Does agglomeration discourage fertility? Evidence from the Japanese General Social Survey 2000–2010

Does agglomeration discourage fertility? Evidence from the Japanese General Social Survey... Abstract This study employs Japanese household-level data to quantify the extent to which congestion diseconomy in large cities affects married couples’ fertility behavior. The theoretical model of this study emphasizes the importance of controlling for preference heterogeneity in the demand for children. The baseline quantification shows that, all else equal, a 10-fold difference in city size generates a spatial variation of −22.13% in the average number of children born to couples aged 30 and a spatial variation of −6.07% at age 49. The narrowing of the gap suggests that the young married couples in larger cities delay childbearing. 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. Glaeser and Maré, 2001; Glaeser and Resseger, 2010; Combes et al., 2012; Combes and Gobillon, 2015; de la Roca and Puga, 2017). Although economists and policymakers consider the economics of agglomeration when designing growth policies, less attention is devoted to the diseconomies brought about by agglomeration. This study aims to shed light on how benefits and congestion costs arising from agglomeration affect socioeconomic behavior. In most developed counties, demographic issues are central to the current policy agendas. These counties have experienced rapid declines in total fertility rates (TFR) with economic growth, and raising fertility rates has become a policy priority in several countries. For example, France, Germany, the UK and the USA have exhibited sharp declines in their TFRs since the 1960s, as have Italy and Japan after the 1970s. Although recent TFRs have remained at ∼2 in France, the UK and the USA, they are less in Germany, Italy and Japan (∼1.4). The low fertility rate has led to acceleration in the aging of the population. Since an unbalanced demographic structure distorts social security systems, governments seek effective policies to recover fertility rates (e.g. Grant et al., 2004). In addition, Krugman (2014) points out that slow population growth precedes reduced demand for new investment and may contribute to secular stagnation. This study attempts to theoretically and empirically clarify how agglomeration discourages fertility behavior. In particular, this study emphasizes spatial rather than temporal views of national fertility. The theoretical model of this study clarifies possible channels through which both agglomeration economies and diseconomies affect the demand for children. For example, Panels (a) and (b) of Figure 1 illustrate fertility rates and population density for Japanese municipalities, respectively. They clearly exhibit a negative relationship, as shown in Panel (c). Figure 1 View largeDownload slide Geographical distribution of total fertility rate and population density. Notes: 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. Source: Created by author based on Vital Statistics by Health Center and Municipality in 2008–2012 and 2010 Population Census. Figure 1 View largeDownload slide Geographical distribution of total fertility rate and population density. Notes: 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. Source: Created by author based on Vital Statistics by Health Center and Municipality in 2008–2012 and 2010 Population Census. There are many possible factors that could explain this negative relationship. For example, Sato (2007) constructs a theoretical model, in which an agglomerated region attracts workers, intensifying the population density and wage rates while reducing fertility rates through agglomeration diseconomies. As empirically studied by Schultz (1986), Sato and Yamamoto (2005), Aiura and Sato (2014), Morita and Yamamoto (2014) and Goto and Minamimura (2015), theoretically, examine the mechanics through which rising real wages in more densely populated areas increase the opportunity cost of childrearing while attracting workers, further elevating the population density and the opportunity cost. This circularity engenders lower fertility rates in more densely populated areas.1 Although these theoretical studies clarify possible channels through which agglomeration affects the demand for children, it remains unclear how agglomeration affects married couples’ decisions to bear children at different ages. In particular, dynamic aspects of fertility behavior across cities are omitted in the existing literature. Figure 2 presents geographical distributions of fertility rates by age cohort and shows regional heterogeneity among age groups. The fertility rates among couples aged 35–39 are relatively high in more densely populated areas, especially in Greater Tokyo and Osaka, although they are lower among couples aged 25–29. The data depicted in Figure 2 imply that individuals residing in large cities postpone parenthood. Figure 2 View largeDownload slide Fertility rate by age group (births per 1000 women). Note: Prefectures are categorized into six quantiles. Source: Created by author based on Specified Report of Vital Statistics in FY2010. Figure 2 View largeDownload slide Fertility rate by age group (births per 1000 women). Note: Prefectures are categorized into six quantiles. Source: Created by author based on Specified Report of Vital Statistics in FY2010. Using household-level microdata, this study aims to quantify the extent to which congestion costs in large cities discourage married couples from bearing children per parental age cohort. As explained in the theoretical model, this study emphasizes that preference heterogeneity in the demand for children leads to the bias when researchers estimate the ex post effect of agglomeration on the demand for children. For example, the spatial sorting of individuals with weak preferences for the demand for children is a possible source of bias.2 To control for preference heterogeneity and self-selected migration, this study employs the Japanese General Social Survey (JGSS) dataset. This study advances the economic geography literature by offering new evidence concerning different patterns of childbearing between large and small cities. Controlling for economic and social factors, this study finds that congestion costs in large cities discourage fertility among married couples, with the magnitude of this effect shrinking as couple’s age. The baseline estimates reveal that, all else equal, a 10-fold increase in population density (in general, the difference between central cities in Japanese rural prefectures and metropolitan areas in Tokyo) reduces fertility by 22% for couples age 30, but by only 6% for couples age 49. Further analyses show that young married couples in large cities postpone having their first child by an average of 5 months in the case of a 10-fold increase in population density. Concerning existing studies in Japan, Sasai (2007) finds that the regional gap in completed fertility shrinks after controlling for social and economic factors, and mentions a possibility that married couples have children later in life. Therefore, my study contributes to the literature by providing supportive evidence for this aspect. In addition, Yamauchi (2016) points out that completed fertility in the Tokyo Metropolitan Area is still lower than that in other areas. Note that my study is consistent with findings in both Sasai (2007) and Yamauchi (2016). Using a more general quantitative analysis by population density, this study reveals that married couples in large cities have children later in life, which decreases the regional gap in completed fertility. However, a slight gap in completed fertility exists.3 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 the birth of the first child and the 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 the effects of housing prices on fertility on homeowners and renters differ owing to differences in the importance of housing’s wealth and price effects. By contrast, this study does not specify each factor of congestions, such as housing and land. This study emphasizes that housing and land are not the only factors that delay the timing of childbearing. For example, high uncertainty of accessibility to nursery schools is another factor, and this factor is highly correlated with city size in Japan. High educational costs in large cities also affect the timing of childbearing. Married couples may wait to have their first child until they have saved enough money. There are also numerous potential costs in large cities that researchers cannot observe directly. Therefore, this study attempts to capture wide-ranging aggregate congestion costs arising from agglomeration by population density. The remainder of this article is organized as follows. Section 2 explains a theoretical model. Section 3 describes the empirical framework. Section 4 presents the dataset. Section 5 discusses the estimation results and a robustness check. Section 6 presents the conclusions. 2. Theoretical explanation This study aims to quantify the extent to which congestion costs arising from agglomeration discourage fertility behavior. Using a simple theoretical model, this study clarifies possible channels through which both agglomeration economies and diseconomies affect the demand for children. Following Becker (1992), Willis (1973) and Sato (2007), this study describes households’ fertility decisions, in which both the number and quality (e.g. the education level) of children are assumed. For simplicity, this study employs a Cobb–Douglas utility function in which all goods are normal, as follows:4  u(xr,yr,qr)=xr1−μ−ξyrμqrξ, 0<μ+ξ<1, 0<μ<1, 0<ξ<1, where xr, yr and qr represent consumption of a composite good, the number of children and the quality per child, respectively. This study assumes that each household is endowed with one unit of time allocated between working and child-rearing. Households must spend a quantity of time byr, where b is a positive constant tied to the time requirement of rearing one child. Thus, the budget constraint is given as follows:5  pxr(nr)xr+pqr(nr)qryr=Ir(nr)+wr(nr)(1−byr)−cr(nr), where nr is the city size variable (e.g. the population density or population size) in region r, pxr(nr) is the price of composite goods in region r, pqr(nr) is the price related with the quality of children, Ir(nr) is the income of a full-time worker in the household (e.g. the husband’s income or the income of a household member who has little time for childrearing) in region r, wr(nr) is the wage rate for a household member who takes care of children (e.g. the wife’s wage) in region r, wr(nr)(1−byr) is the wife’s income and cr(nr) is the congestion cost arising from agglomeration in region r. It is assumed that prices, income, wages and congestion costs depend on the city size. In the budget constraint, bwr(nr)+pqr(nr)qr denotes the marginal cost of rearing one child, in which bwr(nr) captures the opportunity cost of rearing a child relative to working (i.e. the loss of earnings). Importantly, an increase in the wife’s wage rate wr(nr) leads to higher opportunity costs of rearing a child. In addition, agglomeration economies and diseconomies are assumed as follows:   dpxr(nr)dnr⋛0, dpqr(nr)dnr>0, dIr(nr)dnr>0, dwr(nr)dnr>0, and dcr(nr)dnr>0, (1) where the price index, pxr(nr), may increase in nr, whereas if xr also includes differentiated goods, pxr(nr) may decrease in nr (e.g. Ottaviano et al., 2002; Handbury and Weinstein, 2015). As discussed in the Online Appendix, the price related with the quality of children, pqr(nr), might be higher in large cities. As studies in urban economics have established, income and wage rates in more densely populated regions tend to be higher (e.g. Combes and Gobillon, 2015). The congestion costs of agglomeration cr(nr) (e.g. commuting) increase in nr. Households’ utility maximization yields respective demand functions for consumption goods, children and the quality of children, as follows:   xr(Ir(nr),wr(nr),cr(nr),pxr(nr))=(1−μ−ξ)Ir(nr)+wr(nr)−cr(nr)pxr(nr), yr(Ir(nr),wr(nr),cr(nr))=(μ−ξ)Ir(nr)+wr(nr)−cr(nr)bwr(nr), qr(wr(nr),pqr(nr))=ξμ−ξbwr(nr)pqr(nr), (2) where μ−ξ>0 and Ir(nr)+wr(nr)−cr(nr)>0 are assumed to satisfy positive demands. The comparative statics regarding the demand for children yr yield the following relationships:   ∂yr∂Ir(nr)>0, ∂yr∂wr(nr)⋚0 if Ir(nr)−cr(nr)⋛0, and ∂yr∂cr(nr)<0, (3) which clarify that an increase in the husband’s income Ir(nr) raises the demand for children per household. An increase in the wife’s wage wr(nr) has both positive and negative effects depending on the husband’s income and congestion costs. When Ir(nr)−cr(nr)>0, which may hold in many cases, an increase in the wife’s wage reduces the demand for children through the high opportunity costs of rearing children. An increase in the congestion costs of agglomeration cr(nr) reduces the demand for children.6 To connect the theoretical predictions with the empirical analysis, this study discusses these key channels through which agglomeration economies and diseconomies affect the demand for children. Matching the agglomeration economies in Equation (1) with the comparative statics in Equation (3), I find that agglomeration economies have both positive and negative effects on the number of children through income effects and the high opportunity costs of rearing children. By contrast, agglomeration diseconomies have negative effects on the number of children through high congestion costs. In addition, it is important to discuss conditions regarding the total effects of agglomeration on the demand for children based on dyr/dnr. See the Online Appendix for the details of the comparative statics for total effects of agglomeration on demand for children. Another key prediction is that preference heterogeneity in parameters μ and ξ affects the spatial distribution of the number of children. From the demand functions in Equation (2), the following relationships can be derived:   dyrdμ>0, dqrdμ<0, dyrdξ<0, and dqrdξ>0, which mean (i) that consumers with strong preferences for the quantity of children have more children and decrease expenditures on their quality and (ii) that consumers with strong preference for the quality of children have fewer children and increase expenditures on their quality. Importantly, this preference heterogeneity leads to a bias in the empirical analysis when researchers estimate the ex post effects of agglomeration on the demand for children. For example, suppose that consumers with weak preferences for the quantity of children tend to migrate into large cities because the large variety of goods and services available in large cities increases these consumers’ utility compared with having children. This relationship can be written as μs<μr when ns > nr, which generates the negative correlation between the number of children and city size. Therefore, in the empirical analysis, it is important to control for consumers’ preference heterogeneity and their endogenous migration choice. Although the theoretical model uncovers how agglomeration affects fertility behavior in terms of its channels, the total effects of agglomeration on the demand for children become highly complicated. In the empirical analysis, this study uncovers how additional controls for economic and social factors change the aggregate impacts of agglomeration.7 3. Empirical framework 3.1. Estimating 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 TFR). A standard approach is to linearly regress the number of children on population density and other control variables. However, an empirical issue is that the dependent variable takes a discrete value. In that case, a Poisson regression is more appropriate. Therefore, the regression model to be estimated is given by   Pr(Yir=yir)=exp(−λir(θ))(λir(θ))yiryir!, yir=0,1,2,…,λir(θ)≡exp(αlog(Densr(i)t)+γMi+Xiβ+X˜iδ+Dr(i)Regη+DtYearψ), (4) where yir is the number of children in household i residing in region r; Densr(i) is the population density of region r where 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 of 1 if either spouse in couple i has emigrated and 0 otherwise; Xi is a vector of variables denoting household characteristics (age, gender, cohort dummies, employment status, health condition, education, years of working experience, and the husband’s and wife’s incomes), X˜i is a vector of variables for household social characteristics that affect fertility decisions; DrReg is a vector of regional dummies; DtYear is a vector of year dummies; and θ is a vector of parameters (α,γ,β′,δ′,η′,ψ′)′. Thus, the parameter vector that maximizes the log-likelihood function ℓ(y,θ) is estimated as follows:   ℓ(y,θ)=∑i=1N(−λir(θ)+yirlog(λir(θ))−log(yir!)), where N is the number of observations. 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. This study quantifies, holding other factors constant, the extent to which differences in city size affect the number of children per married couple.8 The regression includes customarily unobservable household characteristics X˜i. The use of a social survey dataset mitigates estimation bias arising from spatial sorting driven by heterogeneity in households’ preference. Migration influences the decisions to bear children through its higher financial and nonfinancial costs. For example, nonmigrants residing near their parents have advantages in rearing children. In addition, large cities offer numerous job opportunities and may attract people who are more intent on careers than parenthood. Thus, migrants are expected to have fewer children than nonmigrants. Furthermore, it needs to be considered that this migration choice is endogenously determined. The next question is whether agglomeration affects completed fertility. Focusing on married couples for which the wife’s age is 50 or older (i.e. the outer age for childbearing), I estimate the Poisson regression model as follows:   λir(θ)≡exp(αlog(Densr(i)t50)+γMi+Ziϕ+X˜iδ+Dr(i)Regη+DtYearψ), (5) where Densr(i)t50 denotes the population density of the city where the married couple lived when the wife was age 50 and Zi is limited to the vector of variables capturing husbands’ and wives’ university education because the dataset includes no historical information on income, work experience or health status.9 The interpretations of parameter α in Models (4) and (5) may be ambiguous when the sample includes migrants, even if migration status is controlled for. If possible, it is ideal to control for all of the cities in which migrants have ever resided. Another related issue is that migration itself is highly related with the fertility decision, presenting self-selection bias. Although the method proposed by Dahl (2002) is more appropriate, because of data limitations, the robustness check is based on a classical approach to the selection bias by an endogenous binary-variable model. See Section 5.5 for details of the robustness check. 3.2. Testing the catch-up process in large cities This section examines the observation that married couples residing in more densely populated areas bear children later in life, as shown in Figure 2. To measure the catch-up process in the regression framework, this study introduces a cross-term of population density and wife’s age into the Poisson regression Model (4) as follows:   λir(θ)≡exp(αlog(Densr(i)t)+φlog(Densr(i)t)×Ageiwife+Xiβ+X˜iδ+Dr(i)Regη+DtYearψ), (6) where Ageiwife denotes the wife’s age for married couple i and φ measures the catch-up process on fertility decisions. A positive value of φ suggests that married couples residing in more densely populated areas delay having children and have children when they are older. This regression is estimated using the sample of nonmigrants aged 50 or younger to control for households’ dynamic location choice. This baseline model considers a linear dynamic fertility decision process. In the Online Appendix, this study additionally considers two specifications of the dynamic catch-up process on fertility decisions that include nonlinear and discrete effects of age. To quantify the extent to which congestion costs arising from population concentration discourage households’ fertility behavior, this study emphasizes that a dynamic fertility process should be considered. For example, it is inappropriate to quantify the magnitude of congestion costs simply by comparing married couples across cities at a point in time. The fact that young married couples in large cities tend to have children later in life causes spatial variation in the number of children to be overestimated. Therefore, this study proposes a method of quantifying spatial variations in the number of children per parental age cohort using the estimates of α and φ in Regression (6). Another aspect of the catch-up process is whether agglomeration affects the timing of marriage and the birth of the first child (e.g. Simon and Tamura, 2009). These agglomeration effects are estimated by the following linear regression:   Ageir,kwife=αklog(Densr(i)tAll)+γkMi+Ziϕk+X˜iδk+Dr(i)Regηk+DtYearψk+ui,k, (7) where Ageir,kwife denotes the wife’s age for married couple i at the time of marriage (k = 1) and birth of the first child (k = 2), respectively; Densr(i)tAll denotes the population density and takes the value of Densr(i)t if married couple i is aged 50 or younger and the value of Densr(i)t50 if the wife in couple i is age 50 or older; and ui,k is the error term. In this regression, the sample is not divided by the wife’s age. Parameter αk captures the congestion diseconomy effects on the timing of marriage and the birth of the first child. 3.3. Quantifying spatial variation in fertility The quantification of the spatial variation in the number of children per married couple uses the estimates of α and φ (i.e. the density elasticity of the number of children) of Regression (6). Holding other factors equal, the percentage change in the average number of children per household between two cities s and r can be estimated as:   λs−λrλr=(DenssDensr)α^+φ^×Age−1. Note that this spatial variation in the 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 have 2 children on average, 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 have 2 children on average, then households in city s on average have 1.824 children. Similarly, this study examines how long the congestion diseconomy in large cities delays marriage and the birth of the first child for married couples from Regression (7). Holding other factors equal, differences in a wife’s age between cities s and r can be estimated as:   Ages,kwife−Ager,kwife=α^klog(DenssDensr), where α^k is the estimate of the parameter in Regression (7). 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 and α^2=0.2. In this case, married couples in large cities postpone having their first child by an average of 1.66 ( ≈12×0.2×log(2)) months. 4. Data This study uses the cumulative dataset (i.e. a pooled cross section) of the JGSS, which covers the years 2000, 2001, 2002, 2005, 2006, 2008 and 2010.10 The sample is limited to married couples (i.e. unmarried persons are excluded). Table 1 presents descriptive statistics of the variables. Detailed definitions of the variables used in this study, such as population density, migration and income, are explained in the Online Appendix. The average number of children per household in the sample with wife’s age < 50 is 1.810, whereas the average number of children per household in the sample with wife’s age ≥50 is 2.204.11 Table 1 Descriptive statistics of variables for regression analysis Variables  Sample with wife’s age < 50   Sample with wife’s age ≥ 50   Obs.  Mean  S. D.  Min  Max  Obs.  Mean  S. D.  Min  Max  Number of children  2339  1.810  0.964  0  6  1995  2.204  0.865  0  8  Ideal number of children  2085  2.617  0.604  0  10  1804  2.774  0.610  0  9  Gap in number of children  2085  –0.805  0.987  –8  4  1804  – 0.579  0.978  – 7  4  Log (population density) in survey year  2339  7.431  1.077  4.646  9.628            Log (population density) at age 50            1995  7.359  1.065  4.694  9.597  Log (population density) in 1930  2339  6.732  1.257  3.374  9.492  1995  6.698  1.308  3.374  9.492  D (1 = migration)  2339  0.239  0.427  0  1  1995  0.282  0.450  0  1  D (1 = university or higher for husband)  2339  0.354  0.478  0  1  1995  0.209  0.406  0  1  D (1 = university or higher for wife)  2339  0.239  0.426  0  1  1995  0.114  0.318  0  1  Husband’s income (unit: million yen)  2339  5.510  2.823  0  27.600  1995  3.950  3.954  0  27.600  Wife’s income (unit: million yen)  2339  1.731  1.850  0  20.363  1995  1.410  1.972  0  17.130  Hours worked last week for husband (unit: 10 h)  2339  4.810  1.143  0  8.000  1995  3.350  2.110  0  8.200  Hours worked last week for wife (unit: 10 h)  2339  2.828  1.544  0  6.500  1995  2.318  1.846  0  6.500  D (1 = nonlabor force for husband)  2339  0.007  0.082  0  1  1995  0.203  0.402  0  1  D (1 = nonlabor force for wife)  2339  0.091  0.288  0  1  1995  0.258  0.437  0  1  D (1 = not healthy)  2339  0.139  0.346  0  1  1995  0.155  0.362  0  1  Old-age security index  2339  4.583  1.880  2  10  1995  4.719  2.098  2  10  D (1 = non-necessity of children in a marriage)  2339  0.432  0.495  0  1  1995  0.283  0.450  0  1  Number of siblings  2339  1.715  0.955  0  8  1995  3.225  1.575  0  15  Husband’s age  2339  42.253  7.828  20  66  1995  62.804  8.063  33  91  Wife’s age  2339  39.520  6.684  20  49  1995  60.275  7.563  51  90  Wife’s age at marriage  1034  24.653  3.351  16  45  624  23.962  3.338  16  51  Wife’s age at birth of first child  2019  26.568  3.710  16  41  1861  25.722  3.727  16  50  D (1 = university or higher for father)  2339  0.100  0.300  0  1  1995  0.044  0.204  0  1  D (1 = university or higher for mother)  2339  0.040  0.195  0  1  1995  0.006  0.077  0  1  Variables  Sample with wife’s age < 50   Sample with wife’s age ≥ 50   Obs.  Mean  S. D.  Min  Max  Obs.  Mean  S. D.  Min  Max  Number of children  2339  1.810  0.964  0  6  1995  2.204  0.865  0  8  Ideal number of children  2085  2.617  0.604  0  10  1804  2.774  0.610  0  9  Gap in number of children  2085  –0.805  0.987  –8  4  1804  – 0.579  0.978  – 7  4  Log (population density) in survey year  2339  7.431  1.077  4.646  9.628            Log (population density) at age 50            1995  7.359  1.065  4.694  9.597  Log (population density) in 1930  2339  6.732  1.257  3.374  9.492  1995  6.698  1.308  3.374  9.492  D (1 = migration)  2339  0.239  0.427  0  1  1995  0.282  0.450  0  1  D (1 = university or higher for husband)  2339  0.354  0.478  0  1  1995  0.209  0.406  0  1  D (1 = university or higher for wife)  2339  0.239  0.426  0  1  1995  0.114  0.318  0  1  Husband’s income (unit: million yen)  2339  5.510  2.823  0  27.600  1995  3.950  3.954  0  27.600  Wife’s income (unit: million yen)  2339  1.731  1.850  0  20.363  1995  1.410  1.972  0  17.130  Hours worked last week for husband (unit: 10 h)  2339  4.810  1.143  0  8.000  1995  3.350  2.110  0  8.200  Hours worked last week for wife (unit: 10 h)  2339  2.828  1.544  0  6.500  1995  2.318  1.846  0  6.500  D (1 = nonlabor force for husband)  2339  0.007  0.082  0  1  1995  0.203  0.402  0  1  D (1 = nonlabor force for wife)  2339  0.091  0.288  0  1  1995  0.258  0.437  0  1  D (1 = not healthy)  2339  0.139  0.346  0  1  1995  0.155  0.362  0  1  Old-age security index  2339  4.583  1.880  2  10  1995  4.719  2.098  2  10  D (1 = non-necessity of children in a marriage)  2339  0.432  0.495  0  1  1995  0.283  0.450  0  1  Number of siblings  2339  1.715  0.955  0  8  1995  3.225  1.575  0  15  Husband’s age  2339  42.253  7.828  20  66  1995  62.804  8.063  33  91  Wife’s age  2339  39.520  6.684  20  49  1995  60.275  7.563  51  90  Wife’s age at marriage  1034  24.653  3.351  16  45  624  23.962  3.338  16  51  Wife’s age at birth of first child  2019  26.568  3.710  16  41  1861  25.722  3.727  16  50  D (1 = university or higher for father)  2339  0.100  0.300  0  1  1995  0.044  0.204  0  1  D (1 = university or higher for mother)  2339  0.040  0.195  0  1  1995  0.006  0.077  0  1  Notes: The household who has the maximum number of children and the uppermost 1 percentile of the distribution of hours worked for husband and wife are excluded from the full sample as extreme outliers. Population density is expressed in persons/km2. Table 1 Descriptive statistics of variables for regression analysis Variables  Sample with wife’s age < 50   Sample with wife’s age ≥ 50   Obs.  Mean  S. D.  Min  Max  Obs.  Mean  S. D.  Min  Max  Number of children  2339  1.810  0.964  0  6  1995  2.204  0.865  0  8  Ideal number of children  2085  2.617  0.604  0  10  1804  2.774  0.610  0  9  Gap in number of children  2085  –0.805  0.987  –8  4  1804  – 0.579  0.978  – 7  4  Log (population density) in survey year  2339  7.431  1.077  4.646  9.628            Log (population density) at age 50            1995  7.359  1.065  4.694  9.597  Log (population density) in 1930  2339  6.732  1.257  3.374  9.492  1995  6.698  1.308  3.374  9.492  D (1 = migration)  2339  0.239  0.427  0  1  1995  0.282  0.450  0  1  D (1 = university or higher for husband)  2339  0.354  0.478  0  1  1995  0.209  0.406  0  1  D (1 = university or higher for wife)  2339  0.239  0.426  0  1  1995  0.114  0.318  0  1  Husband’s income (unit: million yen)  2339  5.510  2.823  0  27.600  1995  3.950  3.954  0  27.600  Wife’s income (unit: million yen)  2339  1.731  1.850  0  20.363  1995  1.410  1.972  0  17.130  Hours worked last week for husband (unit: 10 h)  2339  4.810  1.143  0  8.000  1995  3.350  2.110  0  8.200  Hours worked last week for wife (unit: 10 h)  2339  2.828  1.544  0  6.500  1995  2.318  1.846  0  6.500  D (1 = nonlabor force for husband)  2339  0.007  0.082  0  1  1995  0.203  0.402  0  1  D (1 = nonlabor force for wife)  2339  0.091  0.288  0  1  1995  0.258  0.437  0  1  D (1 = not healthy)  2339  0.139  0.346  0  1  1995  0.155  0.362  0  1  Old-age security index  2339  4.583  1.880  2  10  1995  4.719  2.098  2  10  D (1 = non-necessity of children in a marriage)  2339  0.432  0.495  0  1  1995  0.283  0.450  0  1  Number of siblings  2339  1.715  0.955  0  8  1995  3.225  1.575  0  15  Husband’s age  2339  42.253  7.828  20  66  1995  62.804  8.063  33  91  Wife’s age  2339  39.520  6.684  20  49  1995  60.275  7.563  51  90  Wife’s age at marriage  1034  24.653  3.351  16  45  624  23.962  3.338  16  51  Wife’s age at birth of first child  2019  26.568  3.710  16  41  1861  25.722  3.727  16  50  D (1 = university or higher for father)  2339  0.100  0.300  0  1  1995  0.044  0.204  0  1  D (1 = university or higher for mother)  2339  0.040  0.195  0  1  1995  0.006  0.077  0  1  Variables  Sample with wife’s age < 50   Sample with wife’s age ≥ 50   Obs.  Mean  S. D.  Min  Max  Obs.  Mean  S. D.  Min  Max  Number of children  2339  1.810  0.964  0  6  1995  2.204  0.865  0  8  Ideal number of children  2085  2.617  0.604  0  10  1804  2.774  0.610  0  9  Gap in number of children  2085  –0.805  0.987  –8  4  1804  – 0.579  0.978  – 7  4  Log (population density) in survey year  2339  7.431  1.077  4.646  9.628            Log (population density) at age 50            1995  7.359  1.065  4.694  9.597  Log (population density) in 1930  2339  6.732  1.257  3.374  9.492  1995  6.698  1.308  3.374  9.492  D (1 = migration)  2339  0.239  0.427  0  1  1995  0.282  0.450  0  1  D (1 = university or higher for husband)  2339  0.354  0.478  0  1  1995  0.209  0.406  0  1  D (1 = university or higher for wife)  2339  0.239  0.426  0  1  1995  0.114  0.318  0  1  Husband’s income (unit: million yen)  2339  5.510  2.823  0  27.600  1995  3.950  3.954  0  27.600  Wife’s income (unit: million yen)  2339  1.731  1.850  0  20.363  1995  1.410  1.972  0  17.130  Hours worked last week for husband (unit: 10 h)  2339  4.810  1.143  0  8.000  1995  3.350  2.110  0  8.200  Hours worked last week for wife (unit: 10 h)  2339  2.828  1.544  0  6.500  1995  2.318  1.846  0  6.500  D (1 = nonlabor force for husband)  2339  0.007  0.082  0  1  1995  0.203  0.402  0  1  D (1 = nonlabor force for wife)  2339  0.091  0.288  0  1  1995  0.258  0.437  0  1  D (1 = not healthy)  2339  0.139  0.346  0  1  1995  0.155  0.362  0  1  Old-age security index  2339  4.583  1.880  2  10  1995  4.719  2.098  2  10  D (1 = non-necessity of children in a marriage)  2339  0.432  0.495  0  1  1995  0.283  0.450  0  1  Number of siblings  2339  1.715  0.955  0  8  1995  3.225  1.575  0  15  Husband’s age  2339  42.253  7.828  20  66  1995  62.804  8.063  33  91  Wife’s age  2339  39.520  6.684  20  49  1995  60.275  7.563  51  90  Wife’s age at marriage  1034  24.653  3.351  16  45  624  23.962  3.338  16  51  Wife’s age at birth of first child  2019  26.568  3.710  16  41  1861  25.722  3.727  16  50  D (1 = university or higher for father)  2339  0.100  0.300  0  1  1995  0.044  0.204  0  1  D (1 = university or higher for mother)  2339  0.040  0.195  0  1  1995  0.006  0.077  0  1  Notes: The household who has the maximum number of children and the uppermost 1 percentile of the distribution of hours worked for husband and wife are excluded from the full sample as extreme outliers. Population density is expressed in persons/km2. Figure 3 presents differences in the numbers of children between large and small cities in the JGSS dataset. Note that the sample with wife’s age < 50 is used, and migrants are excluded from the sample. Panel (a) of Figure 3 shows that households residing in large cities have fewer children than those residing in small cities. Panel (b) of Figure 3 presents the average number of children per married couple by parental age cohort. An interesting trend is that households with ages averaging from 20–24 in more densely populated areas (exceeding the 75th percentile of population density of 4176 persons/km2) have half as many children as households in less dense areas do. The gap between the two narrows, but a slight gap remains. Figure 3 View largeDownload slide Number of children per married couple between large and small cities. Notes: Sample with wife’s age < 50 is used. Migrants are excluded from the sample. The 75th percentile of population density is calculated from the distribution in the JGSS dataset. Source: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. Figure 3 View largeDownload slide Number of children per married couple between large and small cities. Notes: Sample with wife’s age < 50 is used. Migrants are excluded from the sample. The 75th percentile of population density is calculated from the distribution in the JGSS dataset. Source: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. Figure 4 presents regional variations in the number of children per married couple in the JGSS dataset. I aggregated individual microdata for the geographical unit used in this study. Panel (a) of Figure 4 presents a similar trend to that in Figure 1. Although the JGSS sample size is quite small, it adequately captures the characteristics of the entire country. Panel (b) of Figure 4 presents the spatial variation in completed fertility. The spatial variation in completed fertility becomes small, suggesting that agglomeration affects the timing of childbearing. Figure 4 View largeDownload slide Average number of children per married couple and city size in JGSS cumulative data 2000–2010. Note: The circle size represents the sample size in each geographical unit. Source: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. Figure 4 View largeDownload slide Average number of children per married couple and city size in JGSS cumulative data 2000–2010. Note: The circle size represents the sample size in each geographical unit. Source: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. Figure 5 presents regional variations in the wife’s age at marriage and at the birth of the first child in the JGSS dataset. Panels (a) and (b) of Figure 5 present positive correlations between the wife’s age at marriage and at the birth of the first child and city size suggesting that agglomeration affects the timing of marriage and childbearing. To examine whether agglomeration indeed leads to this relationship, regression analyses are undertaken. Figure 5 View largeDownload slide Average wife’s age and city size in JGSS cumulative data 2000–2010. Note: The circle size represents the sample size in each geographical unit. Source: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. Figure 5 View largeDownload slide Average wife’s age and city size in JGSS cumulative data 2000–2010. Note: The circle size represents the sample size in each geographical unit. Source: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. To control for preference heterogeneity in the demand for children, this study makes use of three variables on social factors. The first variable relates to the motive of security in old age, which predicts that such households have more children.12 The second variable directly captures the household’s preference for children. The JGSS asks a question about households’ opinions of whether children are necessary in a marriage. A dummy variable based on this question takes the value of 1 for households that agree or somewhat agree children are unnecessary and 0 otherwise. The third variable is the number of siblings because couples that have relatively many siblings may have more children. 5. Estimation results 5.1. Agglomeration discourages the fertility behavior of young married couples Table 2 presents the baseline estimation results of Poisson regression Model (4).13 Column (1) shows the aggregate impacts of agglomeration diseconomies on the number of children. The density elasticity of the number of children is significantly negative at the 1% level and its value is –0.075. To decompose channels through which agglomeration affects the demand for children, economic and social factors are controlled for in Columns (2)–(7) of Table 2. Table 2 Poisson regression estimation results for fertility decision and city size Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50   (1)  (2)  (3)  (4)  (5)  (6)  (7)  Log (population density)  –0.074***  –0.069***  –0.061***  –0.080***  –0.082***  –0.071***  –0.067***    (0.015)  (0.015)  (0.014)  (0.015)  (0.016)  (0.016)  (0.015)  Husband’s age  0.090***  0.089***  0.092***  0.085***  0.086***  0.088***  0.080***    (0.029)  (0.028)  (0.028)  (0.028)  (0.028)  (0.028)  (0.027)  Husband’s age squared ( ×1/100)  –0.098***  –0.096***  –0.100***  –0.093***  –0.094***  –0.096***  –0.088***    (0.031)  (0.031)  (0.030)  (0.030)  (0.030)  (0.030)  (0.029)  Wife’s age  0.166***  0.167***  0.168***  0.162***  0.163***  0.166***  0.163***    (0.029)  (0.029)  (0.028)  (0.029)  (0.029)  (0.028)  (0.028)  Wife’s age squared ( ×1/100)  –0.190***  –0.192***  –0.192***  –0.184***  –0.188***  –0.192***  –0.187***    (0.034)  (0.034)  (0.033)  (0.035)  (0.035)  (0.033)  (0.033)  D (1 = migration)    –0.073**          –0.063**      (0.028)          (0.028)  D (1 = university graduate for husband)      –0.122***        –0.121***      (0.026)        (0.023)  D (1 = university graduate for wife)      –0.094***        –0.085***        (0.020)        (0.021)  Husband’s income        0.010***      0.015***          (0.003)      (0.003)  Wife’s income        –0.034***      –0.017***          (0.007)      (0.006)  Hours worked last week for husband          0.009    0.006            (0.011)    (0.010)  Hours worked last week for wife          –0.045***    –0.032***            (0.011)    (0.011)  D (1 = nonlabor force for husband)          –0.136    –0.092            (0.178)    (0.170)  D (1 = nonlabor force for wife)          –0.109**    –0.098*            (0.054)    (0.056)  D (1 = not healthy)            –0.056**  –0.064**              (0.028)  (0.028)  Old-age security motive score            0.009  0.009              (0.006)  (0.006)  D (1 = non-necessity of children)            –0.077***  –0.079***              (0.019)  (0.018)  Number of siblings            0.036***  0.025**              (0.011)  (0.011)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  2339  2339  2339  2339  2339  Log likelihood  –3331.608  –3329.873  –3318.649  –3322.692  –3324.573  –3324.556  –3300.614  AIC  6711.216  6709.745  6689.298  6697.384  6705.145  6705.111  6675.229  Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50   (1)  (2)  (3)  (4)  (5)  (6)  (7)  Log (population density)  –0.074***  –0.069***  –0.061***  –0.080***  –0.082***  –0.071***  –0.067***    (0.015)  (0.015)  (0.014)  (0.015)  (0.016)  (0.016)  (0.015)  Husband’s age  0.090***  0.089***  0.092***  0.085***  0.086***  0.088***  0.080***    (0.029)  (0.028)  (0.028)  (0.028)  (0.028)  (0.028)  (0.027)  Husband’s age squared ( ×1/100)  –0.098***  –0.096***  –0.100***  –0.093***  –0.094***  –0.096***  –0.088***    (0.031)  (0.031)  (0.030)  (0.030)  (0.030)  (0.030)  (0.029)  Wife’s age  0.166***  0.167***  0.168***  0.162***  0.163***  0.166***  0.163***    (0.029)  (0.029)  (0.028)  (0.029)  (0.029)  (0.028)  (0.028)  Wife’s age squared ( ×1/100)  –0.190***  –0.192***  –0.192***  –0.184***  –0.188***  –0.192***  –0.187***    (0.034)  (0.034)  (0.033)  (0.035)  (0.035)  (0.033)  (0.033)  D (1 = migration)    –0.073**          –0.063**      (0.028)          (0.028)  D (1 = university graduate for husband)      –0.122***        –0.121***      (0.026)        (0.023)  D (1 = university graduate for wife)      –0.094***        –0.085***        (0.020)        (0.021)  Husband’s income        0.010***      0.015***          (0.003)      (0.003)  Wife’s income        –0.034***      –0.017***          (0.007)      (0.006)  Hours worked last week for husband          0.009    0.006            (0.011)    (0.010)  Hours worked last week for wife          –0.045***    –0.032***            (0.011)    (0.011)  D (1 = nonlabor force for husband)          –0.136    –0.092            (0.178)    (0.170)  D (1 = nonlabor force for wife)          –0.109**    –0.098*            (0.054)    (0.056)  D (1 = not healthy)            –0.056**  –0.064**              (0.028)  (0.028)  Old-age security motive score            0.009  0.009              (0.006)  (0.006)  D (1 = non-necessity of children)            –0.077***  –0.079***              (0.019)  (0.018)  Number of siblings            0.036***  0.025**              (0.011)  (0.011)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  2339  2339  2339  2339  2339  Log likelihood  –3331.608  –3329.873  –3318.649  –3322.692  –3324.573  –3324.556  –3300.614  AIC  6711.216  6709.745  6689.298  6697.384  6705.145  6705.111  6675.229  Notes: AIC, Akaike’s information criterion. Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Table 2 Poisson regression estimation results for fertility decision and city size Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50   (1)  (2)  (3)  (4)  (5)  (6)  (7)  Log (population density)  –0.074***  –0.069***  –0.061***  –0.080***  –0.082***  –0.071***  –0.067***    (0.015)  (0.015)  (0.014)  (0.015)  (0.016)  (0.016)  (0.015)  Husband’s age  0.090***  0.089***  0.092***  0.085***  0.086***  0.088***  0.080***    (0.029)  (0.028)  (0.028)  (0.028)  (0.028)  (0.028)  (0.027)  Husband’s age squared ( ×1/100)  –0.098***  –0.096***  –0.100***  –0.093***  –0.094***  –0.096***  –0.088***    (0.031)  (0.031)  (0.030)  (0.030)  (0.030)  (0.030)  (0.029)  Wife’s age  0.166***  0.167***  0.168***  0.162***  0.163***  0.166***  0.163***    (0.029)  (0.029)  (0.028)  (0.029)  (0.029)  (0.028)  (0.028)  Wife’s age squared ( ×1/100)  –0.190***  –0.192***  –0.192***  –0.184***  –0.188***  –0.192***  –0.187***    (0.034)  (0.034)  (0.033)  (0.035)  (0.035)  (0.033)  (0.033)  D (1 = migration)    –0.073**          –0.063**      (0.028)          (0.028)  D (1 = university graduate for husband)      –0.122***        –0.121***      (0.026)        (0.023)  D (1 = university graduate for wife)      –0.094***        –0.085***        (0.020)        (0.021)  Husband’s income        0.010***      0.015***          (0.003)      (0.003)  Wife’s income        –0.034***      –0.017***          (0.007)      (0.006)  Hours worked last week for husband          0.009    0.006            (0.011)    (0.010)  Hours worked last week for wife          –0.045***    –0.032***            (0.011)    (0.011)  D (1 = nonlabor force for husband)          –0.136    –0.092            (0.178)    (0.170)  D (1 = nonlabor force for wife)          –0.109**    –0.098*            (0.054)    (0.056)  D (1 = not healthy)            –0.056**  –0.064**              (0.028)  (0.028)  Old-age security motive score            0.009  0.009              (0.006)  (0.006)  D (1 = non-necessity of children)            –0.077***  –0.079***              (0.019)  (0.018)  Number of siblings            0.036***  0.025**              (0.011)  (0.011)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  2339  2339  2339  2339  2339  Log likelihood  –3331.608  –3329.873  –3318.649  –3322.692  –3324.573  –3324.556  –3300.614  AIC  6711.216  6709.745  6689.298  6697.384  6705.145  6705.111  6675.229  Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50   (1)  (2)  (3)  (4)  (5)  (6)  (7)  Log (population density)  –0.074***  –0.069***  –0.061***  –0.080***  –0.082***  –0.071***  –0.067***    (0.015)  (0.015)  (0.014)  (0.015)  (0.016)  (0.016)  (0.015)  Husband’s age  0.090***  0.089***  0.092***  0.085***  0.086***  0.088***  0.080***    (0.029)  (0.028)  (0.028)  (0.028)  (0.028)  (0.028)  (0.027)  Husband’s age squared ( ×1/100)  –0.098***  –0.096***  –0.100***  –0.093***  –0.094***  –0.096***  –0.088***    (0.031)  (0.031)  (0.030)  (0.030)  (0.030)  (0.030)  (0.029)  Wife’s age  0.166***  0.167***  0.168***  0.162***  0.163***  0.166***  0.163***    (0.029)  (0.029)  (0.028)  (0.029)  (0.029)  (0.028)  (0.028)  Wife’s age squared ( ×1/100)  –0.190***  –0.192***  –0.192***  –0.184***  –0.188***  –0.192***  –0.187***    (0.034)  (0.034)  (0.033)  (0.035)  (0.035)  (0.033)  (0.033)  D (1 = migration)    –0.073**          –0.063**      (0.028)          (0.028)  D (1 = university graduate for husband)      –0.122***        –0.121***      (0.026)        (0.023)  D (1 = university graduate for wife)      –0.094***        –0.085***        (0.020)        (0.021)  Husband’s income        0.010***      0.015***          (0.003)      (0.003)  Wife’s income        –0.034***      –0.017***          (0.007)      (0.006)  Hours worked last week for husband          0.009    0.006            (0.011)    (0.010)  Hours worked last week for wife          –0.045***    –0.032***            (0.011)    (0.011)  D (1 = nonlabor force for husband)          –0.136    –0.092            (0.178)    (0.170)  D (1 = nonlabor force for wife)          –0.109**    –0.098*            (0.054)    (0.056)  D (1 = not healthy)            –0.056**  –0.064**              (0.028)  (0.028)  Old-age security motive score            0.009  0.009              (0.006)  (0.006)  D (1 = non-necessity of children)            –0.077***  –0.079***              (0.019)  (0.018)  Number of siblings            0.036***  0.025**              (0.011)  (0.011)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  2339  2339  2339  2339  2339  Log likelihood  –3331.608  –3329.873  –3318.649  –3322.692  –3324.573  –3324.556  –3300.614  AIC  6711.216  6709.745  6689.298  6697.384  6705.145  6705.111  6675.229  Notes: AIC, Akaike’s information criterion. Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. The estimation results in Table 2 show that including migration and education variables reduces the density elasticity of the number of children. After controlling for migration, the density elasticity becomes –0.069 in Column (2), whereas after controlling for university education, the density elasticity becomes –0.061 in Column (3). These results mean that migrants with university education, who tend to have fewer children, are concentrated in large cities, which leads to an overestimation of the impacts of agglomeration diseconomies. By contrast, the inclusion of incomes increases the magnitude of the coefficient on population density. These results mean that individuals with high income, who tend to have more children due to income effects, are concentrated in large cities, which leads to underestimation of the impact of agglomeration diseconomies.14 In Column (6), the inclusion of the social factor variables slightly decreases the magnitude of the effect, which may imply that the spatial sorting of preference heterogeneity is not relevant for this study. These results in Column (7) imply that, holding other factors equal, a 10-fold difference in city size on average generates spatial variation in the per-household number of children by 14.31% ( ≈10−0.067−1). Consider the 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 is 1.714. The spatial gap shows ∼286 children per 1000 households.15 Therefore, the results show that congestion costs in large cities discourage fertility behavior. An interesting finding is that husbands’ and wives’ incomes, which relate highly to city size, have significant positive and negative signs, respectively. This finding can be explained by the simple theoretical model of this study. Agglomeration economies increase income and wages, which have both positive and negative effects on the demand for children through income effects and the opportunity cost of rearing children, respectively. Concerning preference heterogeneity in the demand for children, the dummy denoting that children are unnecessary in a marriage significantly decreases the number of children at the 1% level. In addition, when either the husband or wife has more siblings, they tend to have more children. Indeed, the inclusion of these social characteristics tends to reduce the magnitude of the dummy for wife’s university education, implying that female workers with high earnings simultaneously tend to have the opinion that children are unnecessary in a marriage. These results emphasize the importance for controlling for preference heterogeneity among individuals. In addition, the migration dummy is significantly negative at the 5% level. A household 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 a reverse causality. That is, migration itself may impose substantial costs on having children, but having fewer children may enable households to easily migrate. The robustness check for self-selected migration is carried out in Section 5.5. 5.2. Completed fertility and agglomeration Table 3 presents estimation results for couples whose childbearing years have ended because the wife’s age is 50 or older. This estimation intends to examine whether congestion costs in large cities discourage completed fertility. Table 3 Poisson regression estimation results for completed fertility decision and city size Explanatory variables  Dependent variable: number of children   Sample with wife’s age ≥50   (1)  (2)  (3)  (4)  (5)  Log (population density) at age 50  –0.035***  –0.032**  –0.036***  –0.031**  –0.029**    (0.013)  (0.013)  (0.013)  (0.013)  (0.013)  D (1 = migration)    –0.033*      –0.031*      (0.017)      (0.018)  D (1 = university graduate for husband)      –0.013    –0.005        (0.025)    (0.026)  D (1 = university graduate for wife)      0.046    0.049        (0.033)    (0.031)  D (1 = not healthy)        –0.026  –0.024          (0.029)  (0.029)  Old-age security motive score        –0.000  –0.001          (0.005)  (0.005)  D (1 = non-necessity of children)        –0.088***  –0.087***          (0.020)  (0.020)  Number of siblings        0.016***  0.017**          (0.006)  (0.007)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1995  1995  1995  1995  1995  Log likelihood  –2977.043  –2976.656  –2976.691  –2972.469  –2971.705  AIC  5990.087  5991.312  5993.382  5988.939  5993.409  Explanatory variables  Dependent variable: number of children   Sample with wife’s age ≥50   (1)  (2)  (3)  (4)  (5)  Log (population density) at age 50  –0.035***  –0.032**  –0.036***  –0.031**  –0.029**    (0.013)  (0.013)  (0.013)  (0.013)  (0.013)  D (1 = migration)    –0.033*      –0.031*      (0.017)      (0.018)  D (1 = university graduate for husband)      –0.013    –0.005        (0.025)    (0.026)  D (1 = university graduate for wife)      0.046    0.049        (0.033)    (0.031)  D (1 = not healthy)        –0.026  –0.024          (0.029)  (0.029)  Old-age security motive score        –0.000  –0.001          (0.005)  (0.005)  D (1 = non-necessity of children)        –0.088***  –0.087***          (0.020)  (0.020)  Number of siblings        0.016***  0.017**          (0.006)  (0.007)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1995  1995  1995  1995  1995  Log likelihood  –2977.043  –2976.656  –2976.691  –2972.469  –2971.705  AIC  5990.087  5991.312  5993.382  5988.939  5993.409  Notes: AIC, Akaike’s information criterion. Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Table 3 Poisson regression estimation results for completed fertility decision and city size Explanatory variables  Dependent variable: number of children   Sample with wife’s age ≥50   (1)  (2)  (3)  (4)  (5)  Log (population density) at age 50  –0.035***  –0.032**  –0.036***  –0.031**  –0.029**    (0.013)  (0.013)  (0.013)  (0.013)  (0.013)  D (1 = migration)    –0.033*      –0.031*      (0.017)      (0.018)  D (1 = university graduate for husband)      –0.013    –0.005        (0.025)    (0.026)  D (1 = university graduate for wife)      0.046    0.049        (0.033)    (0.031)  D (1 = not healthy)        –0.026  –0.024          (0.029)  (0.029)  Old-age security motive score        –0.000  –0.001          (0.005)  (0.005)  D (1 = non-necessity of children)        –0.088***  –0.087***          (0.020)  (0.020)  Number of siblings        0.016***  0.017**          (0.006)  (0.007)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1995  1995  1995  1995  1995  Log likelihood  –2977.043  –2976.656  –2976.691  –2972.469  –2971.705  AIC  5990.087  5991.312  5993.382  5988.939  5993.409  Explanatory variables  Dependent variable: number of children   Sample with wife’s age ≥50   (1)  (2)  (3)  (4)  (5)  Log (population density) at age 50  –0.035***  –0.032**  –0.036***  –0.031**  –0.029**    (0.013)  (0.013)  (0.013)  (0.013)  (0.013)  D (1 = migration)    –0.033*      –0.031*      (0.017)      (0.018)  D (1 = university graduate for husband)      –0.013    –0.005        (0.025)    (0.026)  D (1 = university graduate for wife)      0.046    0.049        (0.033)    (0.031)  D (1 = not healthy)        –0.026  –0.024          (0.029)  (0.029)  Old-age security motive score        –0.000  –0.001          (0.005)  (0.005)  D (1 = non-necessity of children)        –0.088***  –0.087***          (0.020)  (0.020)  Number of siblings        0.016***  0.017**          (0.006)  (0.007)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1995  1995  1995  1995  1995  Log likelihood  –2977.043  –2976.656  –2976.691  –2972.469  –2971.705  AIC  5990.087  5991.312  5993.382  5988.939  5993.409  Notes: AIC, Akaike’s information criterion. Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Column (1) of Table 3 shows the impact of wide-ranging aggregate congestion costs arising from agglomeration on completed fertility. The density elasticity of the number of children is –0.035, whereas the density elasticity for the sample with wife’s age < 50 is –0.074, as shown in Table 2. This relationship remains negative after controlling for economic and social household characteristics and migration status, but the density elasticity declines to –0.029 in Column (5). As studied in Yamauchi (2016), the estimation results suggest that the costs associated with agglomeration discourage completed fertility and, holding other factors equal, a 10-fold difference in city size on average generates a spatial variation of 6.40% ( ≈10−0.029−1) in number of children per household. Consider a case where the population of city s is 10 times larger than that of city r. If the average number of children in city r is 2, the average in city s becomes 1.872. The spatial gap shows ∼128 children per 1000 households.16 More importantly, the density elasticity of the number of children decreases between Tables 2 and 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 the average number of children decreases as couples age. Another interesting finding is that the effect of higher education on completed fertility is not significant at the 10% level. Combined with the estimation results in Table 2, this finding suggests that higher education discourages childbearing among young married couples but does not affect completed fertility. These results also imply that, holding other factors equal, university graduates postpone having children. Concerning preference heterogeneity in the demand for children, the dummy variable denoting that children are unnecessary in a marriage has a significant negative effect on completed fertility. In addition, the number of siblings exerts a significantly positive effect on completed fertility. Seeking security in old age shows no significant relationship with completed fertility. The migration dummy also shows negative effects on completed fertility, but it is significant at the 10% level. A robustness check for self-selected migration is carried out in Section 5.5. 5.3. Catch-up process of fertility in more densely populated areas Table 4 presents the estimation results of Poisson regression Model (6), which considers the dynamic process of fertility behavior across different city sizes. This study quantifies spatial variations in average number of children by parents’ ages estimating the cross-term of population density and wife’s age. Note that sample used in Table 4 does not include migrants. Table 4 Poisson regression estimation results for dynamic fertility decision and city size with linear effects of age Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50, nonmigrants   (1)  (2)  (3)  (4)  (5)  (6)  Log (population density)  –0.245***  –0.244***  –0.233***  –0.246***  –0.247***  –0.237***    (0.079)  (0.080)  (0.079)  (0.076)  (0.078)  (0.076)  Log (population density) × wife’s age  0.004**  0.005**  0.004**  0.004**  0.005**  0.004**    (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  Husband’s age  0.070**  0.071**  0.065**  0.067**  0.066**  0.059**    (0.029)  (0.029)  (0.029)  (0.029)  (0.029)  (0.028)  Husband’s age squared ( ×1/100)  –0.074**  –0.074**  –0.069**  –0.070**  –0.070**  –0.062**    (0.032)  (0.031)  (0.032)  (0.031)  (0.032)  (0.031)  Wife’s age  0.124***  0.125***  0.124***  0.125***  0.125***  0.127***    (0.035)  (0.034)  (0.035)  (0.034)  (0.034)  (0.034)  Wife’s age squared ( ×1/100)  –0.186***  –0.189***  –0.180***  –0.186***  –0.190***  –0.188***    (0.041)  (0.041)  (0.041)  (0.041)  (0.040)  (0.040)  D (1 = university graduate for husband)    –0.111***        –0.116***    (0.025)        (0.024)  D (1 = university graduate for wife)    –0.108***        –0.096***    (0.027)        (0.029)  Husband’s income      0.010***      0.015***        (0.004)      (0.004)  Wife’s income      –0.031***      –0.014**        (0.008)      (0.007)  Hours worked last week for husband        0.010    0.006          (0.011)    (0.012)  Hours worked last week for wife        –0.038***    –0.025**          (0.013)    (0.012)  D (1 = nonlabor force for husband)        0.025    0.048          (0.145)    (0.144)  D (1 = nonlabor force for wife)        –0.057    –0.046          (0.057)    (0.055)  D (1 = not healthy)          –0.081***  –0.094***            (0.025)  (0.025)  Old-age security motive score          0.005  0.007            (0.007)  (0.006)  D (1 = non-necessity of children)          –0.076***  –0.077***            (0.025)  (0.024)  Number of siblings          0.044***  0.034***            (0.011)  (0.012)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  1779  1779  1779  1779  1779  1779  Log likelihood  –2536.763  –2527.288  –2531.063  –2532.827  –2530.365  –2515.435  AIC  5123.527  5108.576  5116.127  5123.654  5118.729  5104.871  Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50, nonmigrants   (1)  (2)  (3)  (4)  (5)  (6)  Log (population density)  –0.245***  –0.244***  –0.233***  –0.246***  –0.247***  –0.237***    (0.079)  (0.080)  (0.079)  (0.076)  (0.078)  (0.076)  Log (population density) × wife’s age  0.004**  0.005**  0.004**  0.004**  0.005**  0.004**    (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  Husband’s age  0.070**  0.071**  0.065**  0.067**  0.066**  0.059**    (0.029)  (0.029)  (0.029)  (0.029)  (0.029)  (0.028)  Husband’s age squared ( ×1/100)  –0.074**  –0.074**  –0.069**  –0.070**  –0.070**  –0.062**    (0.032)  (0.031)  (0.032)  (0.031)  (0.032)  (0.031)  Wife’s age  0.124***  0.125***  0.124***  0.125***  0.125***  0.127***    (0.035)  (0.034)  (0.035)  (0.034)  (0.034)  (0.034)  Wife’s age squared ( ×1/100)  –0.186***  –0.189***  –0.180***  –0.186***  –0.190***  –0.188***    (0.041)  (0.041)  (0.041)  (0.041)  (0.040)  (0.040)  D (1 = university graduate for husband)    –0.111***        –0.116***    (0.025)        (0.024)  D (1 = university graduate for wife)    –0.108***        –0.096***    (0.027)        (0.029)  Husband’s income      0.010***      0.015***        (0.004)      (0.004)  Wife’s income      –0.031***      –0.014**        (0.008)      (0.007)  Hours worked last week for husband        0.010    0.006          (0.011)    (0.012)  Hours worked last week for wife        –0.038***    –0.025**          (0.013)    (0.012)  D (1 = nonlabor force for husband)        0.025    0.048          (0.145)    (0.144)  D (1 = nonlabor force for wife)        –0.057    –0.046          (0.057)    (0.055)  D (1 = not healthy)          –0.081***  –0.094***            (0.025)  (0.025)  Old-age security motive score          0.005  0.007            (0.007)  (0.006)  D (1 = non-necessity of children)          –0.076***  –0.077***            (0.025)  (0.024)  Number of siblings          0.044***  0.034***            (0.011)  (0.012)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  1779  1779  1779  1779  1779  1779  Log likelihood  –2536.763  –2527.288  –2531.063  –2532.827  –2530.365  –2515.435  AIC  5123.527  5108.576  5116.127  5123.654  5118.729  5104.871  Notes: AIC, Akaike’s information criterion. Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Table 4 Poisson regression estimation results for dynamic fertility decision and city size with linear effects of age Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50, nonmigrants   (1)  (2)  (3)  (4)  (5)  (6)  Log (population density)  –0.245***  –0.244***  –0.233***  –0.246***  –0.247***  –0.237***    (0.079)  (0.080)  (0.079)  (0.076)  (0.078)  (0.076)  Log (population density) × wife’s age  0.004**  0.005**  0.004**  0.004**  0.005**  0.004**    (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  Husband’s age  0.070**  0.071**  0.065**  0.067**  0.066**  0.059**    (0.029)  (0.029)  (0.029)  (0.029)  (0.029)  (0.028)  Husband’s age squared ( ×1/100)  –0.074**  –0.074**  –0.069**  –0.070**  –0.070**  –0.062**    (0.032)  (0.031)  (0.032)  (0.031)  (0.032)  (0.031)  Wife’s age  0.124***  0.125***  0.124***  0.125***  0.125***  0.127***    (0.035)  (0.034)  (0.035)  (0.034)  (0.034)  (0.034)  Wife’s age squared ( ×1/100)  –0.186***  –0.189***  –0.180***  –0.186***  –0.190***  –0.188***    (0.041)  (0.041)  (0.041)  (0.041)  (0.040)  (0.040)  D (1 = university graduate for husband)    –0.111***        –0.116***    (0.025)        (0.024)  D (1 = university graduate for wife)    –0.108***        –0.096***    (0.027)        (0.029)  Husband’s income      0.010***      0.015***        (0.004)      (0.004)  Wife’s income      –0.031***      –0.014**        (0.008)      (0.007)  Hours worked last week for husband        0.010    0.006          (0.011)    (0.012)  Hours worked last week for wife        –0.038***    –0.025**          (0.013)    (0.012)  D (1 = nonlabor force for husband)        0.025    0.048          (0.145)    (0.144)  D (1 = nonlabor force for wife)        –0.057    –0.046          (0.057)    (0.055)  D (1 = not healthy)          –0.081***  –0.094***            (0.025)  (0.025)  Old-age security motive score          0.005  0.007            (0.007)  (0.006)  D (1 = non-necessity of children)          –0.076***  –0.077***            (0.025)  (0.024)  Number of siblings          0.044***  0.034***            (0.011)  (0.012)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  1779  1779  1779  1779  1779  1779  Log likelihood  –2536.763  –2527.288  –2531.063  –2532.827  –2530.365  –2515.435  AIC  5123.527  5108.576  5116.127  5123.654  5118.729  5104.871  Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50, nonmigrants   (1)  (2)  (3)  (4)  (5)  (6)  Log (population density)  –0.245***  –0.244***  –0.233***  –0.246***  –0.247***  –0.237***    (0.079)  (0.080)  (0.079)  (0.076)  (0.078)  (0.076)  Log (population density) × wife’s age  0.004**  0.005**  0.004**  0.004**  0.005**  0.004**    (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  Husband’s age  0.070**  0.071**  0.065**  0.067**  0.066**  0.059**    (0.029)  (0.029)  (0.029)  (0.029)  (0.029)  (0.028)  Husband’s age squared ( ×1/100)  –0.074**  –0.074**  –0.069**  –0.070**  –0.070**  –0.062**    (0.032)  (0.031)  (0.032)  (0.031)  (0.032)  (0.031)  Wife’s age  0.124***  0.125***  0.124***  0.125***  0.125***  0.127***    (0.035)  (0.034)  (0.035)  (0.034)  (0.034)  (0.034)  Wife’s age squared ( ×1/100)  –0.186***  –0.189***  –0.180***  –0.186***  –0.190***  –0.188***    (0.041)  (0.041)  (0.041)  (0.041)  (0.040)  (0.040)  D (1 = university graduate for husband)    –0.111***        –0.116***    (0.025)        (0.024)  D (1 = university graduate for wife)    –0.108***        –0.096***    (0.027)        (0.029)  Husband’s income      0.010***      0.015***        (0.004)      (0.004)  Wife’s income      –0.031***      –0.014**        (0.008)      (0.007)  Hours worked last week for husband        0.010    0.006          (0.011)    (0.012)  Hours worked last week for wife        –0.038***    –0.025**          (0.013)    (0.012)  D (1 = nonlabor force for husband)        0.025    0.048          (0.145)    (0.144)  D (1 = nonlabor force for wife)        –0.057    –0.046          (0.057)    (0.055)  D (1 = not healthy)          –0.081***  –0.094***            (0.025)  (0.025)  Old-age security motive score          0.005  0.007            (0.007)  (0.006)  D (1 = non-necessity of children)          –0.076***  –0.077***            (0.025)  (0.024)  Number of siblings          0.044***  0.034***            (0.011)  (0.012)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  1779  1779  1779  1779  1779  1779  Log likelihood  –2536.763  –2527.288  –2531.063  –2532.827  –2530.365  –2515.435  AIC  5123.527  5108.576  5116.127  5123.654  5118.729  5104.871  Notes: AIC, Akaike’s information criterion. Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Overall, the Poisson estimation results in Columns (1)–(6) show that the estimated coefficients for the cross-term of population density and wife’s age are significantly positive, which means that young married couples in large cities postpone having children. The results are robust for additional controls for economic and social factors. In Column (6), the coefficient on population density captures the effects of the congestion costs in large cities on the demand for children. An important finding is that the gap in the number of children between large and small cities is large early in life, but it shrinks gradually as couples age. Figure 6 illustrates estimated spatial variations in the average number of children using the estimates in Column (6) of Table 4. Panel (a) of Figure 6 shows the density elasticity of the number of children at different ages. This density elasticity is large for couples in their 20s (e.g. –0.113 at age 29) but declines to –0.027 at age 49. Figure 6 View largeDownload slide Percentage change in the average number of children by city size simulated from Poisson estimates. Notes: The density elasticity of the number of children in Panel (a) is calculated as α^+φ^×Age using the estimates in Column (6) of Table 4. The percentage change in the average number of children in Panel (b) is calculated as [λs(θ^)−λr(θ^)]/λr(θ^)=Ratiosrα^+φ^×Age−1, where Ratiosr is the population density ratio between cities s and r, and households’ characteristics are assumed to be identical. This numerical simulation uses the estimates θ^ in Column (6) of Table 4. The Online Appendix provides two specifications of the dynamic catch-up process on fertility decisions that include nonlinear and discrete effects of age. Figure 6 View largeDownload slide Percentage change in the average number of children by city size simulated from Poisson estimates. Notes: The density elasticity of the number of children in Panel (a) is calculated as α^+φ^×Age using the estimates in Column (6) of Table 4. The percentage change in the average number of children in Panel (b) is calculated as [λs(θ^)−λr(θ^)]/λr(θ^)=Ratiosrα^+φ^×Age−1, where Ratiosr is the population density ratio between cities s and r, and households’ characteristics are assumed to be identical. This numerical simulation uses the estimates θ^ in Column (6) of Table 4. The Online Appendix provides two specifications of the dynamic catch-up process on fertility decisions that include nonlinear and discrete effects of age. Panel (b) of Figure 6 quantifies spatial variations in number of children by wife’s age, showing what percentage change in the average number of children is generated by the difference in city size, holding other variables equal. Among couples age 30, the estimated percentage change in the number of children between one city and a city with 10 times more people is –22.13% ( ≈10−0.237+0.004×30−1). If households in the baseline city have 1.5 children at age 30 on average, households in a city with 10 times more people have 1.168 children on average. The spatial gap shows ∼332 (=1500 − 1168) children per 1000 households. However, the estimated percentage change in the number of children between those cities for couples at age 49 is –6.07% ( ≈10−0.237+0.004×49−1). 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 is 2.066. The spatial gap shows ∼34 (=2200 − 2066) children per 1000 households.17 Although slight spatial variation in the average number of children between large and small cities remains, the important finding is that couples residing in larger cities have children relatively late in life, which reduces the spatial gap in the number of children around age 50. Thus far, the estimation results suggest that congestion costs in large cities discourage younger couples from bearing children, but the gap in completed fertility shrinks between large and small cities as couples age. To offer supportive evidence on this finding, this study examines whether agglomeration affects the timing of childbirth in the next subsection. 5.4. Agglomeration delays the birth of the first child Table 5 presents estimation results concerning how agglomeration affects the wife’s age at marriage. Importantly, in Column (3), the inclusion of dummies for university education decreases the coefficient on population density, which means that the spatial sorting of highly educated people, who tend to have children later in life, leads to an upward bias when the impact of congestion costs on fertility behavior is estimated. Table 5 Wife’s ages at marriage, city size and migration Explanatory variables  Dependent variable: wife’s age at marriage   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.130  0.119  0.077  0.125  0.079    (0.116)  (0.116)  (0.120)  (0.118)  (0.118)  D (1 = migration)    0.115      –0.021      (0.181)      (0.179)  D (1 = university graduate for husband)      0.709***    0.699***        (0.175)    (0.178)  D (1 = university graduate for wife)      1.478***    1.467***        (0.274)    (0.268)  D (1 = not healthy)        –0.245  –0.158          (0.215)  (0.201)  Old-age security motive score        –0.041  –0.041          (0.037)  (0.037)  D (1 = non-necessity of children)        –0.091  –0.139          (0.166)  (0.170)  Number of siblings        –0.104**  –0.032          (0.045)  (0.041)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1658  1658  1658  1658  1658  Adjusted R2  0.045  0.044  0.078  0.046  0.076  Explanatory variables  Dependent variable: wife’s age at marriage   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.130  0.119  0.077  0.125  0.079    (0.116)  (0.116)  (0.120)  (0.118)  (0.118)  D (1 = migration)    0.115      –0.021      (0.181)      (0.179)  D (1 = university graduate for husband)      0.709***    0.699***        (0.175)    (0.178)  D (1 = university graduate for wife)      1.478***    1.467***        (0.274)    (0.268)  D (1 = not healthy)        –0.245  –0.158          (0.215)  (0.201)  Old-age security motive score        –0.041  –0.041          (0.037)  (0.037)  D (1 = non-necessity of children)        –0.091  –0.139          (0.166)  (0.170)  Number of siblings        –0.104**  –0.032          (0.045)  (0.041)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1658  1658  1658  1658  1658  Adjusted R2  0.045  0.044  0.078  0.046  0.076  Notes: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Table 5 Wife’s ages at marriage, city size and migration Explanatory variables  Dependent variable: wife’s age at marriage   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.130  0.119  0.077  0.125  0.079    (0.116)  (0.116)  (0.120)  (0.118)  (0.118)  D (1 = migration)    0.115      –0.021      (0.181)      (0.179)  D (1 = university graduate for husband)      0.709***    0.699***        (0.175)    (0.178)  D (1 = university graduate for wife)      1.478***    1.467***        (0.274)    (0.268)  D (1 = not healthy)        –0.245  –0.158          (0.215)  (0.201)  Old-age security motive score        –0.041  –0.041          (0.037)  (0.037)  D (1 = non-necessity of children)        –0.091  –0.139          (0.166)  (0.170)  Number of siblings        –0.104**  –0.032          (0.045)  (0.041)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1658  1658  1658  1658  1658  Adjusted R2  0.045  0.044  0.078  0.046  0.076  Explanatory variables  Dependent variable: wife’s age at marriage   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.130  0.119  0.077  0.125  0.079    (0.116)  (0.116)  (0.120)  (0.118)  (0.118)  D (1 = migration)    0.115      –0.021      (0.181)      (0.179)  D (1 = university graduate for husband)      0.709***    0.699***        (0.175)    (0.178)  D (1 = university graduate for wife)      1.478***    1.467***        (0.274)    (0.268)  D (1 = not healthy)        –0.245  –0.158          (0.215)  (0.201)  Old-age security motive score        –0.041  –0.041          (0.037)  (0.037)  D (1 = non-necessity of children)        –0.091  –0.139          (0.166)  (0.170)  Number of siblings        –0.104**  –0.032          (0.045)  (0.041)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1658  1658  1658  1658  1658  Adjusted R2  0.045  0.044  0.078  0.046  0.076  Notes: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Although the estimated coefficients on population density are positive in Columns (1)–(5), they are not significant at even the 10% level. It is not evident that agglomeration discourages the timing of marriage. Higher education, specifically for females, markedly delays age at marriage at the 1% level. In the baseline estimation, Column (5) shows that couples in which both spouses have a university education marry about 26 months later than those in which both have a nonuniversity education. Table 6 provides evidence on whether congestion costs in large cities delay the birth of the first child. As noted earlier, the inclusion of dummies for university education decreases the coefficient on population density in Column (3). However, the coefficient on population density remains significant. In the baseline estimation, Column (5) shows that couples in which both spouses have a university education bear their first child about 22 months later than those in which both have a nonuniversity education. Table 6 Wife’s ages at birth of first child, city size and migration Explanatory variables  Dependent variable: wife’s ages at birth of first child   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.290***  0.257***  0.205***  0.281***  0.180**    (0.072)  (0.074)  (0.071)  (0.071)  (0.073)  D (1 = migration)    0.356**      0.242      (0.168)      (0.168)  D (1 = university graduate for husband)      0.844***    0.813***        (0.152)    (0.154)  D (1 = university graduate for wife)      1.090***    1.086***        (0.190)    (0.190)  D (1 = not healthy)        0.034  0.110          (0.189)  (0.190)  Old-age security motive score        –0.030  –0.037          (0.031)  (0.030)  D (1 = non-necessity of children)        0.006  –0.009          (0.129)  (0.128)  Number of siblings        –0.121**  –0.045          (0.054)  (0.054)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  3880  3880  3880  3880  3880  Adjusted R2  0.044  0.045  0.072  0.045  0.072  Explanatory variables  Dependent variable: wife’s ages at birth of first child   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.290***  0.257***  0.205***  0.281***  0.180**    (0.072)  (0.074)  (0.071)  (0.071)  (0.073)  D (1 = migration)    0.356**      0.242      (0.168)      (0.168)  D (1 = university graduate for husband)      0.844***    0.813***        (0.152)    (0.154)  D (1 = university graduate for wife)      1.090***    1.086***        (0.190)    (0.190)  D (1 = not healthy)        0.034  0.110          (0.189)  (0.190)  Old-age security motive score        –0.030  –0.037          (0.031)  (0.030)  D (1 = non-necessity of children)        0.006  –0.009          (0.129)  (0.128)  Number of siblings        –0.121**  –0.045          (0.054)  (0.054)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  3880  3880  3880  3880  3880  Adjusted R2  0.044  0.045  0.072  0.045  0.072  Notes: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Table 6 Wife’s ages at birth of first child, city size and migration Explanatory variables  Dependent variable: wife’s ages at birth of first child   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.290***  0.257***  0.205***  0.281***  0.180**    (0.072)  (0.074)  (0.071)  (0.071)  (0.073)  D (1 = migration)    0.356**      0.242      (0.168)      (0.168)  D (1 = university graduate for husband)      0.844***    0.813***        (0.152)    (0.154)  D (1 = university graduate for wife)      1.090***    1.086***        (0.190)    (0.190)  D (1 = not healthy)        0.034  0.110          (0.189)  (0.190)  Old-age security motive score        –0.030  –0.037          (0.031)  (0.030)  D (1 = non-necessity of children)        0.006  –0.009          (0.129)  (0.128)  Number of siblings        –0.121**  –0.045          (0.054)  (0.054)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  3880  3880  3880  3880  3880  Adjusted R2  0.044  0.045  0.072  0.045  0.072  Explanatory variables  Dependent variable: wife’s ages at birth of first child   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.290***  0.257***  0.205***  0.281***  0.180**    (0.072)  (0.074)  (0.071)  (0.071)  (0.073)  D (1 = migration)    0.356**      0.242      (0.168)      (0.168)  D (1 = university graduate for husband)      0.844***    0.813***        (0.152)    (0.154)  D (1 = university graduate for wife)      1.090***    1.086***        (0.190)    (0.190)  D (1 = not healthy)        0.034  0.110          (0.189)  (0.190)  Old-age security motive score        –0.030  –0.037          (0.031)  (0.030)  D (1 = non-necessity of children)        0.006  –0.009          (0.129)  (0.128)  Number of siblings        –0.121**  –0.045          (0.054)  (0.054)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  3880  3880  3880  3880  3880  Adjusted R2  0.044  0.045  0.072  0.045  0.072  Notes: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Unlike the estimation results for marriage, the estimated coefficients for population density are significantly positive at the 5% level in Columns (1)–(5). In Column (5), the density semi-elasticity of the number of children is 0.180. Using this value, the quantification shows that, holding other variables equal, couples residing in a city that is 10 times more populous delay childbirth by an average of ∼5 ( ≈0.180×log(10)) months.18 In sum, congestion costs strongly defer 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 couple’s age, although a statistically significant slight gap remains. 5.5. Robustness check for self-selected migration As discussed in Section 2, the endogenous migration choices of individuals with preference heterogeneity in the demand for children lead to biases in two ways. First, the magnitude of the effect of agglomeration on the number of children is overestimated when individuals with weak preferences for the quantity of children and with strong preferences for the quality of children migrate into large cities. This bias derives from the spatial sorting of individuals with preference heterogeneity. Second, the coefficient on the migration dummy γ is biased due to this self-selection. This study applies a classical approach to the selectivity bias correction (Heckman, 1979; Maddala, 1986), which is known as an endogenous binary-variable model.19 This study estimates the following regression model:   yir=αlog(Densr(i)t)+γMi+Xiβ+X˜iδ+Dr(i)Regη+DtYearψ+uir,Mi*=Wiπ+X˜iδ+Dr(i)Pref15η+DtYearψ+virMi=1 if Mi*>0, and 0 otherwise, where it is assumed that the error terms uir and vir follow bivariate normal distribution with mean 0 and covariance matrix   (σu2ρσuρσu1). The determinants of migration choice include a vector of household’s characteristics Wi (dummies for whether parents of the married couples are university graduates and the variables included in Zi) and a vector of prefecture dummies at age 15 Dr(i)Pref15, and vir is an error term. Note that a linear rather than a Poisson model is estimated. Therefore, the parameter α is not directly comparable with the corresponding parameter in the Poisson estimates. In the same manner, the wife’s age at marriage and at the birth of the first child is also estimated by this framework. Table 7 presents the estimation results of the endogenous binary-variable model. More importantly, the coefficients on the population density essentially do not change even after controlling for self-selected migration. However, the coefficients on migration drastically change after controlling for self-selection. Comparing Columns (3) and (4) of Table 7, completed fertility is highly affected by the migration experience, implying that migration costs have larger impacts on the demand for children in the long-term. Table 7 Estimation results for fertility decision and self-selected migration choice Explanatory variables  Dependent variable: number of children   Dependent variable: wife’s age at marriage   Dependent variable: wife’s age at birth of first child   Sample with wife’s age < 50   Sample with wife’s age ≥50   Full sample   Full sample   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  Log (population density)  –0.113***  –0.115***  –0.062**  –0.062**  0.079  0.012  0.180**  0.170**    (0.024)  (0.024)  (0.028)  (0.028)  (0.118)  (0.123)  (0.073)  (0.075)  D (1 = migration)  –0.116**  0.171  –0.068*  –0.823***  –0.021  3.970***  0.242  4.830***    (0.049)  (0.213)  (0.038)  (0.230)  (0.179)  (0.606)  (0.168)  (0.373)  D (1 = university graduate for husband)  –0.207***  –0.239***  –0.011  0.119  0.699***  0.210  0.813***  0.208    (0.033)  (0.046)  (0.057)  (0.081)  (0.178)  (0.237)  (0.154)  (0.190)  D (1 = university graduate for wife)  –0.140***  –0.154***  0.107  0.076  1.467***  1.197***  1.086***  0.998***    (0.036)  (0.035)  (0.070)  (0.068)  (0.268)  (0.292)  (0.190)  (0.180)  Husband’s income  0.031***  0.030***                (0.007)  (0.007)              Wife’s income  –0.030***  –0.030***                (0.010)  (0.010)              Hours worked last week for husband  0.013  0.013                (0.018)  (0.018)              Hours worked last week for wife  –0.054***  –0.054***                (0.019)  (0.019)              D (1 = nonlabor force for husband)  –0.069  –0.076                (0.244)  (0.246)              D (1 = nonlabor force for wife)  –0.188*  –0.187**                (0.097)  (0.095)              D (1 = not healthy)  –0.117**  –0.126**  –0.053  –0.074  –0.158  –0.186  0.110  0.088    (0.051)  (0.051)  (0.064)  (0.065)  (0.201)  (0.267)  (0.190)  (0.238)  Old-age security motive score  0.014  0.017  –0.001  –0.003  –0.041  0.015  –0.037  –0.026    (0.011)  (0.011)  (0.011)  (0.011)  (0.037)  (0.045)  (0.030)  (0.033)  D (1 = non-necessity of children)  –0.142***  –0.157***  –0.186***  –0.125***  –0.139  –0.355**  –0.009  –0.280*    (0.031)  (0.034)  (0.042)  (0.043)  (0.170)  (0.174)  (0.128)  (0.146)  Number of siblings  0.051**  0.046**  0.038**  0.043**  –0.032  –0.102*  –0.045  –0.088    (0.022)  (0.022)  (0.015)  (0.018)  (0.041)  (0.055)  (0.054)  (0.062)  Age, cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Control for endogenous migration choice  No  Yes  No  Yes  No  Yes  No  Yes  Explanatory variables  Dependent variable: number of children   Dependent variable: wife’s age at marriage   Dependent variable: wife’s age at birth of first child   Sample with wife’s age < 50   Sample with wife’s age ≥50   Full sample   Full sample   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  Log (population density)  –0.113***  –0.115***  –0.062**  –0.062**  0.079  0.012  0.180**  0.170**    (0.024)  (0.024)  (0.028)  (0.028)  (0.118)  (0.123)  (0.073)  (0.075)  D (1 = migration)  –0.116**  0.171  –0.068*  –0.823***  –0.021  3.970***  0.242  4.830***    (0.049)  (0.213)  (0.038)  (0.230)  (0.179)  (0.606)  (0.168)  (0.373)  D (1 = university graduate for husband)  –0.207***  –0.239***  –0.011  0.119  0.699***  0.210  0.813***  0.208    (0.033)  (0.046)  (0.057)  (0.081)  (0.178)  (0.237)  (0.154)  (0.190)  D (1 = university graduate for wife)  –0.140***  –0.154***  0.107  0.076  1.467***  1.197***  1.086***  0.998***    (0.036)  (0.035)  (0.070)  (0.068)  (0.268)  (0.292)  (0.190)  (0.180)  Husband’s income  0.031***  0.030***                (0.007)  (0.007)              Wife’s income  –0.030***  –0.030***                (0.010)  (0.010)              Hours worked last week for husband  0.013  0.013                (0.018)  (0.018)              Hours worked last week for wife  –0.054***  –0.054***                (0.019)  (0.019)              D (1 = nonlabor force for husband)  –0.069  –0.076                (0.244)  (0.246)              D (1 = nonlabor force for wife)  –0.188*  –0.187**                (0.097)  (0.095)              D (1 = not healthy)  –0.117**  –0.126**  –0.053  –0.074  –0.158  –0.186  0.110  0.088    (0.051)  (0.051)  (0.064)  (0.065)  (0.201)  (0.267)  (0.190)  (0.238)  Old-age security motive score  0.014  0.017  –0.001  –0.003  –0.041  0.015  –0.037  –0.026    (0.011)  (0.011)  (0.011)  (0.011)  (0.037)  (0.045)  (0.030)  (0.033)  D (1 = non-necessity of children)  –0.142***  –0.157***  –0.186***  –0.125***  –0.139  –0.355**  –0.009  –0.280*    (0.031)  (0.034)  (0.042)  (0.043)  (0.170)  (0.174)  (0.128)  (0.146)  Number of siblings  0.051**  0.046**  0.038**  0.043**  –0.032  –0.102*  –0.045  –0.088    (0.022)  (0.022)  (0.015)  (0.018)  (0.041)  (0.055)  (0.054)  (0.062)  Age, cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Control for endogenous migration choice  No  Yes  No  Yes  No  Yes  No  Yes  Explanatory variables  Treatment variable: D (1 = migration)   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  D (1 = university graduate for father)    0.225**    0.241**    0.135    0.280***      (0.107)    (0.098)    (0.112)    (0.070)  D (1 = university graduate for mother)    –0.109    –0.014    –0.146    –0.006      (0.150)    (0.331)    (0.269)    (0.135)  D (1 = university graduate for husband)    0.350***    0.454***    0.375***    0.374***      (0.066)    (0.101)    (0.081)    (0.062)  D (1 = university graduate for wife)    0.149*    –0.137    0.130    0.020      (0.081)    (0.085)    (0.113)    (0.056)  D (1 = not healthy)    0.129    –0.139    –0.003    –0.002      (0.094)    (0.102)    (0.103)    (0.075)  Old-age security motive score    –0.026*    –0.007    –0.040***    –0.007      (0.014)    (0.015)    (0.014)    (0.010)  D (1 = non-necessity of children)    0.151***    0.241***    0.154***    0.154***      (0.057)    (0.065)    (0.058)    (0.045)  Number of siblings    0.053    0.033    0.063**    0.026      (0.038)    (0.023)    (0.027)    (0.020)  Husband’s age    –0.011    –0.122    0.040    0.028      (0.049)    (0.080)    (0.046)    (0.031)  Husband’s age squared ( ×1/100)    0.033    0.082    –0.091**    –0.060**      (0.057)    (0.064)    (0.043)    (0.028)  Wife’s age    0.062    0.219**    0.140**    0.039      (0.063)    (0.091)    (0.063)    (0.035)  Wife’s age squared ( ×1/100)    –0.062    –0.163**    –0.050    0.012      (0.081)    (0.074)    (0.053)    (0.033)  ρ    –0.209    0.523***    –0.674***    –0.690***      (0.158)    (0.127)    (0.080)    (0.048)  σu    0.831***    0.909***    3.624***    4.080***      (0.016)    (0.049)    (0.179)    (0.113)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  1995  1995  1658  1658  3880  3880  Adjusted R2  0.260    0.031    0.076    0.072    Explanatory variables  Treatment variable: D (1 = migration)   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  D (1 = university graduate for father)    0.225**    0.241**    0.135    0.280***      (0.107)    (0.098)    (0.112)    (0.070)  D (1 = university graduate for mother)    –0.109    –0.014    –0.146    –0.006      (0.150)    (0.331)    (0.269)    (0.135)  D (1 = university graduate for husband)    0.350***    0.454***    0.375***    0.374***      (0.066)    (0.101)    (0.081)    (0.062)  D (1 = university graduate for wife)    0.149*    –0.137    0.130    0.020      (0.081)    (0.085)    (0.113)    (0.056)  D (1 = not healthy)    0.129    –0.139    –0.003    –0.002      (0.094)    (0.102)    (0.103)    (0.075)  Old-age security motive score    –0.026*    –0.007    –0.040***    –0.007      (0.014)    (0.015)    (0.014)    (0.010)  D (1 = non-necessity of children)    0.151***    0.241***    0.154***    0.154***      (0.057)    (0.065)    (0.058)    (0.045)  Number of siblings    0.053    0.033    0.063**    0.026      (0.038)    (0.023)    (0.027)    (0.020)  Husband’s age    –0.011    –0.122    0.040    0.028      (0.049)    (0.080)    (0.046)    (0.031)  Husband’s age squared ( ×1/100)    0.033    0.082    –0.091**    –0.060**      (0.057)    (0.064)    (0.043)    (0.028)  Wife’s age    0.062    0.219**    0.140**    0.039      (0.063)    (0.091)    (0.063)    (0.035)  Wife’s age squared ( ×1/100)    –0.062    –0.163**    –0.050    0.012      (0.081)    (0.074)    (0.053)    (0.033)  ρ    –0.209    0.523***    –0.674***    –0.690***      (0.158)    (0.127)    (0.080)    (0.048)  σu    0.831***    0.909***    3.624***    4.080***      (0.016)    (0.049)    (0.179)    (0.113)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  1995  1995  1658  1658  3880  3880  Adjusted R2  0.260    0.031    0.076    0.072    Notes: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Table 7 Estimation results for fertility decision and self-selected migration choice Explanatory variables  Dependent variable: number of children   Dependent variable: wife’s age at marriage   Dependent variable: wife’s age at birth of first child   Sample with wife’s age < 50   Sample with wife’s age ≥50   Full sample   Full sample   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  Log (population density)  –0.113***  –0.115***  –0.062**  –0.062**  0.079  0.012  0.180**  0.170**    (0.024)  (0.024)  (0.028)  (0.028)  (0.118)  (0.123)  (0.073)  (0.075)  D (1 = migration)  –0.116**  0.171  –0.068*  –0.823***  –0.021  3.970***  0.242  4.830***    (0.049)  (0.213)  (0.038)  (0.230)  (0.179)  (0.606)  (0.168)  (0.373)  D (1 = university graduate for husband)  –0.207***  –0.239***  –0.011  0.119  0.699***  0.210  0.813***  0.208    (0.033)  (0.046)  (0.057)  (0.081)  (0.178)  (0.237)  (0.154)  (0.190)  D (1 = university graduate for wife)  –0.140***  –0.154***  0.107  0.076  1.467***  1.197***  1.086***  0.998***    (0.036)  (0.035)  (0.070)  (0.068)  (0.268)  (0.292)  (0.190)  (0.180)  Husband’s income  0.031***  0.030***                (0.007)  (0.007)              Wife’s income  –0.030***  –0.030***                (0.010)  (0.010)              Hours worked last week for husband  0.013  0.013                (0.018)  (0.018)              Hours worked last week for wife  –0.054***  –0.054***                (0.019)  (0.019)              D (1 = nonlabor force for husband)  –0.069  –0.076                (0.244)  (0.246)              D (1 = nonlabor force for wife)  –0.188*  –0.187**                (0.097)  (0.095)              D (1 = not healthy)  –0.117**  –0.126**  –0.053  –0.074  –0.158  –0.186  0.110  0.088    (0.051)  (0.051)  (0.064)  (0.065)  (0.201)  (0.267)  (0.190)  (0.238)  Old-age security motive score  0.014  0.017  –0.001  –0.003  –0.041  0.015  –0.037  –0.026    (0.011)  (0.011)  (0.011)  (0.011)  (0.037)  (0.045)  (0.030)  (0.033)  D (1 = non-necessity of children)  –0.142***  –0.157***  –0.186***  –0.125***  –0.139  –0.355**  –0.009  –0.280*    (0.031)  (0.034)  (0.042)  (0.043)  (0.170)  (0.174)  (0.128)  (0.146)  Number of siblings  0.051**  0.046**  0.038**  0.043**  –0.032  –0.102*  –0.045  –0.088    (0.022)  (0.022)  (0.015)  (0.018)  (0.041)  (0.055)  (0.054)  (0.062)  Age, cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Control for endogenous migration choice  No  Yes  No  Yes  No  Yes  No  Yes  Explanatory variables  Dependent variable: number of children   Dependent variable: wife’s age at marriage   Dependent variable: wife’s age at birth of first child   Sample with wife’s age < 50   Sample with wife’s age ≥50   Full sample   Full sample   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  Log (population density)  –0.113***  –0.115***  –0.062**  –0.062**  0.079  0.012  0.180**  0.170**    (0.024)  (0.024)  (0.028)  (0.028)  (0.118)  (0.123)  (0.073)  (0.075)  D (1 = migration)  –0.116**  0.171  –0.068*  –0.823***  –0.021  3.970***  0.242  4.830***    (0.049)  (0.213)  (0.038)  (0.230)  (0.179)  (0.606)  (0.168)  (0.373)  D (1 = university graduate for husband)  –0.207***  –0.239***  –0.011  0.119  0.699***  0.210  0.813***  0.208    (0.033)  (0.046)  (0.057)  (0.081)  (0.178)  (0.237)  (0.154)  (0.190)  D (1 = university graduate for wife)  –0.140***  –0.154***  0.107  0.076  1.467***  1.197***  1.086***  0.998***    (0.036)  (0.035)  (0.070)  (0.068)  (0.268)  (0.292)  (0.190)  (0.180)  Husband’s income  0.031***  0.030***                (0.007)  (0.007)              Wife’s income  –0.030***  –0.030***                (0.010)  (0.010)              Hours worked last week for husband  0.013  0.013                (0.018)  (0.018)              Hours worked last week for wife  –0.054***  –0.054***                (0.019)  (0.019)              D (1 = nonlabor force for husband)  –0.069  –0.076                (0.244)  (0.246)              D (1 = nonlabor force for wife)  –0.188*  –0.187**                (0.097)  (0.095)              D (1 = not healthy)  –0.117**  –0.126**  –0.053  –0.074  –0.158  –0.186  0.110  0.088    (0.051)  (0.051)  (0.064)  (0.065)  (0.201)  (0.267)  (0.190)  (0.238)  Old-age security motive score  0.014  0.017  –0.001  –0.003  –0.041  0.015  –0.037  –0.026    (0.011)  (0.011)  (0.011)  (0.011)  (0.037)  (0.045)  (0.030)  (0.033)  D (1 = non-necessity of children)  –0.142***  –0.157***  –0.186***  –0.125***  –0.139  –0.355**  –0.009  –0.280*    (0.031)  (0.034)  (0.042)  (0.043)  (0.170)  (0.174)  (0.128)  (0.146)  Number of siblings  0.051**  0.046**  0.038**  0.043**  –0.032  –0.102*  –0.045  –0.088    (0.022)  (0.022)  (0.015)  (0.018)  (0.041)  (0.055)  (0.054)  (0.062)  Age, cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Control for endogenous migration choice  No  Yes  No  Yes  No  Yes  No  Yes  Explanatory variables  Treatment variable: D (1 = migration)   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  D (1 = university graduate for father)    0.225**    0.241**    0.135    0.280***      (0.107)    (0.098)    (0.112)    (0.070)  D (1 = university graduate for mother)    –0.109    –0.014    –0.146    –0.006      (0.150)    (0.331)    (0.269)    (0.135)  D (1 = university graduate for husband)    0.350***    0.454***    0.375***    0.374***      (0.066)    (0.101)    (0.081)    (0.062)  D (1 = university graduate for wife)    0.149*    –0.137    0.130    0.020      (0.081)    (0.085)    (0.113)    (0.056)  D (1 = not healthy)    0.129    –0.139    –0.003    –0.002      (0.094)    (0.102)    (0.103)    (0.075)  Old-age security motive score    –0.026*    –0.007    –0.040***    –0.007      (0.014)    (0.015)    (0.014)    (0.010)  D (1 = non-necessity of children)    0.151***    0.241***    0.154***    0.154***      (0.057)    (0.065)    (0.058)    (0.045)  Number of siblings    0.053    0.033    0.063**    0.026      (0.038)    (0.023)    (0.027)    (0.020)  Husband’s age    –0.011    –0.122    0.040    0.028      (0.049)    (0.080)    (0.046)    (0.031)  Husband’s age squared ( ×1/100)    0.033    0.082    –0.091**    –0.060**      (0.057)    (0.064)    (0.043)    (0.028)  Wife’s age    0.062    0.219**    0.140**    0.039      (0.063)    (0.091)    (0.063)    (0.035)  Wife’s age squared ( ×1/100)    –0.062    –0.163**    –0.050    0.012      (0.081)    (0.074)    (0.053)    (0.033)  ρ    –0.209    0.523***    –0.674***    –0.690***      (0.158)    (0.127)    (0.080)    (0.048)  σu    0.831***    0.909***    3.624***    4.080***      (0.016)    (0.049)    (0.179)    (0.113)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  1995  1995  1658  1658  3880  3880  Adjusted R2  0.260    0.031    0.076    0.072    Explanatory variables  Treatment variable: D (1 = migration)   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  D (1 = university graduate for father)    0.225**    0.241**    0.135    0.280***      (0.107)    (0.098)    (0.112)    (0.070)  D (1 = university graduate for mother)    –0.109    –0.014    –0.146    –0.006      (0.150)    (0.331)    (0.269)    (0.135)  D (1 = university graduate for husband)    0.350***    0.454***    0.375***    0.374***      (0.066)    (0.101)    (0.081)    (0.062)  D (1 = university graduate for wife)    0.149*    –0.137    0.130    0.020      (0.081)    (0.085)    (0.113)    (0.056)  D (1 = not healthy)    0.129    –0.139    –0.003    –0.002      (0.094)    (0.102)    (0.103)    (0.075)  Old-age security motive score    –0.026*    –0.007    –0.040***    –0.007      (0.014)    (0.015)    (0.014)    (0.010)  D (1 = non-necessity of children)    0.151***    0.241***    0.154***    0.154***      (0.057)    (0.065)    (0.058)    (0.045)  Number of siblings    0.053    0.033    0.063**    0.026      (0.038)    (0.023)    (0.027)    (0.020)  Husband’s age    –0.011    –0.122    0.040    0.028      (0.049)    (0.080)    (0.046)    (0.031)  Husband’s age squared ( ×1/100)    0.033    0.082    –0.091**    –0.060**      (0.057)    (0.064)    (0.043)    (0.028)  Wife’s age    0.062    0.219**    0.140**    0.039      (0.063)    (0.091)    (0.063)    (0.035)  Wife’s age squared ( ×1/100)    –0.062    –0.163**    –0.050    0.012      (0.081)    (0.074)    (0.053)    (0.033)  ρ    –0.209    0.523***    –0.674***    –0.690***      (0.158)    (0.127)    (0.080)    (0.048)  σu    0.831***    0.909***    3.624***    4.080***      (0.016)    (0.049)    (0.179)    (0.113)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  1995  1995  1658  1658  3880  3880  Adjusted R2  0.260    0.031    0.076    0.072    Notes: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. In Columns (5)–(8) of Table 7, this robustness check is applied to estimate whether congestion costs in large cities delay marriage and the timing of the birth of the first child, and this study finds that migration costs greatly delay marriage and the birth of the first child. Interestingly, the self-selection model reveals new channels on fertility behavior. Highly educated men tend to migrate, which delays marriage and the birth of the first child. On the contrary, highly educated women directly delay marriage and the birth of the first child regardless of migration costs. In addition, the dummy variable for the non-necessity of children in marriage increases the migration probability, which delays marriage and the birth of the first child. 6. Conclusion This study has examined how agglomeration economies and diseconomies affect married couples’ decisions to bear children at different life stages. By employing a Japanese social survey dataset that inquiries into households’ fertility decisions, this study has been able to control for economic factors alongside preference heterogeneity in the demand for children. In addition, this study has proposed a method to quantify spatial variations in the average number of children born to households per parental age cohort. This study has found that, although congestion costs in large cities significantly discourage couples’ fertility decisions, the magnitude declines as couples age: in the baseline quantification, holding other factors equal, a 10-hold difference in city size generates a spatial variation of –22.13% in the average number of children among couples at age 30 and a variation of –6.07% among married couples at age 49, suggesting that young married couples in larger cities bear children later in life. The results show that congestion costs in large cities delay the birth of the first child by an average of about 5 months among couples living in cities that are 10 times larger than the baseline cities. Despite the acknowledged economic benefits of agglomeration economies (e.g. Combes and Gobillon, 2015), my findings present the important conclusion that agglomeration hampers fertility rates through higher congestion costs. In short, agglomeration-oriented growth policies may accelerate the graying of the population that policymakers struggle to reverse. Policymakers in graying societies need to set effective policies to support couples considering differences in their dynamic fertility behaviors across cities. This study has some limitations. Although the empirical results emphasize the importance of different dynamic fertility behaviors across cities, theoretical studies including this study have not been explored sufficiently in this literature. A dynamic theory that includes space, such as Goto and Minamimura (2015), will be required when considering the conditions of effective fertility policies. This study focuses on married couples, but the decision to marry affects 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. Furthermore, self-selected migration also needs to be studied using a large-sized panel dataset with information on migration history. More densely populated areas are likely to attract single people who will work long-term and will displace married couples with children because of the high cost of living. Households’ endogenous location choices will feature prominently in spatial variations in fertility rates. Distinguishing congestion diseconomy from self-selected migration is an important topic, and clarifying these mechanisms remains for future research. Supplementary material Supplementary data for this paper are available at Journal of Economic Geography online. Footnotes 1 Another explanation for the negative relationship between TFR and city size is the spatial sorting of high-skilled people, who earn higher wages in larger cities. Maruyama and Yamamoto (2010) also provide insightful views on endogenous fertility decisions focusing on the variety expansion effects in large cities. In this literature, Becker (1960) develops the economic analysis of fertility. As Becker and Lewis (1973) explain, the interaction between the quantity and quality of children is important in economic models of fertility. Willis (1973) extends the fertility model to incorporate the opportunity costs of rearing children versus earning wages from working. See Becker (1992), Browning (1992) and Hotz et al. (1997) for details of fertility analysis. 2 Large cities attract high-skilled workers, who tend to have fewer children. Therefore, the negative relationship between TFR and city size may not be explained by ex post effects of agglomeration, such as high opportunity costs of rearing children and congestion costs. This spatial sorting can be viewed as an ex ante effect of agglomeration. 3 There are other existing studies related to this article. Dekle (1990) finds that an increase in the husband’s income tends to increase completed fertility, whereas an increase in women’s real earnings tends to decrease it. His finding is consistent with mine. Koike (2009) shows that rural-to-urban migrants have fewer children than those who stay in urban or rural areas. In the existing literature, some of them discuss city size effects on the number of children, although these studies generally use dummies of region or city size (e.g. Dekle, 1990; Sasai, 2007; Koike, 2009; Yamauchi, 2016). One exception is Kitamura and Miyazaki (2005), who discuss potential sources that generate a negative correlation between TFR and population density using regional data. However, their main focus is on the relationship between marriage experience and childbearing. Unlike the traditional approach, this study uses a continuous variable for city size, specifically population density. 4 This study constructs a simple model based on the Cobb–Douglas utility function. Despite some strong assumptions that the Cobb–Douglas utility function imposes (e.g. there is no cross price elasticity of demand), a specific functional form allows for a more intuitive understanding of the theoretical results. In particular, the Cobb–Douglas specification allows for discussion of the mechanism of spatial sorting in terms of preference heterogeneity in the utility function. 5 This type of simple formulation can be found in Sato (2007). By contrast, Aiura and Sato (2014) consider land/housing consumption in the utility function. The high land/housing price plays a similar role in the congestion costs of agglomeration, but consumers can simultaneously reduce their land/housing consumption. This simple formulation, like that of Sato (2007), omits the latter channel. 6 In addition, an interesting theoretical prediction is that an increase in the wife’s wage rate reduces the number of children per household when Ir(nr)−cr(nr)>0 and simultaneously increases expenditures toward the quality of children. In other words, a shift from quantity to quality occurs in the demand for children. 7 A limitation of this theoretical model is that the dynamic process of fertility behavior is not explicitly considered. This study empirically addresses this issue. 8 Although the sample size becomes small, I examine how the strong preferences for the quality of children affect the demand for children in the Online Appendix. In turn, this study cannot examine how agglomeration affects the demand for the quality of children due to data limitations. 9 For migrants, I calculate the population densities of cities where couples in which the wife is 50 or older lived during the survey year. 10 This study discarded the JGSS 2003 dataset because it omits questions about the number of siblings. Its surveyed population consists of men and women ages 20–89 as of 1 September of the particular survey year, and the survey subjects are selected by a stratified two-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. This study constructs regional variables based on three groups of cities in each prefecture by taking the averages of the corresponding municipalities. The sample sizes of valid response vary from 2023 (in 2005) to 5003 (in 2010). Detailed information about the JGSS sampling design is available from the website (URL: http://jgss.daishodai.ac.jp/english/index.html). 11 Heterogeneity in having children across generations exists between couples with ages over and under 50. Importantly, the number of siblings captures the completed fertility of an individual’s parents. In Table 1, the average number of siblings for people younger than 50 is 1.715, whereas that for individuals older than 50 is 3.225. This study controls for these generation heterogeneities using cohort dummies. 12 For example, city dwellers might hold different opinions about parenthood than rural residents or the desire for security during old age may motivate having children, particularly in rural areas (Nugent and Gillaspy, 1983; Nugent, 1985; Rendall and Bahchieva, 1998). 13 IV Poisson estimation results are provided in the Online Appendix. In some situations, a negative binominal model may be more appropriate than a Poisson model. As shown in Figure 3, the mode of the number of children is 2, and thus, the number of children per married couple is not bounded below by 0. In fact, the Poisson and negative binominal estimation results are almost identical. 14 In this case, the husband’s income effects are larger than those of the wife’s opportunity costs of rearing children. In the Online Appendix, I show the regression results in which the husband’s income and the wife’s income are included separately. 15 Here is another numerical example. Holding other factors equal, doubling the difference in city size on average generates spatial variation in the per-household number of children by 4.54% ( ≈2−0.067−1). 16 Holding other factors equal, doubling the difference in city size on average generates spatial variation in the number of children per household by 1.97% ( ≈2−0.029−1). 17 Here is another numerical example. Among couples age 30, the estimated percentage change in the number of children between one city and a city with twice as many people is –7.25% ( ≈2−0.237+0.004×30−1). However, among couples age 49, the estimated percentage change in the number of children between those cities is –1.87% ( ≈2−0.237+0.004×49−1). 18 Here is another numerical example. Holding other factors equal, couples residing in a city that is twice as populous delay childbirth by an average of 2 ( ≈0.181×log(2)) months. The detailed numerical simulation results are provided in the Online Appendix. 19 The method proposed by Dahl (2002) may be appropriate to address the selectivity issue when individuals face multiple choices. However, data limitations of the JGSS (i.e. a small sample for interregional migration flows) make the gravity estimation of migration flows difficult. Greene (2012, Ch. 19.6.1) provides a detailed explanation for an endogenous binary-variable model. Acknowledgements I am greatly indebted to two anonymous reviewers, 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 in the RIETI Luncheon Seminar, the Urban Economic Workshop at Kyoto University, the 28th annual meeting of the ARSC, the RIETI DP Seminar, the RIETI-TIER-KIET Workshop, the 62nd Annual North American Meetings of the Regional Science Association International and 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 and Mayumi Kobayashi for their generous research support. 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( 1979) Sample selection bias as a specification error. Econometrica , 47: 153– 161. Google Scholar CrossRef Search ADS   Hotz V. J., Klerman J. A., Willis R. J. ( 1997) The economics of fertility in developed countries. In Rosenzweig M. R., Stark and O. (eds) Handbook of Population and Family Economics , vol. 1A, chapter 7, pp. 275– 347. Amsterdam: Elsevier. Google Scholar CrossRef Search ADS   Kitamura Y., Miyazaki T. ( 2005) Regional gap in marriage experience and fertility: an empirical survey. Hi-Stat Discussion Paper series No. d05-124 (in Japanese). Koike S. ( 2009) On the relation of migration and fertility behavior: focusing on the migrants to metropolitan areas before first marriage. Journal of Population Problems (Jinko Mondai Kenkyu) , 65: 3– 20 (in Japanese). Krugman P. ( 2014) Four observations on secular stagnation. In Teulings C., Baldwin R. (eds) Secular Stagnation: Facts, Causes, and Cures , chapter 4, pp. 61– 68. London: Centre for Economic Policy Research Press. 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This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Economic Geography Oxford University Press

Does agglomeration discourage fertility? Evidence from the Japanese General Social Survey 2000–2010

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Abstract

Abstract This study employs Japanese household-level data to quantify the extent to which congestion diseconomy in large cities affects married couples’ fertility behavior. The theoretical model of this study emphasizes the importance of controlling for preference heterogeneity in the demand for children. The baseline quantification shows that, all else equal, a 10-fold difference in city size generates a spatial variation of −22.13% in the average number of children born to couples aged 30 and a spatial variation of −6.07% at age 49. The narrowing of the gap suggests that the young married couples in larger cities delay childbearing. 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. Glaeser and Maré, 2001; Glaeser and Resseger, 2010; Combes et al., 2012; Combes and Gobillon, 2015; de la Roca and Puga, 2017). Although economists and policymakers consider the economics of agglomeration when designing growth policies, less attention is devoted to the diseconomies brought about by agglomeration. This study aims to shed light on how benefits and congestion costs arising from agglomeration affect socioeconomic behavior. In most developed counties, demographic issues are central to the current policy agendas. These counties have experienced rapid declines in total fertility rates (TFR) with economic growth, and raising fertility rates has become a policy priority in several countries. For example, France, Germany, the UK and the USA have exhibited sharp declines in their TFRs since the 1960s, as have Italy and Japan after the 1970s. Although recent TFRs have remained at ∼2 in France, the UK and the USA, they are less in Germany, Italy and Japan (∼1.4). The low fertility rate has led to acceleration in the aging of the population. Since an unbalanced demographic structure distorts social security systems, governments seek effective policies to recover fertility rates (e.g. Grant et al., 2004). In addition, Krugman (2014) points out that slow population growth precedes reduced demand for new investment and may contribute to secular stagnation. This study attempts to theoretically and empirically clarify how agglomeration discourages fertility behavior. In particular, this study emphasizes spatial rather than temporal views of national fertility. The theoretical model of this study clarifies possible channels through which both agglomeration economies and diseconomies affect the demand for children. For example, Panels (a) and (b) of Figure 1 illustrate fertility rates and population density for Japanese municipalities, respectively. They clearly exhibit a negative relationship, as shown in Panel (c). Figure 1 View largeDownload slide Geographical distribution of total fertility rate and population density. Notes: 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. Source: Created by author based on Vital Statistics by Health Center and Municipality in 2008–2012 and 2010 Population Census. Figure 1 View largeDownload slide Geographical distribution of total fertility rate and population density. Notes: 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. Source: Created by author based on Vital Statistics by Health Center and Municipality in 2008–2012 and 2010 Population Census. There are many possible factors that could explain this negative relationship. For example, Sato (2007) constructs a theoretical model, in which an agglomerated region attracts workers, intensifying the population density and wage rates while reducing fertility rates through agglomeration diseconomies. As empirically studied by Schultz (1986), Sato and Yamamoto (2005), Aiura and Sato (2014), Morita and Yamamoto (2014) and Goto and Minamimura (2015), theoretically, examine the mechanics through which rising real wages in more densely populated areas increase the opportunity cost of childrearing while attracting workers, further elevating the population density and the opportunity cost. This circularity engenders lower fertility rates in more densely populated areas.1 Although these theoretical studies clarify possible channels through which agglomeration affects the demand for children, it remains unclear how agglomeration affects married couples’ decisions to bear children at different ages. In particular, dynamic aspects of fertility behavior across cities are omitted in the existing literature. Figure 2 presents geographical distributions of fertility rates by age cohort and shows regional heterogeneity among age groups. The fertility rates among couples aged 35–39 are relatively high in more densely populated areas, especially in Greater Tokyo and Osaka, although they are lower among couples aged 25–29. The data depicted in Figure 2 imply that individuals residing in large cities postpone parenthood. Figure 2 View largeDownload slide Fertility rate by age group (births per 1000 women). Note: Prefectures are categorized into six quantiles. Source: Created by author based on Specified Report of Vital Statistics in FY2010. Figure 2 View largeDownload slide Fertility rate by age group (births per 1000 women). Note: Prefectures are categorized into six quantiles. Source: Created by author based on Specified Report of Vital Statistics in FY2010. Using household-level microdata, this study aims to quantify the extent to which congestion costs in large cities discourage married couples from bearing children per parental age cohort. As explained in the theoretical model, this study emphasizes that preference heterogeneity in the demand for children leads to the bias when researchers estimate the ex post effect of agglomeration on the demand for children. For example, the spatial sorting of individuals with weak preferences for the demand for children is a possible source of bias.2 To control for preference heterogeneity and self-selected migration, this study employs the Japanese General Social Survey (JGSS) dataset. This study advances the economic geography literature by offering new evidence concerning different patterns of childbearing between large and small cities. Controlling for economic and social factors, this study finds that congestion costs in large cities discourage fertility among married couples, with the magnitude of this effect shrinking as couple’s age. The baseline estimates reveal that, all else equal, a 10-fold increase in population density (in general, the difference between central cities in Japanese rural prefectures and metropolitan areas in Tokyo) reduces fertility by 22% for couples age 30, but by only 6% for couples age 49. Further analyses show that young married couples in large cities postpone having their first child by an average of 5 months in the case of a 10-fold increase in population density. Concerning existing studies in Japan, Sasai (2007) finds that the regional gap in completed fertility shrinks after controlling for social and economic factors, and mentions a possibility that married couples have children later in life. Therefore, my study contributes to the literature by providing supportive evidence for this aspect. In addition, Yamauchi (2016) points out that completed fertility in the Tokyo Metropolitan Area is still lower than that in other areas. Note that my study is consistent with findings in both Sasai (2007) and Yamauchi (2016). Using a more general quantitative analysis by population density, this study reveals that married couples in large cities have children later in life, which decreases the regional gap in completed fertility. However, a slight gap in completed fertility exists.3 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 the birth of the first child and the 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 the effects of housing prices on fertility on homeowners and renters differ owing to differences in the importance of housing’s wealth and price effects. By contrast, this study does not specify each factor of congestions, such as housing and land. This study emphasizes that housing and land are not the only factors that delay the timing of childbearing. For example, high uncertainty of accessibility to nursery schools is another factor, and this factor is highly correlated with city size in Japan. High educational costs in large cities also affect the timing of childbearing. Married couples may wait to have their first child until they have saved enough money. There are also numerous potential costs in large cities that researchers cannot observe directly. Therefore, this study attempts to capture wide-ranging aggregate congestion costs arising from agglomeration by population density. The remainder of this article is organized as follows. Section 2 explains a theoretical model. Section 3 describes the empirical framework. Section 4 presents the dataset. Section 5 discusses the estimation results and a robustness check. Section 6 presents the conclusions. 2. Theoretical explanation This study aims to quantify the extent to which congestion costs arising from agglomeration discourage fertility behavior. Using a simple theoretical model, this study clarifies possible channels through which both agglomeration economies and diseconomies affect the demand for children. Following Becker (1992), Willis (1973) and Sato (2007), this study describes households’ fertility decisions, in which both the number and quality (e.g. the education level) of children are assumed. For simplicity, this study employs a Cobb–Douglas utility function in which all goods are normal, as follows:4  u(xr,yr,qr)=xr1−μ−ξyrμqrξ, 0<μ+ξ<1, 0<μ<1, 0<ξ<1, where xr, yr and qr represent consumption of a composite good, the number of children and the quality per child, respectively. This study assumes that each household is endowed with one unit of time allocated between working and child-rearing. Households must spend a quantity of time byr, where b is a positive constant tied to the time requirement of rearing one child. Thus, the budget constraint is given as follows:5  pxr(nr)xr+pqr(nr)qryr=Ir(nr)+wr(nr)(1−byr)−cr(nr), where nr is the city size variable (e.g. the population density or population size) in region r, pxr(nr) is the price of composite goods in region r, pqr(nr) is the price related with the quality of children, Ir(nr) is the income of a full-time worker in the household (e.g. the husband’s income or the income of a household member who has little time for childrearing) in region r, wr(nr) is the wage rate for a household member who takes care of children (e.g. the wife’s wage) in region r, wr(nr)(1−byr) is the wife’s income and cr(nr) is the congestion cost arising from agglomeration in region r. It is assumed that prices, income, wages and congestion costs depend on the city size. In the budget constraint, bwr(nr)+pqr(nr)qr denotes the marginal cost of rearing one child, in which bwr(nr) captures the opportunity cost of rearing a child relative to working (i.e. the loss of earnings). Importantly, an increase in the wife’s wage rate wr(nr) leads to higher opportunity costs of rearing a child. In addition, agglomeration economies and diseconomies are assumed as follows:   dpxr(nr)dnr⋛0, dpqr(nr)dnr>0, dIr(nr)dnr>0, dwr(nr)dnr>0, and dcr(nr)dnr>0, (1) where the price index, pxr(nr), may increase in nr, whereas if xr also includes differentiated goods, pxr(nr) may decrease in nr (e.g. Ottaviano et al., 2002; Handbury and Weinstein, 2015). As discussed in the Online Appendix, the price related with the quality of children, pqr(nr), might be higher in large cities. As studies in urban economics have established, income and wage rates in more densely populated regions tend to be higher (e.g. Combes and Gobillon, 2015). The congestion costs of agglomeration cr(nr) (e.g. commuting) increase in nr. Households’ utility maximization yields respective demand functions for consumption goods, children and the quality of children, as follows:   xr(Ir(nr),wr(nr),cr(nr),pxr(nr))=(1−μ−ξ)Ir(nr)+wr(nr)−cr(nr)pxr(nr), yr(Ir(nr),wr(nr),cr(nr))=(μ−ξ)Ir(nr)+wr(nr)−cr(nr)bwr(nr), qr(wr(nr),pqr(nr))=ξμ−ξbwr(nr)pqr(nr), (2) where μ−ξ>0 and Ir(nr)+wr(nr)−cr(nr)>0 are assumed to satisfy positive demands. The comparative statics regarding the demand for children yr yield the following relationships:   ∂yr∂Ir(nr)>0, ∂yr∂wr(nr)⋚0 if Ir(nr)−cr(nr)⋛0, and ∂yr∂cr(nr)<0, (3) which clarify that an increase in the husband’s income Ir(nr) raises the demand for children per household. An increase in the wife’s wage wr(nr) has both positive and negative effects depending on the husband’s income and congestion costs. When Ir(nr)−cr(nr)>0, which may hold in many cases, an increase in the wife’s wage reduces the demand for children through the high opportunity costs of rearing children. An increase in the congestion costs of agglomeration cr(nr) reduces the demand for children.6 To connect the theoretical predictions with the empirical analysis, this study discusses these key channels through which agglomeration economies and diseconomies affect the demand for children. Matching the agglomeration economies in Equation (1) with the comparative statics in Equation (3), I find that agglomeration economies have both positive and negative effects on the number of children through income effects and the high opportunity costs of rearing children. By contrast, agglomeration diseconomies have negative effects on the number of children through high congestion costs. In addition, it is important to discuss conditions regarding the total effects of agglomeration on the demand for children based on dyr/dnr. See the Online Appendix for the details of the comparative statics for total effects of agglomeration on demand for children. Another key prediction is that preference heterogeneity in parameters μ and ξ affects the spatial distribution of the number of children. From the demand functions in Equation (2), the following relationships can be derived:   dyrdμ>0, dqrdμ<0, dyrdξ<0, and dqrdξ>0, which mean (i) that consumers with strong preferences for the quantity of children have more children and decrease expenditures on their quality and (ii) that consumers with strong preference for the quality of children have fewer children and increase expenditures on their quality. Importantly, this preference heterogeneity leads to a bias in the empirical analysis when researchers estimate the ex post effects of agglomeration on the demand for children. For example, suppose that consumers with weak preferences for the quantity of children tend to migrate into large cities because the large variety of goods and services available in large cities increases these consumers’ utility compared with having children. This relationship can be written as μs<μr when ns > nr, which generates the negative correlation between the number of children and city size. Therefore, in the empirical analysis, it is important to control for consumers’ preference heterogeneity and their endogenous migration choice. Although the theoretical model uncovers how agglomeration affects fertility behavior in terms of its channels, the total effects of agglomeration on the demand for children become highly complicated. In the empirical analysis, this study uncovers how additional controls for economic and social factors change the aggregate impacts of agglomeration.7 3. Empirical framework 3.1. Estimating 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 TFR). A standard approach is to linearly regress the number of children on population density and other control variables. However, an empirical issue is that the dependent variable takes a discrete value. In that case, a Poisson regression is more appropriate. Therefore, the regression model to be estimated is given by   Pr(Yir=yir)=exp(−λir(θ))(λir(θ))yiryir!, yir=0,1,2,…,λir(θ)≡exp(αlog(Densr(i)t)+γMi+Xiβ+X˜iδ+Dr(i)Regη+DtYearψ), (4) where yir is the number of children in household i residing in region r; Densr(i) is the population density of region r where 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 of 1 if either spouse in couple i has emigrated and 0 otherwise; Xi is a vector of variables denoting household characteristics (age, gender, cohort dummies, employment status, health condition, education, years of working experience, and the husband’s and wife’s incomes), X˜i is a vector of variables for household social characteristics that affect fertility decisions; DrReg is a vector of regional dummies; DtYear is a vector of year dummies; and θ is a vector of parameters (α,γ,β′,δ′,η′,ψ′)′. Thus, the parameter vector that maximizes the log-likelihood function ℓ(y,θ) is estimated as follows:   ℓ(y,θ)=∑i=1N(−λir(θ)+yirlog(λir(θ))−log(yir!)), where N is the number of observations. 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. This study quantifies, holding other factors constant, the extent to which differences in city size affect the number of children per married couple.8 The regression includes customarily unobservable household characteristics X˜i. The use of a social survey dataset mitigates estimation bias arising from spatial sorting driven by heterogeneity in households’ preference. Migration influences the decisions to bear children through its higher financial and nonfinancial costs. For example, nonmigrants residing near their parents have advantages in rearing children. In addition, large cities offer numerous job opportunities and may attract people who are more intent on careers than parenthood. Thus, migrants are expected to have fewer children than nonmigrants. Furthermore, it needs to be considered that this migration choice is endogenously determined. The next question is whether agglomeration affects completed fertility. Focusing on married couples for which the wife’s age is 50 or older (i.e. the outer age for childbearing), I estimate the Poisson regression model as follows:   λir(θ)≡exp(αlog(Densr(i)t50)+γMi+Ziϕ+X˜iδ+Dr(i)Regη+DtYearψ), (5) where Densr(i)t50 denotes the population density of the city where the married couple lived when the wife was age 50 and Zi is limited to the vector of variables capturing husbands’ and wives’ university education because the dataset includes no historical information on income, work experience or health status.9 The interpretations of parameter α in Models (4) and (5) may be ambiguous when the sample includes migrants, even if migration status is controlled for. If possible, it is ideal to control for all of the cities in which migrants have ever resided. Another related issue is that migration itself is highly related with the fertility decision, presenting self-selection bias. Although the method proposed by Dahl (2002) is more appropriate, because of data limitations, the robustness check is based on a classical approach to the selection bias by an endogenous binary-variable model. See Section 5.5 for details of the robustness check. 3.2. Testing the catch-up process in large cities This section examines the observation that married couples residing in more densely populated areas bear children later in life, as shown in Figure 2. To measure the catch-up process in the regression framework, this study introduces a cross-term of population density and wife’s age into the Poisson regression Model (4) as follows:   λir(θ)≡exp(αlog(Densr(i)t)+φlog(Densr(i)t)×Ageiwife+Xiβ+X˜iδ+Dr(i)Regη+DtYearψ), (6) where Ageiwife denotes the wife’s age for married couple i and φ measures the catch-up process on fertility decisions. A positive value of φ suggests that married couples residing in more densely populated areas delay having children and have children when they are older. This regression is estimated using the sample of nonmigrants aged 50 or younger to control for households’ dynamic location choice. This baseline model considers a linear dynamic fertility decision process. In the Online Appendix, this study additionally considers two specifications of the dynamic catch-up process on fertility decisions that include nonlinear and discrete effects of age. To quantify the extent to which congestion costs arising from population concentration discourage households’ fertility behavior, this study emphasizes that a dynamic fertility process should be considered. For example, it is inappropriate to quantify the magnitude of congestion costs simply by comparing married couples across cities at a point in time. The fact that young married couples in large cities tend to have children later in life causes spatial variation in the number of children to be overestimated. Therefore, this study proposes a method of quantifying spatial variations in the number of children per parental age cohort using the estimates of α and φ in Regression (6). Another aspect of the catch-up process is whether agglomeration affects the timing of marriage and the birth of the first child (e.g. Simon and Tamura, 2009). These agglomeration effects are estimated by the following linear regression:   Ageir,kwife=αklog(Densr(i)tAll)+γkMi+Ziϕk+X˜iδk+Dr(i)Regηk+DtYearψk+ui,k, (7) where Ageir,kwife denotes the wife’s age for married couple i at the time of marriage (k = 1) and birth of the first child (k = 2), respectively; Densr(i)tAll denotes the population density and takes the value of Densr(i)t if married couple i is aged 50 or younger and the value of Densr(i)t50 if the wife in couple i is age 50 or older; and ui,k is the error term. In this regression, the sample is not divided by the wife’s age. Parameter αk captures the congestion diseconomy effects on the timing of marriage and the birth of the first child. 3.3. Quantifying spatial variation in fertility The quantification of the spatial variation in the number of children per married couple uses the estimates of α and φ (i.e. the density elasticity of the number of children) of Regression (6). Holding other factors equal, the percentage change in the average number of children per household between two cities s and r can be estimated as:   λs−λrλr=(DenssDensr)α^+φ^×Age−1. Note that this spatial variation in the 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 have 2 children on average, 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 have 2 children on average, then households in city s on average have 1.824 children. Similarly, this study examines how long the congestion diseconomy in large cities delays marriage and the birth of the first child for married couples from Regression (7). Holding other factors equal, differences in a wife’s age between cities s and r can be estimated as:   Ages,kwife−Ager,kwife=α^klog(DenssDensr), where α^k is the estimate of the parameter in Regression (7). 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 and α^2=0.2. In this case, married couples in large cities postpone having their first child by an average of 1.66 ( ≈12×0.2×log(2)) months. 4. Data This study uses the cumulative dataset (i.e. a pooled cross section) of the JGSS, which covers the years 2000, 2001, 2002, 2005, 2006, 2008 and 2010.10 The sample is limited to married couples (i.e. unmarried persons are excluded). Table 1 presents descriptive statistics of the variables. Detailed definitions of the variables used in this study, such as population density, migration and income, are explained in the Online Appendix. The average number of children per household in the sample with wife’s age < 50 is 1.810, whereas the average number of children per household in the sample with wife’s age ≥50 is 2.204.11 Table 1 Descriptive statistics of variables for regression analysis Variables  Sample with wife’s age < 50   Sample with wife’s age ≥ 50   Obs.  Mean  S. D.  Min  Max  Obs.  Mean  S. D.  Min  Max  Number of children  2339  1.810  0.964  0  6  1995  2.204  0.865  0  8  Ideal number of children  2085  2.617  0.604  0  10  1804  2.774  0.610  0  9  Gap in number of children  2085  –0.805  0.987  –8  4  1804  – 0.579  0.978  – 7  4  Log (population density) in survey year  2339  7.431  1.077  4.646  9.628            Log (population density) at age 50            1995  7.359  1.065  4.694  9.597  Log (population density) in 1930  2339  6.732  1.257  3.374  9.492  1995  6.698  1.308  3.374  9.492  D (1 = migration)  2339  0.239  0.427  0  1  1995  0.282  0.450  0  1  D (1 = university or higher for husband)  2339  0.354  0.478  0  1  1995  0.209  0.406  0  1  D (1 = university or higher for wife)  2339  0.239  0.426  0  1  1995  0.114  0.318  0  1  Husband’s income (unit: million yen)  2339  5.510  2.823  0  27.600  1995  3.950  3.954  0  27.600  Wife’s income (unit: million yen)  2339  1.731  1.850  0  20.363  1995  1.410  1.972  0  17.130  Hours worked last week for husband (unit: 10 h)  2339  4.810  1.143  0  8.000  1995  3.350  2.110  0  8.200  Hours worked last week for wife (unit: 10 h)  2339  2.828  1.544  0  6.500  1995  2.318  1.846  0  6.500  D (1 = nonlabor force for husband)  2339  0.007  0.082  0  1  1995  0.203  0.402  0  1  D (1 = nonlabor force for wife)  2339  0.091  0.288  0  1  1995  0.258  0.437  0  1  D (1 = not healthy)  2339  0.139  0.346  0  1  1995  0.155  0.362  0  1  Old-age security index  2339  4.583  1.880  2  10  1995  4.719  2.098  2  10  D (1 = non-necessity of children in a marriage)  2339  0.432  0.495  0  1  1995  0.283  0.450  0  1  Number of siblings  2339  1.715  0.955  0  8  1995  3.225  1.575  0  15  Husband’s age  2339  42.253  7.828  20  66  1995  62.804  8.063  33  91  Wife’s age  2339  39.520  6.684  20  49  1995  60.275  7.563  51  90  Wife’s age at marriage  1034  24.653  3.351  16  45  624  23.962  3.338  16  51  Wife’s age at birth of first child  2019  26.568  3.710  16  41  1861  25.722  3.727  16  50  D (1 = university or higher for father)  2339  0.100  0.300  0  1  1995  0.044  0.204  0  1  D (1 = university or higher for mother)  2339  0.040  0.195  0  1  1995  0.006  0.077  0  1  Variables  Sample with wife’s age < 50   Sample with wife’s age ≥ 50   Obs.  Mean  S. D.  Min  Max  Obs.  Mean  S. D.  Min  Max  Number of children  2339  1.810  0.964  0  6  1995  2.204  0.865  0  8  Ideal number of children  2085  2.617  0.604  0  10  1804  2.774  0.610  0  9  Gap in number of children  2085  –0.805  0.987  –8  4  1804  – 0.579  0.978  – 7  4  Log (population density) in survey year  2339  7.431  1.077  4.646  9.628            Log (population density) at age 50            1995  7.359  1.065  4.694  9.597  Log (population density) in 1930  2339  6.732  1.257  3.374  9.492  1995  6.698  1.308  3.374  9.492  D (1 = migration)  2339  0.239  0.427  0  1  1995  0.282  0.450  0  1  D (1 = university or higher for husband)  2339  0.354  0.478  0  1  1995  0.209  0.406  0  1  D (1 = university or higher for wife)  2339  0.239  0.426  0  1  1995  0.114  0.318  0  1  Husband’s income (unit: million yen)  2339  5.510  2.823  0  27.600  1995  3.950  3.954  0  27.600  Wife’s income (unit: million yen)  2339  1.731  1.850  0  20.363  1995  1.410  1.972  0  17.130  Hours worked last week for husband (unit: 10 h)  2339  4.810  1.143  0  8.000  1995  3.350  2.110  0  8.200  Hours worked last week for wife (unit: 10 h)  2339  2.828  1.544  0  6.500  1995  2.318  1.846  0  6.500  D (1 = nonlabor force for husband)  2339  0.007  0.082  0  1  1995  0.203  0.402  0  1  D (1 = nonlabor force for wife)  2339  0.091  0.288  0  1  1995  0.258  0.437  0  1  D (1 = not healthy)  2339  0.139  0.346  0  1  1995  0.155  0.362  0  1  Old-age security index  2339  4.583  1.880  2  10  1995  4.719  2.098  2  10  D (1 = non-necessity of children in a marriage)  2339  0.432  0.495  0  1  1995  0.283  0.450  0  1  Number of siblings  2339  1.715  0.955  0  8  1995  3.225  1.575  0  15  Husband’s age  2339  42.253  7.828  20  66  1995  62.804  8.063  33  91  Wife’s age  2339  39.520  6.684  20  49  1995  60.275  7.563  51  90  Wife’s age at marriage  1034  24.653  3.351  16  45  624  23.962  3.338  16  51  Wife’s age at birth of first child  2019  26.568  3.710  16  41  1861  25.722  3.727  16  50  D (1 = university or higher for father)  2339  0.100  0.300  0  1  1995  0.044  0.204  0  1  D (1 = university or higher for mother)  2339  0.040  0.195  0  1  1995  0.006  0.077  0  1  Notes: The household who has the maximum number of children and the uppermost 1 percentile of the distribution of hours worked for husband and wife are excluded from the full sample as extreme outliers. Population density is expressed in persons/km2. Table 1 Descriptive statistics of variables for regression analysis Variables  Sample with wife’s age < 50   Sample with wife’s age ≥ 50   Obs.  Mean  S. D.  Min  Max  Obs.  Mean  S. D.  Min  Max  Number of children  2339  1.810  0.964  0  6  1995  2.204  0.865  0  8  Ideal number of children  2085  2.617  0.604  0  10  1804  2.774  0.610  0  9  Gap in number of children  2085  –0.805  0.987  –8  4  1804  – 0.579  0.978  – 7  4  Log (population density) in survey year  2339  7.431  1.077  4.646  9.628            Log (population density) at age 50            1995  7.359  1.065  4.694  9.597  Log (population density) in 1930  2339  6.732  1.257  3.374  9.492  1995  6.698  1.308  3.374  9.492  D (1 = migration)  2339  0.239  0.427  0  1  1995  0.282  0.450  0  1  D (1 = university or higher for husband)  2339  0.354  0.478  0  1  1995  0.209  0.406  0  1  D (1 = university or higher for wife)  2339  0.239  0.426  0  1  1995  0.114  0.318  0  1  Husband’s income (unit: million yen)  2339  5.510  2.823  0  27.600  1995  3.950  3.954  0  27.600  Wife’s income (unit: million yen)  2339  1.731  1.850  0  20.363  1995  1.410  1.972  0  17.130  Hours worked last week for husband (unit: 10 h)  2339  4.810  1.143  0  8.000  1995  3.350  2.110  0  8.200  Hours worked last week for wife (unit: 10 h)  2339  2.828  1.544  0  6.500  1995  2.318  1.846  0  6.500  D (1 = nonlabor force for husband)  2339  0.007  0.082  0  1  1995  0.203  0.402  0  1  D (1 = nonlabor force for wife)  2339  0.091  0.288  0  1  1995  0.258  0.437  0  1  D (1 = not healthy)  2339  0.139  0.346  0  1  1995  0.155  0.362  0  1  Old-age security index  2339  4.583  1.880  2  10  1995  4.719  2.098  2  10  D (1 = non-necessity of children in a marriage)  2339  0.432  0.495  0  1  1995  0.283  0.450  0  1  Number of siblings  2339  1.715  0.955  0  8  1995  3.225  1.575  0  15  Husband’s age  2339  42.253  7.828  20  66  1995  62.804  8.063  33  91  Wife’s age  2339  39.520  6.684  20  49  1995  60.275  7.563  51  90  Wife’s age at marriage  1034  24.653  3.351  16  45  624  23.962  3.338  16  51  Wife’s age at birth of first child  2019  26.568  3.710  16  41  1861  25.722  3.727  16  50  D (1 = university or higher for father)  2339  0.100  0.300  0  1  1995  0.044  0.204  0  1  D (1 = university or higher for mother)  2339  0.040  0.195  0  1  1995  0.006  0.077  0  1  Variables  Sample with wife’s age < 50   Sample with wife’s age ≥ 50   Obs.  Mean  S. D.  Min  Max  Obs.  Mean  S. D.  Min  Max  Number of children  2339  1.810  0.964  0  6  1995  2.204  0.865  0  8  Ideal number of children  2085  2.617  0.604  0  10  1804  2.774  0.610  0  9  Gap in number of children  2085  –0.805  0.987  –8  4  1804  – 0.579  0.978  – 7  4  Log (population density) in survey year  2339  7.431  1.077  4.646  9.628            Log (population density) at age 50            1995  7.359  1.065  4.694  9.597  Log (population density) in 1930  2339  6.732  1.257  3.374  9.492  1995  6.698  1.308  3.374  9.492  D (1 = migration)  2339  0.239  0.427  0  1  1995  0.282  0.450  0  1  D (1 = university or higher for husband)  2339  0.354  0.478  0  1  1995  0.209  0.406  0  1  D (1 = university or higher for wife)  2339  0.239  0.426  0  1  1995  0.114  0.318  0  1  Husband’s income (unit: million yen)  2339  5.510  2.823  0  27.600  1995  3.950  3.954  0  27.600  Wife’s income (unit: million yen)  2339  1.731  1.850  0  20.363  1995  1.410  1.972  0  17.130  Hours worked last week for husband (unit: 10 h)  2339  4.810  1.143  0  8.000  1995  3.350  2.110  0  8.200  Hours worked last week for wife (unit: 10 h)  2339  2.828  1.544  0  6.500  1995  2.318  1.846  0  6.500  D (1 = nonlabor force for husband)  2339  0.007  0.082  0  1  1995  0.203  0.402  0  1  D (1 = nonlabor force for wife)  2339  0.091  0.288  0  1  1995  0.258  0.437  0  1  D (1 = not healthy)  2339  0.139  0.346  0  1  1995  0.155  0.362  0  1  Old-age security index  2339  4.583  1.880  2  10  1995  4.719  2.098  2  10  D (1 = non-necessity of children in a marriage)  2339  0.432  0.495  0  1  1995  0.283  0.450  0  1  Number of siblings  2339  1.715  0.955  0  8  1995  3.225  1.575  0  15  Husband’s age  2339  42.253  7.828  20  66  1995  62.804  8.063  33  91  Wife’s age  2339  39.520  6.684  20  49  1995  60.275  7.563  51  90  Wife’s age at marriage  1034  24.653  3.351  16  45  624  23.962  3.338  16  51  Wife’s age at birth of first child  2019  26.568  3.710  16  41  1861  25.722  3.727  16  50  D (1 = university or higher for father)  2339  0.100  0.300  0  1  1995  0.044  0.204  0  1  D (1 = university or higher for mother)  2339  0.040  0.195  0  1  1995  0.006  0.077  0  1  Notes: The household who has the maximum number of children and the uppermost 1 percentile of the distribution of hours worked for husband and wife are excluded from the full sample as extreme outliers. Population density is expressed in persons/km2. Figure 3 presents differences in the numbers of children between large and small cities in the JGSS dataset. Note that the sample with wife’s age < 50 is used, and migrants are excluded from the sample. Panel (a) of Figure 3 shows that households residing in large cities have fewer children than those residing in small cities. Panel (b) of Figure 3 presents the average number of children per married couple by parental age cohort. An interesting trend is that households with ages averaging from 20–24 in more densely populated areas (exceeding the 75th percentile of population density of 4176 persons/km2) have half as many children as households in less dense areas do. The gap between the two narrows, but a slight gap remains. Figure 3 View largeDownload slide Number of children per married couple between large and small cities. Notes: Sample with wife’s age < 50 is used. Migrants are excluded from the sample. The 75th percentile of population density is calculated from the distribution in the JGSS dataset. Source: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. Figure 3 View largeDownload slide Number of children per married couple between large and small cities. Notes: Sample with wife’s age < 50 is used. Migrants are excluded from the sample. The 75th percentile of population density is calculated from the distribution in the JGSS dataset. Source: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. Figure 4 presents regional variations in the number of children per married couple in the JGSS dataset. I aggregated individual microdata for the geographical unit used in this study. Panel (a) of Figure 4 presents a similar trend to that in Figure 1. Although the JGSS sample size is quite small, it adequately captures the characteristics of the entire country. Panel (b) of Figure 4 presents the spatial variation in completed fertility. The spatial variation in completed fertility becomes small, suggesting that agglomeration affects the timing of childbearing. Figure 4 View largeDownload slide Average number of children per married couple and city size in JGSS cumulative data 2000–2010. Note: The circle size represents the sample size in each geographical unit. Source: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. Figure 4 View largeDownload slide Average number of children per married couple and city size in JGSS cumulative data 2000–2010. Note: The circle size represents the sample size in each geographical unit. Source: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. Figure 5 presents regional variations in the wife’s age at marriage and at the birth of the first child in the JGSS dataset. Panels (a) and (b) of Figure 5 present positive correlations between the wife’s age at marriage and at the birth of the first child and city size suggesting that agglomeration affects the timing of marriage and childbearing. To examine whether agglomeration indeed leads to this relationship, regression analyses are undertaken. Figure 5 View largeDownload slide Average wife’s age and city size in JGSS cumulative data 2000–2010. Note: The circle size represents the sample size in each geographical unit. Source: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. Figure 5 View largeDownload slide Average wife’s age and city size in JGSS cumulative data 2000–2010. Note: The circle size represents the sample size in each geographical unit. Source: Author’s calculation from Japanese General Social Surveys Cumulative Data 2000–2010. To control for preference heterogeneity in the demand for children, this study makes use of three variables on social factors. The first variable relates to the motive of security in old age, which predicts that such households have more children.12 The second variable directly captures the household’s preference for children. The JGSS asks a question about households’ opinions of whether children are necessary in a marriage. A dummy variable based on this question takes the value of 1 for households that agree or somewhat agree children are unnecessary and 0 otherwise. The third variable is the number of siblings because couples that have relatively many siblings may have more children. 5. Estimation results 5.1. Agglomeration discourages the fertility behavior of young married couples Table 2 presents the baseline estimation results of Poisson regression Model (4).13 Column (1) shows the aggregate impacts of agglomeration diseconomies on the number of children. The density elasticity of the number of children is significantly negative at the 1% level and its value is –0.075. To decompose channels through which agglomeration affects the demand for children, economic and social factors are controlled for in Columns (2)–(7) of Table 2. Table 2 Poisson regression estimation results for fertility decision and city size Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50   (1)  (2)  (3)  (4)  (5)  (6)  (7)  Log (population density)  –0.074***  –0.069***  –0.061***  –0.080***  –0.082***  –0.071***  –0.067***    (0.015)  (0.015)  (0.014)  (0.015)  (0.016)  (0.016)  (0.015)  Husband’s age  0.090***  0.089***  0.092***  0.085***  0.086***  0.088***  0.080***    (0.029)  (0.028)  (0.028)  (0.028)  (0.028)  (0.028)  (0.027)  Husband’s age squared ( ×1/100)  –0.098***  –0.096***  –0.100***  –0.093***  –0.094***  –0.096***  –0.088***    (0.031)  (0.031)  (0.030)  (0.030)  (0.030)  (0.030)  (0.029)  Wife’s age  0.166***  0.167***  0.168***  0.162***  0.163***  0.166***  0.163***    (0.029)  (0.029)  (0.028)  (0.029)  (0.029)  (0.028)  (0.028)  Wife’s age squared ( ×1/100)  –0.190***  –0.192***  –0.192***  –0.184***  –0.188***  –0.192***  –0.187***    (0.034)  (0.034)  (0.033)  (0.035)  (0.035)  (0.033)  (0.033)  D (1 = migration)    –0.073**          –0.063**      (0.028)          (0.028)  D (1 = university graduate for husband)      –0.122***        –0.121***      (0.026)        (0.023)  D (1 = university graduate for wife)      –0.094***        –0.085***        (0.020)        (0.021)  Husband’s income        0.010***      0.015***          (0.003)      (0.003)  Wife’s income        –0.034***      –0.017***          (0.007)      (0.006)  Hours worked last week for husband          0.009    0.006            (0.011)    (0.010)  Hours worked last week for wife          –0.045***    –0.032***            (0.011)    (0.011)  D (1 = nonlabor force for husband)          –0.136    –0.092            (0.178)    (0.170)  D (1 = nonlabor force for wife)          –0.109**    –0.098*            (0.054)    (0.056)  D (1 = not healthy)            –0.056**  –0.064**              (0.028)  (0.028)  Old-age security motive score            0.009  0.009              (0.006)  (0.006)  D (1 = non-necessity of children)            –0.077***  –0.079***              (0.019)  (0.018)  Number of siblings            0.036***  0.025**              (0.011)  (0.011)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  2339  2339  2339  2339  2339  Log likelihood  –3331.608  –3329.873  –3318.649  –3322.692  –3324.573  –3324.556  –3300.614  AIC  6711.216  6709.745  6689.298  6697.384  6705.145  6705.111  6675.229  Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50   (1)  (2)  (3)  (4)  (5)  (6)  (7)  Log (population density)  –0.074***  –0.069***  –0.061***  –0.080***  –0.082***  –0.071***  –0.067***    (0.015)  (0.015)  (0.014)  (0.015)  (0.016)  (0.016)  (0.015)  Husband’s age  0.090***  0.089***  0.092***  0.085***  0.086***  0.088***  0.080***    (0.029)  (0.028)  (0.028)  (0.028)  (0.028)  (0.028)  (0.027)  Husband’s age squared ( ×1/100)  –0.098***  –0.096***  –0.100***  –0.093***  –0.094***  –0.096***  –0.088***    (0.031)  (0.031)  (0.030)  (0.030)  (0.030)  (0.030)  (0.029)  Wife’s age  0.166***  0.167***  0.168***  0.162***  0.163***  0.166***  0.163***    (0.029)  (0.029)  (0.028)  (0.029)  (0.029)  (0.028)  (0.028)  Wife’s age squared ( ×1/100)  –0.190***  –0.192***  –0.192***  –0.184***  –0.188***  –0.192***  –0.187***    (0.034)  (0.034)  (0.033)  (0.035)  (0.035)  (0.033)  (0.033)  D (1 = migration)    –0.073**          –0.063**      (0.028)          (0.028)  D (1 = university graduate for husband)      –0.122***        –0.121***      (0.026)        (0.023)  D (1 = university graduate for wife)      –0.094***        –0.085***        (0.020)        (0.021)  Husband’s income        0.010***      0.015***          (0.003)      (0.003)  Wife’s income        –0.034***      –0.017***          (0.007)      (0.006)  Hours worked last week for husband          0.009    0.006            (0.011)    (0.010)  Hours worked last week for wife          –0.045***    –0.032***            (0.011)    (0.011)  D (1 = nonlabor force for husband)          –0.136    –0.092            (0.178)    (0.170)  D (1 = nonlabor force for wife)          –0.109**    –0.098*            (0.054)    (0.056)  D (1 = not healthy)            –0.056**  –0.064**              (0.028)  (0.028)  Old-age security motive score            0.009  0.009              (0.006)  (0.006)  D (1 = non-necessity of children)            –0.077***  –0.079***              (0.019)  (0.018)  Number of siblings            0.036***  0.025**              (0.011)  (0.011)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  2339  2339  2339  2339  2339  Log likelihood  –3331.608  –3329.873  –3318.649  –3322.692  –3324.573  –3324.556  –3300.614  AIC  6711.216  6709.745  6689.298  6697.384  6705.145  6705.111  6675.229  Notes: AIC, Akaike’s information criterion. Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Table 2 Poisson regression estimation results for fertility decision and city size Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50   (1)  (2)  (3)  (4)  (5)  (6)  (7)  Log (population density)  –0.074***  –0.069***  –0.061***  –0.080***  –0.082***  –0.071***  –0.067***    (0.015)  (0.015)  (0.014)  (0.015)  (0.016)  (0.016)  (0.015)  Husband’s age  0.090***  0.089***  0.092***  0.085***  0.086***  0.088***  0.080***    (0.029)  (0.028)  (0.028)  (0.028)  (0.028)  (0.028)  (0.027)  Husband’s age squared ( ×1/100)  –0.098***  –0.096***  –0.100***  –0.093***  –0.094***  –0.096***  –0.088***    (0.031)  (0.031)  (0.030)  (0.030)  (0.030)  (0.030)  (0.029)  Wife’s age  0.166***  0.167***  0.168***  0.162***  0.163***  0.166***  0.163***    (0.029)  (0.029)  (0.028)  (0.029)  (0.029)  (0.028)  (0.028)  Wife’s age squared ( ×1/100)  –0.190***  –0.192***  –0.192***  –0.184***  –0.188***  –0.192***  –0.187***    (0.034)  (0.034)  (0.033)  (0.035)  (0.035)  (0.033)  (0.033)  D (1 = migration)    –0.073**          –0.063**      (0.028)          (0.028)  D (1 = university graduate for husband)      –0.122***        –0.121***      (0.026)        (0.023)  D (1 = university graduate for wife)      –0.094***        –0.085***        (0.020)        (0.021)  Husband’s income        0.010***      0.015***          (0.003)      (0.003)  Wife’s income        –0.034***      –0.017***          (0.007)      (0.006)  Hours worked last week for husband          0.009    0.006            (0.011)    (0.010)  Hours worked last week for wife          –0.045***    –0.032***            (0.011)    (0.011)  D (1 = nonlabor force for husband)          –0.136    –0.092            (0.178)    (0.170)  D (1 = nonlabor force for wife)          –0.109**    –0.098*            (0.054)    (0.056)  D (1 = not healthy)            –0.056**  –0.064**              (0.028)  (0.028)  Old-age security motive score            0.009  0.009              (0.006)  (0.006)  D (1 = non-necessity of children)            –0.077***  –0.079***              (0.019)  (0.018)  Number of siblings            0.036***  0.025**              (0.011)  (0.011)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  2339  2339  2339  2339  2339  Log likelihood  –3331.608  –3329.873  –3318.649  –3322.692  –3324.573  –3324.556  –3300.614  AIC  6711.216  6709.745  6689.298  6697.384  6705.145  6705.111  6675.229  Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50   (1)  (2)  (3)  (4)  (5)  (6)  (7)  Log (population density)  –0.074***  –0.069***  –0.061***  –0.080***  –0.082***  –0.071***  –0.067***    (0.015)  (0.015)  (0.014)  (0.015)  (0.016)  (0.016)  (0.015)  Husband’s age  0.090***  0.089***  0.092***  0.085***  0.086***  0.088***  0.080***    (0.029)  (0.028)  (0.028)  (0.028)  (0.028)  (0.028)  (0.027)  Husband’s age squared ( ×1/100)  –0.098***  –0.096***  –0.100***  –0.093***  –0.094***  –0.096***  –0.088***    (0.031)  (0.031)  (0.030)  (0.030)  (0.030)  (0.030)  (0.029)  Wife’s age  0.166***  0.167***  0.168***  0.162***  0.163***  0.166***  0.163***    (0.029)  (0.029)  (0.028)  (0.029)  (0.029)  (0.028)  (0.028)  Wife’s age squared ( ×1/100)  –0.190***  –0.192***  –0.192***  –0.184***  –0.188***  –0.192***  –0.187***    (0.034)  (0.034)  (0.033)  (0.035)  (0.035)  (0.033)  (0.033)  D (1 = migration)    –0.073**          –0.063**      (0.028)          (0.028)  D (1 = university graduate for husband)      –0.122***        –0.121***      (0.026)        (0.023)  D (1 = university graduate for wife)      –0.094***        –0.085***        (0.020)        (0.021)  Husband’s income        0.010***      0.015***          (0.003)      (0.003)  Wife’s income        –0.034***      –0.017***          (0.007)      (0.006)  Hours worked last week for husband          0.009    0.006            (0.011)    (0.010)  Hours worked last week for wife          –0.045***    –0.032***            (0.011)    (0.011)  D (1 = nonlabor force for husband)          –0.136    –0.092            (0.178)    (0.170)  D (1 = nonlabor force for wife)          –0.109**    –0.098*            (0.054)    (0.056)  D (1 = not healthy)            –0.056**  –0.064**              (0.028)  (0.028)  Old-age security motive score            0.009  0.009              (0.006)  (0.006)  D (1 = non-necessity of children)            –0.077***  –0.079***              (0.019)  (0.018)  Number of siblings            0.036***  0.025**              (0.011)  (0.011)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  2339  2339  2339  2339  2339  Log likelihood  –3331.608  –3329.873  –3318.649  –3322.692  –3324.573  –3324.556  –3300.614  AIC  6711.216  6709.745  6689.298  6697.384  6705.145  6705.111  6675.229  Notes: AIC, Akaike’s information criterion. Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. The estimation results in Table 2 show that including migration and education variables reduces the density elasticity of the number of children. After controlling for migration, the density elasticity becomes –0.069 in Column (2), whereas after controlling for university education, the density elasticity becomes –0.061 in Column (3). These results mean that migrants with university education, who tend to have fewer children, are concentrated in large cities, which leads to an overestimation of the impacts of agglomeration diseconomies. By contrast, the inclusion of incomes increases the magnitude of the coefficient on population density. These results mean that individuals with high income, who tend to have more children due to income effects, are concentrated in large cities, which leads to underestimation of the impact of agglomeration diseconomies.14 In Column (6), the inclusion of the social factor variables slightly decreases the magnitude of the effect, which may imply that the spatial sorting of preference heterogeneity is not relevant for this study. These results in Column (7) imply that, holding other factors equal, a 10-fold difference in city size on average generates spatial variation in the per-household number of children by 14.31% ( ≈10−0.067−1). Consider the 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 is 1.714. The spatial gap shows ∼286 children per 1000 households.15 Therefore, the results show that congestion costs in large cities discourage fertility behavior. An interesting finding is that husbands’ and wives’ incomes, which relate highly to city size, have significant positive and negative signs, respectively. This finding can be explained by the simple theoretical model of this study. Agglomeration economies increase income and wages, which have both positive and negative effects on the demand for children through income effects and the opportunity cost of rearing children, respectively. Concerning preference heterogeneity in the demand for children, the dummy denoting that children are unnecessary in a marriage significantly decreases the number of children at the 1% level. In addition, when either the husband or wife has more siblings, they tend to have more children. Indeed, the inclusion of these social characteristics tends to reduce the magnitude of the dummy for wife’s university education, implying that female workers with high earnings simultaneously tend to have the opinion that children are unnecessary in a marriage. These results emphasize the importance for controlling for preference heterogeneity among individuals. In addition, the migration dummy is significantly negative at the 5% level. A household 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 a reverse causality. That is, migration itself may impose substantial costs on having children, but having fewer children may enable households to easily migrate. The robustness check for self-selected migration is carried out in Section 5.5. 5.2. Completed fertility and agglomeration Table 3 presents estimation results for couples whose childbearing years have ended because the wife’s age is 50 or older. This estimation intends to examine whether congestion costs in large cities discourage completed fertility. Table 3 Poisson regression estimation results for completed fertility decision and city size Explanatory variables  Dependent variable: number of children   Sample with wife’s age ≥50   (1)  (2)  (3)  (4)  (5)  Log (population density) at age 50  –0.035***  –0.032**  –0.036***  –0.031**  –0.029**    (0.013)  (0.013)  (0.013)  (0.013)  (0.013)  D (1 = migration)    –0.033*      –0.031*      (0.017)      (0.018)  D (1 = university graduate for husband)      –0.013    –0.005        (0.025)    (0.026)  D (1 = university graduate for wife)      0.046    0.049        (0.033)    (0.031)  D (1 = not healthy)        –0.026  –0.024          (0.029)  (0.029)  Old-age security motive score        –0.000  –0.001          (0.005)  (0.005)  D (1 = non-necessity of children)        –0.088***  –0.087***          (0.020)  (0.020)  Number of siblings        0.016***  0.017**          (0.006)  (0.007)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1995  1995  1995  1995  1995  Log likelihood  –2977.043  –2976.656  –2976.691  –2972.469  –2971.705  AIC  5990.087  5991.312  5993.382  5988.939  5993.409  Explanatory variables  Dependent variable: number of children   Sample with wife’s age ≥50   (1)  (2)  (3)  (4)  (5)  Log (population density) at age 50  –0.035***  –0.032**  –0.036***  –0.031**  –0.029**    (0.013)  (0.013)  (0.013)  (0.013)  (0.013)  D (1 = migration)    –0.033*      –0.031*      (0.017)      (0.018)  D (1 = university graduate for husband)      –0.013    –0.005        (0.025)    (0.026)  D (1 = university graduate for wife)      0.046    0.049        (0.033)    (0.031)  D (1 = not healthy)        –0.026  –0.024          (0.029)  (0.029)  Old-age security motive score        –0.000  –0.001          (0.005)  (0.005)  D (1 = non-necessity of children)        –0.088***  –0.087***          (0.020)  (0.020)  Number of siblings        0.016***  0.017**          (0.006)  (0.007)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1995  1995  1995  1995  1995  Log likelihood  –2977.043  –2976.656  –2976.691  –2972.469  –2971.705  AIC  5990.087  5991.312  5993.382  5988.939  5993.409  Notes: AIC, Akaike’s information criterion. Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Table 3 Poisson regression estimation results for completed fertility decision and city size Explanatory variables  Dependent variable: number of children   Sample with wife’s age ≥50   (1)  (2)  (3)  (4)  (5)  Log (population density) at age 50  –0.035***  –0.032**  –0.036***  –0.031**  –0.029**    (0.013)  (0.013)  (0.013)  (0.013)  (0.013)  D (1 = migration)    –0.033*      –0.031*      (0.017)      (0.018)  D (1 = university graduate for husband)      –0.013    –0.005        (0.025)    (0.026)  D (1 = university graduate for wife)      0.046    0.049        (0.033)    (0.031)  D (1 = not healthy)        –0.026  –0.024          (0.029)  (0.029)  Old-age security motive score        –0.000  –0.001          (0.005)  (0.005)  D (1 = non-necessity of children)        –0.088***  –0.087***          (0.020)  (0.020)  Number of siblings        0.016***  0.017**          (0.006)  (0.007)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1995  1995  1995  1995  1995  Log likelihood  –2977.043  –2976.656  –2976.691  –2972.469  –2971.705  AIC  5990.087  5991.312  5993.382  5988.939  5993.409  Explanatory variables  Dependent variable: number of children   Sample with wife’s age ≥50   (1)  (2)  (3)  (4)  (5)  Log (population density) at age 50  –0.035***  –0.032**  –0.036***  –0.031**  –0.029**    (0.013)  (0.013)  (0.013)  (0.013)  (0.013)  D (1 = migration)    –0.033*      –0.031*      (0.017)      (0.018)  D (1 = university graduate for husband)      –0.013    –0.005        (0.025)    (0.026)  D (1 = university graduate for wife)      0.046    0.049        (0.033)    (0.031)  D (1 = not healthy)        –0.026  –0.024          (0.029)  (0.029)  Old-age security motive score        –0.000  –0.001          (0.005)  (0.005)  D (1 = non-necessity of children)        –0.088***  –0.087***          (0.020)  (0.020)  Number of siblings        0.016***  0.017**          (0.006)  (0.007)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1995  1995  1995  1995  1995  Log likelihood  –2977.043  –2976.656  –2976.691  –2972.469  –2971.705  AIC  5990.087  5991.312  5993.382  5988.939  5993.409  Notes: AIC, Akaike’s information criterion. Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Column (1) of Table 3 shows the impact of wide-ranging aggregate congestion costs arising from agglomeration on completed fertility. The density elasticity of the number of children is –0.035, whereas the density elasticity for the sample with wife’s age < 50 is –0.074, as shown in Table 2. This relationship remains negative after controlling for economic and social household characteristics and migration status, but the density elasticity declines to –0.029 in Column (5). As studied in Yamauchi (2016), the estimation results suggest that the costs associated with agglomeration discourage completed fertility and, holding other factors equal, a 10-fold difference in city size on average generates a spatial variation of 6.40% ( ≈10−0.029−1) in number of children per household. Consider a case where the population of city s is 10 times larger than that of city r. If the average number of children in city r is 2, the average in city s becomes 1.872. The spatial gap shows ∼128 children per 1000 households.16 More importantly, the density elasticity of the number of children decreases between Tables 2 and 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 the average number of children decreases as couples age. Another interesting finding is that the effect of higher education on completed fertility is not significant at the 10% level. Combined with the estimation results in Table 2, this finding suggests that higher education discourages childbearing among young married couples but does not affect completed fertility. These results also imply that, holding other factors equal, university graduates postpone having children. Concerning preference heterogeneity in the demand for children, the dummy variable denoting that children are unnecessary in a marriage has a significant negative effect on completed fertility. In addition, the number of siblings exerts a significantly positive effect on completed fertility. Seeking security in old age shows no significant relationship with completed fertility. The migration dummy also shows negative effects on completed fertility, but it is significant at the 10% level. A robustness check for self-selected migration is carried out in Section 5.5. 5.3. Catch-up process of fertility in more densely populated areas Table 4 presents the estimation results of Poisson regression Model (6), which considers the dynamic process of fertility behavior across different city sizes. This study quantifies spatial variations in average number of children by parents’ ages estimating the cross-term of population density and wife’s age. Note that sample used in Table 4 does not include migrants. Table 4 Poisson regression estimation results for dynamic fertility decision and city size with linear effects of age Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50, nonmigrants   (1)  (2)  (3)  (4)  (5)  (6)  Log (population density)  –0.245***  –0.244***  –0.233***  –0.246***  –0.247***  –0.237***    (0.079)  (0.080)  (0.079)  (0.076)  (0.078)  (0.076)  Log (population density) × wife’s age  0.004**  0.005**  0.004**  0.004**  0.005**  0.004**    (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  Husband’s age  0.070**  0.071**  0.065**  0.067**  0.066**  0.059**    (0.029)  (0.029)  (0.029)  (0.029)  (0.029)  (0.028)  Husband’s age squared ( ×1/100)  –0.074**  –0.074**  –0.069**  –0.070**  –0.070**  –0.062**    (0.032)  (0.031)  (0.032)  (0.031)  (0.032)  (0.031)  Wife’s age  0.124***  0.125***  0.124***  0.125***  0.125***  0.127***    (0.035)  (0.034)  (0.035)  (0.034)  (0.034)  (0.034)  Wife’s age squared ( ×1/100)  –0.186***  –0.189***  –0.180***  –0.186***  –0.190***  –0.188***    (0.041)  (0.041)  (0.041)  (0.041)  (0.040)  (0.040)  D (1 = university graduate for husband)    –0.111***        –0.116***    (0.025)        (0.024)  D (1 = university graduate for wife)    –0.108***        –0.096***    (0.027)        (0.029)  Husband’s income      0.010***      0.015***        (0.004)      (0.004)  Wife’s income      –0.031***      –0.014**        (0.008)      (0.007)  Hours worked last week for husband        0.010    0.006          (0.011)    (0.012)  Hours worked last week for wife        –0.038***    –0.025**          (0.013)    (0.012)  D (1 = nonlabor force for husband)        0.025    0.048          (0.145)    (0.144)  D (1 = nonlabor force for wife)        –0.057    –0.046          (0.057)    (0.055)  D (1 = not healthy)          –0.081***  –0.094***            (0.025)  (0.025)  Old-age security motive score          0.005  0.007            (0.007)  (0.006)  D (1 = non-necessity of children)          –0.076***  –0.077***            (0.025)  (0.024)  Number of siblings          0.044***  0.034***            (0.011)  (0.012)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  1779  1779  1779  1779  1779  1779  Log likelihood  –2536.763  –2527.288  –2531.063  –2532.827  –2530.365  –2515.435  AIC  5123.527  5108.576  5116.127  5123.654  5118.729  5104.871  Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50, nonmigrants   (1)  (2)  (3)  (4)  (5)  (6)  Log (population density)  –0.245***  –0.244***  –0.233***  –0.246***  –0.247***  –0.237***    (0.079)  (0.080)  (0.079)  (0.076)  (0.078)  (0.076)  Log (population density) × wife’s age  0.004**  0.005**  0.004**  0.004**  0.005**  0.004**    (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  Husband’s age  0.070**  0.071**  0.065**  0.067**  0.066**  0.059**    (0.029)  (0.029)  (0.029)  (0.029)  (0.029)  (0.028)  Husband’s age squared ( ×1/100)  –0.074**  –0.074**  –0.069**  –0.070**  –0.070**  –0.062**    (0.032)  (0.031)  (0.032)  (0.031)  (0.032)  (0.031)  Wife’s age  0.124***  0.125***  0.124***  0.125***  0.125***  0.127***    (0.035)  (0.034)  (0.035)  (0.034)  (0.034)  (0.034)  Wife’s age squared ( ×1/100)  –0.186***  –0.189***  –0.180***  –0.186***  –0.190***  –0.188***    (0.041)  (0.041)  (0.041)  (0.041)  (0.040)  (0.040)  D (1 = university graduate for husband)    –0.111***        –0.116***    (0.025)        (0.024)  D (1 = university graduate for wife)    –0.108***        –0.096***    (0.027)        (0.029)  Husband’s income      0.010***      0.015***        (0.004)      (0.004)  Wife’s income      –0.031***      –0.014**        (0.008)      (0.007)  Hours worked last week for husband        0.010    0.006          (0.011)    (0.012)  Hours worked last week for wife        –0.038***    –0.025**          (0.013)    (0.012)  D (1 = nonlabor force for husband)        0.025    0.048          (0.145)    (0.144)  D (1 = nonlabor force for wife)        –0.057    –0.046          (0.057)    (0.055)  D (1 = not healthy)          –0.081***  –0.094***            (0.025)  (0.025)  Old-age security motive score          0.005  0.007            (0.007)  (0.006)  D (1 = non-necessity of children)          –0.076***  –0.077***            (0.025)  (0.024)  Number of siblings          0.044***  0.034***            (0.011)  (0.012)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  1779  1779  1779  1779  1779  1779  Log likelihood  –2536.763  –2527.288  –2531.063  –2532.827  –2530.365  –2515.435  AIC  5123.527  5108.576  5116.127  5123.654  5118.729  5104.871  Notes: AIC, Akaike’s information criterion. Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Table 4 Poisson regression estimation results for dynamic fertility decision and city size with linear effects of age Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50, nonmigrants   (1)  (2)  (3)  (4)  (5)  (6)  Log (population density)  –0.245***  –0.244***  –0.233***  –0.246***  –0.247***  –0.237***    (0.079)  (0.080)  (0.079)  (0.076)  (0.078)  (0.076)  Log (population density) × wife’s age  0.004**  0.005**  0.004**  0.004**  0.005**  0.004**    (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  Husband’s age  0.070**  0.071**  0.065**  0.067**  0.066**  0.059**    (0.029)  (0.029)  (0.029)  (0.029)  (0.029)  (0.028)  Husband’s age squared ( ×1/100)  –0.074**  –0.074**  –0.069**  –0.070**  –0.070**  –0.062**    (0.032)  (0.031)  (0.032)  (0.031)  (0.032)  (0.031)  Wife’s age  0.124***  0.125***  0.124***  0.125***  0.125***  0.127***    (0.035)  (0.034)  (0.035)  (0.034)  (0.034)  (0.034)  Wife’s age squared ( ×1/100)  –0.186***  –0.189***  –0.180***  –0.186***  –0.190***  –0.188***    (0.041)  (0.041)  (0.041)  (0.041)  (0.040)  (0.040)  D (1 = university graduate for husband)    –0.111***        –0.116***    (0.025)        (0.024)  D (1 = university graduate for wife)    –0.108***        –0.096***    (0.027)        (0.029)  Husband’s income      0.010***      0.015***        (0.004)      (0.004)  Wife’s income      –0.031***      –0.014**        (0.008)      (0.007)  Hours worked last week for husband        0.010    0.006          (0.011)    (0.012)  Hours worked last week for wife        –0.038***    –0.025**          (0.013)    (0.012)  D (1 = nonlabor force for husband)        0.025    0.048          (0.145)    (0.144)  D (1 = nonlabor force for wife)        –0.057    –0.046          (0.057)    (0.055)  D (1 = not healthy)          –0.081***  –0.094***            (0.025)  (0.025)  Old-age security motive score          0.005  0.007            (0.007)  (0.006)  D (1 = non-necessity of children)          –0.076***  –0.077***            (0.025)  (0.024)  Number of siblings          0.044***  0.034***            (0.011)  (0.012)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  1779  1779  1779  1779  1779  1779  Log likelihood  –2536.763  –2527.288  –2531.063  –2532.827  –2530.365  –2515.435  AIC  5123.527  5108.576  5116.127  5123.654  5118.729  5104.871  Explanatory variables  Dependent variable: number of children   Sample with wife’s age < 50, nonmigrants   (1)  (2)  (3)  (4)  (5)  (6)  Log (population density)  –0.245***  –0.244***  –0.233***  –0.246***  –0.247***  –0.237***    (0.079)  (0.080)  (0.079)  (0.076)  (0.078)  (0.076)  Log (population density) × wife’s age  0.004**  0.005**  0.004**  0.004**  0.005**  0.004**    (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  (0.002)  Husband’s age  0.070**  0.071**  0.065**  0.067**  0.066**  0.059**    (0.029)  (0.029)  (0.029)  (0.029)  (0.029)  (0.028)  Husband’s age squared ( ×1/100)  –0.074**  –0.074**  –0.069**  –0.070**  –0.070**  –0.062**    (0.032)  (0.031)  (0.032)  (0.031)  (0.032)  (0.031)  Wife’s age  0.124***  0.125***  0.124***  0.125***  0.125***  0.127***    (0.035)  (0.034)  (0.035)  (0.034)  (0.034)  (0.034)  Wife’s age squared ( ×1/100)  –0.186***  –0.189***  –0.180***  –0.186***  –0.190***  –0.188***    (0.041)  (0.041)  (0.041)  (0.041)  (0.040)  (0.040)  D (1 = university graduate for husband)    –0.111***        –0.116***    (0.025)        (0.024)  D (1 = university graduate for wife)    –0.108***        –0.096***    (0.027)        (0.029)  Husband’s income      0.010***      0.015***        (0.004)      (0.004)  Wife’s income      –0.031***      –0.014**        (0.008)      (0.007)  Hours worked last week for husband        0.010    0.006          (0.011)    (0.012)  Hours worked last week for wife        –0.038***    –0.025**          (0.013)    (0.012)  D (1 = nonlabor force for husband)        0.025    0.048          (0.145)    (0.144)  D (1 = nonlabor force for wife)        –0.057    –0.046          (0.057)    (0.055)  D (1 = not healthy)          –0.081***  –0.094***            (0.025)  (0.025)  Old-age security motive score          0.005  0.007            (0.007)  (0.006)  D (1 = non-necessity of children)          –0.076***  –0.077***            (0.025)  (0.024)  Number of siblings          0.044***  0.034***            (0.011)  (0.012)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  1779  1779  1779  1779  1779  1779  Log likelihood  –2536.763  –2527.288  –2531.063  –2532.827  –2530.365  –2515.435  AIC  5123.527  5108.576  5116.127  5123.654  5118.729  5104.871  Notes: AIC, Akaike’s information criterion. Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Overall, the Poisson estimation results in Columns (1)–(6) show that the estimated coefficients for the cross-term of population density and wife’s age are significantly positive, which means that young married couples in large cities postpone having children. The results are robust for additional controls for economic and social factors. In Column (6), the coefficient on population density captures the effects of the congestion costs in large cities on the demand for children. An important finding is that the gap in the number of children between large and small cities is large early in life, but it shrinks gradually as couples age. Figure 6 illustrates estimated spatial variations in the average number of children using the estimates in Column (6) of Table 4. Panel (a) of Figure 6 shows the density elasticity of the number of children at different ages. This density elasticity is large for couples in their 20s (e.g. –0.113 at age 29) but declines to –0.027 at age 49. Figure 6 View largeDownload slide Percentage change in the average number of children by city size simulated from Poisson estimates. Notes: The density elasticity of the number of children in Panel (a) is calculated as α^+φ^×Age using the estimates in Column (6) of Table 4. The percentage change in the average number of children in Panel (b) is calculated as [λs(θ^)−λr(θ^)]/λr(θ^)=Ratiosrα^+φ^×Age−1, where Ratiosr is the population density ratio between cities s and r, and households’ characteristics are assumed to be identical. This numerical simulation uses the estimates θ^ in Column (6) of Table 4. The Online Appendix provides two specifications of the dynamic catch-up process on fertility decisions that include nonlinear and discrete effects of age. Figure 6 View largeDownload slide Percentage change in the average number of children by city size simulated from Poisson estimates. Notes: The density elasticity of the number of children in Panel (a) is calculated as α^+φ^×Age using the estimates in Column (6) of Table 4. The percentage change in the average number of children in Panel (b) is calculated as [λs(θ^)−λr(θ^)]/λr(θ^)=Ratiosrα^+φ^×Age−1, where Ratiosr is the population density ratio between cities s and r, and households’ characteristics are assumed to be identical. This numerical simulation uses the estimates θ^ in Column (6) of Table 4. The Online Appendix provides two specifications of the dynamic catch-up process on fertility decisions that include nonlinear and discrete effects of age. Panel (b) of Figure 6 quantifies spatial variations in number of children by wife’s age, showing what percentage change in the average number of children is generated by the difference in city size, holding other variables equal. Among couples age 30, the estimated percentage change in the number of children between one city and a city with 10 times more people is –22.13% ( ≈10−0.237+0.004×30−1). If households in the baseline city have 1.5 children at age 30 on average, households in a city with 10 times more people have 1.168 children on average. The spatial gap shows ∼332 (=1500 − 1168) children per 1000 households. However, the estimated percentage change in the number of children between those cities for couples at age 49 is –6.07% ( ≈10−0.237+0.004×49−1). 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 is 2.066. The spatial gap shows ∼34 (=2200 − 2066) children per 1000 households.17 Although slight spatial variation in the average number of children between large and small cities remains, the important finding is that couples residing in larger cities have children relatively late in life, which reduces the spatial gap in the number of children around age 50. Thus far, the estimation results suggest that congestion costs in large cities discourage younger couples from bearing children, but the gap in completed fertility shrinks between large and small cities as couples age. To offer supportive evidence on this finding, this study examines whether agglomeration affects the timing of childbirth in the next subsection. 5.4. Agglomeration delays the birth of the first child Table 5 presents estimation results concerning how agglomeration affects the wife’s age at marriage. Importantly, in Column (3), the inclusion of dummies for university education decreases the coefficient on population density, which means that the spatial sorting of highly educated people, who tend to have children later in life, leads to an upward bias when the impact of congestion costs on fertility behavior is estimated. Table 5 Wife’s ages at marriage, city size and migration Explanatory variables  Dependent variable: wife’s age at marriage   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.130  0.119  0.077  0.125  0.079    (0.116)  (0.116)  (0.120)  (0.118)  (0.118)  D (1 = migration)    0.115      –0.021      (0.181)      (0.179)  D (1 = university graduate for husband)      0.709***    0.699***        (0.175)    (0.178)  D (1 = university graduate for wife)      1.478***    1.467***        (0.274)    (0.268)  D (1 = not healthy)        –0.245  –0.158          (0.215)  (0.201)  Old-age security motive score        –0.041  –0.041          (0.037)  (0.037)  D (1 = non-necessity of children)        –0.091  –0.139          (0.166)  (0.170)  Number of siblings        –0.104**  –0.032          (0.045)  (0.041)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1658  1658  1658  1658  1658  Adjusted R2  0.045  0.044  0.078  0.046  0.076  Explanatory variables  Dependent variable: wife’s age at marriage   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.130  0.119  0.077  0.125  0.079    (0.116)  (0.116)  (0.120)  (0.118)  (0.118)  D (1 = migration)    0.115      –0.021      (0.181)      (0.179)  D (1 = university graduate for husband)      0.709***    0.699***        (0.175)    (0.178)  D (1 = university graduate for wife)      1.478***    1.467***        (0.274)    (0.268)  D (1 = not healthy)        –0.245  –0.158          (0.215)  (0.201)  Old-age security motive score        –0.041  –0.041          (0.037)  (0.037)  D (1 = non-necessity of children)        –0.091  –0.139          (0.166)  (0.170)  Number of siblings        –0.104**  –0.032          (0.045)  (0.041)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1658  1658  1658  1658  1658  Adjusted R2  0.045  0.044  0.078  0.046  0.076  Notes: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Table 5 Wife’s ages at marriage, city size and migration Explanatory variables  Dependent variable: wife’s age at marriage   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.130  0.119  0.077  0.125  0.079    (0.116)  (0.116)  (0.120)  (0.118)  (0.118)  D (1 = migration)    0.115      –0.021      (0.181)      (0.179)  D (1 = university graduate for husband)      0.709***    0.699***        (0.175)    (0.178)  D (1 = university graduate for wife)      1.478***    1.467***        (0.274)    (0.268)  D (1 = not healthy)        –0.245  –0.158          (0.215)  (0.201)  Old-age security motive score        –0.041  –0.041          (0.037)  (0.037)  D (1 = non-necessity of children)        –0.091  –0.139          (0.166)  (0.170)  Number of siblings        –0.104**  –0.032          (0.045)  (0.041)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1658  1658  1658  1658  1658  Adjusted R2  0.045  0.044  0.078  0.046  0.076  Explanatory variables  Dependent variable: wife’s age at marriage   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.130  0.119  0.077  0.125  0.079    (0.116)  (0.116)  (0.120)  (0.118)  (0.118)  D (1 = migration)    0.115      –0.021      (0.181)      (0.179)  D (1 = university graduate for husband)      0.709***    0.699***        (0.175)    (0.178)  D (1 = university graduate for wife)      1.478***    1.467***        (0.274)    (0.268)  D (1 = not healthy)        –0.245  –0.158          (0.215)  (0.201)  Old-age security motive score        –0.041  –0.041          (0.037)  (0.037)  D (1 = non-necessity of children)        –0.091  –0.139          (0.166)  (0.170)  Number of siblings        –0.104**  –0.032          (0.045)  (0.041)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  1658  1658  1658  1658  1658  Adjusted R2  0.045  0.044  0.078  0.046  0.076  Notes: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Although the estimated coefficients on population density are positive in Columns (1)–(5), they are not significant at even the 10% level. It is not evident that agglomeration discourages the timing of marriage. Higher education, specifically for females, markedly delays age at marriage at the 1% level. In the baseline estimation, Column (5) shows that couples in which both spouses have a university education marry about 26 months later than those in which both have a nonuniversity education. Table 6 provides evidence on whether congestion costs in large cities delay the birth of the first child. As noted earlier, the inclusion of dummies for university education decreases the coefficient on population density in Column (3). However, the coefficient on population density remains significant. In the baseline estimation, Column (5) shows that couples in which both spouses have a university education bear their first child about 22 months later than those in which both have a nonuniversity education. Table 6 Wife’s ages at birth of first child, city size and migration Explanatory variables  Dependent variable: wife’s ages at birth of first child   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.290***  0.257***  0.205***  0.281***  0.180**    (0.072)  (0.074)  (0.071)  (0.071)  (0.073)  D (1 = migration)    0.356**      0.242      (0.168)      (0.168)  D (1 = university graduate for husband)      0.844***    0.813***        (0.152)    (0.154)  D (1 = university graduate for wife)      1.090***    1.086***        (0.190)    (0.190)  D (1 = not healthy)        0.034  0.110          (0.189)  (0.190)  Old-age security motive score        –0.030  –0.037          (0.031)  (0.030)  D (1 = non-necessity of children)        0.006  –0.009          (0.129)  (0.128)  Number of siblings        –0.121**  –0.045          (0.054)  (0.054)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  3880  3880  3880  3880  3880  Adjusted R2  0.044  0.045  0.072  0.045  0.072  Explanatory variables  Dependent variable: wife’s ages at birth of first child   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.290***  0.257***  0.205***  0.281***  0.180**    (0.072)  (0.074)  (0.071)  (0.071)  (0.073)  D (1 = migration)    0.356**      0.242      (0.168)      (0.168)  D (1 = university graduate for husband)      0.844***    0.813***        (0.152)    (0.154)  D (1 = university graduate for wife)      1.090***    1.086***        (0.190)    (0.190)  D (1 = not healthy)        0.034  0.110          (0.189)  (0.190)  Old-age security motive score        –0.030  –0.037          (0.031)  (0.030)  D (1 = non-necessity of children)        0.006  –0.009          (0.129)  (0.128)  Number of siblings        –0.121**  –0.045          (0.054)  (0.054)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  3880  3880  3880  3880  3880  Adjusted R2  0.044  0.045  0.072  0.045  0.072  Notes: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Table 6 Wife’s ages at birth of first child, city size and migration Explanatory variables  Dependent variable: wife’s ages at birth of first child   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.290***  0.257***  0.205***  0.281***  0.180**    (0.072)  (0.074)  (0.071)  (0.071)  (0.073)  D (1 = migration)    0.356**      0.242      (0.168)      (0.168)  D (1 = university graduate for husband)      0.844***    0.813***        (0.152)    (0.154)  D (1 = university graduate for wife)      1.090***    1.086***        (0.190)    (0.190)  D (1 = not healthy)        0.034  0.110          (0.189)  (0.190)  Old-age security motive score        –0.030  –0.037          (0.031)  (0.030)  D (1 = non-necessity of children)        0.006  –0.009          (0.129)  (0.128)  Number of siblings        –0.121**  –0.045          (0.054)  (0.054)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  3880  3880  3880  3880  3880  Adjusted R2  0.044  0.045  0.072  0.045  0.072  Explanatory variables  Dependent variable: wife’s ages at birth of first child   Full sample   (1)  (2)  (3)  (4)  (5)  Log (population density)  0.290***  0.257***  0.205***  0.281***  0.180**    (0.072)  (0.074)  (0.071)  (0.071)  (0.073)  D (1 = migration)    0.356**      0.242      (0.168)      (0.168)  D (1 = university graduate for husband)      0.844***    0.813***        (0.152)    (0.154)  D (1 = university graduate for wife)      1.090***    1.086***        (0.190)    (0.190)  D (1 = not healthy)        0.034  0.110          (0.189)  (0.190)  Old-age security motive score        –0.030  –0.037          (0.031)  (0.030)  D (1 = non-necessity of children)        0.006  –0.009          (0.129)  (0.128)  Number of siblings        –0.121**  –0.045          (0.054)  (0.054)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Number of observations  3880  3880  3880  3880  3880  Adjusted R2  0.044  0.045  0.072  0.045  0.072  Notes: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Unlike the estimation results for marriage, the estimated coefficients for population density are significantly positive at the 5% level in Columns (1)–(5). In Column (5), the density semi-elasticity of the number of children is 0.180. Using this value, the quantification shows that, holding other variables equal, couples residing in a city that is 10 times more populous delay childbirth by an average of ∼5 ( ≈0.180×log(10)) months.18 In sum, congestion costs strongly defer 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 couple’s age, although a statistically significant slight gap remains. 5.5. Robustness check for self-selected migration As discussed in Section 2, the endogenous migration choices of individuals with preference heterogeneity in the demand for children lead to biases in two ways. First, the magnitude of the effect of agglomeration on the number of children is overestimated when individuals with weak preferences for the quantity of children and with strong preferences for the quality of children migrate into large cities. This bias derives from the spatial sorting of individuals with preference heterogeneity. Second, the coefficient on the migration dummy γ is biased due to this self-selection. This study applies a classical approach to the selectivity bias correction (Heckman, 1979; Maddala, 1986), which is known as an endogenous binary-variable model.19 This study estimates the following regression model:   yir=αlog(Densr(i)t)+γMi+Xiβ+X˜iδ+Dr(i)Regη+DtYearψ+uir,Mi*=Wiπ+X˜iδ+Dr(i)Pref15η+DtYearψ+virMi=1 if Mi*>0, and 0 otherwise, where it is assumed that the error terms uir and vir follow bivariate normal distribution with mean 0 and covariance matrix   (σu2ρσuρσu1). The determinants of migration choice include a vector of household’s characteristics Wi (dummies for whether parents of the married couples are university graduates and the variables included in Zi) and a vector of prefecture dummies at age 15 Dr(i)Pref15, and vir is an error term. Note that a linear rather than a Poisson model is estimated. Therefore, the parameter α is not directly comparable with the corresponding parameter in the Poisson estimates. In the same manner, the wife’s age at marriage and at the birth of the first child is also estimated by this framework. Table 7 presents the estimation results of the endogenous binary-variable model. More importantly, the coefficients on the population density essentially do not change even after controlling for self-selected migration. However, the coefficients on migration drastically change after controlling for self-selection. Comparing Columns (3) and (4) of Table 7, completed fertility is highly affected by the migration experience, implying that migration costs have larger impacts on the demand for children in the long-term. Table 7 Estimation results for fertility decision and self-selected migration choice Explanatory variables  Dependent variable: number of children   Dependent variable: wife’s age at marriage   Dependent variable: wife’s age at birth of first child   Sample with wife’s age < 50   Sample with wife’s age ≥50   Full sample   Full sample   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  Log (population density)  –0.113***  –0.115***  –0.062**  –0.062**  0.079  0.012  0.180**  0.170**    (0.024)  (0.024)  (0.028)  (0.028)  (0.118)  (0.123)  (0.073)  (0.075)  D (1 = migration)  –0.116**  0.171  –0.068*  –0.823***  –0.021  3.970***  0.242  4.830***    (0.049)  (0.213)  (0.038)  (0.230)  (0.179)  (0.606)  (0.168)  (0.373)  D (1 = university graduate for husband)  –0.207***  –0.239***  –0.011  0.119  0.699***  0.210  0.813***  0.208    (0.033)  (0.046)  (0.057)  (0.081)  (0.178)  (0.237)  (0.154)  (0.190)  D (1 = university graduate for wife)  –0.140***  –0.154***  0.107  0.076  1.467***  1.197***  1.086***  0.998***    (0.036)  (0.035)  (0.070)  (0.068)  (0.268)  (0.292)  (0.190)  (0.180)  Husband’s income  0.031***  0.030***                (0.007)  (0.007)              Wife’s income  –0.030***  –0.030***                (0.010)  (0.010)              Hours worked last week for husband  0.013  0.013                (0.018)  (0.018)              Hours worked last week for wife  –0.054***  –0.054***                (0.019)  (0.019)              D (1 = nonlabor force for husband)  –0.069  –0.076                (0.244)  (0.246)              D (1 = nonlabor force for wife)  –0.188*  –0.187**                (0.097)  (0.095)              D (1 = not healthy)  –0.117**  –0.126**  –0.053  –0.074  –0.158  –0.186  0.110  0.088    (0.051)  (0.051)  (0.064)  (0.065)  (0.201)  (0.267)  (0.190)  (0.238)  Old-age security motive score  0.014  0.017  –0.001  –0.003  –0.041  0.015  –0.037  –0.026    (0.011)  (0.011)  (0.011)  (0.011)  (0.037)  (0.045)  (0.030)  (0.033)  D (1 = non-necessity of children)  –0.142***  –0.157***  –0.186***  –0.125***  –0.139  –0.355**  –0.009  –0.280*    (0.031)  (0.034)  (0.042)  (0.043)  (0.170)  (0.174)  (0.128)  (0.146)  Number of siblings  0.051**  0.046**  0.038**  0.043**  –0.032  –0.102*  –0.045  –0.088    (0.022)  (0.022)  (0.015)  (0.018)  (0.041)  (0.055)  (0.054)  (0.062)  Age, cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Control for endogenous migration choice  No  Yes  No  Yes  No  Yes  No  Yes  Explanatory variables  Dependent variable: number of children   Dependent variable: wife’s age at marriage   Dependent variable: wife’s age at birth of first child   Sample with wife’s age < 50   Sample with wife’s age ≥50   Full sample   Full sample   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  Log (population density)  –0.113***  –0.115***  –0.062**  –0.062**  0.079  0.012  0.180**  0.170**    (0.024)  (0.024)  (0.028)  (0.028)  (0.118)  (0.123)  (0.073)  (0.075)  D (1 = migration)  –0.116**  0.171  –0.068*  –0.823***  –0.021  3.970***  0.242  4.830***    (0.049)  (0.213)  (0.038)  (0.230)  (0.179)  (0.606)  (0.168)  (0.373)  D (1 = university graduate for husband)  –0.207***  –0.239***  –0.011  0.119  0.699***  0.210  0.813***  0.208    (0.033)  (0.046)  (0.057)  (0.081)  (0.178)  (0.237)  (0.154)  (0.190)  D (1 = university graduate for wife)  –0.140***  –0.154***  0.107  0.076  1.467***  1.197***  1.086***  0.998***    (0.036)  (0.035)  (0.070)  (0.068)  (0.268)  (0.292)  (0.190)  (0.180)  Husband’s income  0.031***  0.030***                (0.007)  (0.007)              Wife’s income  –0.030***  –0.030***                (0.010)  (0.010)              Hours worked last week for husband  0.013  0.013                (0.018)  (0.018)              Hours worked last week for wife  –0.054***  –0.054***                (0.019)  (0.019)              D (1 = nonlabor force for husband)  –0.069  –0.076                (0.244)  (0.246)              D (1 = nonlabor force for wife)  –0.188*  –0.187**                (0.097)  (0.095)              D (1 = not healthy)  –0.117**  –0.126**  –0.053  –0.074  –0.158  –0.186  0.110  0.088    (0.051)  (0.051)  (0.064)  (0.065)  (0.201)  (0.267)  (0.190)  (0.238)  Old-age security motive score  0.014  0.017  –0.001  –0.003  –0.041  0.015  –0.037  –0.026    (0.011)  (0.011)  (0.011)  (0.011)  (0.037)  (0.045)  (0.030)  (0.033)  D (1 = non-necessity of children)  –0.142***  –0.157***  –0.186***  –0.125***  –0.139  –0.355**  –0.009  –0.280*    (0.031)  (0.034)  (0.042)  (0.043)  (0.170)  (0.174)  (0.128)  (0.146)  Number of siblings  0.051**  0.046**  0.038**  0.043**  –0.032  –0.102*  –0.045  –0.088    (0.022)  (0.022)  (0.015)  (0.018)  (0.041)  (0.055)  (0.054)  (0.062)  Age, cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Control for endogenous migration choice  No  Yes  No  Yes  No  Yes  No  Yes  Explanatory variables  Treatment variable: D (1 = migration)   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  D (1 = university graduate for father)    0.225**    0.241**    0.135    0.280***      (0.107)    (0.098)    (0.112)    (0.070)  D (1 = university graduate for mother)    –0.109    –0.014    –0.146    –0.006      (0.150)    (0.331)    (0.269)    (0.135)  D (1 = university graduate for husband)    0.350***    0.454***    0.375***    0.374***      (0.066)    (0.101)    (0.081)    (0.062)  D (1 = university graduate for wife)    0.149*    –0.137    0.130    0.020      (0.081)    (0.085)    (0.113)    (0.056)  D (1 = not healthy)    0.129    –0.139    –0.003    –0.002      (0.094)    (0.102)    (0.103)    (0.075)  Old-age security motive score    –0.026*    –0.007    –0.040***    –0.007      (0.014)    (0.015)    (0.014)    (0.010)  D (1 = non-necessity of children)    0.151***    0.241***    0.154***    0.154***      (0.057)    (0.065)    (0.058)    (0.045)  Number of siblings    0.053    0.033    0.063**    0.026      (0.038)    (0.023)    (0.027)    (0.020)  Husband’s age    –0.011    –0.122    0.040    0.028      (0.049)    (0.080)    (0.046)    (0.031)  Husband’s age squared ( ×1/100)    0.033    0.082    –0.091**    –0.060**      (0.057)    (0.064)    (0.043)    (0.028)  Wife’s age    0.062    0.219**    0.140**    0.039      (0.063)    (0.091)    (0.063)    (0.035)  Wife’s age squared ( ×1/100)    –0.062    –0.163**    –0.050    0.012      (0.081)    (0.074)    (0.053)    (0.033)  ρ    –0.209    0.523***    –0.674***    –0.690***      (0.158)    (0.127)    (0.080)    (0.048)  σu    0.831***    0.909***    3.624***    4.080***      (0.016)    (0.049)    (0.179)    (0.113)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  1995  1995  1658  1658  3880  3880  Adjusted R2  0.260    0.031    0.076    0.072    Explanatory variables  Treatment variable: D (1 = migration)   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  D (1 = university graduate for father)    0.225**    0.241**    0.135    0.280***      (0.107)    (0.098)    (0.112)    (0.070)  D (1 = university graduate for mother)    –0.109    –0.014    –0.146    –0.006      (0.150)    (0.331)    (0.269)    (0.135)  D (1 = university graduate for husband)    0.350***    0.454***    0.375***    0.374***      (0.066)    (0.101)    (0.081)    (0.062)  D (1 = university graduate for wife)    0.149*    –0.137    0.130    0.020      (0.081)    (0.085)    (0.113)    (0.056)  D (1 = not healthy)    0.129    –0.139    –0.003    –0.002      (0.094)    (0.102)    (0.103)    (0.075)  Old-age security motive score    –0.026*    –0.007    –0.040***    –0.007      (0.014)    (0.015)    (0.014)    (0.010)  D (1 = non-necessity of children)    0.151***    0.241***    0.154***    0.154***      (0.057)    (0.065)    (0.058)    (0.045)  Number of siblings    0.053    0.033    0.063**    0.026      (0.038)    (0.023)    (0.027)    (0.020)  Husband’s age    –0.011    –0.122    0.040    0.028      (0.049)    (0.080)    (0.046)    (0.031)  Husband’s age squared ( ×1/100)    0.033    0.082    –0.091**    –0.060**      (0.057)    (0.064)    (0.043)    (0.028)  Wife’s age    0.062    0.219**    0.140**    0.039      (0.063)    (0.091)    (0.063)    (0.035)  Wife’s age squared ( ×1/100)    –0.062    –0.163**    –0.050    0.012      (0.081)    (0.074)    (0.053)    (0.033)  ρ    –0.209    0.523***    –0.674***    –0.690***      (0.158)    (0.127)    (0.080)    (0.048)  σu    0.831***    0.909***    3.624***    4.080***      (0.016)    (0.049)    (0.179)    (0.113)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  1995  1995  1658  1658  3880  3880  Adjusted R2  0.260    0.031    0.076    0.072    Notes: Heteroskedasticity-consistent standard errors clustered by cohort year are in parentheses. Constant is not reported. *,**,***Statistical significance at the 10, 5 and 1% levels, respectively. Table 7 Estimation results for fertility decision and self-selected migration choice Explanatory variables  Dependent variable: number of children   Dependent variable: wife’s age at marriage   Dependent variable: wife’s age at birth of first child   Sample with wife’s age < 50   Sample with wife’s age ≥50   Full sample   Full sample   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  Log (population density)  –0.113***  –0.115***  –0.062**  –0.062**  0.079  0.012  0.180**  0.170**    (0.024)  (0.024)  (0.028)  (0.028)  (0.118)  (0.123)  (0.073)  (0.075)  D (1 = migration)  –0.116**  0.171  –0.068*  –0.823***  –0.021  3.970***  0.242  4.830***    (0.049)  (0.213)  (0.038)  (0.230)  (0.179)  (0.606)  (0.168)  (0.373)  D (1 = university graduate for husband)  –0.207***  –0.239***  –0.011  0.119  0.699***  0.210  0.813***  0.208    (0.033)  (0.046)  (0.057)  (0.081)  (0.178)  (0.237)  (0.154)  (0.190)  D (1 = university graduate for wife)  –0.140***  –0.154***  0.107  0.076  1.467***  1.197***  1.086***  0.998***    (0.036)  (0.035)  (0.070)  (0.068)  (0.268)  (0.292)  (0.190)  (0.180)  Husband’s income  0.031***  0.030***                (0.007)  (0.007)              Wife’s income  –0.030***  –0.030***                (0.010)  (0.010)              Hours worked last week for husband  0.013  0.013                (0.018)  (0.018)              Hours worked last week for wife  –0.054***  –0.054***                (0.019)  (0.019)              D (1 = nonlabor force for husband)  –0.069  –0.076                (0.244)  (0.246)              D (1 = nonlabor force for wife)  –0.188*  –0.187**                (0.097)  (0.095)              D (1 = not healthy)  –0.117**  –0.126**  –0.053  –0.074  –0.158  –0.186  0.110  0.088    (0.051)  (0.051)  (0.064)  (0.065)  (0.201)  (0.267)  (0.190)  (0.238)  Old-age security motive score  0.014  0.017  –0.001  –0.003  –0.041  0.015  –0.037  –0.026    (0.011)  (0.011)  (0.011)  (0.011)  (0.037)  (0.045)  (0.030)  (0.033)  D (1 = non-necessity of children)  –0.142***  –0.157***  –0.186***  –0.125***  –0.139  –0.355**  –0.009  –0.280*    (0.031)  (0.034)  (0.042)  (0.043)  (0.170)  (0.174)  (0.128)  (0.146)  Number of siblings  0.051**  0.046**  0.038**  0.043**  –0.032  –0.102*  –0.045  –0.088    (0.022)  (0.022)  (0.015)  (0.018)  (0.041)  (0.055)  (0.054)  (0.062)  Age, cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Control for endogenous migration choice  No  Yes  No  Yes  No  Yes  No  Yes  Explanatory variables  Dependent variable: number of children   Dependent variable: wife’s age at marriage   Dependent variable: wife’s age at birth of first child   Sample with wife’s age < 50   Sample with wife’s age ≥50   Full sample   Full sample   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  Log (population density)  –0.113***  –0.115***  –0.062**  –0.062**  0.079  0.012  0.180**  0.170**    (0.024)  (0.024)  (0.028)  (0.028)  (0.118)  (0.123)  (0.073)  (0.075)  D (1 = migration)  –0.116**  0.171  –0.068*  –0.823***  –0.021  3.970***  0.242  4.830***    (0.049)  (0.213)  (0.038)  (0.230)  (0.179)  (0.606)  (0.168)  (0.373)  D (1 = university graduate for husband)  –0.207***  –0.239***  –0.011  0.119  0.699***  0.210  0.813***  0.208    (0.033)  (0.046)  (0.057)  (0.081)  (0.178)  (0.237)  (0.154)  (0.190)  D (1 = university graduate for wife)  –0.140***  –0.154***  0.107  0.076  1.467***  1.197***  1.086***  0.998***    (0.036)  (0.035)  (0.070)  (0.068)  (0.268)  (0.292)  (0.190)  (0.180)  Husband’s income  0.031***  0.030***                (0.007)  (0.007)              Wife’s income  –0.030***  –0.030***                (0.010)  (0.010)              Hours worked last week for husband  0.013  0.013                (0.018)  (0.018)              Hours worked last week for wife  –0.054***  –0.054***                (0.019)  (0.019)              D (1 = nonlabor force for husband)  –0.069  –0.076                (0.244)  (0.246)              D (1 = nonlabor force for wife)  –0.188*  –0.187**                (0.097)  (0.095)              D (1 = not healthy)  –0.117**  –0.126**  –0.053  –0.074  –0.158  –0.186  0.110  0.088    (0.051)  (0.051)  (0.064)  (0.065)  (0.201)  (0.267)  (0.190)  (0.238)  Old-age security motive score  0.014  0.017  –0.001  –0.003  –0.041  0.015  –0.037  –0.026    (0.011)  (0.011)  (0.011)  (0.011)  (0.037)  (0.045)  (0.030)  (0.033)  D (1 = non-necessity of children)  –0.142***  –0.157***  –0.186***  –0.125***  –0.139  –0.355**  –0.009  –0.280*    (0.031)  (0.034)  (0.042)  (0.043)  (0.170)  (0.174)  (0.128)  (0.146)  Number of siblings  0.051**  0.046**  0.038**  0.043**  –0.032  –0.102*  –0.045  –0.088    (0.022)  (0.022)  (0.015)  (0.018)  (0.041)  (0.055)  (0.054)  (0.062)  Age, cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Control for endogenous migration choice  No  Yes  No  Yes  No  Yes  No  Yes  Explanatory variables  Treatment variable: D (1 = migration)   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  D (1 = university graduate for father)    0.225**    0.241**    0.135    0.280***      (0.107)    (0.098)    (0.112)    (0.070)  D (1 = university graduate for mother)    –0.109    –0.014    –0.146    –0.006      (0.150)    (0.331)    (0.269)    (0.135)  D (1 = university graduate for husband)    0.350***    0.454***    0.375***    0.374***      (0.066)    (0.101)    (0.081)    (0.062)  D (1 = university graduate for wife)    0.149*    –0.137    0.130    0.020      (0.081)    (0.085)    (0.113)    (0.056)  D (1 = not healthy)    0.129    –0.139    –0.003    –0.002      (0.094)    (0.102)    (0.103)    (0.075)  Old-age security motive score    –0.026*    –0.007    –0.040***    –0.007      (0.014)    (0.015)    (0.014)    (0.010)  D (1 = non-necessity of children)    0.151***    0.241***    0.154***    0.154***      (0.057)    (0.065)    (0.058)    (0.045)  Number of siblings    0.053    0.033    0.063**    0.026      (0.038)    (0.023)    (0.027)    (0.020)  Husband’s age    –0.011    –0.122    0.040    0.028      (0.049)    (0.080)    (0.046)    (0.031)  Husband’s age squared ( ×1/100)    0.033    0.082    –0.091**    –0.060**      (0.057)    (0.064)    (0.043)    (0.028)  Wife’s age    0.062    0.219**    0.140**    0.039      (0.063)    (0.091)    (0.063)    (0.035)  Wife’s age squared ( ×1/100)    –0.062    –0.163**    –0.050    0.012      (0.081)    (0.074)    (0.053)    (0.033)  ρ    –0.209    0.523***    –0.674***    –0.690***      (0.158)    (0.127)    (0.080)    (0.048)  σu    0.831***    0.909***    3.624***    4.080***      (0.016)    (0.049)    (0.179)    (0.113)  Cohort groups, region and year dummies  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Number of observations  2339  2339  1995  1995  1658  1658  3880  3880  Adjusted R2  0.260    0.031    0.076    0.072    Explanatory variables  Treatment variable: D (1 = migration)   (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  D (1 = university graduate for father)    0.225**    0.241**    0.135    0.280***      (0.107)    (0.098)    (0.112)    (0.070)  D (1 = university graduate for mother)    –0.109    –0.014    –0.146    –0.006      (0.150)    (0.331)    (0.269)    (0.135)  D (1 = university graduate for husband)    0.350***    0.454***    0.375***    0.374***      (0.066)    (0.101)    (0.081)    (0.062)  D (1 = university graduate for wife)    0.149*    –0.137    0.130    0.020      (0.081)    (0.085)    (0.113)    (0.056)  D (1 = not healthy)    0.129    –0.139    –0.003    –0.002      (0.094)    (0.102)    (0.103)    (0.075)  Old-age security motive score    –0.026*    –0.007    –0.040***    –0.007      (0.014)    (0.015)    (0.014)    (0.010)  D (1 = non-necessity of children)    0.151***    0.241***    0.154***    0.154***