2.1.1 Direct effects: Intergenerational human capital investment.

From the perspective of life cycle theory, delaying marriage provides individuals with a critical time window to complete educational attainment (prolonging schooling), establish career trajectories (accumulating professional capital), and achieve psychological maturity (enhancing non-cognitive skills). This maturation effect directly influences intergenerational human capital investment, shaping children’s educational outcomes.

Life cycle theory conceptualizes life as a continuous developmental process in which individuals assume different social roles and face distinct developmental tasks at each stage [9–10]. Early marriage often coincides with critical periods of academic and career development, during which economic instability limits parents’ ability to invest in their children’s education and health [11–14]. Additionally, parents in the early stages of their careers tend to prioritize work commitments, reducing their availability for childcare and educational engagement. Young parenthood, mainly when unplanned or occurring outside of marriage, can introduce an external shock to family planning, further constraining the resources available for child development [15–16]. Under such circumstances, parenting often arises from external pressures rather than intrinsic motivation, which may diminish the intentionality and effectiveness of educational investment.

In contrast, delaying marriage allows individuals to extend their years of education [6,17] and transition into a phase of career stability [18]). Marriage at a more mature stage provides a stable social role and emotional support network, which broadens individuals’ perspectives and enhances professional prospects, ultimately leading to higher household incomes [19]. When material capital is sufficient, parents who marry later can allocate more significant financial resources toward high-quality educational investments, including conducive learning environments, educational expenditures, and nutritional support. Furthermore, greater psychological maturity enhances parents’ awareness of the long-term value of education, prompting them to adopt a strategic and sustained approach to educational planning [20–23]. For these parents, childbearing tends to be a deliberate decision embedded in long-term life planning [24], optimizing intergenerational human capital investment throughout the child’s life cycle.

However, excessively delayed marriage may also impose constraints on children’s educational outcomes. First, although late-marrying parents may be well-prepared for parenthood, their advanced career commitments could limit the time and energy available for child-rearing and academic involvement, potentially impeding children’s cognitive and non-cognitive skill development [25–26]. Second, intergenerational age misalignment may introduce financial and caregiving pressures, particularly as older parents enter retirement while their children are still in school. This dynamic may lead children to forgo higher education in favor of early labor market entry, thereby constraining their human capital accumulation. Third, more significant generational gaps between parents and children could impede effective communication and intergenerational understanding, weakening the educational environment [27–28].

These arguments suggest that parental marriage age exhibits a non-monotonic effect on children’s educational human capital, initially promoting and subsequently inhibiting educational outcomes as marriage age increases.

2.1.2 Indirect effects: Marital stability.

Extensive research has established that marital stability is a critical determinant of child development [29–30], and declining marital stability can negatively impact children’s educational human capital accumulation [31]. Marital instability disrupts the family environment and fosters economic insecurity, elevating psychological stress among children and adolescents, potentially compromising their educational attainment [32–35].

Parental marriage age is closely linked to marital stability, yet this relationship is not linear. Early marriage is associated with an increased risk of divorce, as insufficient premarital information and emotional immaturity contribute to marital instability [36–38]. However, delayed marriage does not unconditionally enhance marital stability. Recent studies indicate that beyond a certain threshold, further increases in marriage age elevate the risk of divorce, as individuals may face heightened social pressure to marry “less compatible” or “suboptimal” partners [36,39,40].

This marginal effect suggests a non-linear relationship between marriage age and marital stability, indicating a potential U-shaped link to children’s human capital [41]. Within a moderate range, delaying marriage enhances marital resilience, leading to a more stable environment for child-rearing [42]. Stable marital unions facilitate more outstanding parental commitment to intergenerational human capital investment, yielding more decisive arithmetic and literacy outcomes in children [5]. However, excessive delays in marriage may introduce new sources of marital strain, ultimately undermining the benefits of late marriage for children’s educational development.

Drawing on these theoretical insights, this study proposes the following hypothesis:

4.1.1 Benchmark regression results.

Table 4 reports the estimated effects of parental marriage age on their children’s education outcomes. OLS regression results from columns (1) and (2) show that the parents’ late marriage significantly impacts their children’s education (The first column is the category of children’s education, with a value range of 1–8. The second column is the length of education of the children, with a value range of 0–22. The same is as below). However, when parents marry later than a certain age, this positive effect will turn negative. This means there is an inverted U-shaped relationship between the marriage age of parents and the accumulation of human capital in children’s education. Further calculations have shown that, on the one hand, when parents married one year later, their children’s average years of schooling increased by 0.29 years, and about 2.35% (the average age of children in the sample is 12.22 years). This article calculates through a formula that the marriage age at the turning point is approximately 29.49 years old, which means when parents get married before the age of 29.49, getting married later is more beneficial for their children’s human capital; When parents get married beyond the age, getting married later may harm their children’s acquisition of education.

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Table 4. Regression results of parents’ marriage age on children’s education.

https://doi.org/10.1371/journal.pone.0322151.t004

The estimated coefficients of the control variables are consistent with existing research. Due to the scarcity of resources within the family, the greater the number of children, the lower the average educational investment the children receive and the lower the education years. The higher the family income, the longer the parent’s education, the higher the education outcomes of the children. An interesting finding is that the estimated coefficient for the gender of children is significantly negative, indicating that in recent years, the education level of girls has gradually improved, even surpassing that of boys. The possible reason is that with the implementation of the Family Planning Policy, when a family is limited to only one child, even if it is a daughter, parents will invest in their children’s human capital. Finally, compared to the children of rural families, the education outcomes of children in urban families are higher.

This article also changes the estimation model and the selection of research objects to demonstrate the robustness of the results. Considering the discrete characteristics of the education variable, this study draws on the ordered Probit model as a robustness test of OLS regression. The results are shown in columns (3) and (4) from Table 4, the significance and estimated parameter signs support the benchmark regression results. At the same time, parents’ higher education and higher family income increase children’s education probability.

Since the enrollment age for eligible children in China is 6 years old and the nine-year compulsory education system is implemented, eligible children enjoy nine years of basic free school education. After the age of 15, children will face three choices: not being able to attend high school and directly participating in work, vocational high school (with a term of 3 or 5 years, making it challenging to enter undergraduate universities), and ordinary high school (with a term of 3 years, a way to participating in the college entrance examination typically). The educational results under each choice are entirely different. Therefore, this article also replaces the limit of “completed education” in the benchmark regression with “15 years old and above (excluding 15 years old)”, and the regression results are shown in columns (5) and (6) of Table 4. The estimated coefficients confirm the robustness of the benchmark conclusion.

4.1.2 Robustness tests.

1. ① Introducing instrumental variables. Although children’s educational human capital does not affect the age at which their parents first marry, there may still be omissions of unobservable variables or self-selection, leading to endogeneity issues. For example, some individuals choose to delay marriage to provide their children with a better material foundation. To alleviate potential endogeneity issues, this article adopts “the closest distance from the province where the parents are located to the coastal port” (The data on the shortest distance from each province to the nearest coastal port came from PPData database) as an instrumental variable for the age at marriage of parents. The reason for selecting this variable is that being closer to coastal ports means more exposure to diverse cultures worldwide, accepting more concepts such as free love and independence at the marriage, and being more likely to choose to delay marriage [55]. Meanwhile, natural geographic variables have gained widespread recognition in research due to their homogeneity. Therefore, this variable can better meet the two conditions of correlation and homogeneity. From the second column of Table 5, it can be observed that the farther away from coastal ports, the earlier the age of marriage. The second-stage regression results in column (3) show that the positive effect of marriage age on children’s education is still significant.

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Table 5. Estimation results of instrumental variables.

https://doi.org/10.1371/journal.pone.0322151.t005

1. ② Group regression by turning point. The conclusion of Table 4 indicates an inverted U-shaped relationship between the accumulation of educational human capital of parents at marriage age and their children. But does the estimated turning point of the quadratic equation have economic significance? This article further divides the sample into two groups based on the calculated marriage age turning point of 29.49 that affects children’s education (since age is an integer, a value of 30 is taken here). The regression results are presented in columns (1) and (2) of Table 6. It is found that for couples married before the age of 30, the age of marriage significantly positively impacts their children’s education, and the coefficients are more significant than the estimated coefficients of the baseline regression. For couples who get married after age 30, the influence of marriage age turns negative, but it is not statistically significant. This may be because, for most eligible young people in China, relatively few get married after 30, with only 147 samples.
2. ③ Group regression by parents’ age. Parents born in different years have different historical backgrounds. For example, couples born in the era of the Family Planning Policy are limited in the number of children they can have. When there is only one child in the family, all the capital in the family is invested in that child, and their educational human capital is also higher. Therefore, this article divides parents into three categories based on their birth years: “1950-1960”, “1960-1970”, and “1970-1980” (due to the small sample of parents born after 1980, only 12 were included in the regression, so this group was discarded) and grouped for regression. The results of OLS regression after the regroup in columns (3) to (5) of Table 6 show that after changing the grouping standard, the estimated coefficient of marriage age on children’s education is positive at a significant level of 1%. The extension of the marriage age significantly improved the education of the children. In summary, the conclusion that late marriage improves children’s education is robust.

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Table 6. Estimation results of group regression.

https://doi.org/10.1371/journal.pone.0322151.t006

4.2.1 Benchmark regression results.

Existing studies have shown that mothers spend more time caring and educating for their children than fathers [42]. Then, is there a difference in the influence of fathers and mothers on their children’s education? The article next examines the impact of the marriage age of fathers and mothers on the education outcomes of their children to test Hypothesis 2. From the results reported in columns (1) and (4) of Table 7, it can be found that just the marriage age of the mother can significantly improve the education outcomes of the children. Also, we adopted the SUEST, testing based on a Seemingly Unrelated Regression (SUR), to statistically test whether there is a significant difference between the two coefficients. The P-values of the estimated coefficients for marriage age and the square term of marriage age are 0.012 and 0.015, respectively, indicating that the difference between fathers and mothers is statistically significant. The results based on the ordered probit model of columns (2) and (5) confirm the robustness of the results. Further regress and perform SUR tests on parents whose first marriage age is before 30. It was found that although the estimated coefficient of 1.615 for the mother’s marriage age is slightly higher than the estimated coefficient of 1.114 for the father’s marriage age, it is not statistically significant (The P-values of the estimated coefficients for marriage age and the square term of marriage age are 0.374 and 0.387).

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Table 7. Regression results of parents’ marriage age and children’s education.

https://doi.org/10.1371/journal.pone.0322151.t007

4.2.2 Considering changes in historical context and gender roles.

Over different historical periods, shifts in the availability of educational resources, societal attitudes toward marriage, and family structures have influenced the effect of parental marital age on children’s education. So, have parental characteristics changed over time and subsequently influenced children’s education? As female educational attainment has improved and labor force participation has risen, the role of mothers in children’s education has evolved across different periods. In earlier historical contexts, mothers primarily assumed caregiving responsibilities within the household. However, as modern women engage more actively in the workforce, their support for children’s education may have shifted from direct time investment to financial contributions or access to educational resources. To further examine whether the effect of parental marital age varies across historical periods, we conducted an in-depth analysis from two perspectives:

First, according to Section 4.1.2, we performed subgroup regression analysis based on parental birth cohorts. We categorized parents into three cohorts (born before 1960, between 1960 and 1970, and between 1970 and 1980) to investigate whether differences in historical contexts led to variations in how parental marital age influences children’s education. The empirical results in Table 8 show that the inverted U-shaped relationship between maternal marital age and children’s education is significant across all cohorts, with the peak effect consistently observed between ages 24 and 27. This indicates that the impact pattern of maternal marital age on children’s education remains stable across generations. In contrast, the effect of paternal marital age is insignificant for fathers born before 1960. Still, it becomes significant for those born between 1960 and 1970 and between 1970 and 1980, with a stable peak effect between ages 22 and 27. These findings suggest two key insights. First, while parental characteristics may have evolved, the fundamental influence of marital age on children’s education has not undergone systematic distortions. Second, consistent with our baseline results, the educational benefits associated with maternal marital age are more pronounced than those of paternal marital age.

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Table 8. Parental differences (Subgroup regression results by parental birth cohorts).

https://doi.org/10.1371/journal.pone.0322151.t008

Second, we conducted a period-based regression analysis based on parental marriage timing. Given the variations in marriage patterns across different historical periods in China, we categorized parents into two groups based on their marriage timing to examine whether the effect of marital age on children’s education has adjusted over time. Specifically, we divided marriage timing into two periods: before 1980 and 1980 or later, and performed separate regressions for each. This classification is primarily based on enacting the new marriage law in 1980, which introduced revised legal marriage age requirements. Before 1981, China adhered to the 1970s’ late marriage and late childbirth policy, resulting in relatively high average marriage ages. However, after 1981, the legal marriage age was set at 22 for men and 20 for women, leading to a decline in marriage age. Accordingly, we used this historical policy shift for our subgroup regression analysis.

The empirical results presented in Table 9 indicate that the effect of maternal marital age on children’s education remains significant before and after 1980, consistently exhibiting an inverted U-shaped relationship. This suggests that regardless of whether a mother married before or after 1980, both early and late marriages negatively affect children’s educational outcomes. In contrast, marriage at an optimal age yields the most positive impact. This finding may be attributed to the primary caregiving role of mothers within the family—despite changes in the broader social environment, a mother’s direct involvement in early childhood education (such as time spent with children and participation in early learning activities) remains a crucial determinant of educational success. Additionally, since the biological window for childbirth is relatively stable, an appropriately timed marriage is more likely to allow mothers to give birth within an optimal reproductive age, benefiting both children’s physical development and educational investment.

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Table 9. Parental differences (Subgroup regression results by parental marriage timing).

https://doi.org/10.1371/journal.pone.0322151.t009

In contrast, the effect of paternal marital age remains significant for fathers who married before 1980, following an inverted U-shaped pattern. However, for those who married after 1980, while the estimated coefficients maintain a similar direction, the overall effect is no longer statistically significant. This shift may be attributed to the relatively delayed role of fathers in family education and their greater susceptibility to societal changes. Compared to mothers, fathers tend to have less direct involvement in children’s education, with their contributions primarily reflected in economic support and the accumulation of social capital. As female educational attainment increased and female labor force participation rose in the post-1980 era, family caregiving dynamics underwent significant transformations. With mothers contributing more economically, the influence of paternal marital age on children’s education may have diminished as a key determinant.

Overall, these findings suggest that in the context of post-1980 social transformations, the influence of maternal marital age on children’s education has remained robust. In contrast, the effect of paternal marital age has weakened due to socioeconomic development and shifts in family caregiving structures. This further supports the notion that social changes shape family decision-making and intergenerational transmission mechanisms, highlighting the need to consider gender differences and their evolution across historical periods when examining the effects of marital age.