2.1 Families in Japan

Confucianism has strongly affected the family system in Asian countries, where repaying parents is considered a virtue; the philosophical rationale for strong family ties is traced to Catholicism in Europe (Koyano, Reference Koyano1996; Esping-Andersen, Reference Esping-Andersen1997; Tsutsui et al., Reference Tsutsui, Muramatsu and Higashino2014), resulting in a relatively large reliance on families rather than on society. In Japan, filial piety remains relatively strong, with caring for older parents traditionally being a family affair. According to Ministry of Health, Labour and Welfare (2020), in 2019, 28.2% of the primary caregivers for older adults requiring long-term care (LTC) were coresident couples of the younger generation (the older adults’ children and their partners). This figure is more than double the 12.1% of the care was provided by paid caregivers. Thus, the burden of care on the younger generation is still not being shouldered by the market.

Until the end of the WWII, Japan’s inheritance system was patrilineal, with the eldest son inheriting the family head’s entire estate. In 1947, the law was amended to allow family members other than the heir (typically, the eldest son) to inherit equally. However, for families that have existed for a long time or in farm families, a culture of inheritance by the family head (i.e., eldest son) still exists, along with heavier obligations attached to this role.

Moreover, the burden of care tends to be on a specific child and their spouse, who may live with that child’s parents. If the child living with the parents is the eldest son and heir, his wife tends to make her marriage decision with the understanding that she may eventually care for the parents-in-law (Ogawa and Ermisch, Reference Ogawa and Ermisch1996).Footnote ⁵

However, it should be mentioned that the masculine norm is slowly fading and that the tendency to care for one’s own parents has increased. Thus, while patrilineal co-residence remains more common (and although the practice of co-residence with parents is still stronger in Japan than in many advanced countries, co-residence itself has been declining over time), the gap between living with the husband’s parents and with the wife’s parents has been narrowing (National Institute of Population and Social Security Research, 2020).Footnote ⁶

2.2 Only children in Japan

A survey that has been conducted since 1940 shows that the percentage of only child families has gradually increased since the 1990s (Cabinet Office, 2021), indicating an increase from 10% in 2002 to 18.6% in 2015. Meanwhile, the percentage of families with two children has remained stable at around 50% for almost 40 years. The rise in only child families can also be attributed to the decline in households with three or more children since the early 2000s.

In Japan’s male-dominated society, relatively strong family norms persist, and the burden tends to be concentrated on the offspring, especially a specific child. Here, being a male or female only child is a unique characteristic in postmarital life (Yu and Hertog, Reference Yu and Hertog2018; Uchikoshi et al., Reference Uchikoshi, Raymo and Yoda2023). When an only child reaches adulthood, they automatically become the parents’ heir. If the only child is a male, they automatically become the eldest son. If the only child is female, no eldest son exists to serve as the typical successor, while no other siblings exist to share the burden within the natal family. Consequently, the natal families of only child women have to give up not only intergenerational relations but also their surnames and family lines at the time of their marriage, all of which have been preserved over generations.Footnote ⁷ Encouragingly, the trend toward masculine domination is weakening (as discussed earlier). With this shift, only children, regardless of gender, are increasingly expected to bear the responsibility of caring for their own parents, particularly among younger generations.

Notably, an only child has the advantage that they can enjoy transfers from their parents throughout their lives. A prime example of postmarital income transfers are bequests from their parents.Footnote ⁸ Combined with the discussion on investment in education, which is examined later, only children seem not merely to be at a disadvantage but also to benefit from intergenerational relations.

Finally, despite the prevalent preference for sons in Asia, the male-to-female ratio among only children is nearly equal, as will be demonstrated with data in Section 3.Footnote ⁹ Thus, in Japan, the preference for sons may not be as pronounced as in other Asian countries where the sex ratio at birth is more distorted. Furthermore, families that exhibit a strong son preference often place significant value on upholding traditional family structures. These families are more inclined to pursue having multiple children to ensure the continuation of family leadership or adhering to the customary norm of having two children. Consequently, one-child families are more likely to reflect family planning based on the desired number of children rather than only on gender preference.

3.1 The national survey on migration

The National Survey on Migration is a nationally representative survey from Japan, encompassing data on sibling configuration, birthplace prefecture, year of birth, and marital status of each family member. The data are collected by the National Institute of Population and Social Security Research through a random sampling method.Footnote ¹⁰ The surveyors distribute and collect the questionnaires for each household. This study uses the latest available waves from 1991, 1996, 2001, 2006, and 2011.Footnote ¹¹ The collection rates for each wave are 89.4%, 95.8%, 85.5%, 74.0%, and 74.7%, respectively. In this study, we use the following information for the analyses.

1. Only child dummy: The survey asks for the number of surviving older brothers, older sisters, younger brothers, and younger sisters. When none of these are present, the only child dummy equals one for these individuals. All others are assigned a value of 0.

2. Age at the time of the survey: To account for changing trends over five-year intervals, we control for the age of respondents at the time of the survey, along with information on the year of birth.

3. Years of schooling: The number of years of schooling for the individual is calculated from the highest school graduated category.

4. Birth year: The respondent’s year of birth is used.

5. Regional block: The survey asks for the prefecture where the respondent was born. In the analyses, the 47 prefectures are classified into ten blocks and used to account for regional characteristics.Footnote ¹²

3.2 Sample selection

Before examining the data, we highlight the key points regarding our samples. As explained later, this research explores marriage patterns of only children along with surplus analysis following the Choo and Siow (Reference Choo and Siow2006)’s framework. Then, we examine spousal SES matching based on the approach of Chiappori et al. (Reference Chiappori, Oreffice and Quintana-Domeque2018).

For the analyses of marriage patterns, we use information on the number of both single and married individuals. Ideally, the entire sample would be used for this analysis. However, due to data limitations discussed later, certain samples are excluded. Specifically, in the analyses of marriage patterns, while all single individuals from the survey are included, the sample of married individuals is restricted to household heads and their spouses. That is, married individuals who are not household heads or their spouses are excluded.

The issue with the dataset is that, while information on household members is available, detailed information about their spouses is not consistently provided. This information, such as the sibling composition, is only available for household heads and their spouses. Therefore, cases not involving household heads or their spouses must be excluded.Footnote ¹³

Next, for the analysis of spousal matching characteristics, following Chiappori et al. (Reference Chiappori, Oreffice and Quintana-Domeque2018), we use data from household heads and their spouses for whom all relevant information was available. Consequently, singles and married individuals who are not household heads or their spouses are excluded from this analysis (the former exclusion is due to the definition of the analysis).

Formally, the sample is restricted to individuals aged between 23 and 65 in the survey year, for whom complete educational background information is available. The upper age limit is set due to the definition of the sibling structure variable. The number of siblings in the questionnaire is limited to those who are still alive. This restriction helps exclude older respondents who may have lost a sibling after entering the marriage market. Furthermore, the sample is limited to individuals for whom information on sibling composition, year of birth, and home prefecture is available.

Given these restrictions, unmarried individuals are limited to those who have never been married. The sample of married couples is restricted to those for whom information on both spouses is available; specifically, it includes couples where the respondent is either the household head or the spouse of the household head, and who are currently married. Individuals who are divorced, widowed, or separated are excluded. In addition, the sample is limited to couples in which both the respondent and their spouse reside in the same household. To ensure this, the sample is further restricted to households with at least two members. As a result of these sample restrictions, the number of observations decreased from 66,468 to 55,752.

3.3 Summary statistics

Table 1 presents the descriptive statistics for each respondent’s gender and only-child status. For continuous variables, the figures indicate the median within each subsample, while percentages or the 25th and 75th percentiles within the subsample are provided in parentheses. For categorical variables, the figures represent the number of samples and the percentage within each group. The following key points can be observed from these data.

Table 1. Summary statistics

Notes: Continuous variables are reported as medians with 25th and 75th percentiles in parentheses. Categorical variables are reported as counts with within-group percentages. See Section 3 for details on data and sample construction.

First, the sample size of only children is necessarily small. Note that, as discussed in Section 2, no gender difference is observed for this variable, with the percentage of only children being about 7% each for men (=2032/(26,945+2032)) and women (=1921/(24,854+1921)). Second, only children’s marital status is more likely to be single than that of non-only children at the descriptive level. Third, the average birth year of only children is later than that of non-only children. This may reflect the increasing prevalence of only-child families over time.

Finally, the key variable of interest, educational background, exhibits a noticeable difference based on only-child status. Specifically, only children tend to have slightly higher education levels. Regarding the years of education by gender, men generally have a higher level of education. Specifically, a large proportion of men in the 12-year high school graduate category as well as in the highest 16-year category. Conversely, women are concentrated in the high school diploma group and the second-highest educational level (14 years of schooling). This suggests that the polarization of educational attainment is more pronounced among men.

4.1. Comparison with random matching

To capture the overall trend in marriage patterns among only children, we first compare the observed marriage patterns based on only-child status with those generated via random matching. For this purpose, we construct a counterfactual sample of randomly matched couples, following the permutation procedure employed by Chiappori et al. (Reference Chiappori, Oreffice and Quintana-Domeque2018). We assign pseudo-random IDs drawn from a uniform distribution to men and women, rank them accordingly, and match them based on these ranks.

Table 2 presents the observed and randomly generated patterns. Only children are more likely to marry other only children. Although the percentage difference in marriages between only children may seem small at first glance, it becomes striking when viewed from the only child’s perspective. For example, in the random matching scenario, the share of marriages between only children is 7.3% among men (96/1319) and 7.7% among women (96/1242). Meanwhile, in the observed data, it rises to 14.5% for men (191/1319) and 15.4% for women (191/1242). Formally, the chi-squared test strongly rejects the null hypothesis that only-child status and matching patterns are independent ( ${\chi ^2}\left( 1 \right) = 166.2$ , $p \lt 0.001$ ).

Table 2. Observed versus randomly matched marriage patterns

Notes: This table compares the observed marriage patterns with those generated under random matching. The columns indicate whether the husband is an only child, and the rows indicate the same for the wife. Each cell reports the number of couples for each combination, with the proportion relative to the total number of couples shown in parentheses. Random couples are generated by applying a random permutation to the observed married individuals, following the procedure of Chiappori et al. (Reference Chiappori, Oreffice and Quintana-Domeque2018). Men and women are each assigned IDs drawn from a uniform distribution, ranked accordingly, and then matched based on these ranks.

Despite the tendency of positive assortative matching, mixed marriages between only and non-only children also occur. As discussed above, according to Chiappori et al. (Reference Chiappori, Oreffice and Quintana-Domeque2018), perfect assortative matching would arise under a symmetric case wherein male and female characteristics play the same role in the surplus function, and the distributions of these characteristics are the same across genders (Proposition 1, p.169). This requires: (i) the distribution of only-child status is the same across genders; (ii) the distribution of SES is the same across genders; (iii) only-child status plays a symmetric role in the marital surplus function; (iv) SES plays a symmetric role as well. At the observable level, Table 1 in Section 3.3 shows that the proportion of only children is nearly identical for men and women, suggesting symmetry in this dimension. Conversely, men tend to have higher educational attainment and greater variance in schooling. Thus, the distribution of education, which we use as an SES proxy, already violates one of the conditions for the symmetric case, which may hinder perfect assortative matching from fully holding.

4.2 Formal analysis of marriage patterns

This subsection statistically verifies the two trends previously observed in the marriage patterns of only children. Specifically, we examine the likelihood of each marriage pattern. Specifically, the estimand is the average values of the following:

(1) $$E\left[ {Typ{e^{partner}}\left| {OnlyChild=1,X\left] { - E} \right[Typ{e^{partner}}} \right|OnlyChild=0,X} \right]$$

This equation shows the expected difference in the likelihood of marriage outcomes between only and non-only children, where ${Typ{e^{partner}} \in}$ ${\left\{ {onlychild,non{\hbox{-}}onlychild,single} \right\}}$ is defined as follows: $onlychild$ indicates that the partner is an only child, $non{\hbox{-}}onlychild$ indicates that the partner has siblings, and $single$ indicates that the individual remains unmarried. Here, $OnlyChild$ on the right-hand side denotes a dummy variable that equals one if the individual is an only child.

Then, we present the estimates of how marital status differs between only and non-only children, controlling for gender, year of birth, age, and birthplace, as shown in Eq.(1).Footnote ¹⁶

In the estimation, we employ the double-debiased machine learning for augmented inverse probability weighting estimator (Robins and Rotnitzky, Reference Robins and Rotnitzky1995; Chernozhukov et al., Reference Chernozhukov, Chetverikov, Demirer, Duflo, Hansen, Newey and Robins2018). While ordinary least squares (OLS) provides consistent estimators when the model is correctly specified, it can yield large biases under misspecification. Given the complexity of the confounding factors in the marriage market, strong reliance on linear specifications is risky, which motivates our use of double-debiased machine learning.

Double-debiased machine learning builds on augmented inverse probability weighting and incorporates cross-fitting, which mitigates the risk of overfitting and ensures asymptotic unbiasedness even when flexible machine learning methods are used. Nevertheless, double-debiased machine learning is not without limitations. It can suffer from large variance when the estimated propensity scores are close to zero or one, although this issue is not severe in our application (the minimum estimated propensity score is 0.038). Moreover, the protection against overfitting is only asymptotic; with small samples, this risk may not be fully alleviated. However, because our dataset is sufficiently large, these concerns are unlikely to affect our results. As shown in Table 1, our analysis is based on $N = 55,752$ individuals.Footnote ¹⁷

Finally, the specific method can be summarized as follows: In the first stage, we estimate the nuisance functions that model the relationship between the partner’s type and individual’s own only-child status, conditional on the control variables. To flexibly capture conditional means without relying on parametric assumptions, we implement a stacking algorithm that combines OLS, random forests, and Bayesian additive regression trees. In the second stage, these estimates are incorporated into the augmented inverse probability weighting procedure to obtain the final estimator. Formally, the nuisance functions are expressed as $\Pr [Typ{e^{partner}}|OnlyChild,X]$ and $\Pr[OnlyChild|X]$ . $X$ denotes the control variables including years of one’s own schooling, birth year, age, and region of birth. Note that we use robust standard error clustering at the household-level. We estimate this equation for each male and female sample. Technically, the estimator captures the percentage-point difference in the share of individuals in each marital status, defined by $Typ{e^{partner}}$ , between only children and non-only children. Intuitively, it shows how being an only child relates to the likelihood of each marriage state.

Figure 1 shows the estimated associations for $OnlyChild$ conditional on the type of marriage partner (as well as single status), which are sorted by own gender. The left panels show the results for singles, while the right panels show the results for marriage with only children. Note that we only present the results for the two statuses, as the values for the remaining group of those marrying non-only children are automatically calculated using these two results.

Figure 1. Estimated associations between only-child status and partner type.

Notes: This figure shows the different marital statuses according to only child status, namely, single (left graph) and married to an only child (right graph), estimated by Eq.(1), along with the 95% confidence intervals; thin lines show Bonferroni-corrected confidence intervals. All nuisance functions are estimated using the stacking method (Wolpert, Reference Wolpert1992; Breiman, Reference Breiman1996), which consists of OLS (including squared terms of age, birth year, and years of schooling), random forests (Breiman, Reference Breiman2001), and Bayesian additive regression trees (Chipman et al., Reference Chipman, George and McCulloch2006; Chipman et al., Reference Chipman, George and McCulloch2010). Standard errors clustered at the household level are in parentheses. We compare groups of only children and non-only children, and the estimates represent the differences in the likelihood of being in each status. Specifically, they indicate the likelihood of being single for only children minus that for non-only children, and the likelihood of marrying another only child for only children minus that for non-only children, respectively.

Comparing the estimated associations across the panels, we obtain four main insights: First, considering the panel as a whole, we observe similar trends in each panel regardless of gender. Second, the panel of singles reveals that only children are more likely to remain single than non-only children. The estimated differences are 0.07 for men and 0.05 for women. Although the point estimates are somewhat larger for men, the gender difference is not statistically significant.Footnote ¹⁸ Third, only children are more likely to marry only-child partners. The related values are 0.05 for men and 0.06 for women. Finally, inextricably associated with the above results, the only-child status reduces the likelihood of marrying a non-only-child partner by 0.12 for men and 0.11 for women.

These results highlight two important points. First, people choose mates in a positive assortative manner regarding only-child status.Footnote ¹⁹ Second, only children are less likely to get married. These results indicate that family size tends to increase with marriage for non-only children. Consequently, family-size disparities are heightened by dynamics within the marriage market.

4.3 Systematic returns to marriage

Here, we estimate marriage returns, thus offering a structural perspective on the trends observed in the previous subsections. We first estimate the household-level marriage gain. According to Choo and Siow (Reference Choo and Siow2006), the total systematic gain to marriage for a type $i$ male and type $j$ female can be identified by estimating the logarithm of the following variable:

(2) $${\Pi _{i{\rm{*}}j}} = {{{\mu _{ij}}} \over {\sqrt {{\mu _{i0}} \times {\mu _{0j}}} }}$$

where ${\mu _i}$ represents the number of marriages between type $i$ males and type $j$ females, whereas ${\mu _{i0}}$ and ${\mu _{0j}}$ denote the number of single males and females of each respective type. The larger this value, the greater the relative return on marriage for types $i$ and $j$ compared to remaining single. As noted in Choo and Siow (Reference Choo and Siow2006), the calculation normalizes by the number of singles, eliminating scale effects.

Additionally, individual-level systematic return can be computed. The return from marriage for a type $i$ male to a type $j$ female is given by:

(3) $${n_{ij}} = {\rm{ln}}\left( {{{{\mu _{ij}}} \over {{\mu _{i0}}}}} \right)$$

Similarly, the systematic return from marriage for a type $j$ female to a type $i$ male is:

(4) $${N_{ij}} = {\rm{ln}}\left( {{{{\mu _{ij}}} \over {{\mu _{0j}}}}} \right)$$

which can be identified through this estimation.

Table 3 shows the estimated household- and individual-level returns to marriage by type $ij$ , specifically focusing on the combinations of the spouses’ only-child statuses. Table 3 categorizes marriage patterns by only-child status, naming combinations in the order of male and female. Each row corresponds to a specific marriage pattern. For instance, a marriage between a non-only child male and an only child female is labeled as “Non-only child – Only child marriage.” The three columns report the total return to marriage in Eq.(2), male’s individual return in Eq.(3), and female’s individual return in Eq.(4).

Table 3. Systematic returns to marriage

Notes: This table reports the estimated household-level and individual-level returns to marriage by spouse-type combination, based on each partner’s only-child status. Marriage types are labeled according to the only-child status of the male and female spouse, respectively. For example, a union between a non-only child male and an only child female is labeled as “Non-only child – Only child marriage.” Each row corresponds to a specific marriage pattern. The three columns report: the total return to marriage in Eq.(2); the male individual return in Eq.(3); and the female individual return in Eq.(4).

The highest total return is observed for marriages between non-only children, followed by mixed marriages where the female is an only child, then mixed marriages where the male is an only child. The lowest return is observed in marriages between two only children. This suggests that marriages involving only children tend to have lower returns. Furthermore, a comparison between mixed marriages where the husband is an only child and those where the wife is an only child reveals that the surplus size is generally similar. Thus, the presence of an only child has limited gender-based impact on the total household surplus. At the individual level, two main findings emerge: On the one hand, in homogeneous marriages concerning only-child status, females generally have higher returns. On the other hand, in mixed marriages, the only-child partner consistently attains higher individual returns than the non-only-child partner, regardless of gender. In addition, the gender difference in the surplus loss from marrying an only child appears small, with no clear pattern emerging.

5.1 Estimand

This subsection presents the estimands that are estimated in the following sections. Let $SE{S^{partner}}$ denote the partner’s SES. The estimand here is the average values of the following expression:

(5) $$E\left[ {SE{S^{\ partner}}{\rm{\;}}\left| {{\rm{\;}}OnlyChild=1,X\left] { - E} \right[SE{S^{\ partner}}{\rm{\;}}} \right|{\rm{\;}}OnlyChild=0,X} \right].$$

Eq.(5) shows that only children’s partners are likely to be more or less educated than non-only children’s partners. Note that if we assume $E[SE{S^{partner}}|OnlyChild,X] = {\beta _0} + {\beta _1}OnlyChild + \beta {\bf{X}} $ , we can use the same approach as in Chiappori et al. (Reference Chiappori, Oreffice and Quintana-Domeque2018). However, the following section proposes a more flexible estimation strategy rather than relying on such a linear specification.

In the following analyses, we use SES as a proxy for a partner’s attractiveness other than only-child status. As in Chiappori et al. (Reference Chiappori, Oreffice and Quintana-Domeque2018), we assume that, holding other conditions constant, individuals want a marriage partner with a higher SES. Thus, when Eq.(5) takes negative values, the married partner’s SES is lower for the only child, suggesting the existence of an only child penalty and vice versa.

5.2 Estimation method

We estimate how the partner’s SES differs between only and non-only children, controlling for $X$ , as described in Eq.(5) and its estimand. The dependent variable is $SE{S^{partner}}$ , which captures attractiveness other than only-child status. Operationally, following Chiappori et al. (Reference Chiappori, Oreffice and Quintana-Domeque2018), we proxy $SE{S^{partner}}$ by the partner’s years of schooling. As in the previous analysis, $OnlyChild$ , our variable of interest, is a dummy variable that equals one for an only child. $X$ includes own years of schooling, birth year, age, and birth region. Again, we control for the individual’s years of schooling to focus on the disparity in adulthood and to consider positive assortativity on education for couples. Note that the same machine-learning procedure is followed as in the previous analysis in Section 4.2.

5.3 Results: partner’s years of schooling (Pooled sample analysis)

Figure 2 shows the estimated associations of $OnlyChild$ using the total sample by gender. The panel presents the estimated relationship between only-child status and the spouse’s years of schooling. Figure 2 does not show a significant only-child-matching premium or penalty in the pooled sample for either men or women.

Figure 2. Estimated differences in partners’ years of schooling by only-child status (Pooled sample).

Notes: This figure shows the difference in partners’ years of schooling according to only child status, estimated by Eq.(5), along with the 95% confidence intervals; thin lines show Bonferroni-corrected confidence intervals. All nuisance functions are estimated using the stacking method (Wolpert, Reference Wolpert1992; Breiman, Reference Breiman1996), which consists of OLS (including squared terms of age, birth year, and years of schooling), random forests (Breiman, Reference Breiman2001), and Bayesian additive regression trees (Chipman et al., Reference Chipman, George and McCulloch2006; Chipman et al., Reference Chipman, George and McCulloch2010). Standard errors clustered at the household level are in parentheses. We compare groups of only children and non-only children, and the estimates represent the differences in their partners’ years of schooling after controlling for other variables. Specifically, they indicate the years of schooling of only children’s partners minus those of non-only children’s partners.

5.4 Results: partner’s years of schooling (Subsample analysis by partner’s status)

As we have seen, the difference is small and unclear in the results for the pooled sample. However, considering that the benefits of larger family size may differ, the partner’s only child status may matter in determining the premium/penalty. Therefore, we analyze the SES penalty using subsamples characterized by the partner’s only child status.

Figure 3 presents the results for this subsample analysis, restricted to the respondent’s gender and the marriage partner’s only-child status. Similar to the pooled-sample figure (Figure 2), the upper and lower parts of this figure correspond to the male and female samples, respectively. Furthermore, we show the results for the left-hand panels with individuals whose marriage partner is a non-only child, and the right panels for individuals whose partner is an only child.

Figure 3. Estimated differences in partners’ years of schooling by only-child status (Subsample analysis).

Notes: This figure shows the difference in partners’ years of schooling for subsamples defined by partner type, namely, married to a non-only child (left graph) and married to an only child (right graph), estimated by Eq.(5), along with the 95% confidence intervals; thin lines show Bonferroni-corrected confidence intervals. All nuisance functions are estimated using the stacking method (Wolpert, Reference Wolpert1992; Breiman, Reference Breiman1996), which consists of OLS (including squared terms of age, birth year, and years of schooling), random forests (Breiman, Reference Breiman2001), and Bayesian additive regression trees (Chipman et al., Reference Chipman, George and McCulloch2006; Chipman et al., Reference Chipman, George and McCulloch2010). Standard errors clustered at the household level are in parentheses. We compare groups of only children and non-only children, and the estimates represent the differences in their partners’ years of schooling after controlling for other variables. Specifically, they are calculated as the years of schooling of only children’s partners minus those of non-only children’s partners.

Figure 3 shows that the results vary considerably by the respondent’s gender and the partner’s only-child status. In the subsample in which the spouse is a non-only child, the estimated associations for both men and women are close to zero, indicating that an individual’s only-child status is not significantly related to their partner’s years of schooling in such marriages. However, in the subsample where the partner is an only child, gender-specific patterns emerge: the association for men remains near zero (−0.03, not significant at the 5 % level), whereas the association for women is notably negative at −0.63 and statistically significant. The penalty for female only-children married to male only-children (−0.63) is nearly twice the average gender gap observed in the full sample (0.34). Given that a gap of 0.34 years is already substantial, this comparison illustrates the considerable magnitude of the estimated association. A more detailed interpretation of these findings is presented in Section 6.

7.1 Heterogeneity in only-child marriage matching outcomes

Here, we examine how only-child marriage matching outcomes vary with heterogeneity. In particular, we focus on two types of heterogeneity. The first is the demographic characteristics such as birth year and age. The meaning of being an only child may change over time, and individuals may change their marriage behaviors depending on their own age. The second is educational background. A higher level of education may increase one’s attractiveness and mitigate the penalty associated with being an only child. In addition, if caregiving duties are critical for their attractiveness, one may purchase these services from the market if they can sufficiently afford to do so.

To explore these issues, we analyze the patterns of heterogeneity separately for men and women. Specifically, we estimate a linear approximation model of the conditional mean differences using the double-debiased machine learning framework. Semenova and Chernozhukov (Reference Semenova and Chernozhukov2021) extended the work of Chernozhukov et al. (Reference Chernozhukov, Chetverikov, Demirer, Duflo, Hansen, Newey and Robins2018) and proposed a method to estimate such linear approximation models for mean differences. This method reduces misspecification errors while preserving asymptotic unbiasedness and normality, similar to the augmented inverse probability weighting estimator, and allows for approximate computation of confidence intervals. For these reasons, we employ this method in our heterogeneity analysis.

Figure 4 shows the results of the heterogeneity analysis of marriage patterns. We first examine the association with birth year. The results show that the more recent the respondent’s birth cohort, the stronger the main patterns: only children are somewhat more likely to remain single (though this estimated association is not statistically significant), tend to marry other only children, and are correspondingly less likely to marry non-only children. Regarding age, being older at the time of the survey is not significantly related to the likelihood of remaining single, but it shows a stronger tendency for only children to marry other only children. For education, the magnitudes of the main patterns become weaker. We next interpret these results from the perspective of economic incentives to form larger families and parental monetary transfers.

Figure 4. Estimated associations between only-child status and partner type (Heterogeneity analysis).

Notes: This figure shows the best linear projection of the conditional difference in marital outcomes by only-child status, single (left graph) and married to an only child partner (right graph), along with the 95% confidence intervals; thin lines show Bonferroni-corrected confidence intervals. All nuisance functions are estimated using the stacking method (Wolpert, Reference Wolpert1992; Breiman, Reference Breiman1996), which consists of OLS (including squared terms of age, birth year, and years of schooling), random forests (Breiman, Reference Breiman2001), and Bayesian additive regression trees (Chipman et al., Reference Chipman, George and McCulloch2006; Chipman et al., Reference Chipman, George and McCulloch2010). Standard errors clustered at the household level are in parentheses. We compare groups of only children and non-only children. Each variable is interpreted as follows. The coefficient for women is relative to men (the omitted category). Years of schooling, birth year, and age estimates represent the association between the dependent variable and a one – standard-deviation change from the mean of these variables, respectively.

Figure 4 shows results for birth year that can be understood if we account for the circumstances in which Japan has experienced the gradual socialization of older adults’ care through public policies (and slowly fading social norms regarding filial obligations).Footnote ²¹ However, this trend of socialization of care may also reflect the trend of women’s advancement in society and the decrease in their labor in households. Women who were typically used to care for their parents and the parents-in-law are now more difficult to rely on as caregivers. Consequently, the difficulty of caregiving arrangements within households may lead to the enhanced trend that people choose mates in a positive assortative manner based on only child status (i.e., only children are less likely to be chosen as a marital partners at the market level, even though those who do marry are more likely to marry another only child). In terms of other factors, such as monetary transfer, only children’s attractiveness may be weakened by the declining relative importance of parental monetary transfers compared with their own economic capabilities.

Regarding the heterogeneity in age, the main trend becomes more prominent as respondents get older at the time of the survey. Given that younger individuals remain single, this result reflects that the trend regarding the choice of marriage partner becomes even stronger when comparing those who are already married and young compared to those who are older. This suggests that individuals who marry at a later age may be selecting partners with a more realistic understanding of caregiving responsibilities. The results for education level may reflect that only children can overcome their disadvantages if one’s educational background is higher, as discussed above.

Finally, Figure 5 shows the estimates of the matching premium/penalty measured by the partner’s SES. The main results are not significantly related to either own birth year, age, or education. In summary, heterogeneity appears to influence the choice of marital partner based only on sibling structure and not the partner’s SES.

Figure 5. Estimated differences in partners’ years of schooling by only-child status (Heterogeneity analysis).

Notes: This figure shows the best linear projection of the conditional difference in partners’ years of schooling, along with the 95% confidence intervals; thin lines show Bonferroni-corrected confidence intervals. All nuisance functions are estimated using the stacking method (Wolpert, Reference Wolpert1992; Breiman, Reference Breiman1996), which consists of OLS (including the squared terms of age, birth year, and years of schooling), random forests (Breiman, Reference Breiman2001), and Bayesian additive regression trees (Chipman et al., Reference Chipman, George and McCulloch2006; Chipman et al., Reference Chipman, George and McCulloch2010). Standard errors clustered at the household level are in parentheses. We compare groups of only children and non-only children. Each variable is interpreted as follows. The coefficient for women is relative to men (the omitted category). For the partner variable, the coefficient for only children is relative to marriages with partners who are non-only children (the omitted category). Years of schooling, birth year, and age estimates represent the association between the dependent variable and a one-standard-deviation change from the mean of these variables, respectively.

7.2 Excluding education from controls

This subsection examines whether our main result holds when education is not controlled for. As discussed in the main text, only children tend to be more educated, which may offset the penalty. Thus, we also explore how our main results change once positive educational assortativity is taken into account. In Appendix C, we follow the same procedure as in the main text but exclude the respondent’s own education from the control variables.

According to Appendix C, only children are more likely to remain single and more likely to marry another only child, consistent with the main results obtained without controlling for education. However, the results for years of schooling show a modest deviation from the main findings. A clear difference emerges depending on the type of marriage partner: Being married to a non-only child is associated with a significantly higher partner education level for only children, although the estimated difference is relatively small. Conversely, the partner’s education tends to decrease for both male and female only children who marry another only child. As the main results show, this is particularly evident for women, with estimated associations that are significant and of similar magnitude.

In summary, although the impact is small, a notable difference from the main result is the presence of a premium for those married to non-only children. This pattern is likely due to the omission of education controls and reflects the well-documented positive correlation in educational attainment between spouses. However, this does not contradict our main finding of a penalty associated with marrying an only child.

7.3 Alternative sibling positions

Thus far, we have examined the relationships between being an only child and marriage patterns. However, the underlying factors driving these patterns remain to be understood. To gain further insights, we conduct an additional analysis that considers alternative sibling positions and interprets them in terms of intergenerational relationships. If such relationships account for the disadvantages experienced by only children in the marriage market, policy interventions, such as promoting the socialization of informal care, could help mitigate these penalties.

In this context, we explore two alternative sibling positions: the status of being the eldest son and that of being the eldest child. In Japan, the eldest son (and their wife) traditionally bears certain obligations, including caring for their parents. Similarly, the eldest daughter with no male siblings is expected to assume this role. While the influence of the eldest son is widely known, the concept of primogeniture, wherein inheritance goes to the eldest child, suggests that birth order may be more significant than simply being the eldest son. Recent trends indicate a growing preference for individuals to take care of their own parents and expect their own children to care for them. Additionally, considering the persistent gender gap in the provision of informal care, women are expected to care for their parents even if they have younger brothers. If two siblings have a significant age difference, the first-born effect may be even more pronounced than that of the eldest son. Considering these two cases, we test whether and how these sibling positions matter in shaping marriage patterns. To focus on sibling position, we analyze samples from families with only two siblings. This approach allows us to extend our main findings on only-child marriage matching outcomes and make meaningful comparisons (for the detailed analysis, see Appendix D).

Two key findings emerge. First, patrilineal heiresses who marry only children exhibit patterns that, while not statistically significant, are partially consistent with the main results regarding the marital matching patterns based on their partners’ types and educational background of only-child women. Specifically, the observed association for patrilineal heiresses married to an only child aligns with our main findings, indicating a sizable difference; however, it is not statistically significant. The absence of a partner education penalty for heiresses married to individuals who are non-only children also coincides with our results for only children.

Second, among men expected to bear family responsibilities, especially patrilineal heirs, we observe clear tendencies in partner selection. Specifically, they tend to have a higher probability of remaining single and are more likely to avoid marrying only children. They may themselves be avoided due to their family responsibilities, which mirrors the patterns observed for only children. Moreover, the tendency of eldest sons with siblings to avoid only children does not contradict the main result of positive assortativity by only-child status. Instead, it may suggest that these eldest sons, who are likely to bear heavier familial duties, are more cautious in choosing a spouse who, as an only child, may prioritize caring for their own parents.

These findings do not dismiss the possibility that the strength of intergenerational relationships plays a role in the penalties faced by only children. Furthermore, the penalty associated with being an only child exceeds that of being an heir with one sibling, as suggested by the analyses based on the two definitions. This highlights the potential challenges faced by only children who lack the support of siblings; conversely, heirs under either of the two definitions can share their responsibilities among siblings.