DP
RIETI Discussion Paper Series 15-E-067
Does Agglomeration Discourage Fertility?
Evidence from the Japanese General Social Survey 2000-2010
(Revised)
KONDO Keisuke
RIETI
The Research Institute of Economy, Trade and Industry
http://www.rieti.go.jp/en/
RIETI Discussion Paper Series 15-E-067
First draft: May 2015
Revised: June 2016
Does Agglomeration Discourage Fertility?
Evidence from the Japanese General Social Survey 2000–2010*
KONDO Keisuke †
Research Institute of Economy, Trade and Industry
Abstract
This study employs household-level data to quantify how agglomeration externalities affect
the number of children born to Japanese married couples, the ages at which couples bear the
first child, and spatial variations in the average number of children born to couples at different
ages. Controlling for economic and social household characteristics, we find that
agglomeration externalities significantly discourage married couples from bearing children,
but that the magnitude of its effect declines as couples age. Our quantification shows that,
holding other things equal, a 10-fold difference in city size generates a spatial variation of
-27.71% in the average number of children born to couples aged 30 and a spatial variation of
-9.56% at age 49, suggesting that young married couples in bigger cities bear children later in
life. Further empirical results show that although agglomeration delays couples’ decision to
bear their first child, it does not significantly affect the age at which they marry.
Keywords: Fertility, Agglomeration, Social survey, Migration
JEL classification: J10, J13, R23
RIETI Discussion Papers Series aims at widely disseminating research results in the form of
professional papers, thereby stimulating lively discussion. The views expressed in the papers are
solely those of the author(s), and neither represent those of the organization to which the author(s)
belong(s) nor the Research Institute of Economy, Trade and Industry.
I am greatly indebted to Ryo Arawatari and Yasuhiro Sato for their invaluable comments. I thank Hirobumi Akagi,
Deokho Cho, Masahisa Fujita, Hiroshi Goto, Mitsuo Inada, Ryo Ito, Shinichiro Iwata, Tatsuaki Kuroda, Ke-Shaw LIAN,
Miwa Matsuo, Tomoya Mori, Masayuki Morikawa, Se-il Mun, Atsushi Nakajima, Kentaro Nakajima, Makoto Ogawa,
Takashi Unayama, Isamu Yamauchi, Ting Yin, Kazufumi Yugami, and participants at the luncheon meeting of the
Research Institute of Economy, Trade and Industry (RIETI), in the Urban Economic Workshop at Kyoto University, in the
28th annual meeting of the Applied Regional Science Conference, in the RIETI Discussion Paper Seminar, in the
RIETI-TIER-KIET Workshop, in the 62nd Annual North American Meetings of the Regional Science Association
International, and in the Rokko Forum at Kobe University for their helpful comments and suggestions. Naturally, any
remaining errors are my own. This study is a part of research results undertaken at RIETI. I am grateful to Maya Kimura
for her generous research support. The 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
accredited by 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, “JGSS,” was provided by the Social Science Japan
Data Archive, Center for Social Research and Data Archives, Institute of Social Science, The University of Tokyo.
†Research Institute of Economy, Trade and Industry: 1-3-1 Kasumigaseki, Chiyoda-ku, Tokyo, 100-8901, Japan.
(E-mail: kondo-keisuke@rieti.go.jp)
*
2
1 Introduction
Recent literature in economic geography has emphasized the benefits of agglomeration economies,
including higher productivity and faster human capital accumulation in more densely populated areas
(e.g., Combes et al., 2008, 2010, 2012; Glaeser and Maré, 2001; Glaeser and Resseger, 2010; de la Roca
and Puga, 2012). Although economists and policymakers attend to the economics of agglomeration
when designing growth policies, they still insufficiently understand how agglomeration externalities
negatively affect socioeconomic behavior. Following Sato (2007), who considers a strong connection
between agglomeration and fertility rates, we focus on demographic issues that are central to the
current policy agendas in most developed counties. Krugman (2014) points out that slow population
growth precedes reduced demand for new investment and may contribute to secular stagnation. As
such, our concern is to empirically examine whether agglomeration discourages fertility. In particular,
we aim to quantify the extent to which agglomeration externalities discourage the completed fertility
(total number of children that married couples have during their lifetimes) and the timing of childbirth.
Fertility rates in most developed countries have declined rapidly with economic growth, and
raising fertility rates has become a policy priority in several countries. Panels (a) and (b) of Figure
1 present trends in total fertility rates and share of population aged 65 and older for selected OECD
countries. France, Germany, the United Kingdom (UK), and the United States (US) exhibit sharp
declines in total fertility rates since the 1960s, as have Italy and Japan after the 1970s. Although recent
total fertility rates have remained at approximately 2 in France, the UK, and the US, they are less in
Germany, Italy, and Japan and are accelerating the graying of those countries, as shown in Panel (b)
of Figure 1. As unbalanced demographic structures distort social security systems, governments seek
effective policies to recover fertility rates (e.g., Grant et al., 2004).
[Figure 1]
This study presents a new focus on spatial rather than temporal views of national fertility. Panel (a)
and Panel (b) of Figure 2 illustrate fertility rates and population density for Japanese municipalities,
respectively. A negative relationship between these is evident, as shown in Panel (c). Although
innumerable factors explain this negative relationship, it may best be explained by a model of Sato
(2007) in which an agglomerated region attracts workers, intensifying population density and wage
rates while reducing fertility rates through agglomeration diseconomies. Sato and Yamamoto (2005),
Aiura and Sato (2014), Morita and Yamamoto (2014), and Goto and Minamimura (2015) examine
the mechanics whereby rising real wages in more densely populated areas increase the opportunity
3
cost of childrearing while attracting workers, further elevating population density and opportunity
cost. This circularity engenders lower fertility rates in more densely populated areas.1 Schultz (1986)
shows that higher wages for wives increase the opportunity cost of motherhood.2
[Figure 2]
Although these theoretical studies predict that agglomeration reduces fertility rates, it remains
unclear how it affects married couples’ decisions to bear children at different ages. Figure 3 presents
geographical distributions of fertility rates by age and shows regional heterogeneity among age
groups. Fertility rates among ages 35–39 are relatively high in more densely populated areas, especially Greater Tokyo and Osaka, although they are lower among ages 25–29. Figure 3 implies that
individuals residing in bigger cities postpone parenthood.
[Figure 3]
Using household-level micro-data, we quantify the extent to which agglomeration externalities
discourage married couples from bearing children. To draw meaningful policy implications, we
measure how extensively agglomeration generates spatial variations in the number of children per
parental age cohort. In doing so, it is crucial to control for unobservable household characteristics,
not merely economic and educational factors to assure that spatial sorting of their fertility preferences
does not generate statistical bias.3 For example, city dwellers might hold different opinions about
parenthood than rural residents, or the desire for security during old age motivates having children,
particularly in rural area (Nugent and Gillaspy, 1983; Nugent, 1985; Rendall and Bahchieva, 1998). In
addition, big cities offer numerous job opportunities and may attract people who are more intent on
careers than parenthood. A social survey dataset provides insights into spatial sorting of household
characteristics.
This study advances the literature of economic geography by offering new evidence concerning
childbearing by married couples in big cities. Controlling for economic and social household char1
Sato and Yamamoto (2009) and Maruyama and Yamamoto (2010) provide insightful views on endogenous fertility
decisions. Becker (1960) develops the economic analysis of fertility. As Becker and Lewis (1973) explain, the interaction
between quantity and quality of children is important in economic models of fertility. Willis (1973) extends the fertility
model to incorporate opportunity costs of rearing children versus wages from working. See Becker (1992), Browning (1992),
and Hotz et al. (1997) for details of fertility analysis.
2
Another explanation for this negative relationship is that the geographic concentration of highly educated people, also
related to city size, explains the spatial variations in total fertility rates.
3
Another important aspect of the empirics of agglomeration economies is to use spatial variation, not temporal variation.
One might consider regional panel data analysis to control for fixed effects of cities, extending municipal data in Figure 2.
However, the regional fixed-effect model uses within-city variation and drops information concerning level variation across
space, which means that spatial variation associated with city size is ignored. See Combes et al. (2010) for more details.
4
acteristics and an endogenous issue between number of children and city size using long-lagged
population density as instruments, we find that agglomeration externalities particularly discourage
young married couples’ fertility behavior; however, the numerical magnitude per household shrinks
as couples age. Our quantification reveals that, holding other things equal, a 10-fold difference in
population density (in general, differences between central cities in rural prefectures and metropolitan
areas in Tokyo) yields to a spatial variation of −27.71% in the average number of children born to
couples at age 30 and a variation of −9.56% at age 49. Furthermore, our results assert that young
married couples in big cities postpone having their first child by an average of 5 months in the case
of 10-fold increase in population density. However, agglomeration does not significantly affect age at
which couples marry.
This study also extends the literature concerning fertility and housing prices. Simon and Tamura
(2009) investigate the effects of housing rents on age at first marriage, age at birth of the first child, and
number of children. They find that higher rents delay marriage and childbirth and reduce the number
of children per household. Given that rents are higher in more densely populated areas, this study
complements their findings. In addition, Lovenheim and Mumford (2013) and Dettling and Kearney
(2014) show that housing prices heterogeneously affects fertility between homeowners and renters
through the wealth and price effects. This study uses population density instead of using housing
prices to capture aggregate effects of costs associated with agglomeration because population density
captures numerous other childrearing costs.
The remainder of this paper is organized as follows. Section 2 discusses relationships between
low Japanese fertility rates and costs associated with agglomeration. Section 3 provides a theoretical
overview. Section 4 describes the empirical framework. Section 5 presents our dataset. Section 6
discusses estimation results. Section 7 presents the conclusions.
2 Low Japanese Fertility Rates and Costs Associated with Agglomeration
Japan’s National Institute of Population and Social Security Research (2012) regularly surveys fertility
rates. As Figure 4(a) shows, high costs of rearing and educating children are major reasons why
households do not have ideal numbers of children. Figure 4(b) shows that both reasons provoke
decreases in the planned number of children, compared to the ideal number of children. Thus, higher
costs of rearing children drive lower fertility rates.
[Figure 4]
5
To establish regions with higher childrearing costs, we employ surveys by Japan’s Ministry of
Education, Culture, Sports, Science and Technology (2009). Panel (a) of Figure 5 shows annual costs
of extramural activities for public school students by city size. Clearly, households in bigger cities
pay more for extramural activities. Two possibilities arise from these data: (1) extramural activities
cost more in bigger cities and (2) households with students there consume more such services. Panel
(b) of Figure 5 shows regional difference indices of tutorial fees. A stylized fact is that price indices of
educational services in more densely populated areas exceed those in less dense areas. Thus, even if
consumption of educational services is identical across areas, educational costs differ regionally.
[Figure 5]
3 Theoretical Background
To clarify points raised in our view of theoretical studies, we summarize possible channels through
which population concentration affects fertility decisions. Following Becker (1992), Willis (1973) and
Sato (2007), we describe households’ fertility decisions, in which both the number and quality (e.g.,
education level) of children are assumed. We employ a standard (concave) utility function in which
all goods are normal, as follows:
u(x, y, q),
where x, y, and q represent consumption of a composite good, number of children, and quality per
child, respectively. We assume that each household is endowed with one unit of time allocated
between working and childrearing. Households must spend quantity of time by, where b is a positive
constant tied to time requirement of rearing one child. Thus, the budget constraint is given by
pxr (nr )x + pqr (nr )qy = Hr (nr ) + wr (nr )(1 − by) − cr (nr ),
where pxr (nr ) is the price of composite goods in region r; pqr (nr ) is the price related with quality
of children (e.g., education, training, health); Hr (nr ) is household’s non-labor income or husband’s
income (treated as an exogenous variable) in region r; wr (nr ) is the wage rate in region r; cr (nr ) is the
cost of living in region r; and nr is its population in region r.
Because composite good x includes consumption of housing, its price, pxr (nr ), may increase in nr ,
whereas it also includes various goods (possibly differentiated ones) and pxr (nr ), partly represents
the price index, implying that pxr (nr ) may decrease in nr (Ottaviano et al., 2002). The term bwr (nr )
6
captures the opportunity cost of rearing children versus working (loss of earnings). As studies in
urban economics have established (e.g., Combes and Gobillon, 2015), wage rates in more densely
populated regions tend to be higher and thus opportunity cost will be higher there. The price related
to quality of children, pqr (nr ), might be higher in large cities, as discussed in Section 2. The cost of living
cr (nr ), which is related to negative agglomeration externalities (e.g., commuting and congestion), will
increase in nr .
Households’ utility optimization yields respective demand functions for consumption goods,
children, and quality of children as follows:
xr (nr ) = x pxr (nr ), pqr (nr ), Hr (nr ), wr (nr ), cr (nr ) ,
yr (nr ) = y pxr (nr ), pqr (nr ), Hr (nr ), wr (nr ), cr (nr ) ,
qr (nr ) = q pxr (nr ), pqr (nr ), Hr (nr ), wr (nr ), cr (nr ) .
We draw theoretical implications concerning fertility, yr (nr ). A higher pxr (nr ) or pqr (nr ) may increase
yr (nr ) through the substitution effect or reduce it through the income effect. A higher wage rate wr (nr )
may reduce yr (nr ) by elevating the opportunity cost of childrearing or increase yr (nr ) through the
income effect. Higher exogenous income Hr (nr ) increases yr (nr ) through the income effect. Higher cost
of living cr (nr ) reduces disposable income, which prompt a decrease in yr (nr ). Regional population,
nr , affects all these variables, implying that a larger nr exerts positive and negative effects on yr (nr )
through these channels.
Although theoretical works have uncovered various channels through which population concentration affects fertility, their conclusions do not explain to what extent population concentration has
negative externalities on households’ fertility decisions after controlling for these channels. In other
words, this study examines the negative relationship observed in Figure 2 by estimating demand
function of children, yr (nr ), at the household level.
4 Empirical Framework
4.1 Measuring Agglomeration Effects on Fertility
This study estimates the demand function for children, yir , among married couples i in which the wife
is of childbearing age (15–49 years old as per the definition of total fertility rate). A standard approach
is to regress linearly the number of children on population density and other control variables.
However, an empirical issue is that the dependent variable takes a discrete number. If so, the Poisson
7
regression is more appropriate. Therefore, our regression model to be estimated is given by
Pr(Yir = yir ) =
yir
exp −λir (θ) λir (θ)
yir !
,
yir = 0, 1, 2, . . . ,
Reg
ψ,
λir (θ) ≡ exp α log(Densr(i)t ) + γMi + X i β + X̃ i δ + Dr(i) η + DYear
t
(1)
where yir is the number of children in household i residing in region r; Densr(i) is the population density
of region r where married couple i lives during the study period; α is our parameter of interest, which
captures the density elasticity of the number of children and is expected to be negative; Mi is a
dummy that takes the value 1 if either spouse in household i has emigrated and 0 otherwise; X i is
a vector of variables denoting household characteristics (age, gender, cohort dummies, employment
status, condition of health, education, years of working experience, and each income for husband
and wife); X̃ i is a vector of variables for household social characteristics that affect fertility decisions;
Reg
Dr
is a vector of regional dummies; DYear
is a vector of year dummies; θ is a vector of parameters
t
(α, γ, β , δ , η , ψ ) . Thus, the parameter vector that maximizes the log-likelihood function (y, θ) is
estimated as follows:
n −λir (θ) + yir log λir (θ) − log(yir !) ,
(y, θ) =
i=1
where n is number of observations.
The regression includes customarily unobservable household characteristics X̃ i . Using a social
survey dataset mitigates estimation bias arising from spatial sorting driven by households’ qualitative
factors. Migration influences decisions to bear children through the higher financial and non-financial
costs. For example, non-migrants residing near their parents have advantages for rearing children.
Thus, migrants are expected to have fewer children than non-migrants.
A key feature of the Poisson regression model is that λir (θ) can be seen as a predicted average
number of children per household. Therefore, α can be interpreted as an elasticity that captures spatial
variations in the number of children born to households in terms of city size. We quantify, holding
other things constant, to what extent the difference in city sizes affects the number of children.
Our next question is whether agglomeration affects completed fertility. Focusing on married
couples among whom the wife is aged 50 or older, the outer age for childbearing in definitions of
fertility rates, we estimate this Poisson regression model:
Reg
Year
)
+
γM
+
Z
ϕ
+
X̃
δ
+
D
η
+
D
ψ
,
λir (θ) ≡ exp α log(Dens50
i
i
i
t
r(i)t
r(i)
(2)
8
where Dens50
r(i)t denotes the population density of cities where the married couples lived when the
wife was aged 50, and Zi is limited to the vector of variables capturing husbands’ and wifes’ education
because no historical information itemizes the income, work experience, and health status for married
couples aged 50 and over.4
Interpretations of parameter α in models (1) and (2) may be ambiguous when the sample includes
migrants, even if migration status is controlled for. In other words, it is desired to control for
the cities in which migrants have previously resided, a task requiring long-term household-level
panel data. Another related issue is that migration itself is highly related with fertility decision,
presenting self-selection bias. Because of data limitations, we estimate Poisson regression models
for two samples—one that includes a migration dummy and one that exclude migrants from the
sample—to distinguish effects of migration and costs associated with agglomeration as a robustness
check.5
4.2 Testing Catch-Up Process in Bigger Cities
This section examines how married couples residing in more densely populated areas bear children
later in life, as shown in Figure 3. To measure the catch-up process, we introduce a cross term of
population density and wife’s age into the Poisson regression model (1) as follows:
Reg
+ X i β + X̃ i δ + Dr(i) η + DYear
ψ,
λir (θ) ≡ exp α log(Densr(i)t ) + φ log(Densr(i)t ) × Agewife
t
i
(3)
denotes the wife’s age for married couple i, and φ measures the catch-up process
where Agewife
i
on fertility decisions: positive value of φ suggests that married couples residing in more densely
populated areas delay having children and have children when older. This regression is estimated
for non-migrants aged 50 or younger to exclude households’ dynamic location choice.
We seek to quantify to what extent externalities from population concentration discourage households’ fertility behavior, and thus we emphasize that a dynamic fertility process should be considered.
For example, it is inappropriate to quantify its magnitude simply by comparing married couples across
cities. The fact that young married couples in big cities tend to have children later causes an overestimation of spatial variation in the number of children. This study quantifies spatial differences in the
average number of children per parental cohort age using the estimates of α and φ in regression (3).
4
For migrants, we calculate population densities of cities where couples in which the wife is 50 or older lived during
the survey year.
5
Estimation results without migrants are available on the online supplemental file.
9
Another aspect of the catch-up process is whether agglomeration affects the timing of marriage
and birth of the first child (e.g., Simon and Tamura, 2009). In this regression, the sample is not divided
by wife’s age. Effects of agglomeration are simply estimated by this OLS regression:
Reg
All
Year
=
α
log
Dens
ψk + ui,k ,
Agewife
k
r(i)t + γk Mi + Zi ϕk + X̃ i δk + Dr(i) ηk + Dt
ir,k
(4)
where Agewife
ir,k denotes the wife’s age for married couple i at time of marriage (k = 1) and birth of the
first child (k = 2), respectively; DensAll
r(i)t denotes the population density, takes the value of Densr(i)t if
married couple i is aged 50 or younger and the value of Dens50
r(i)t if its wife i is aged 50 and above; and
ui,k is the error term. Parameter αk captures agglomeration effects on the timing of marriage and birth
of the first child, respectively.
4.3 Solving Endogeneity in Population Density
An estimation issue in the demand function for children relates to the fact that number of children has
positive impacts on the population density unless children born to households migrate to other cities.
Although our aim is to measure the extent to which costs associated with agglomeration discourage
married couples from bearing children, this magnitude may be underestimated owing to the opposite
force.
To solve this endogeneity issue, the literature on economic geography proposes the method of
IV estimation. A possible candidate of instrumental variables is a long-lagged population density,
as used by Ciccone and Hall (1996). A long-lagged population density is highly correlated with the
current city size (in this paper, the correlation coefficient between population densities in survey year
and in 1930 is 0.744). On the correlation between an error term and population density, its validity of
historical lags relies on the hypothesis that the population agglomeration in the past is not related to
current fertility decisions of couples. This study uses the logarithm of population density in 1930 and
its squared as instruments term and estimates demand function for children by the IV Poisson method
assuming an additive error term. We check the validity of our instruments by overidentification tests.
4.4 Quantifying Spatial Variation in Fertility
Our quantification uses the estimates of α and φ (i.e., density elasticity of number of children) of
model (3). Holding other things equal, the percentage change in average number of children per
10
household between two cities s and r can be estimated as
Denss α̂+φ̂×Age
λs − λr
=
− 1.
λr
Densr
Note that this spatial variation in average number of children per household is measured at a relative
level, not an absolute level. For example, consider the case where there are two cities s and r. City s
has twice the population of city r. The density elasticity of the number of children is −0.04 at a certain
age. In this case, the percentage change is calculated as −2.73% (≈ 2−0.04 − 1). If households in city r
on average have 2 children, then households in city s on average have 1.95 children. Similarly, if city
s has 10 times the population of city r, the percentage change in average number of children becomes
−8.80% (≈ 10−0.04 − 1). If households in city r on average have 2 children, then households in city s on
average have 1.824 children.
Similarly, we examine to what extent externalities of agglomeration delay marriage and birth of
the first child for married couples from model (4). Holding other things equal, differences in a wife’s
age between cities s and r can be estimated as
Agewife
s,k
−
Agewife
r,k
Denss
= α̂k log
,
Densr
where α̂k is the parameter estimate in model (4). Note that the spatial variation in wife’s age is
measured at the absolute level. For example, consider the case where city s has twice the population
of city r. In this case, spatial variation in the wives’ ages between is calculated as α̂k × log(2).
5 Data
To control for unobservable household characteristics affecting fertility decision, we use the cumulative dataset (i.e., pooled cross section) of the Japan General Social Surveys (JGSS), which covers the
years 2000, 2001, 2002, 2005, 2006, 2008, and 2010.6 The sample is limited to married couples (i.e.,
unmarried persons are excluded).
6
We discarded the JGSS 2003 dataset because it omits questions about number of siblings. Its surveyed population
consists of men and women aged not under 20 to 89 as of September 1st of the particular survey year, and survey subjects
are selected by a stratified 2-stage sampling method. In the first step, stratification is conducted among six regional blocks
(Hokkaido/Tohoku, Kanto, Chubu, Kinki, Chugoku/Shikoku, and Kyushu). Then, cities and districts in each block are
classified into three groups of the largest cities, other cities, and towns/villages. We construct our regional variables based
on three groups of cities in each prefecture by taking averages of corresponding municipalities. Sample sizes of valid
response vary from 2,023 (in 2005) to 5,003 (in 2010). Detailed information about the JGSS sampling design is available from
the web-site (URL: http://jgss.daishodai.ac.jp/english/index.html).
11
Table 1 presents descriptive statistics of variables. Definitions of variables used in this study, such
as population density, migration, and income, are in Appendix A. The average number of children per
household in the sample is approximately 1.98. Average numbers of children by parental age cohort
appear in Figure 6. Panel (a) of Figure 6 displays differences in numbers of children by dividing the
75th percentile point for population density (DensAll
r(i)t ). Households with ages averaging 20–24 in more
densely populated areas (exceeding the 75th percentile of population density of 4,176 persons/km2)
have half as many children as households in less dense areas. The gap between the two narrows,
but a slight gap remains. Panel (b) of Figure 6 presents average ideal numbers of children by cohort
group. We see the younger generation tending toward lower ideal numbers, but no geographical gap
appears in relation to population density. People in the same generation desire the same number of
children regardless of where they live.
Panels (a) and (b) of Figure 7 present distributions by city size for the wife’s age at marriage and
at birth of the first child, respectively. Approximately, couples residing in more densely populated
areas tend to marry and have children later than couples in less dense areas. This finding associates
agglomeration with delayed childbearing among married couples.
The JGSS asks two questions about how households perceive the roles of government and family
in providing security for the elderly (1: Governments, 5: Individuals and Families): (1) responsibility
for livelihood of the elderly (2) responsibility for medical and nursing care of the elderly. The old
age security score in Table 1 indicates the sum of two values. Minimum and maximum values are 2
and 10. Greater values indicate how households are responsible within the families in their old age.
The motive to be secure in old age predicts that such households have more children. Furthermore,
the JGSS asks a question about households’ opinions whether children are necessary in a marriage.
A dummy variable takes the value 1 for households that agree or somewhat agree children are
unnecessary and 0 otherwise.
[Table 1 and Figures 6–7]
We include number of siblings because couples who have relatively many siblings may have more
children. JGSS polls the number of siblings for both spouses but often only one answers this question.
Our question merges spousal responses. If both answer, the average number of siblings is used; if
one answers the question, the number that he or she provided is used.
12
6 Estimation Results
6.1 Agglomeration Discourages Fertility
Table 2 presents estimation results of model (1) by Poisson and IV Poisson estimations. Column (1)
shows that density elasticity of number of children is significantly negative at the 1% level and its
value is −0.075. However, the elasticity obtained by IV Poisson is −0.102. As predicted, the Poisson
estimation generates a downward bias, which arises from that rising number of children increases
population density. The IV estimation captures that the causal effects of bigger cities on the fertility
decision is greater. These values offer an aggregate relationship between the number of children
and population density. These results are the benchmark for comparison with results controlled for
household characteristics.
Estimation results in Table 2 show that additional control for household characteristics gradually
reduces the density elasticity of number of children. The density elasticity becomes −0.067 in Column
(3), whereas the density elasticity obtained by IV Poisson becomes −0.091 in Column (6). These results
imply that, holding other things equal, a 10-fold difference in city size on average generates spatial
variation in the per-household number of children by 18.77% (≈ 10−0.091 − 1). Consider a case where
city s is 10 times the population of city r. If the average number of children in city r is 2, the average in
city s becomes 1.625 (the spatial gap is approximately 375 children per 1,000 households).7 Therefore,
our results show that negative externalities of agglomeration discourage fertility behavior.
An interesting finding is that that husbands’ and wives’ incomes, which related highly to city
size, have significant positive and negative signs, respectively. Indeed, husband’s higher income in
big cities reduces the density elasticity if we do not control for this variable. This finding implies
that differences in city size determine spatial variation in demand for children through conflicting
channels between husband’s higher income and wife’s greater opportunity costs of having children.
Household characteristics are additionally controlled for in Columns (2)–(3) and (5)–(6). Overall,
results indicate that both spouses’ high educations negatively affect demand for children. As mentioned, households in which husbands earn higher incomes tend to have more children, suggesting
that progressive increases in the husband’s income has income effect. On the other hand, the wife’s
income shows a negative sign, suggesting that wife’s higher income discourages fertility decision
owing to higher opportunity cost. These findings are also theoretically supported.
In Columns (3) and (6), a dummy denoting that children are unnecessary in a marriage demon7
Here is another numerical example. Holding other things equal, double difference in city size on average generates
spatial variation in the per-household number of children by 6.07% (≈ 2−0.091 − 1).
13
strates notably negative effects on the number of children at the 1% significance level. If either
husband or wife has more siblings, they tend to have more children. The number of siblings might
affect their preference for children. However, the motive for security in old age has no significant
relationship with the number of children. Inclusion of these social characteristics tends to reduce
magnitudes of the dummy denoting university graduates.
Columns (2)–(3) and (5)–(6) show that the migration dummy is significant negative at the 5% or
10% level. Households in which either spouse has migration experience tend to have fewer children
than those in which neither has migration experience. The negative sign may derive from both a
causal relationship and from self-selection. That is, migration itself may impose substantial costs
on having children, or having fewer children may enable households to easily migrate. We do not
distinguish these two channels and merely note the negative relationship between number of children
and migration.
[Table 2]
6.2 Completed Fertility and Agglomeration
Table 3 presents estimation results for couples whose child-bearing years have ended because the wife
is age 50 or older. This estimation examines whether costs of agglomeration discourage completed
fertility.
Columns (1) and (3) show density elasticities of total number of children in the benchmark
estimation, and these values are −0.035 in Column (1) and −0.045 in Column (4). As mentioned
earlier, the standard Poisson estimation generates a downward bias to the density elasticity of number
of children. This negative relationship holds after we control for economic and social household
characteristics and migration status, but the density elasticities decline to −0.029 in Column (3)
and −0.039 in Column (6). Therefore, our estimation results suggest that costs associated with
agglomeration discourage completed fertility and, holding other things equal, a 10-fold difference
in city size on average generates a spatial variation of 8.63% (≈ 10−0.039 − 1) in number of children
per household. Consider a case where the population of city s is 10 times lager than city r. If the
average number of children in city r is 2, the average in city s becomes 1.827 (here, the spatial gap is
approximately 173 children per 1000 households).8
More importantly, we note that the density elasticity of number of children decreases compared
8
Holding other things equal, double difference in city size on average generates spatial variation in number of children
per household by 2.68% (≈ 2−0.039 − 1).
14
with results in Table 2: in the case of IV estimation, −0.091 in Column (6) of Table 2 versus −0.039 in
Column (6) of Table 3. This finding suggests that costs associated with agglomeration affect the timing
of childbirth. The two numerical examples above also imply that the regional gap in average number
of children decreases as couples age. This statistical test is the main topic of the next subsections.
Another interesting finding is that the effect of higher education on completed fertility is not
significant at the 10% level. Combining with estimation results in Table 2, our findings suggest
that higher education discourages childbearing among young married couples but does not affect
completed fertility. These results also imply that, holding other things equal, university graduates
postpone having children.
Similarly, dummy variables for couples who do not view children as necessary and for the number
of siblings exert significantly negative and positive effects, respectively, on the number of children.
Seeking security in old age shows no significant relationship with number of children. Our estimation
results suggest that social characteristics are crucial in determining preferences for having children.
The migration dummy also shows negative effects on completed fertility in Columns (2)–(3)
and (5)–(6). Migration correlates negatively with fertility, but more rigorous analysis is required to
distinguish between causality and self-selection via the decision to migrate.
[Table 3]
6.3 Catch-Up Process of Fertility in More Densely Populated Areas
Table 4 presents estimation results of Poisson regression model (3), which considers the dynamic
process of fertility behavior across different city sizes. We seek to quantify regional gaps in average
number of children by parents’ ages. To do so, we test whether the cross-term of population density
and wife’s age shows significant positive effects on number of children. Note that samples used in
Table 4 do not include migrants.
Poisson estimation results in Columns (1) and (2) show that the estimated coefficient for the crossterm of population density and wife’s age is significantly positive, which means that young married
couples in big cities postpone having children. IV Poisson estimation results in Columns (3) and (4)
also support this finding, but the magnitudes obtained by IV estimation are bigger than standard
ones. An important finding is that the gap in number of children between denser and less dense areas
is larger early in life and shrinks gradually as couples age.
Figure 8 illustrates estimated spatial variations in average number of children using estimates in
Column (4) of Table 4. Panel (a) shows the density elasticity of number of children at different ages.
15
Spatial variation in number of children is grater for couples in their 20s (e.g., −0.146 at age 29) but
declines to −0.044 at age 49.
Panel (b) of Figure 8 quantifies spatial variations in number of children by couples’ ages, showing
what percent of the change in average number of children is generated by difference in city size,
holding other things equal. Among couples age 30, the estimated percentage change in number of
children between a city and a city with 10 times more people is −27.71% (≈ 10−0.295+0.005×30 − 1). If
households in the baseline city on average have 1.5 children at age 30, households in a city with 10
times more people on average have 1.084 children (the spatial gap is approximately 426 children per
1,000 households). However, the estimated percentage change in the number of children between
those cities for couples at age 49 is −9.56% (≈ 10−0.295+0.005×49 − 1). If the average number of children
per household at age 49 in the baseline city is 2.2, the average in a city with 10 times more people
becomes 1.990 (the spatial gap is approximately 210 children per 1,000 households).9 Although slight
spatial variation in average number of children between denser and less dense areas remains, our
important finding is that couples residing in bigger cities have children relatively late in life, which
reduces the spatial gap in the number of children around age 50.
Thus far, our estimation results suggest that agglomeration discourages younger couples from
bearing children, but the completed fertility shrinks between denser and less dense areas as couples
age. Therefore, our results may emphasize that agglomeration affects the timing of childbirth rather
than number of children. That prospect is statistically tested in the next subsection.
[Table 4 and Figure 8]
6.4 Agglomeration Delays Birth of First Child
Table 5 presents estimation results concerning how agglomeration affects the wife’s age at marriage.
Estimated coefficient for population density are positive in Columns (1)–(3), but are not significant
even at the 10% level. It is not evident that agglomeration discourages the timing of marriage.
However, higher education level markedly delays age at marriage at the 1% level. Column (3) shows
that couples in which both spouses are university graduates marry about 26 months later than couples
in which both are not university graduates.
Table 5 provides evidence on whether agglomeration delays birth of first child. Unlike the
estimation results for marriage, estimated coefficient for population density are significantly positive
9
Here is another numerical example. Among couples age 30, the estimated percentage change in number of children
between a city and a city with twice more people is −9.31% (≈ 2−0.295+0.005×30 − 1). However, among couples age 49, the
estimated percentage change in number of children between those cities is −2.98% (≈ 2−0.295+0.005×49 − 1).
16
at the 5% level in Columns (4)–(6), with the value reaching 0.181 in Column (6). Using it, our
quantification shows, holding other things equal, that couples residing in a 10 times more populous
city delay childbirth by an average of approximately 5 months (≈ 0.181 × log(10)).10
As with the timing of marriage, higher education markedly delays the first child’s birth at the 1%
significance level. Column (6) shows that couples in which both spouses are university graduates bear
their first child about 22 months later than couples in which neither spouse is a university graduate.
In sum, agglomeration strongly defers childbirth decisions among younger couples, but married
couples in more densely populated areas generally have children later in life, whereas couples in less
dense areas have children early and stop after approximately two or three children. As a result, spatial
variation in the number of children per household diminishes as couples age, although the statistically
significant slight gap remains. Agglomeration delays birth of first child but not necessarily the timing
of marriage.
[Table 5]
7 Conclusion
This study has examined how agglomeration externalities affect married couples’ decisions to bear
children at different life stages. By employing a Japanese social survey dataset that inquires into
households’ fertility decisions, we have been able to control for economic factors alongside customarily unobservable household characteristics. Controlling for an endogeneity between number of
children and city size, we have quantified the extent to which agglomeration externalities generate
spatial variations in average number of children born to households.
We have found that, although agglomeration externalities significantly discourage couples’ fertility decisions, the magnitude declines as couples age: holding other things equal, a 10-hold difference
in city size generates a spatial variation of −27.71% in average number of children among couples at
age 30 and a variation of −9.56% among married couples at age 49, suggesting that young married
couples in bigger cities bear children later in life. Our results show that agglomeration externalities
delay birth of the first child by an average of about five months among couples living in cities that 10
times lager than the benchmark cities. Despite the acknowledged economic benefits of agglomeration
(e.g., Combes and Gobillon, 2015), our findings present the important conclusion that agglomeration
10
Here is another numerical example. Holding other things equal, couples residing in a twice more populous city delay
childbirth by an average of approximately 2 months (≈ 0.181 × log(2)).
17
hampers fertility rates through higher costs associated from agglomeration. In short, agglomerationoriented growth policies may accelerate the graying of population that policymakers struggle to
reverse. Policymakers in graying societies need to care about demographic issues associated with
agglomeration.
Future research needs to address two limitations in this research. We focus on married couples, but
decisions to marry affect national fertility rates. Thus, it should be noted that low fertility rates in more
densely populated areas also originate from their high proportions of unmarried people. Following
Baudin et al. (2015), childlessness should be studied in detail. Self-selected migration also needs to be
addressed. More densely populated areas are likely to attract single people who will work long term
and displace married couples with children because of high cost of living. Households’ endogenous
choices of location will feature prominently in spatial variations of fertility rates. Clarifying these
mechanisms remains for future research.
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Appendix A
Definitions of Variables
Number of Children
Total number of children (including deceased) that married couples had by
the date of survey.
Population Density
Total population divided by inhabitable area (in km2 ). The municipal panel
dataset was constructed from 1980, 1985, 1990, 1995, 2000, 2005, and 2010 population censuses. The
reference date for geographical information is April 1, 2011, when Japan had 1,747 municipalities
(excluding the Northern Territories). Tokyo’s 23 wards are counted individually. Cities designated by
government ordinance (Seirei Shitei Toshi) are counted as cities (shi), rather than subcategories ku. The
20
corresponding cities are Sapporo-shi, Sendai-shi, Saitama-shi, Chiba-shi, Yokohama-shi, Kawasakishi, Sagamihara-shi, Niigata-shi, Shizuoka-shi, Hamamatsu-shi, Nagoya-shi, Kyoto-shi, Osaka-shi,
Sakai-shi, Kobe-shi, Okayama-shi, Hiroshima-shi, Kitakyushu-shi, and Fukuoka-shi. Since some
municipalities merged between 1980 and 2011, their populations are re-aggregated from relevant
information. Linear interpolation is implemented between the census years. Average population
density is calculated by unit based on the combinations of prefectures and city size (Seirei Shitei
Toshi, Other City, and Village). Population densities at wife’s age 50 (Dens50
r(i) ) are replaced by those
in 1980 if wives reached age 50 before 1980. Population density in 1930 is computed from 1930
population census by administrative unit as of April 1, 2011, and then the average population density
is calculated by unit based on the combinations of prefectures and city size (Seirei Shitei Toshi, Other
City, and Village).
Migration Dummy Takes the value 1 if respondents’ current residential prefecture differs from
prefectures where either spouse lived at age 15 and 0 otherwise.
Old Age Security Score Ranges from 2 to 10, which is the sum of two questions about how households perceive the roles of government and family in providing security for the elderly (1: Governments, 5: Individuals and Families): (1) responsibility for livelihood of the elderly (2) responsibility
for medical and nursing care of the elderly. Greater values indicate how households are responsible
within the families in their old age.
Dummy for Non-Necessity of Children in a Marriage
Takes the value 1 for households that agree
or somewhat agree children are unnecessary in a marriage and 0 otherwise.
Number of Siblings is calculated by merging spousal responses. If both answer, the average
number of siblings is used; if one answers the question, the number that he or she provided is used.
Husband’s and Wife’s Incomes Class values (0, 35, 85, 115, 145, 200, 300, 400, 500, 600, 700, 800, 925,
1100, 1300, 1500, 1725, 2075, and 2300 in 10,000 JPY). The maximum class value is multiplied by 1.2.
Income is deflated by the consumer price index (2010=100)
Working Hours Total weekly worked during the past week (in 10 hours).
21
Dummy for Non-Labor Force Takes the value 1 if a respondent has never worked (i.e., a person
who answered 0 years of work experience) and 0 otherwise.
Dummy for University Graduate Takes the value 1 if a respondent graduated from university or
graduate school and 0 otherwise.
Dummy for Not Healthy
Takes the value 1 if answers are 4 or 5 on a one-to-five scale (1=good,
5=bad).
Dummies for Cohort Groups Take the value 1 if the wife in married couple i was born in 1944 and
earlier, 1945–1949, 1950–1954, 1955–1959, 1960–1964, 1965–1969, 1970–1974, or 1975 and later, and 0
otherwise.
Dummies for Survey Years
Take the value 1 if married couple i answers the questionnaire either in
the 2000, 2001, 2002, 2005, 2006, 2008, or 2010 survey and 0 otherwise.
Dummies for Regions Take the value 1 if married couple i lives either in Hokkaido–Tohoku
(Hokkaido, Aomori, Iwate, Miyagi, Akita, Yamagata, Fukushima), Kanto (Ibaraki, Tochigi, Gunma,
Saitama, Chiba, Tokyo, and Kanagawa), Chubu (Niigata, Toyama, Ishikawa, Fukui, Yamanashi,
Nagano, Gifu, Shizuoka, Aichi, and Mie), Kinki (Shiga, Kyoto, Osaka, Hyogo, Nara, and Wakayama),
Chugoku–Shikoku (Tottori, Shimane, Okayama, Hiroshima, Yamaguchi, Tokushima, Kagawa, Ehime,
and Kochi), or Kyushu (Fukuoka, Saga, Nagasaki, Kumamoto, Oita, Miyazaki, Kagoshima, Okinawa)
and 0 otherwise.
0.94
3401.08
3395.07
1.98
0.48
1.48
0.44
0.45
0.39
3.48
1.91
1.81
1.71
0.30
0.37
12.96
12.55
1.09
3.36
3.74
2042.81
4.65
0.36
2.41
0.26
0.29
0.18
4.79
1.58
4.14
2.59
0.10
0.17
51.71
49.07
2.35
24.39
26.16
S.D.
1.99
2908.21
Mean
29
2
0
0
0
0
0
0
0
0
0
0
0
20
20
1
16
16
0
104
Min
13253
10
1
15
1
1
1
28
20
8
7
1
1
91
90
5
51
50
8
15182
Max
3323.26
1.88
0.50
0.96
0.43
0.48
0.43
2.82
1.85
1.14
1.54
0.08
0.29
7.83
6.68
1.06
3.35
3.71
3423.62
2987.73
2014.00
4.58
0.43
1.72
0.24
0.35
0.24
5.51
1.73
4.81
2.83
0.01
0.09
42.25
39.52
2.32
24.65
26.57
0.96
S.D.
1.81
Mean
29
2
0
0
0
0
0
0
0
0
0
0
0
20
20
1
16
16
104
0
Min
13253
10
1
8
1
1
1
28
20
8
7
1
1
66
49
5
45
41
15182
6
Max
Sample of Wife’s Age < 50
2814.98
2076.59
4.72
0.28
3.23
0.28
0.21
0.11
3.95
1.41
3.35
2.32
0.20
0.26
62.80
60.28
2.38
23.96
25.72
2.20
Mean
3372.92
3477.92
2.10
0.45
1.58
0.45
0.41
0.32
3.95
1.97
2.11
1.85
0.40
0.44
8.06
7.56
1.12
3.34
3.73
0.87
S.D.
109
29
2
0
0
0
0
0
0
0
0
0
0
0
33
51
1
16
16
0
Min
14715
13253
10
1
15
1
1
1
28
17
8
7
1
1
91
90
5
51
50
8
Max
Sample of Wife’s Age ≥ 50
Note: The numbers of observations for full sample, sample (wife’s age < 50), and sample (wife’s age ≥ 50) are 4,334, 2,339, and 1,995, respectively. The numbers of observations for
wife’s age at marriage are 1,658, 1,034, and 624, respectively. The numbers of observations for wife’s age at birth of first child are 3,880, 2,019, and 1,861, respectively. The household
who has the maximum number of children and the uppermost 1 percentile of the distribution of working hours for husband and wife are excluded from the full sample as extreme
outliers. Population density is expressed in persons/km2. Working hours are expressed in 10-hour units.
Number of Children
Population Density for All
Population Density in Survey Year
Population Density at Age 50
Population Density (Persons/km2 ) in 1930
Old-Age Security Index
D(1=Non-Necessity of Children in a Marriage)
Number of Brothers and Sisters
D(1=Migration)
D(1=University Graduate for Husband)
D(1=University Graduate for Wife)
Husband’s Income (Million yen)
Wife’s Income (Million yen)
Working Hours Last Week for Husband
Working Hours Last Week for Wife
D(1=Non-Labor Force for Husband)
D(1=Non-Labor Force for Wife)
Husband’s Age
Wife’s Age
D(1=Not Healthy)
Wife’s Age at Marriage
Wife’s Age at Birth of First Child
Variables
Full Sample
Table 1: Descriptive Statistics of Variables for Regression Analysis
22
23
Table 2: Poisson Regression Estimation Results from Sample (Wife’s Age < 50)
Dependent Variable: Number of Children
Poisson
Explanatory Variables
Log(Population Density)
(1)
(2)
(3)
(4)
(5)
(6)
−0.075***
(0.016)
−0.069***
(0.014)
−0.127***
(0.024)
−0.095***
(0.020)
0.015***
(0.003)
−0.016***
(0.006)
0.005
(0.010)
−0.029***
(0.011)
−0.087
(0.177)
−0.091*
(0.054)
0.082***
(0.028)
−0.090***
(0.030)
0.166***
(0.028)
−0.190***
(0.034)
−0.028***
(0.009)
−0.062**
(0.029)
−0.102***
(0.019)
−0.093***
(0.017)
−0.122***
(0.023)
−0.090***
(0.019)
0.016***
(0.003)
−0.018***
(0.006)
0.007
(0.010)
−0.032***
(0.011)
−0.079
(0.177)
−0.097*
(0.053)
0.096***
(0.025)
−0.106***
(0.027)
0.158***
(0.028)
−0.181***
(0.034)
−0.025***
(0.009)
−0.058**
(0.029)
Yes
Yes
−0.067***
(0.015)
−0.120***
(0.023)
−0.087***
(0.021)
0.015***
(0.003)
−0.016***
(0.006)
0.006
(0.010)
−0.032***
(0.011)
−0.085
(0.175)
−0.096*
(0.054)
0.081***
(0.027)
−0.089***
(0.029)
0.164***
(0.028)
−0.188***
(0.033)
−0.027***
(0.009)
−0.061**
(0.029)
0.009
(0.006)
−0.079***
(0.018)
0.025**
(0.011)
Yes
Yes
Yes
−0.091***
(0.018)
−0.114***
(0.022)
−0.080***
(0.020)
0.016***
(0.003)
−0.018***
(0.006)
0.007
(0.010)
−0.034***
(0.011)
−0.081
(0.175)
−0.101*
(0.053)
0.097***
(0.025)
−0.108***
(0.027)
0.155***
(0.027)
−0.178***
(0.032)
−0.024***
(0.009)
−0.056*
(0.029)
0.006
(0.006)
−0.074***
(0.018)
0.026**
(0.011)
Yes
2339
2339
2339
0.051
0.102
0.073
Dummy (1=University Graduate for Husband)
Dummy (1=University Graduate for Wife)
Husband’s Income
Wife’s Income
Hours Worked Last Week for Husband
Hours Worked Last Week for Wife
Dummy (1=Non-Labor Force for Husband)
Dummy (1=Non-Labor Force for Wife)
Husband’s Age
Husband’s Age Squared (1/100)
Wife’s Age
Wife’s Age Squared (1/100)
Dummy (1=Not Healthy)
Dummy (1=Migration)
Old-Age Security Motive Score
Dummy (1=Non-Necessity of Children)
Number of Siblings
Cohort Groups, Region, and Year Dummies
Number of Observations
Log Likelihood
AIC
Overidentification (p-value)
IV Poisson
2339
2339
2339
−3360.628 −3304.877 −3299.954
6761.255
6677.755
6673.908
Note: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Instrumental variables for
the population density are the logarithm of population density in 1930 and its squared variable. Constant is not reported.
* denotes statistical significance at the 10% level, ** at the 5% level, and *** at the 1% level.
24
Table 3: Poisson Regression Estimation Results from Sample (Wife’s Age ≥ 50)
Dependent Variable: Number of Children
Poisson
Explanatory Variables
Log(Population Density at Age 50)
(1)
(2)
(3)
(4)
(5)
(6)
−0.035***
(0.013)
−0.032**
(0.013)
−0.011
(0.025)
0.045
(0.033)
−0.033*
(0.017)
−0.045***
(0.015)
−0.043***
(0.015)
−0.011
(0.024)
0.049
(0.032)
−0.030*
(0.016)
Yes
Yes
−0.029**
(0.013)
−0.004
(0.026)
0.050
(0.031)
−0.031*
(0.018)
−0.000
(0.005)
−0.087***
(0.020)
0.017**
(0.007)
Yes
Yes
Yes
−0.039***
(0.015)
−0.006
(0.025)
0.055*
(0.030)
−0.029*
(0.016)
−0.000
(0.005)
−0.083***
(0.019)
0.016**
(0.007)
Yes
1995
1995
1995
0.636
0.653
0.569
Dummy (1=University Graduate for Husband)
Dummy (1=University Graduate for Wife)
Dummy (1=Migration)
Old-Age Security Motive Score
Dummy (1=Non-Necessity of Children)
Number of Siblings
Cohort Groups, Region, and Year Dummies
Number of Observations
Log Likelihood
AIC
Overidentification (p-value)
IV Poisson
1995
1995
1995
−2977.043 −2976.321 −2971.868
5990.087
5994.643
5991.736
Note: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Instrumental variables for
the population density are the logarithm of population density in 1930 and its squared variable. Constant is not reported.
* denotes statistical significance at the 10% level, ** at the 5% level, and *** at the 1% level.
25
Table 4: Poisson Regression Estimation Results from Sample (Wife’s Age < 50, Non-Migrants)
Dependent Variable: Number of Children
Poisson
Explanatory Variables
Log(Population Density)
Log(Population Density) × Wife’s Age
Dummy (1=University Graduate for Husband)
Dummy (1=University Graduate for Wife)
Husband’s Income
Wife’s Income
Hours Worked Last Week for Husband
Hours Worked Last Week for Wife
Dummy (1=Non-Labor Force for Husband)
Dummy (1=Non-Labor Force for Wife)
Husband’s Age
Husband’s Age Squared (1/100)
Wife’s Age
Wife’s Age Squared (1/100)
Dummy (1=Not Healthy)
(1)
(2)
(3)
(4)
−0.232***
(0.078)
0.004**
(0.002)
−0.120***
(0.025)
−0.109***
(0.027)
0.015***
(0.004)
−0.014**
(0.007)
0.006
(0.011)
−0.023*
(0.012)
0.053
(0.152)
−0.039
(0.053)
0.064**
(0.029)
−0.067**
(0.031)
0.128***
(0.036)
−0.188***
(0.042)
−0.031***
(0.009)
−0.277***
(0.094)
0.005**
(0.002)
−0.113***
(0.024)
−0.120***
(0.026)
0.015***
(0.004)
−0.015**
(0.007)
0.005
(0.010)
−0.027**
(0.012)
0.043
(0.150)
−0.034
(0.053)
0.074***
(0.025)
−0.078***
(0.027)
0.116***
(0.039)
−0.177***
(0.040)
−0.030***
(0.009)
Yes
−0.237***
(0.077)
0.004**
(0.002)
−0.116***
(0.024)
−0.097***
(0.028)
0.015***
(0.004)
−0.013**
(0.007)
0.006
(0.012)
−0.025**
(0.012)
0.055
(0.150)
−0.046
(0.054)
0.061**
(0.029)
−0.065**
(0.031)
0.126***
(0.035)
−0.188***
(0.041)
−0.031***
(0.009)
0.007
(0.006)
−0.077***
(0.024)
0.034***
(0.012)
Yes
Yes
−0.295***
(0.091)
0.005**
(0.002)
−0.109***
(0.024)
−0.109***
(0.027)
0.016***
(0.004)
−0.014**
(0.007)
0.004
(0.011)
−0.029**
(0.012)
0.042
(0.148)
−0.039
(0.054)
0.072***
(0.024)
−0.078***
(0.026)
0.111***
(0.039)
−0.176***
(0.039)
−0.030***
(0.009)
0.006
(0.006)
−0.071***
(0.023)
0.035***
(0.012)
Yes
1779
−2519.496
5106.992
1779
−2515.319
5104.639
1779
1779
0.432
0.378
Old-Age Security Motive Score
Dummy (1=Non-Necessity of Children)
Number of Siblings
Cohort Groups, Region, and Year Dummies
Number of Observations
Log Likelihood
AIC
Overidentification (p-value)
IV Poisson
Note: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Instrumental variables for
the population density and cross-term of population density and wife’s age are the logarithm of population density in 1930,
its squared variable, and cross-terms of these two variables and wife’s age. Constant is not reported. * denotes statistical
significance at the 10% level, ** at the 5% level, and *** at the 1% level.
26
Table 5: Wife’s Ages at Marriage and at Birth of First Child
Dependent Variable:
Wife’s Age at Marriage
Explanatory Variables
Log(Population Density)
(1)
(2)
(3)
(4)
(5)
(6)
0.130
(0.116)
0.079
(0.118)
0.710***
(0.178)
1.479***
(0.272)
−0.021
(0.181)
0.290***
(0.072)
0.185**
(0.073)
0.825***
(0.156)
1.089***
(0.189)
0.237
(0.167)
Yes
Yes
0.077
(0.118)
0.701***
(0.179)
1.477***
(0.272)
−0.021
(0.179)
−0.039
(0.037)
−0.140
(0.170)
−0.032
(0.041)
Yes
Yes
Yes
0.181**
(0.073)
0.813***
(0.154)
1.080***
(0.192)
0.242
(0.168)
−0.038
(0.029)
−0.008
(0.129)
−0.045
(0.054)
Yes
1658
0.045
1658
0.077
1658
0.076
3880
0.044
3880
0.072
3880
0.072
Dummy (1=University Graduate for Husband)
Dummy (1=University Graduate for Wife)
Dummy (1=Migration)
Old-Age Security Motive Score
Dummy (1=Non-Necessity of Children)
Number of Siblings
Cohort Groups, Region, and Year Dummies
Number of Observations
Adjusted R2
Dependent Variable:
Wife’s Age at Birth of First Child
Note: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported.
* denotes statistical significance at the 10% level, ** at the 5% level, and *** at the 1% level.
4.0
Total Fertility Rate
3.5
Japan
Germany
United Kingdom
France
Italy
United States
3.0
2.5
2.0
1.5
1.0
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Year
(a) Total Fertility Rate
Population aged 65 and above (% of Total)
27
25
Japan
Germany
United Kingdom
France
Italy
United States
20
15
10
5
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Year
(b) Share of Population Aged 65 and Above
Figure 1: Total Fertility Rates and Population Aging Rate of Selective Developed Countries
Note: Created by author. Japan’s fertility data are obtained from the Vital Statistics of the Ministry of Health,
Labour and Welfare. Other data are obtained from the World DataBank of the World Bank.
28
1.67 or more
2570 or more
1.55-1.67
1177-2570
1.48-1.55
785-1177
1.40-1.48
533- 785
1.31-1.40
318- 533
less than 1.31
less than 318
Total Fertility Rate
Population Density
(a) Total Fertility Rate, 2008–2012
(b) Population Density, 2010
3.0
Total Fertility Rate
log(TFR) = 0.671 - 0.042 log(Dens)
2.5
2.0
1.5
1.0
0.5
8
16
32
64
128
256
512 1024 2048 4096 8192 16384
Population Density
(c) Relationship between Total Fertility Rate and Population Density
Figure 2: Geographical Distribution of Total Fertility Rate and Population Density
Note: Created by author based on Vital Statistics by Health Center and Municipality in 2008–2012 and 2010
Population Census. Municipalities are categorized into six quantiles. Population densities are calculated as total
population divided by inhabitable area. Spatially smoothed population densities are calculated by including
neighboring municipalities that lie within the circle of 30 km radius from the centroid of municipality. Several
municipalities lacking data are classified into the lowest group.
29
103.4 or more
45.3 or more
98.2-103.4
43.9-45.3
95.1- 98.2
42.5-43.9
91.8- 95.1
41.5-42.5
79.4- 91.8
39.1-41.5
less than 79.4
less than 39.1
Age 25-29
(a) Age Group 25–29
Age 35-39
(b) Age Group 35–39
Figure 3: Fertility Rate by Age Group (Births per 1,000 Women)
Note: Created by author based on Specified Report of Vital Statistics in FY2010. Prefectures are categorized
into six quantiles.
30
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
Total
(1835)
Under 30
(90)
30-34
(233)
35-39
(519)
40-49
(993)
Very high costs of rearing children and education
Small living space
Dislike giving birth at a later stage in life
Want children but cannot have
(a) By Age Group
0
Total
Ideal No. ≥ 1
Ideal No. ≥ 2
Ideal No. ≥ 3
(Planned No. = 0) (Planned No. = 1) (Planned No. ≥ 2)
Very high costs of rearing children and education
Small living space
Dislike giving birth at a later stage in life
Want children but cannot have
(b) Compared with Planned Number of Children
Figure 4: Reasons Why Households Do Not Have Ideal Number of Children (Multiple answers
allowed, %)
Note: Created by author based on 2010 Japanese National Fertility Survey Volume I, National Institute of
Population and Social Security Research.
31
400
350
300
u
o
h
T
:
t
i
n
U
(
250
200
150
100
50
0
Kindergarten
Elementary School
Junior High School
Population<50,000
50,000≤Population<150,000
Population≥150,000
Shitei Toshi and Tokubetsu-ku
(a) Annual costs of extramural activities for public school students by city size, 2012 (Current Price)
Log(Price Index for Tutorial Fees)
)
n
e
Y
d
n
a
s
5.5
11214
11245 13214
25206
13209
24205
27210
11202
22213
9208
12212
29205 28204 11230 13210
13203
13211
14211 27220
11225
13224
11224
13208
27211 11235
9204 22100
29209
27203
27214
27227
12211
23207
23201
14214
12227
14203
27222
17210
21201
27219 13201
14205
14207
1320413100
14213
8204
27215
28219
12220
28214 12221
25201
12224
34205
33100
11221
11237 13207
28217 14201
22203 2610023219
27209
27216
20201
27205
12204
13212
34212
13205
28100
12100 27140
1100
4100
13222
13206
27100
11227
320138202
28202
8217
11219
14130
21204
26204
11100
9201
23100
23202
11222
12203
14100
19201
2920114206
4202
11208
10204
14150 11201
38201
25213 23211 822034207
24202
22206
25202
12216 13229
17201
1221727204 13202
37202
23206
8203
44201
44202
12206
33202
15206
23204
42202
18201
1220727223
11215
10201
47208
4010027202
40130
9205 1213
24207
4721323220
40218
14216
40203
14204
34100
43202
14215
27217
28203
23213
11203
34204
20202
22130 12219
72021204
46201
33203
24204
22212
31202 21213
5201
16201
11218
47201
38206
17203
8202
8227 10202
2020515222
21202
15100
32203
39201
20203
7203 6201
1620242201
3215
41202
23205
22214
8201
13213
9213 120722207
12222
2201
35208
27212
1208
620434213 2202
7201 38205
43201
28207
41201
28210
24203
20217
27218
14212
24216 45202
23222
47211
28201
5203 46218
40205 92023720112208
31201 35201
24201 35202
30201
32051206
35215
35203
7204 42204
11217
32201 1217
3209
36201
23212 23210
10203
6203 46215
27207
1020540202
1202 120334202
23203
22210
22211
45203 4620315202
8221
35206
4215 15204
2203
45201
5.0
4.5
4.0
4
5
6
7
8
9
10
Log(Population Density)
(b) Price Index for Tutorial Fees, 2007
Figure 5: Costs of Education and Agglomeration
Note: Created by author. Panel (a) is based on 2012 Survey on Household Expenditures on Education per
Student (Ministry of Education, Culture, Sports, Science and Technology). Panel (b) is based on tutorial fees
from 2007 National Survey of Prices (Ministry of Internal Affairs and Communications). Average population
densities are calculated using 2005 and 2010 population censuses.
32
Ideal Number of Children
Number of Children
2.5
2.0
1.5
1.0
0.5
0.0
20−24
Population Density > 75th Percentile
Population Density ≤ 75th Percentile
25−29
30−34
35−39
40−44
45−49
50−54
Age Group
(a) Number of Children by Age Group
55−
3.0
2.5
2.0
1.5
−1944
Population Density > 75th Percentile
Population Density ≤ 75th Percentile
1950−1954
1960−1964
1970−74
1945−1949
1955−1959
1965−1969
1975−
Cohort Group
(b) Ideal Number of Children by Cohort Group
Figure 6: Average Number of Children per Married Couple
Note: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. Sample is
limited to non-migrants in Table 1. The 75th percentile is based on population densities for all in Table 1.
Differences in population densities across years are not controlled for in the calculation of the 75 percentile.
33
0.20
0.20
Pop. Density > 75th PCTL
Pop. Density ≤ 75th PCTL
0.15
Fraction
Fraction
0.15
Pop. Density > 75th PCTL
Pop. Density ≤ 75th PCTL
0.10
0.05
0.10
0.05
0.00
0.00
15
20
25
30
35
Wife’s Age
(a) Wife’s Age at Marriage
40
45
50
15
20
25
30
35
40
45
50
Wife’s Age
(b) Wife’s Age at Birth of the First Child
Figure 7: Wife’s Age at Marriage and at Birth of First Child
Note: Author’s calculation from the Japanese General Social Surveys Cumulative Data 2000–2010. Sample
is limited to non-migrants in Table 1. The 75th percentile is based on population densities for all in Table 1.
Differences in population densities across years are not controlled for in the calculation of the 75 percentile.
-0.02
-0.04
-0.06
-0.08
-0.10
-0.12
-0.14
-0.16
-0.18
-0.20
20
25
30
35
40
45
Wife’s Age
(a) Density Elasticity of Number of Children
50
% Change in Average Number of Children
Density Elasticity on Number of Children
34
0%
-5%
-10%
-15%
-20%
-25%
-30%
-35%
-40%
-45%
At Age 25
At Age 30
At Age 35
2
At Age 40
At Age 45
At Age 49
4
6
8
10
12
14
Ratio of Population Density between Two Cities
16
(b) Spatial Variation in Average Number of Children
Figure 8: Percentage Change in Average Number of Children by City Size
Note: The density elasticity of number of children is calculated as α̂ + φ̂ × Age using the estimates in Columns
(4) of Table 4. The percentage change in average number of children is calculated as [λs (θ̂) − λr (θ̂)]/λr (θ̂) =
α̂+φ̂×Age
Ratiosr
− 1, where Ratiosr is the ratio of population density between cities s and r, and households’
characteristics are assumed to be identical. This numerical simulation uses the estimates θ̂ in Columns (4) of
Table 4.