.912
0.873
0.828

0.104
0.161
0.146
0.195

0.000
0.000
0.000
0.000

71957
67338
64010

3.255
12.503
13.587

10.71718.70418.74230.92131.31728.884

2.215
3.900
4.761

0.000
0.000
0.000

70552
67555
61746

0.741
0.451
0.797

1.557
1.098
1.561

2.135
1.458
1.802

0.691
0.183
0.245

0.000
0.000
0.000

71817
72046

0.041
0.168

0.199
0.374

0.493
0.541

0.024
0.054

0.000
0.000

71817
72046

0.039
0.113

0.193
0.316

0.303
0.305

0.029
0.054

0.000
0.000

71817
72046

0.040
0.042

0.195
0.200

0.069
0.058

0.039
0.037

0.000
0.000

Source: LSN21.
Note: The sample includes two-parent families. Parents’ ages and education are measured when child is 0.5 and 1.5 year old,
respectively. Not all labor market outcomes are available at all ages.

19and Kato (2013)). Information on employment type is available when the child isaged 0.5 and 1.5 years. The fraction of regular workers is slightly higher than thatof nonregular workers, and only 4% of mothers are self-employed.
Table 4: Share of Childcare Mode for Working Mothers

Care ModeAge 0.5
Age 1.5
Age 2.5
Age 3.5

Childcare
Center
0.241
0.633
0.733
0.712

Sitter/ Parents
Grandparents Nannies Only
0.334
0.062
0.362
0.198
0.031
0.138
0.150
0.020
0.098
0.101
0.070
0.117

Source: LSN21
Note: Childcare mode is mutually exclusive and collectively exhaustive as defined by the following
rule. If enrollment for a childcare center is reported, this is considered as the primary mode, because
most enrolled children attend fulltime. If a child is cared by grandparents only, the primary caregiver is grandparents. If any caregiver other than a childcare center and grandparents is reported,
the primary caregiver is a child sitter. If no caregiver except is reported, parents are the primary
caregiver.

Many working mothers use informal childcare arrangements, and their choiceof childcare mode changes with child’s age. Table 4 shows the share of childcare
mode for working mothers. When the child is 0.5 years old, only 24.1% of working
mothers use a childcare center. Most children at age 0.5 years are cared for by theirparents or grandparents. The use of babysitters and nannies is rare, at 6.2%.
While most working mothers of infants do not use formal childcare, it is themost common childcare mode for working mothers of older children aged 1.5−3.5
years. At age 1.5 years, 63.3% of working mothers use childcare, and more than
70% of working mothers use childcare when the child is 2.5−3.5 years old. The useof informal care by grandparents becomes less common as the child grows older.
The use of babysitters or nannies is rare regardless of the child’s age. About 10%of the children of working mothers are cared for by parents only.

20

6

Results

We show our main results in three steps so that the econometric model becomesincreasingly complex. First, in Section 6.1, we show the estimates for the first-stage
and reduced-form regressions. Our estimates indicate that the childcare coveragerate indeed increases childcare enrollment and maternal employment rates, which
implies that our instrument, the childcare coverage rate, is not weak. Second, in
Section 6.2, assuming an homogeneous treatment effect for tractability, we show
the estimates for the treatment effect of childcare enrollment by conventional IV
regression and bivariate probit model. We hope that the analysis here is usefulfor readers, because these econometric methods are used routinely. In addition, theestimates can be compared with those from previous studies that use IV regressions.
Third and finally, we allow for heterogeneity in the treatment effect in Section 6.3.
There, we show estimates for the marginal treatment effects that vary by unobserved
propensity for childcare enrollment.

6.1

Effects of Childcare Coverage Rate on Enrollment andMaternal Employment

We begin our analysis by presenting region-level evidence. The panels in the left
column of Figure 1 present the relationship between the region-level coverage rateand childcare enrollment rate by child’s age, after removing the effects of prereform
regional characteristics, parental characteristics, and region and year fixed effects(see the note on Figure 1 for details). The panels in the right column show the
relationship between the coverage rate and mothers’ employment rate at the region
level.
In all graphs, the slope is positive and statistically significant at the 10% level
for all ages from 0.5 to 3.5 years. Note that the results do not seem to be driven byan outlier. The graphs provide prima facie evidence that the expansion of childcare
slots increases the enrollment of children and the employment of their mothers.
These graphs make our identification strategy transparent; however, the residual
plot can only help us visualize the linear relationship. The marginal effect of the21Residualized WorkAge 0.5

0.1
0.0
−0.1
−0.05

0.00

0.05

−0.10

−0.05

0.00

0.05

Age 1.5

Age 1.5

−0.1
−0.05

0.00

0.05

0.0
−0.1

0.10

−0.10

−0.05

0.00

0.05

Age 2.5

Age 2.5
Residualized Work

Residualized Coverage Rate

0.0
−0.1
−0.05

0.00

0.05

0.0
−0.1

0.10

−0.10

−0.05

0.00

0.05

Residualized Coverage Rate

Age 3.5

Age 3.5

0.0
−0.1
−0.05

0.00

0.05

0.10

Residualized Coverage Rate

0.10

0.1

Residualized Coverage Rate

0.1

0.10

0.1

Residualized Coverage Rate

0.1

−0.10

−0.1
Residualized Coverage Rate

0.0

−0.10

0.0

0.10

0.1

−0.10

0.1

Residualized Coverage Rate

Residualized Work

−0.10

Residualized Work

Residualized Enrollment
Residualized Enrollment
Residualized Enrollment
Residualized Enrollment

Age 0.5

0.10

0.1
0.0
−0.1
−0.10

−0.05

0.00

0.05

0.10

Residualized Coverage Rate

Figure 1: Coverage Rate and Childcare Enrollment by Region
Source: Authors’ calculation based on LSN21.
Note: Residualized coverage, childcare enrollment, and maternal employment rates are calculated
as follows. We regress each of the variables on parents’ age and education, regional characteristics
at the 2000, and year and region dummies, and then, take averages of the residuals by region. The
size of the bubbles indicates the number of observations in the region. The fitted line is estimatedby the weighted least squares and shown with the 90% confidence interval.

22

coverage rate on the enrollment rate may vary by the coverage rate, but that ismasked in these graphs. To examine potential nonlinearity between the coveragerate and outcomes, we estimate a flexible probit model that includes up to thirdorder polynomials of the coverage rate and parents’ and regional characteristics.
The top-left panel of Figure 2 shows the effects of the coverage rate on childcare
enrollment by child’s age. The enrollment rate increases with the coverage rate
for all age groups, which confirms the results from the region-level analysis. In
addition, the graph indicates that the enrollment rate changes with the coveragerate. The graph for children aged 3.5 years shows a concave profile, implying that
their enrollment rate does not increase much at a higher coverage rate. This ispresumably because many 3.5-year-old children choose to enroll in kindergarten
instead of childcare, even if childcare is available. Kindergarten is not an option
for younger children aged 0.5−2.5 years. By contrast to 3.5-year-old children, theirenrollment increases with the coverage rate at an increasing rate.
The top-right panel of Figure 2 shows the effects of the coverage rate on thefraction of working mothers. It increases with the coverage rate and the child’sage. Note that the fractions of working mothers and childcare users do not generally coincide for two reasons. First, some working mothers use informal childcarearrangements. Second, the municipal governments accept applications from mothers who do not work but are unable to care for their children because of sickness,disability, schooling, looking for work, etc. These eligible but nonworking mothers
are given low priority but are able to use childcare when the coverage rate is high.
To see whether an expansion of childcare crowds out informal childcare arrangements for working mothers, we estimate probit models for the joint choice ofmothers’ work and childcare mode. The bottom-left panel shows how the coverage rate affects the fraction of mothers who work and use a childcare center. The
fraction increases with the coverage rate and the child’s age. The graph is concavefor 3.5-year-old children, while it is convex for younger children. The bottom-rightpanel shows how the coverage rate affects the fraction of mothers who work anduse an informal childcare arrangement. It decreases with the coverage rate, but noclear pattern can be seen by the child’s age.
Many working mothers rely on informal childcare arrangements when the cov23

0.5

1.5

2.5

Age

3.5

0.8

0.8

0.6

0.6

Prob. of Work

Enrollment Rate

Age

0.4

0.2

0.0

0.5

2.5

3.5

0.4

0.2

0.0
0.2

0.4

0.6

0.8

0.2

Coverage Rate

0.5

1.5

2.5

0.4

0.2

0.0
0.4

0.6

Age

3.5

0.6

0.2

0.4

0.6

0.8

Coverage Rate

Prob. of Work & Informal Care

Age
Prob. of Work & Childcare Ctr.

1.5

0.8

Coverage Rate

0.5

1.5

2.5

3.5

0.16

0.12

0.08

0.04
0.2

0.4

0.6

0.8

Coverage Rate

Figure 2: Coverage Rate, Childcare Enrollment, and Mother’s Work
Note: Estimates are based on the probit model in which the explanatory variables include the coverage rate up to the third-order polynomial, parents’ age and education, regional characteristics in
2000, and region and year fixed effects. The polynomials of the coverage rate are interacted withparents’ characteristics.

24

erage rate is low, but informal childcare is increasingly substituted with formalchildcare centers as the coverage rate increases. This result implies that the expansion of childcare supply crowds out informal childcare among working mothers.
Even though parents’ work is effectively a prerequisite for the use of a childcare
center, providing a new childcare slot does not necessarily add a mother to the labormarket, because some of them simply substitute informal childcare arrangements
and continue to work.
Childcare enrollment and mothers’ work are also affected by parents’ age andeducation. Table 5 shows the average marginal effects of parental characteristics
based on the probit model.
Mothers’ education is positively correlated with the enrollment rate. Rememberthat parents’ work is virtually required for childcare use. Skilled mothers are more
likely to work and to use childcare, because their opportunity cost of staying at
home is high. In addition, the rationing rule gives a higher priority to mothers withstronger labor market attachment, which is positively correlated with education.
Father’s age and education are negatively correlated. If a wife takes her husband’s earnings as given, her labor supply and childcare use are negatively correlated with her husband’s earnings because of the income effect, which accounts forwhy childcare use is negatively correlated with father’s age and education.
We show that the childcare coverage rate increases the mothers’ employment
rate, but the interpretation of the result is not necessarily straightforward. This isbecause the effect of the coverage rate on mothers’ employment is the product of
the effect on childcare enrollment and the treatment effect of childcare enrollment.
In the following subsections, we show estimates for the treatment effect of childcare
enrollment.

6.2

Estimating Treatment Effects by IV Regression andBivariate Probit

In this subsection, we present estimates for treatment effects on mothers’ labormarket outcomes using a conventional IV regression and bivariate probit model,
assuming that treatment effects are homogeneous. Because these methods are well25

Table 5: Marginal Effects of Coverage Rate on Childcare Enrollment

Childcare Enrollment
Mother’s Age
Less Than HS (Mother)
HS (Mother)
2-Yr College (Mother)
Father’s Age
Less Than HS (Father)
HS (Father)
2-Yr College (Father)
Mother’s Work
Mother’s Age
Less Than HS (Mother)
HS (Mother)
2-Yr College (Mother)
Father’s Age
Less Than HS (Father)
HS (Father)
2-Yr College (Father)Age 0.5

Age 1.5

Age 2.5

Age 3.5

0.001(0.000)-0.001(0.004)-0.007(0.002)-0.001(0.002)-0.000(0.000)0.034(0.004)0.020(0.002)0.013(0.002)0.002(0.001)-0.095(0.008)-0.099(0.005)-0.055(0.005)-0.002(0.000)0.111(0.007)0.056(0.004)0.055(0.005)0.001(0.001)-0.098(0.010)-0.104(0.006)-0.071(0.005)-0.001(0.000)0.148(0.008)0.078(0.004)0.072(0.005)-0.000(0.001)-0.075(0.010)-0.078(0.006)-0.058(0.005)-0.001(0.001)
0.185(0.008)0.101(0.005)0.091(0.005)0.003(0.000)0.011(0.007)-0.014(0.004)-0.008(0.004)0.002(0.000)0.111(0.006)0.059(0.003)0.059(0.004)0.004(0.001)-0.144(0.009)-0.136(0.006)-0.083(0.005)-0.001(0.000)0.160(0.008)0.093(0.004)0.091(0.005)0.004(0.001)-0.124(0.010)-0.119(0.006)-0.072(0.005)-0.001(0.001)0.183(0.008)0.111(0.005)0.098(0.005)0.005(0.001)-0.071(0.011)-0.078(0.006)-0.054(0.005)-0.000(0.001)0.222(0.008)0.127(0.005)0.115(0.006)

Note: Standard errors are in parenthesis. Estimates are based on the probit model in which the
explanatory variables include the coverage rate up to the third-order polynomial, parents’ age andeducation, regional characteristics in 2000, and region and year fixed effects. The polynomials of
the coverage rate are interacted with parents’ characteristics. The reference group for education isthose with 4-year university education or higher.

26known and commonly used, our estimates can be compared with those in the previous studies in the literature.
We use the propensity score as an instrument rather than the coverage rate itself.
The propensity score is a function of the coverage rate and other exogenous variables, but the use of the propensity score as an instrument has advantages over theuse of the coverage rate in our context. First, it is required by the local IV estimator
for the MTE. By using the same instrument across different models (IV, probit, andlocal IV models), the estimates become comparable. In particular, an IV estimate
can be interpreted as a weighted average of the MTE (see Heckman and Vytlacil(2005)). Second, the propensity score provides the efficient IV if it is correctly
specified (see Wooldridge (2010)). Note that this method produces a consistent IV
estimate even if the propensity score is not modeled correctly.
The first column of Table 6 shows the effects of childcare use on mothers’ work
estimated by OLS. The estimates range from 0.619 to 0.754, and the treatment
effects decrease with age. Of course, they cannot be interpreted as causal becauseof possible endogenous selection into treatment.
The estimates from the IV regression are reported in the second column. The
estimated effect on mothers of children aged 0.5 years is incredibly large. Given
that only about 13% of them work and only about 3% of them use a childcare
center (see Table 3), the implausible estimate is caused by poor approximation by
the linear probability model. For this age group, accounting for nonlinearity by the
probit model seems to be important. The IV estimates for other age groups range
from 0.426 to 0.685 and are smaller than the OLS estimates. The treatment effects
decrease with child’s age. Note that we soundly reject the null hypothesis that our
instrument is weak, as shown in the third column.
To account for nonlinearity, we estimate the treatment effects using probit models. The fourth column shows the estimates of a univariate probit model, which does
not address possible endogeneity biases. They are very similar to estimates by OLS.
The fifth and last column shows estimates of a bivariate probit model that is comparable to the IV regression as they both use an instrument. The bivariate-probit estimates are smaller than those of a univariate probit for all age groups. Moreover, thedifference between univariate and bivariate probit estimates increases with child’s
27

Table 6: Treatment Effects on Mother’s Market WorkAge 0.5
Age 1.5
Age 2.5
Age 3.5

Linear Models
F-stat for
Weak IV
OLS
IV
0.754
1.142
206.639(0.008) (0.155)
0.744
0.685
147.599(0.010) (0.086)
0.723
0.661
95.613(0.012) (0.089)
0.619
0.426
106.285(0.015) (0.108)

Nonlinear Models
Bivariate
ProbitProbit0.752
0.731(0.007) (0.064)
0.744
0.690
(0.003) (0.040)
0.723
0.498
(0.003) (0.069)
0.618
0.144
(0.003) (0.070)

Note: Standard errors are in parenthesis and those for OLS and IV are clustered at the region level.
The dependent variable is a dummy for mother’s market work. The endogenous variable is a dummy
for the use of a childcare center. The IV is the propensity score estimated by the flexible probit (seeSection 6.1). Other exogenous variables include parents’ age and education, regional characteristics
in 2000, and year and region fixed effects.

age, suggesting that endogeneity bias is more severe for older children.
Although estimates vary between the IV regression and the bivariate probit,
they share some important features: the estimated treatment effect is positive andsignificant, and decreases with child’s age. The treatment effect is smaller for older
children, because informal childcare is more readily available. In particular, children aged 3.5 years are eligible to enroll in kindergarten. Providing a childcare
slot to an older child does not change his/her mother’s work hours, because it only
crowds out the existing informal childcare. Our estimates from the IV and bivariate
probit models help to interpret the ITT effects. The ITT effects are small for mothers of very young children, because they are less likely to use a childcare center,even though their treatment effects are greater than those of the mothers of older
children.

28

6.3

Estimating Marginal Treatment Effect by Local IV Regression

We estimate the MTE using the local IV estimator outlined in Section 4.1.2. Compared with the IV regression and bivariate probit models, the local IV regression
is more flexible because we allow for heterogeneous treatment effects using unobserved characteristics. In the following, we discuss the results for mothers ofchildren aged 1.5−3.5 years. The estimator does not provide reasonable estimatesfor mothers of children aged 0.5 years, because both the enrollment rate and thefraction of working mothers are very low, and the linear probability model in thesecond stage regression provides a poor approximation.
Figure 3 shows how the MTE on various labor market outcomes changes with
the quantile of the unobserved resistance to treatment uD . The MTE is averaged
over observed characteristics and shown with the 90% confidence interval. The
three panels in the top row show the MTE curves for mothers’ market work bychild’s age. They are all significantly above zero and increase with the resistanceto treatment, which implies a reverse selection on the treatment effect. Rememberthat those with a lower value of resistance to treatment are more likely to be enrolled in childcare. The upward-sloping MTE curves imply a negative relationshipbetween the treatment effect and the propensity for childcare use; that is, those withweak treatment effects are more likely to be given a childcare slot, while those withstronger treatment effects are less likely to be given a childcare slot.
The panels in the second row show the MTE on weekly hours of work. Work
hours are not included in the data when the child is age 1.5 years. Again, the MTE
is positive and significant and increases with the unobserved resistance. The panelsin the third row show the MTE on annual earnings in million JPY (≈ 10,000 USD).
The MTE on earnings is positive and significant except for very low values of uD
and increases with the unobserved resistance.
Figure 4 shows the MTE on the choice of employment types that are unavailable when the child is 2.5 and 3.5 years old. Market work is categorized into either
regular work, nonregular work, or self-employment. A typical regular worker is afull-time worker, better paid, with more fringe benefits, and under a permanent con-

29

1.0
0.5
0.0
0.0

0.5

1.5
1.0
0.5
0.0

1.0

0.0

ud (Resistance to Treatment)

Market Work at Age 3.5
Marginal Treatment Effect

1.5

Market Work at Age 2.5
Marginal Treatment EffectMarginal Treatment EffectMarket Work at Age 1.5

0.5

1.5
1.0
0.5
0.0

1.0

0.0

ud (Resistance to Treatment)

60
40
20
0

80
60
40
20
0

0.0

0.5

1.0

0.0

ud (Resistance to Treatment)

Marginal Treatment EffectMarginal Treatment Effect1.0

Earnings at Age 3.5

4
2
0
0.5

0.5

ud (Resistance to Treatment)

Earnings at Age 1.5

6

0.0

1.0

Work Hours at Age 3.5
Marginal Treatment EffectMarginal Treatment EffectWork Hours at Age 2.5

80

0.5

ud (Resistance to Treatment)

1.0

6
4
2
0
0.0

ud (Resistance to Treatment)

0.5

1.0

ud (Resistance to Treatment)

Figure 3: Marginal Treatment Effect Curve
Note: The MTE is averaged over observed characteristics and shown with the 90% confidence interval. Standard errors are clustered at the region level and estimated by a bootstrap with 100 replications. The dependent variables are employment (0 or 1), weekly hours of work, and annual earnings
in million JPY. The explanatory variables used in the local IV estimator include the propensity score
up to the second-order term, parents’ age and education, regional characteristics in 2000 interactedwith year dummies, and sets of year and region dummies. To allow for heterogeneous treatment
effects by observed characteristics, we interact the propensity score with parents’ characteristics.

30

tract, while a typical nonregular worker is not. The MTE on regular work is positiveand significant for a broad range of the resistance to treatment, while the MTE on
nonregular work is positive and marginally insignificant. We find no effects on selfemployment. These graphs indicate that childcare use increases mothers’ market
work largely through regular work instead of nonregular work or self-employment.

1.0
0.5
0.0

0.0

0.5

1.0

ud (Resistance to Treatment)

Selp−Empl. at Age 1.5
Marginal Treatment EffectNon−Reg. Work at Age 1.5
Marginal Treatment EffectMarginal Treatment EffectRegular Work at Age 1.5

1.0
0.5
0.0

0.0

0.5

1.0

ud (Resistance to Treatment)

1.0
0.5
0.0

0.0

0.5

1.0

ud (Resistance to Treatment)

Figure 4: Marginal Treatment Effect Curve on Employment Type
Note: The MTE is averaged over observed characteristics and shown with the 90% confidence
interval. See the note for Figure 3 for details.

The MTE also varies by observed characteristics as shown in Table 7. The treatment effect increases with mothers’ age for most outcomes. The effects on work andwork hours are smaller for mothers with low (less-than-high-school) or high (fouryear university or above) education than a mother with medium education (highschool or two-year college education). A possible explanation is that many lowand high-education mothers have alternative informal childcare options. In LSN21,
25% of low-education mothers live with their parents or in-laws, while 20% of
medium-education mothers do so. This implies that informal childcare by grandparents is more available for low-education mothers than for medium-education
mothers. Fewer high-education mothers live with their parents or in-laws, but they
may have a greater willingness to pay for informal childcare services or to seek
help from their parents. For both low- and high-education mothers, the provision ofchildcare is more likely to cause crowding out of their informal care arrangement
than it is for medium-education mothers.
While the MTE on participation and hours is nonlinear in mothers’ education,
31

the MTE on earnings increases largely with mothers’ education. This is because
the hourly wage increases with mothers’ education, which dominates the effects onparticipation and hours. A similar difference by mothers’ education is also seen for
employment type. The MTE on regular work increases with education, while thaton nonregular work decreases with education.
The MTEs tend to decrease with father’s age and education, although someestimates are noisy. Because the primary earner is typically the father in Japan,
mothers’ labor supply decreases with father’s earnings. When father’s earnings are
low, the mother tries hard to find informal childcare and to work to raise her family.
Providing a childcare slot to this mother is likely to crowd out her informal childcare
without affecting her labor market outcomes.
Aggregate treatment effect parameters including the ATE, TT, and TUT can becalculated by taking a weighted average of the MTE. The weights for the aggregate
treatment effect parameters are graphically presented in Figure 5 when the child isaged 1.5 years (see Appendix A for details). For the TT, greater weight is given to
those with lower values of resistance to treatment. In contrast, for the TUT, greater
weight is given to those with higher values of resistance to treatment. The weights
are similar for other age groups.
0.04

Weight

0.03
TT

0.02

TUT
0.01
0.00
0.00

0.25

0.50

0.75

1.00

ud (Resistance to Treatment)

Figure 5: Weights for Treatment Effects on the Treated and UntreatedNote: Weights for TT and TUT for mothers of children age 1.5 are presented. The details for weights
are given in Appendix A.

32

33-0.007(0.004)-0.101(0.080)-0.057(0.049)0.086(0.060)0.009(0.005)0.018(0.110)0.161(0.066)0.149(0.072)-0.005(0.003)-0.044(0.086)0.003(0.055)0.016(0.050)0.012(0.004)-0.042(0.080)0.136(0.059)0.169(0.047)-0.005(0.002)-0.268(0.114)-0.116(0.077)-0.047(0.078)0.008(0.004)-0.081(0.077)0.143(0.056)0.208(0.051)-0.298(0.155)-3.792(3.192)-0.150(2.397)2.163(1.991)

0.503(0.160)-3.025(3.571)
2.693(2.234)5.715(1.824)-0.319(0.117)-4.133(4.022)-1.277(2.654)2.099(2.886)0.548(0.175)-8.142(2.732)0.209(2.048)3.970(1.802)Work Hours
Age 2.5 Age 3.5

0.001(0.013)-0.466(0.177)-0.354(0.144)-0.209(0.193)0.045(0.015)-0.190(0.166)-0.191(0.168)0.011(0.171)-0.017(0.012)-1.082(0.342)-0.839(0.247)-0.475(0.276)0.039(0.013)-0.663(0.218)-0.558(0.202)-0.095(0.194)

Earnings
Age 1.5 Age 3.5-0.005(0.004)-0.039(0.063)-0.029(0.048)0.100(0.066)0.013(0.004)-0.146(0.063)-0.138(0.060)0.014(0.062)Reg.
Work
Age 1.5-0.002(0.003)-0.028(0.066)0.024(0.041)
0.032(0.039)-0.007(0.003)0.186(0.069)0.259(0.061)0.135(0.051)

Non-Reg.
Work
Age 1.5

0.001(0.002)0.028(0.040)-0.003(0.020)-0.014(0.029)0.002(0.002)-0.001(0.055)0.041(0.024)0.021(0.022)

SelfEmpl.
Age 1.5

Note: Standard errors are in parenthesis. They are clustered at the region level and estimated by a bootstrap with 100 replications. The dependent
variables are employment (0 or 1), weekly hours of work, and annual earnings in million JPY. The explanatory variables used in the local IV
estimator include the propensity score up to the second-order term, parents’ age and education, regional characteristics in 2000 interacted withyear dummies, and sets of year and region dummies. To allow for heterogeneous treatment effects by observed characteristics, we interact thepropensity score with parents’ characteristics.

2-Yr College

HS

Less Than HS

FatherAge

2-Yr College

HS

Less Than HS

MotherAge

Market WorkAge 1.5 Age 2.5 Age 3.5

Table 7: Treatment Effect Heterogeneity by Observed Characteristics

Table 8 presents estimates for the aggregate treatment effect parameters. The
ATE on mothers’ work ranges from 0.543 to 0.703 and decreases with child’s age.
For all age groups, the TT on mothers’ work is smaller than the TUT, which implies
negative selection into treatment. This result is consistent with the upward-sloping
MTE curves seen in Figure 3. The analysis here takes into account not only unobserved but also observed heterogeneity and hence gives a more complete picture of
the relationship between the treatment effect and selection pattern.
The ATE on weekly hours of work is positive and significant and decreases
with child’s age, while the ATE on annual earnings is positive and significant, andincreases with child’s age. For all of these outcomes, the TT is smaller than the
TUT, and the differences are statistically significant except for work hours when
the child is at age 3.5 years.
ATE on regular work is about three times greater than ATE on nonregular work,
while they are both positive and significant. The TT is smaller than the TUT for
both types of work. We find no effect on self-employment.

7

Discussion

7.1

Robustness Checks

We examine the robustness of our main results from different perspectives. The
first issue is endogenous fertility. The identifying variation of the causal effects is
the regional variation of the childcare coverage rate, which is given by the numberof childcare slots per child. Because the coverage rate is a measure of childcare
availability, it may also affect fertility and hence the coverage rate itself. To avoid
this concern from endogenous fertility, we use an alternative instrument given by the
number of childcare slot per woman aged 20−44 years. Arguably, this instrument
is more likely to be exogenous than the coverage rate.
The second issue is selective migration. If mothers with stronger labor market
attachment move to a region where childcare is more readily available, our estimates
are upward biased. To assess the extent of biases from selective migration, we
estimate the model using the coverage rate and other regional characteristics at the34

35

Work Hours
Age 2.5 Age 3.5
28.02920.946(4.425) (5.487)
18.46717.950(5.110) (4.553)
32.45522.698(5.855) (8.091)-13.988 -4.748(7.430) (9.010)

Earnings
Age 1.5 Age 3.5
1.644
2.052
(0.390) (0.544)
0.176
1.113
(0.384) (0.378)
2.087
2.595
(0.476) (0.771)-1.911-1.482(0.556) (0.763)

Reg.
Work
Age 1.5
0.503(0.113)0.201(0.147)0.596(0.143)-0.395(0.210)Non-Reg.
Work
Age 1.5
0.161(0.093)0.064(0.106)
0.191(0.114)-0.127(0.145)

SelfEmpl.
Age 1.5
0.001(0.060)0.092(0.077)-0.027(0.079)0.119(0.118)

Note: Standard errors are in parenthesis and clustered at the region level. The ATE is the average treatment effect, TT is the treatment effect on
the treated, and TUT is the treatment effect on the untreated.

TT - TUT

TUT

TT

ATE

Market WorkAge 1.5 Age 2.5 Age 3.5
0.703
0.594
0.543
(0.118) (0.103) (0.150)
0.386
0.567
0.455
(0.153) (0.121) (0.138)
0.801
0.606
0.595
(0.142) (0.133) (0.209)-0.415-0.039-0.139(0.194) (0.168) (0.227)

Table 8: Aggregate Treatment Effects

province level, which is a more aggregated level than the preferred specification.
Evidence from the Employment Structure Survey 2012 shows that 9.5% of mothersof children under 6 years of age moved within the same city for childrearing andeducation in their last move, but only 1.4% moved from other provinces. Hence,
we have much less concern about biases from selective migration in this alternative
specification.
The third issue is the role of siblings. We do not include the number of siblingsin the preferred specification, because fertility may be affected by the availability ofchildcare. However, if it is exogenous and relevant for childcare enrollment and/or
mothers’ labor supply, controlling for the number of siblings can reduce the sizeof the standard errors. Indeed, municipal governments prefer an application froma family in which an older sibling has already attended childcare. We estimate
the propensity score and the outcome equations using a model that includes thenumbers of younger and older siblings.
The fourth issue is concerned with the model for childcare enrollment. In our
preferred specification, we use the coverage rate in the current year only, but childcare enrollment may also be affected by the coverage rates in previous years. Thisis because some children started childcare at an earlier age, and they can remain
enrolled if they wish. The enrollment status of these children is not affected by thecurrent coverage rate but by the coverage rates in previous years. Although leaving
out the coverage rates in previous years does not bias our estimates, the estimates
may become more precise by using these additional variables. We estimate thepropensity score using a probit model augmented by the second-order polynomialsof the coverage rates from age 0.5 years to the current age.
The fifth and last issue is model specification. While we assume that the MTEchanges linearly with the unobserved resistance to treatment uD , this assumption
may be restrictive. We allow for nonlinearity of the MTE curve by including polynomial terms up to the fourth order in the outcome equations.
We assess the sensitivity of our main results by comparing the estimates of theaggregate treatment effect parameters in the benchmark model with those of thealternative models. Table 9 reports the estimates for selected outcomes. Our estimates are largely robust to the issues raised above, although statistical significance36

may change across specifications. The estimates are significantly different from thebaseline specification when the fourth-order term of the propensity score is includedin the local IV regression. The point estimates do not seem to be reasonable, andtheir standard errors are large, which suggests that the fourth-order term is irrelevant for outcomes, and including it only increases noise in the estimates. Overall,
our main results seem to be robust to the endogenous fertility, selective migration,and model specification issues.

7.2

Interpretation

Our analysis indicates that mothers with weaker treatment effects are more likely to
be treated, while mothers with stronger treatment effects are less likely to be treated.
To understand why selection has a negative effect on the treatment effect, consider
how childcare enrollment is determined. Families decide on whether they apply fora childcare center given the pecuniary and nonpecuniary benefits of the childcare
use relative to nonuse. If there are more applications than available slots, the local
governments rank their applications by how many hours their parents work when
they use a childcare center. This ranking corresponds to the unobserved resistanceto treatment uD in our model. Hence, uD should be interpreted as (the negative of)the unobserved component of the preference for work.
Why is the MTE negatively associated with the unobserved preference for work?
The treatment effect is the difference in an outcome (e.g., labor market participation) between the treated and untreated states. In the treated state in which families use childcare, most mothers work because it is effectively a prerequisite forchildcare use. However, in the nontreated state, the probability of labor market participation may vary considerably by individual depending on the availability andaffordability of alternative childcare arrangements.
Mothers with a strong preference for work (or low uD ) are likely to make anextra effort to find an informal childcare arrangement. For example, young families
may choose to live close to their parents or in-laws so that grandparents can takecare of the children (see Compton and Pollak (2014)). Seeking help from in-laws
may not be painless depending on the relationship, given that old Japanese people

37

38
1.644
(0.390)0.176(0.384)2.087(0.476)-1.911(0.556)28.029(4.425)18.467(5.110)32.455(5.855)-13.988(7.430)0.703(0.118)0.386(0.153)0.801(0.142)-0.415(0.194)1.673(0.446)0.551(0.465)2.011(0.517)-1.460(0.558)22.822(4.078)13.739(5.391)27.027(5.587)-13.288(8.039)0.675(0.123)0.473(0.170)0.737(0.159)-0.264(0.246)(2) Endogenous
Fertility

1.672(0.371)0.603(0.473)1.994(0.429)-1.390(0.557)38.423(5.552)35.371(5.627)39.836(6.883)-4.465(7.257)0.703(0.180)0.692(0.293)0.706(0.218)-0.014(0.367)(3) Migration

1.474(0.294)-0.072(0.358)1.940(0.345)-2.012(0.449)41.979(3.482)22.371(4.636)51.060(4.130)-28.689(5.693)0.607(0.097)0.258(0.143)0.715(0.118)-0.457(0.181)(4) Siblings

1.630(0.417)0.141(0.404)2.079(0.510)-1.938(0.588)27.520(4.683)16.700(5.494)32.529(5.582)-15.829(6.389)0.691(0.135)0.374(0.148)0.789(0.170)-0.415(0.219)(5) Lagged
Cov. Rate

1.040(0.922)-0.138(0.543)1.394(1.082)-1.532(0.802)32.728(6.759)22.760(7.325)37.342(7.653)-14.582(7.330)0.793(0.481)0.433(0.254)0.904(0.567)-0.471(0.403)(6) 3rdOrder

2.933(3.266)-0.568(0.617)3.988(4.353)-4.556(4.702)27.877(11.419)27.280(10.786)28.154(18.869)-0.874(26.222)1.573(1.320)0.255(0.270)1.981(1.762)-1.726(1.875)(7) 4thOrder

Note: Standard errors are in parenthesis and clustered at the region level. The ATE is the average treatment effect, TT is the treatment effect on
the treated, and TUT is the treatment effect on the untreated. Model (1) is the baseline model. In model (2), the instrument is the number ofchildcare slots per women aged 20-44. In model (3), regional variables are aggregated to the province level. In model (4), the numbers of younger
and older siblings are included. In model (5), the coverage rates in previous years since age 0.5 are also included in the set of instruments. Inmodels (6) and (7), up to the third and fourth order polynomials of the propensity score are included, respectively.

TT-TUT

TUT

TT

Earnings at Age 1.5
ATE

TT-TUT

TUT

TTWork Hours at Age 2.5
ATE

TT-TUT

TUT

TT

Market Work at Age 1.5
ATE(1) Baseline

Table 9: Robustness of Main Results

tend to have the traditional family value that the mother should stay at home toraise her children. However, a mother with a stronger preference for work may
not hesitate to ask in-laws to take care of her children, because she is desperate forchildcare. This mother is likely to work even in the untreated state in which she is
not given a childcare slot. This implies that the treatment effect is small for thosewith low uD .
In contrast, mothers with a weak preference for work are unlikely to exert much
effort to find an informal childcare arrangement in the untreated state. They arewilling to work only if they are given a slot in a childcare center. This implies thatthe treatment effect is large for those with high uD .

7.3

Policy Simulations

Using the estimated model, we simulate childcare reforms that increase the coverage rate. These reforms do not change the distribution of the treatment effects, but
their policy effects vary because different policies induce different individuals into
treatment.
In the first simulation, we evaluate a policy that changes the coverage rate from
0.28 to 0.35, which corresponds to the change from 2002 to 2011. This simulation
is useful for understanding the effects of childcare expansion during this period. In
the second simulation, the coverage rate is raised from the 2011 level (= 0.35) to
0.42. The size of the change in the coverage rate is the same as that in the firstsimulation. In the third simulation, the coverage rate is further increased from 0.42
to 0.82, which is the highest coverage rate in the sample.
Policies are evaluated by aggregating the MTE to the policy-relevant treatment
effect (see Heckman and Vytlacil (2005)). Suppose that a new policy changes thepropensity score for an individual i from pi to p0i . Let p̄ and p̄0 be the sample meansof the propensity score in the baseline policy and a new policy, respectively. The
policy-relevant treatment effect PRT E is given by0

1 N pi − pi
MT Ei ,PRT E =
0N∑
i p̄ − p̄39where N is the number of individuals in the sample, and MT Ei is the MTE for
individual i. Details are provided in Appendix A.
The weights for policy-relevant treatment effects are graphically presented in
Figure 6. As the coverage rate increases from one policy to another, greater weightis given to individuals with a higher unobserved resistance to treatment uD . Thisimplies that individuals with a higher resistance to treatment are induced gradually
into treatment, as childcare reforms progress.

0.04

Weight0.03
Policy (1)0.02

Policy (2)Policy (3)

0.01
0.00
0.00

0.25

0.50

0.75

1.00

ud (Resistance to Treatment)

Figure 6: Weights for Policy-Relevant Treatment Effects
Note: In policy (1), the coverage rate is increased from 0.28 to 0.35. In policy (2), the coverage rateis increased from 0.35 to 0.42. In policy (3), the coverage rate is increased from 0.42 to 0.82.

Table 10 summarizes the results. The childcare expansion during 2002−2011
increased the coverage rate from 0.28 to 0.35, which eventually changed the childcare enrollment or propensity score from 0.214 to 0.257 for children aged 1.5 years.
The corresponding policy-relevant treatment effects on mothers’ work and earnings
are 0.497 and 0.693, respectively. If the coverage rate continues to increase by thesame extent from 0.35 to 0.42, the enrollment rate increases from 0.257 to 0.306.
While the change in the enrollment rate is similar to that in the first simulation, thepolicy-relevant treatment effects on work and earnings are 0.554 and 0.956, respectively, which are greater than those in the first simulation.
A further childcare expansion has even stronger effects. Raising the coveragerate from 0.42 to 0.82 increases the enrollment rate to 0.632 for children aged 1.540years, which is close to the enrollment rate for children aged 0−2 years in formalchildcare in Denmark, where the participation rate is highest among the OECD
countries (see NOSOSCO (2015)). The policy-relevant treatment effects of thethird simulation are 0.676 for work and 1.517 for earnings, which are greater thanthose of the first two simulations.
The simulation results for children aged 2.5 and 3.5 years are also reported inTable 10. For both age groups, the simulated policies increase childcare enrollment,
mothers’ work, hours of work, and earnings. The policy-relevant treatment effects
become increasingly stronger as the coverage rate increases.
Table 10: Counterfactual Simulations of Policies to Increase the Coverage Rate

Age 1.5(1) Raise Coverage Rate from 0.28 to 0.35
(2) Raise Coverage Rate from 0.35 to 0.42
(3) Raise Coverage Rate from 0.42 to 0.82
Age 2.5(1) Raise Coverage Rate from 0.28 to 0.35
(2) Raise Coverage Rate from 0.35 to 0.42
(3) Raise Coverage Rate from 0.42 to 0.82
Age 3.5(1) Raise Coverage Rate from 0.28 to 0.35
(2) Raise Coverage Rate from 0.35 to 0.42
(3) Raise Coverage Rate from 0.42 to 0.82

Policy-Relevant
Treatment Effect

Propensity Score
New
Baseline Policy

Work

0.214
(0.010)0.257(0.014)0.306(0.026)0.257(0.014)0.306(0.026)
0.632(0.108)0.497(0.114)0.554(0.110)0.676(0.133)0.282(0.012)0.340(0.014)0.401(0.021)0.340(0.014)0.401(0.021)
0.786(0.072)0.580(0.084)0.586(0.076)0.600(0.086)23.141(3.874)25.501(3.785)30.326(4.620)0.326(0.014)0.389(0.013)0.437(0.020)0.389(0.013)0.437(0.020)0.562(0.111)0.499(0.133)0.514(0.139)0.538(0.161)19.426(4.479)19.938(4.912)20.771(6.211)

Hours

Earnings
0.693(0.340)0.956(0.339)1.517(0.444)1.578(0.482)1.738(0.543)1.998(0.681)

Note: Standard errors are in parenthesis. They are calculated by bootstrap with 100 replications andclustered at the region level.

41

Overall, our simulations indicate that the policy-relevant treatment effects become increasingly stronger as childcare reforms progress. Mothers with weak labormarket attachment would be strongly affected by the treatment, but they are unlikely to use a childcare center, because the rationing rule gives them a lower rank.
As the coverage rate increases, mothers with weak labor force attachment gradually start to use a childcare center, which explains why the treatment effects become
increasingly stronger. Our analysis suggests that the current rationing rule causes
inefficient allocation of mothers’ labor supply is concerned. Even if the governmentis unable to use a price mechanism for political ideologies, not ranking applications
by how much parents work may improve the efficacy of a childcare reform.

8

Conclusion

We estimate the MTE of childcare enrollment on mothers’ labor market outcomesby exploiting regional variations in the growth of the childcare coverage rate. The
demand for subsidized childcare exceeds the supply in many regions, and the local
governments rank childcare applications by how much parents work in order toassign a childcare slot to families in need. Mothers’ labor force attachment is a key
determinant for a successful application, but it is not observed in the data. The MTE
framework enables us to estimate variation in the treatment effects by unobserved
propensity for treatment.
Our estimates indicate that mothers with stronger MTE are less likely to use
childcare, whereas mothers with weaker MTE are more likely to find a childcare
slot. The rationing rule prioritizes mothers with stronger labor market attachment,
but they are likely to exert extra effort to find an alternative informal childcare arrangement if they are not given a childcare slot. Because these mothers are likely towork regardless of the availability of subsidized childcare, the treatment effects onthese mothers are small. Mothers with weak labor market attachment are unlikely towork without subsidized childcare, which implies that the treatment effects on thesemothers are strong. As long as mothers’ labor market outcomes are concerned, ouranalysis suggests that the current rationing rule may be inefficient.
We also find significant treatment effect heterogeneity by the child’s age. The
42

estimates show that the treatment effect on mothers’ labor market outcomes decrease with the child’s age, which is robust to alternative modeling assumptions.
However, note that this result does not necessarily imply that a childcare slot should
be assigned to mothers of infants, because infant care is particularly expensive.
The main limitation of this paper is that we have not identified an optimal rationing rule and only suggested a potential problem with the current rationing rule.
An optimal rationing rule should take into account not only the mothers’ labor market outcomes but also child development11 and other dimensions of family welfare
in the long run. We leave this important research agenda for future work.

References
A NDRESEN , M. E. AND T. H AVNES (2016): “Child Care and Parental Labor Supply: A New
Look,” University of Oslo.
AOBA WARD , C ITY OF YOKOHAMA (2009): “Guidance for Enrollment in Childcare in 2010,”
Yokohama.
A SAI , Y. (2015): “Parental Leave Reforms And The Employment of New Mothers: QuasiExperimental Evidence from Japan,” Labour Economics, 36, 72–83.
A SAI , Y., R. K AMBAYASHI , AND S. YAMAGUCHI (2015): “Childcare Availability, Household
Structure, and Maternal Employment,” Journal of the Japanese and International Economies,
38, 172–192.
——— (2016): “Crowding-Out Effect of Subsidized Childcare,” McMaster University.
BAKER , M., J. G RUBER , AND K. M ILLIGAN (2008): “Universal Child Care, Maternal Labor
Supply, and Family Well-Being,” Journal of Political Economy, 116, 709–745.
BAUERNSCHUSTER , S. AND M. S CHLOTTER (2015): “Public Child Care and Mothers’ Labor
Supply-Evidence from Two Quasi-Experiments,” Journal of Public Economics, 123, 1–16.
B ERLINSKI , S. AND S. G ALIANI (2007): “The effect of a large expansion of pre-primary school
facilities on preschool attendance and maternal employment,” Labour Economics, 14, 665 – 680.
B JÖRKLUND , A. AND R. M OFFITT (1987): “The Estimation of Wage Gains and Welfare Gains in
Self-Selection Models,” The Review of Economics and Statistics, 69, 42–49.
11 See Yamaguchi, Asai, and Kambayashi (2017).

43

B RINCH , C., M. M OGSTAD , AND M. W ISWALL (forthcoming): “Beyond LATE with a Discrete
Instrument,” Journal of Political Economy.
C ABINET O FFICE (2010): “A Project for Eliminating Wait-Listed Children by the National andMunicipality Governments,” available from http://www.kantei.go.jp/jp/singi/taikijidou.
C ASCIO , E. U. (2009): “Maternal Labor Supply and the Introduction of Kindergartens into American Public Schools,” Journal of Human Resources, 44, 140–170.
C OMPTON , J. AND R. A. P OLLAK (2014): “Family Proximity, Childcare, and Women’s Labor
Force Attachment,” Journal of Urban Economics, 79, 72–90.
C ORNELISSEN , T., C. D USTMANN , A. R AUTE , AND U. S CHÖNBERG (2016): “From LATE to
MTE: Alternative Methods for The Evaluation of Policy Interventions,” Labour Economics, 41,
47 – 60, sOLE/EALE Conference Issue 2015.
F ITZPATRICK , M. D. (2010): “Preschoolers Enrolled and Mothers at Work? The Effects of Universal Prekindergarten,” Journal of Labor Economics, 28, 51–85.
——— (2012): “Revising Our Thinking About the Relationship Between Maternal Labor Supply
and Preschool,” Journal of Human Resources, 47, 583–612.
G ELBACH , J. B. (2002): “Public Schooling for Young Children and Maternal Labor Supply,” American Economic Review, 92, 307–322.
G OUX , D. AND E. M AURIN (2010): “Public school availability for two-year olds and mothers’
labour supply,” Labour Economics, 17, 951–962.
H AVNES , T. AND M. M OGSTAD (2011): “Money for nothing? Universal child care and maternal
employment,” Journal of Public Economics, 95, 1455–1465.
H ECKMAN , J. J., S. U RZUA , AND E. V YTLACIL (2006): “Understanding Instrumental Variables
in Models with Essential Heterogeneity,” The Review of Economics and Statistics, 88, 389–432.
H ECKMAN , J. J. AND E. V YTLACIL (2005): “Structural Equations, Treatment Effects, and Econometric Policy Evaluation,” Econometrica, 73, 669–738.
K AMBAYASHI , R. AND T. K ATO (2013): “Good Jobs, Bad Jobs, and the Great Recession: Lessons
from Japan’s Lost Decade,” Center on Japanese Economy and Business Working Papers 326,
Columbia University.
L EFEBVRE , P. AND P. M ERRIGAN (2008): “Child-Care Policy and the Labor Supply of Motherswith Young Children: A Natural Experiment from Canada,” Journal of Labor Economics, 26,
519–548.

44

L UNDIN , D., E. M ÖRK , AND B. Ö CKERT (2008): “How Far Can Reduced Childcare Prices Push
Female Labour Supply?” Labour Economics, 15, 647–659.
M INISTRY OF H EALTH , L ABOUR AND W EALTH (2008): “Basic Policy Stance for Making a
New Policy Scheme to Support the Development of the Next Generation,” Available fromhttp://www.mhlw.go.jp/shingi/2008/05/s0520-6.html.
——— (2009): “Summary of the Survey of Regional Child Welfare Services 2009,” Available fromhttp://www.mhlw.go.jp/toukei/saikin/hw/jidou/09/dl/80.pdf.
N ISHITATENO , S. AND M. S HIKATA (2017): “Has Improved Daycare Accessibility Increased
Japan’s Maternal Employment Rate? Municipal Evidence from 2000-2010,” Journal of theJapanese and International Economies, 44, 67–77.
N OLLENBERGER , N. AND N. RODRIGUEZ -P LANAS (2015): “Full-time universal childcare in acontext of low maternal employment: Quasi-experimental evidence from Spain,” Labour Economics, 36, 124 – 136.
NOSOSCO (2015): Social Protection in Nordic Countries.
W OOLDRIDGE , J. M. (2010): Econometric Analysis of Cross Section and Panel Data, vol. 1 of MIT
Press Books, The MIT Press.
YAMAGUCHI , S. (2016): “Effects of Parental Leave Policies on Female Career and Fertility
Choices,” McMaster University.
YAMAGUCHI , S., Y. A SAI , AND R. K AMBAYASHI (2017): “How Does Early Childcare Enrollment
Affect Children, Parents, and Their Interactions?” McMaster University.

A

Treatment Parameters

We calculate treatment parameters following the method outlined by Cornelissen
et al. (2016). Let xi and pi be a vector of control variables and the propensity score0
for family i. The unobserved component of the MTE is denoted by K (uD ). The
sample mean of the propensity score is p̄ = 1/N ∑N
i=1 pi . The ATE, TT, and TUT
are given by

45

ˆ 1
0
1 N
K (u)duATE =xi (β1 − β0 ) +
∑
N i=1
0
ˆ 1
0
1/N ∑N
1 N pii=1 I(pi > u)TT =K (u) ·xi (β1 − β0 ) +du∑
N i=1 p̄p̄0
ˆ 1
0
1/N ∑N1 N 1 − pi
i=1 I(pi ≤ u)
K
(u)
·
TUT =
x
(β
−
β
)
+
du.
i 1
0
∑
N i=1 1 − p̄
1 − p̄
0
The integral can be easily calculated by discretizing the grid for uD .
Denote the propensity score under the baseline policy by pi and the propensity
0
score under the alternative policy by pi . The sample means of the propensity scores
0
under these two policies are denoted by p̄ and p̄ . The PRTE is given by
ˆ 1
0
0
N
0
1/N ∑N
1 N pi − pi
i=1 I(pi > u) − 1/N ∑i=1 I(pi > u)du.
PRTE =0∑ p̄0 − p̄ xi(β1 − β0) + 0 K (u) ·N i=1p̄ − p̄

46