Introduction

With respect to the rise and fall of the country and the well-being of the people, fertility is a basic and overarching strategic issue. However, in response to the dual pressures of an aging population and decreasing numbers of children, the fertility issues faced by China have become increasingly complex and severe (Campisi et al. 2020). Accordingly, China gradually relaxed its fertility policy and successively implemented a “two-child” fertility policy for couples in which either the husband or the wife is from a single-child family as well as “universal two-child” and “universal three-child” policies. However, the effects of these policies have not yet been optimized. As shown in Fig. 1, since the implementation of the universal two-child policy in 2016, China’s birth rate has repeatedly reached new lows, decreasing from 13.57% in 2016 to 6.77% in 2022, and China is currently experiencing ultralow fertility levels. The relaxation of the fertility “access threshold” has not effectively alleviated the issue of these continuing low fertility rates. Therefore, how can the problem of endogenous low fertility levels be addressed, and how can the effects of fertility policies be improved? In this context, it is necessary to start by examining the willingness of groups targeted by these policies to have multiple children, that is, to improve the response of first-time mothers to the two- and three-child policies. In this context, it is important to clarify the key factors affecting family multichild behavior at present and to formulate corresponding support measures to increase the potential of fertility policies and promote the long-term balanced development of the population.Footnote 1

Fig. 1
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Fertility in China: 2016–2022.

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Moreover, the high demand of Chinese people for equal access to quality educational opportunities has also caused the country to attach a great deal of importance to the problem of educational inequality. Since 2013, government work reports have emphasized “educational equality” and attempted to address educational inequality by implementing various measures, such as increasing the level of public education investment (Tang et al. 2020) and expanding educational enrollment (Luo et al. 2018). However, inequality in the field of education remains prominent. Due to increasing educational inequality, problems such as impoverished families that are hardly able to nurture outstanding children and the solidification of social classes are becoming increasingly prominent, resulting in the Matthew effect, according to which “the strong get stronger, the weak get weaker”; this situation has serious negative effects on economic growth, social stability and personal development (Lutz and McGillivray 2015). Therefore, has educational inequality become a “roadblock” with regard to families’ desire to have additional children?

According to previous research, the explicit costs of education have a negative effect on family multichild behavior. For example, Baizan and Nie (2024) reported that fierce competition for education increases the education costs associated with children, especially the explicit education costs associated with having a second child. Therefore, families that pay attention to the quality of education usually consider whether they should have a second child carefully. In the context of educational inequality, parents aim to increase the competitiveness of their children in the struggle for high-quality education resources by purchasing houses in key school districts (Li 2024), spending money on school selection (Liu and Liu 2024), and strengthening after-school tutoring (Zhou and Chen 2023), among other approaches, thus increasing the explicit costs of education for families. In theory, educational inequality negatively affects family multichild behavior by aggravating the explicit costs of education.

In fact, in addition to the explicit costs of education, educational inequality has led to the increasingly common phenomenon of “accompanying students”, according to which mothers take full responsibility for their children’s lives and education. Due to the increasing amounts of time and energy spent educating children, women also face the risk of a “wage penalty” caused by their reduced working hours, which greatly increases the opportunity costs and time costs faced by families, particularly by women; that is, the implicit costs of education faced by families increase in this context (Luo et al. 2022), thus further affecting families’ childbearing behavior with respect to multiple children. However, most previous studies have focused on the explicit costs of education and failed to explore the impact of educational inequality on multichild behavior from the perspective of the implicit costs of education. Therefore, from a perspective that takes both these explicit and implicit costs into account, this paper explores the mechanism underlying the effect of educational inequality on multichild behavior with the goals of enriching and contributing to the literature on this topic.

Given the fact that educational inequality is increasing, it is particularly important to determine the extent to which educational inequality affects families’ multichild behavior. Unfortunately, the literature has not provided a complete theoretical and empirical framework for exploring the relationship between educational inequality and multichild behavior. Accordingly, the following questions are investigated in depth with the goal of addressing this deficiency. Does educational inequality affect the fertility rate of families? If this effect is confirmed, then what is the main mechanism underlying it? Are these issues heterogeneous depending on women’s education level, urban or rural classification, and urban grade? In addition, give that decreasing fertility rates are due not only to the decline in the actual number of births in families (i.e., the quantity effect) but also to days in women’s childbearing time (i.e., the progress effect) (Yu and Han 2022), this paper further analyzes the impact of educational inequality on the birth intervals of families with two childrenFootnote 2.

One challenge in attempts to address these questions is the issue of how educational inequality should be measured. First, educational inequality encompasses three dimensions: inequality in terms of educational starting points, process, and outcomes (Li 2006). Therefore, indicators that have commonly been used in the literature, such as enrollment rates (Li 2014), family education input (Chen and Wang 2018), and students’ cognitive ability (Fang and Huang 2020), are insufficient. Second, with respect to basic education at this stage, it is crucial to focus on ensuring “equality in quality” (Lai et al. 2016). Previous measures of educational inequality, such as the standard deviation, range, Theil index, Gini coefficient and other macroaggregate indicators, have focused primarily on inequality in terms of the quantity of education (Shi and Zhang 2018). Therefore, this paper uses the presence of “super high schools” within cities as a measure of educational inequality.

Hitherto, no clear definition of “super high school” has been accepted in academic circles, and due to the different mechanisms by which this phenomenon can emerge, the nature and categories of “super high schools” also differFootnote 3. However, most scholars have maintained that “in China’s social transformation, the combination of government administrative impetus, market supply and demand mechanisms and individual rational choice are formed, and the large scale of high-quality students (monopolizing high-quality local students), rich educational resources (monopolizing high-quality local teachers and facilities), and especially the high enrollment rate (monopolizing the opportunities for admission to domestic first-class universities)” represent the core characteristics of super high schools (Fang and Lu 2022; Wang et al. 2023).

On the one hand, the existence of “super high schools” fully embodies the three dimensions of educational inequality. Inequality in terms of educational starting points is reflected by the inconsistency of school requirements and the unequal means of admission; inequality in terms of educational processes is reflected by significant differences in basic facilities, unequal levels of teachers and uneven degrees of social support; and inequality in terms of educational outcomes is reflected by differences in the modes of educational achievement, unequal pay-to-income ratios and inconsistent readiness for higher education on the part of students (Feng and Li 2014). On the other hand, with regard to “super high schools”, which represent upgraded versions of key high schools, in addition to their reliance on public resources, favorable conditions for school operation have been the target of considerable parental input. According to this pattern of school operation, children from middle- and low-class families who exhibit excellent character and academic performance are largely crowded out, thus exacerbating the education gap in the long term and failing to achieve the goal of the balanced development of high-quality education (Yu 2019).

In summary, this paper combines municipal panel data from 2010 to 2018 with data drawn from the China Family Panel Studies (CFPS), determines the potential existence of a “super high school” phenomenon in a city, which is used as a proxy variable for educational inequality, and employs a fixed effects model to explore the influence of educational inequality on the fertility rate of families and the mechanism underlying this impact. A heterogeneity test is performed to investigate both microindividual and city characteristics. Furthermore, on the basis of data drawn from the 2018 CFPS, a Cox regression model is used to explore the impact of educational inequality on families’ second-child intervals with the goal of obtaining a comprehensive overview of the impact of educational inequality on family multichild behavior.

In contrast to the extant literature on this topic, this paper’s contributions pertain primarily to the following aspects. First, from a research perspective, the Chinese government attaches a great deal of importance to the task of promoting long-term balanced population development. This paper conducts a detailed analysis with the goal of investigating the role of educational inequality in population development, examines the impact of educational inequality on fertility rates, and explores both the theoretical and empirical dimensions of the corresponding transmission mechanism. Furthermore, heterogeneity in terms of the influence of educational inequality on family fertility rates is confirmed on the basis of factors such as female education level, urban‒rural classification, and urban grade. This investigation not only expands the scope of research on the factors affecting multichild behavior but also has significant implications for efforts to address ultralow fertility rates and improve China’s fertility policies in the new era. Second, from an indicator selection perspective, this paper introduces the notion of “super high schools” as a proxy index that can be used to measure educational inequality at the city level for the first time. This study expands on existing measurement methods by providing a more detailed analysis of within-city differences in educational inequality. Consequently, this approach can help governments formulate targeted educational regulations. Third, from a theoretical perspective, this paper identifies the cost of education as a relevant mechanism, thereby taking into account not only the explicit costs of education, which are dominated by monetary economic input, but also the implicit costs of education in terms of nonmonetary input, including time and energy; both of these factors are used to explain the mechanism underlying the effect of educational inequality on family multichild behavior in a comprehensive manner, thus enriching relevant research. This research also refines and deepens our understanding of the internal relationship between educational inequality and family fertility behavior. Fourth, building on the exploration of whether educational inequality inhibits fertility, this paper further analyses whether such inequality prolongs birth intervals among families with two children. This comprehensive examination helps us understand how educational inequality influences families’ multichild behaviors through both the quantity effect and the progress effect.

The remainder of this paper is structured as follows. The second part presents a literature review. The third part presents the theoretical analysis and research hypotheses. The fourth part presents the research design, including the model setting, index selection and data description. The fifth part contains the empirical results, including the baseline regression, endogeneity treatment and robustness test results. The sixth part presents the mechanism analysis. The seventh part presents the heterogeneity analysis. The eighth part presents the expansion analysis. Finally, the ninth part presents the conclusions of this research alongside corresponding policy implications.

Literature review

To provide new evidence regarding the effects of educational inequality on family fertility rates and the underlying transmission mechanism, this study discusses first discusses previous studies that have explored the factors influencing multichild behavior, which have mostly focused on the quantity effect. (1) In terms of individual characteristics, the role and status of women, as the main actors involved in reproduction, have been identified as powerful explanations for the low fertility rates observed in China. An improvement in women’s education level, an increase in the labor participation rate among women and the dual pressures that women face due to the need to balance their families with their careers have restrictive effects on the number of family births (Zhang 2020). In addition, factors such as women’s salary level and occupation type also affect the number of family births (Hickman et al. 2018). (2) In terms of family characteristics, fertility behavior is not an independent behavior on the part of female individuals, and family characteristics also have important effects on the number of births. Scholars have reported that family economic status, family structure, marital satisfaction and child-rearing costs are important factors that impact fertility rates at the family level. Jiang and Liu (2016) further reported that fathers’ participation in child rearing and paternal care can reduce the child-rearing costs faced by women, thereby increasing their probability of having a second child; this effect is more obvious among highly educated, working and urban women. However, in the context of an increasingly aging population, ancestral care can only mitigate the rate of decline in family fertility rates; that is, it cannot reverse this downward trend (Yu and Gong 2021). (3) Social and economic factors also play important roles in shaping the multichild behaviors of families, especially among families in large cities facing concentrated negative externalities. Due to rapid economic development, increasing economic costs, especially those pertaining to education, medical care, and housing, have become the “three new mountains” faced by residents; these issues thus directly restrict the fertility of individuals in the childbearing age group (Jia et al. 2021). Liu et al. (2020) reported that increasing housing prices significantly reduce the number of fertile families and have stronger negative effects on the number of fertile low-income and renting families.

Several scholars have explored the factors influencing multichild behavior from the perspective of the progress effect (Wilson et al. 2021; Yu and Han 2022; Dhir et al., 2021; Khan and Khanam 2023). In a typical study in this context, Wilson et al. (2021) confirmed that parents tend to decrease birth interval to ensure that their children can have closer relationships with each other, whereas factors such as dystocia before this process and unsatisfactory postpartum recovery can increase the birth interval between two children. Yu and Han (2022) reported that ancestral care decreases the interval between the births of two children within a single family. Dahir et al. (2023) noted that young parents with higher education levels are more likely to extend the birth interval of their second child. Khan and Khanam (2023) reported that a reduction in women’s participation in fertility decision-making leads to a decrease in the interval between the birth of two children. In general, the literature on the factors influencing the family birth interval requires expansion to a greater degree than does the literature on the factors influencing the number of family births.

In addition, educational policy is viewed as an important factor that affects whether families have multiple children. The decision to have more children in a single family is based on rational analysis, and education policies affect many components of such rational analysis, mainly in terms of cost compensation and increased work-family compatibility. Consider the example of preschool education policies. By expanding public education funding, government departments can provide childcare, education services and subsidies for preschool children to a certain extent, reduce family education investments, balance families’ financial budgets and improve mothers’ participation in the labor force. In contrast, when the cost of children’s education is very high, parents’ desire for children may be weakened by factors such as gender division in terms of education and paid work or family finances, thus directly affecting families’ fertility intentions and behaviors (Huang and Qin 2023). The formulation of educational policies is closely related to educational equality. The deficiencies of educational policies in terms of resource allocation, management systems, enrollment systems, charging systems and legal supervision mechanisms have gradually highlighted the practical problems associated with educational inequality. Some scholars have further investigated families’ multichild behavior from the perspective of educational inequality and discussed it at a theoretical level. Xu and Pak (2021) noted that educational inequality gives rise to serious educational competition, which is an important factor leading to low fertility rates. Yang et al. (2021) further reported that in contexts featuring inequalities in terms of basic education, families face enormous education costs—that is, the combined effects of economic, time and opportunity costs. In particular, women of childbearing age face the dilemma of balancing their career development with the education of their children, which thus reduces multichild behavior within families.

In summary, although the literature played an important guiding role in the research content of this paper, it has also exhibited the following deficiencies. First, empirical studies of the relationship between educational inequality and family multichild behavior have been relatively scarce, and no unified understanding or consensus has been reached regarding the main ways in which educational inequality affects family multichild behavior. At the theoretical level, starting with the cost of family education, this paper improves our theoretical understanding of the influence of educational inequality on family multichild behavior. At the empirical level, a fixed effects model is used to test the influence of educational inequality on the number of family births, and the mechanism underlying this influence is further subdivided into explicit and implicit education costs, thus making the policy implications of the findings and conclusions of this paper more reliable. Second, the proxy variables used to measure educational inequality must be expanded. Most of the literature on this topic has focused on measuring and discussing certain connotations of educational inequality, and the total index for measuring educational inequality at the macrolevel reflects inequality mostly in terms of the quantity of education, thereby ignoring differences in the quality of education. This paper focuses on the current research gap and explores the possibility of a “super high school” phenomenon in cities, which is used as a proxy variable for educational inequality, thereby not only reflecting the connotations of educational inequality more comprehensively but also providing a new perspective on and ideas for measuring such inequality. Third, most domestic studies have focused on the single aspect such as the number of family births or the family birth interval and thus failed to conduct a panoramic survey of the multichild behaviors of families. Therefore, this paper extends the analysis of the impact of educational inequality on families’ second-child interval to include the overall impact of such inequality on the multichild behavior of families.

Theoretical analysis and research hypotheses

Due to the increasing importance of education in the era of the knowledge economy, individuals’ educational demands are shifting from a focus on “receiving education” to an emphasis on “receiving high-quality education”. Even parents with various disadvantages typically have high expectations concerning their children’s educational trajectories (Lin 2018). To secure an advantageous position for their children at the outset, families’ investments in comparative education exacerbate the financial burdens they face. In addition to its direct impact on living standards, this practice is certain to influence families’ fertility decisions and birth intervals. Early human capital investment theory defines family educational investment narrowly in terms of the economic expenditure allocated by parents to their children’s education—namely, the explicit costs of education. Broadly speaking, family educational investment encompasses not only such explicit costs but also the time and opportunity costs faced by parents, which are referred to as the implicit costs of education.

In recent years, the phenomenon of “super high schools” has exacerbated educational inequality and attracted public attention. These “super high schools” monopolize local educational development due to their advantages, which is a prominent manifestation of imbalanced educational resources. The exceptional resource quality and high enrollment rates of such schools have also been highly sought after by society (Feng and Li 2014). Consequently, many families are willing to make investments to pay the explicit costs of education with the goals of compensating for a lack of high-quality educational resources and ensuring that their children can obtain competitive advantages (Lin 2018). For example, paying school selection fees or purchasing homes within specific districts can offer families additional admission qualifications with regard to “high-quality schools” (Fang 2019), whereas educational tutoring remains a common method through which families seek to obtain a superior education for their children. Undeniably, the exorbitant costs associated with such explicit education resulting from the phenomenon of “super high schools” serve as a deterrent with respect to family multichild behavior.

Liu and Xie (2015) further emphasized the fact that a family’s financial resources can have only a limited influence on a child’s academic achievement. The implicit investments made by families in education, including those pertaining to educational value, time allocation, and emotional contributions, play a more crucial role in children’s development. The increasing significance of family education motivates parents to dedicate additional time and effort to the task of nurturing their children. The emergence of “super high schools” has undeniably increased people’s levels of anxiety regarding higher education and raised their expectations regarding educational outcomes. In addition to parents’ efforts to help their children with their homework and parents’ participation in weekly school activities, the practice of “accompanying students” is becoming increasingly prevalent among parents. This situation entails not only significant economic costs for families but also substantial sacrifices in terms of time and opportunity costs. Yang (2018) developed the concept of a “momager”, which indicates that mothers allocate additional time and energy to the task of planning for their children’s education, thus enabling their children to benefit from competitive schooling environments. However, the implicit costs of education paid by women, including the allocation of labor time and monetary resources, exhibit certain degrees of substitutability. When mothers want to devote additional time and energy to the education of their children, they face a “time penalty” and “wage penalty” in the labor market; that is, they face the risk of potential income loss, such as through career interruption, reductions in their number of working hours, and the need to perform low-income work (Adda et al. 2017), all of which can inhibit multichild behavior among families.

On the basis of the preceding analysis, the following hypotheses are proposed:

H1: Educational inequality has a negative effect on family multichild behavior.

H2: Educational inequality has a negative effect on multichild behavior by increasing the educational costs faced by families, including both the explicit and implicit costs of education.

Research design

Model construction

To capture the net effect of educational inequality on family multichild behavior effectively, a fixed effects model is used to control for the influence of missing variables and multicollinearity problems. The benchmark model constructed is as follows:

$${Y}_{{ijt}}={\alpha }_{0}+{\alpha }_{1}{Z}_{{jt}}+\delta {{control}}_{{ijt}}+{\mu }_{j}+{\lambda }_{t}+{\varepsilon }_{{ijt}}$$
(1)

where i represents the family, j represents the city, t represents the period, and the dependent variable \({Y}_{{ijt}}\) represents the number of births among i interviewed families in city j during period t. The independent variable \({{Z}}_{{jt}}\) represents a virtual variable that indicates whether the city is experiencing a “super high school” phenomenon. If city j is experiencing such a phenomenon during period t, then it is assigned a value of 1 in the current year and subsequent years; otherwise, it is assigned a value of 0. The coefficient \({\alpha }_{1}\) measures the impact of educational inequality on multichild behavior among families. If the coefficient\(\,{\alpha }_{1}\) is significantly negative, then the “super high school” phenomenon in cities inhibits multichild behavior among families. \({{control}}_{{ijt}}\) refers to a series of control variables, which mainly include individual, family and urban characteristics. \({\mu }_{j}\), \({\lambda }_{t}\), and \({\varepsilon }_{{ijt}}\) represent the regional fixed effects, time fixed effects and residual term, respectively. To avoid the influence of the correlation between households within the region on the estimation results, standard errors are clustered at the city level to facilitate the intragroup correlation of the error terms at the city level.

Variable selection

Dependent variable

Family multichild behavior (Child_num). This paper uses the number of children in families of childbearing age as a measure of this factor.

Core independent variable

The binary virtual variable for the presence of a “super high school” phenomenon in a city (Pilotrt) is measured by the interaction term between the two virtual variables of city and time. Since indicators such as student quality and quality teachers are difficult to quantify and collect from the perspective of operability, this paper draws on the research of Guo et al. (2021) and defines high schools that exhibit a rate of student enrollment at top universities in China that is more than two standard deviations higher than the average student enrollment rate of all schools within a province as “super high schools” in the city in question. When a city features one or more super high schools, a “super high school” phenomenon is said to be present in the city.

Mechanism variables

  1. (1)

    Families’ explicit costs of education (Ln_Cost). The questionnaire asked respondents the following question: “How much did your family spend on your child’s education in the past year?”. The CFPS questionnaire included 9 items pertaining to family educational expenditure for children who had officially started school, including books, tuition and miscellaneous fees, school accommodation fees, school meal fees, transportation expenses incurred due to study, school selection fees, educational software fees, after-school tutoring class fees/tutoring fees, and other expenses; the total expenditure was calculated as the sum of these 9 items.

  2. (2)

    Families’ implicit costs of education. On the one hand, on the basis of the research conducted by Wang et al. (2021), this paper used the number of weekly working hours (Work_hrs)Footnote 4 to reflect the opportunity costs faced by women; in this context, the number of “weekly working hours” in the CFPS questionnaire was used for measurement, and respondents who had worked less than 30 h or more than 84 h weekly were excluded (Li and You 2020). In line with the approach taken by Liu (2017), participation in education (Edu_time) was used to measure mothers’ investment of time and energy in their children’s education. The participants responded to the following six questions in the CFPS questionnaire: “When your child is studying, do you often give up watching your favorite TV programs to avoid interfering with their learning?”, “Since the beginning of this school year/last semester, have you discussed school matters with your child often?”, “Do you often ask your children to complete their homework?”, “Do you often check your child’s homework?”, “Do you often prevent your child from watching TV?”, and “Do you often limit the types of TV shows that your children watch?”. The response options included “never”, “rarely” (once per month), “occasionally” (1–2 times per week), “often” (2–3 times per week), and “very often” (6–7 times per week); total scores ranged from 1 to 5. The score for “participation in education” was obtained by summing the scores associated with the six questions.

Control variables

To reduce the problem of endogeneity resulting from missing variables to the greatest extent possible, the following control variables were selected by reference to common practices in relevant studies (Li et al. 2020; Yu and Gong 2021): (1) the individual characteristic variables included female age (Age), female age squared (Age_sq), education level (Edu) and wage (Ln_wage); (2) the family characteristic variables included annual household income (Ln_finc) and residence (Urban); and (3) the urban characteristic variables included the urbanization rate (Urb), economic development level (Ln_eco), traditional financial development level (Fina), housing price (Ln_hou) and unemployment rate (Rate).

Data description

This paper relies on three main data sourcesFootnote 5. First, the dependent variable and individual-level and household-level control variables referenced in this paper were all drawn from the microscopic data provided by the CFPS regarding the period 2010 to 2018. Second, the original data concerning the core independent variable in this paper were collected from the websites of provincial education departments, municipal education bureaus and the official websites of relevant schools. Third, the control variables at the city level included in this paper were drawn from the Chinese Urban Statistical Yearbook.

In this paper, the data were processed as follows. First, the data drawn from the CFPS in 2010 were screened to obtain cross-sectional data samples. In the first step, married women who were aged between 20 and 50 years and had at least one child were selected as mother samples from the adult database, and relevant information such as respondent’s age, residence, years of education, wage income and weekly working hours were determined. In the second step, since the CFPS does not directly provide information regarding the number of children in a family, the family member database was consulted to obtain the sample code for each child, which corresponds to each individual. Based on the family relationship database, a new variable was constructed, and information indicating the absence of children was assigned a value of 0. Information indicating the presence of children was assigned to a value of 1. Then, the horizontal sum could be calculated to obtain the number of children in the family. The third step involved using the children’s database to identify various variables such as the children’s age and school stage. Using the family economic database, total expenditures in family education, family income and other variables were identified. The fourth step involved matching and summarizing the data drawn from the CFPS adult database, children’s database, family relationship database and family economy database in accordance with personal codes and family codes; the development of a matching database containing female characteristics and family information; and the deletion of respondents for whom key information was missing. Second, the data drawn from 2012, 2014, 2016 and 2018 were vertically merged with the data from 2010 to obtain the data needed for the development of the microdatabase. Finally, samples of municipalities that were directly under the central government were excluded at the city level, and the macrodata at the city level were matched based on the code of the prefecture-level city where the respondents resided according to the CFPS data. After data cleaning, effective data pertaining to 80 cities were ultimately matched. To avoid the influence of extreme values, the continuous variables were considered at levels of 1 and 99%. To alleviate problems pertaining to serial correlation and heteroscedasticity, some continuous variables were processed logarithmically. After data cleaning, the valid data pertaining to these 80 cities were ultimately matched. The specific descriptive statistics are presented in Table 1.

Table 1 Descriptive statistics of the variables.
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Empirical results

Unit root test

To avoid spurious regression due to the nonstationarity of the data, a stationarity test of the variables was performed using the ADF unit root test method, and the test results are shown in Table 2. Table 2 shows that all the variables pass the Augmented Dickey–Fuller (ADF) test at the significance level of 1 or 5%, thereby rejecting the null hypothesis of the existence of a unit root and indicating that all the variables are stationary and can be included in the regression analysis.

Table 2 ADF unit root test.
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Benchmark regression

Table 3 reports the impact of educational inequality on families’ multichild behavior. Columns (1) and (3) report the estimated results regarding the random effects (RE), and columns (2) and (4) report the estimated results concerning the fixed effects (FE). Column (1) and column (2) reveal that regardless of which estimation model is used, the estimation coefficient of Pilotrt remains significantly negative. The applicability of the RE and the FE are further analyzed via the Hausman test. The results reveal that the P value of the statistics associated with the model is much lower than 0.01, thus indicating that the FE are correlated with other explanatory variables in the model; thus, the hypothesis regarding the RE is rejected. Therefore, the results regarding the FE presented in column (4) of Table 3 are primarily used as an example to analyze the results. As shown in column (4), the estimated coefficient of Pilotrt remains significantly negative after the individual-, family- and city-level control variables are added, thus indicating that the “super middle school” phenomenon in cities has a significant negative effect on families’ multichild behavior; accordingly, H1 is confirmed.

Table 3 Benchmark regression.
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Endogeneity test

This paper further used the instrumental variable method to reduce the degree of endogeneity bias as a test of the robustness of the empirical results. In line with the research conducted by Xia and Lu (2019), the total number of Jinshi (successful candidates on the highest-level imperial examinations) during the Ming and Qing Dynasties for each city was used to construct the instrumental variables. Reasonable instrumental variables should satisfy both correlation and externality requirements. In terms of relevance, the formation of a city’s culture requires long-term accumulation, and developed ancient imperial areas are considered to be the core areas for Chinese culture and education (Shen 2004). Therefore, previous studies have often used the number of Jinshi in the Ming and Qing Dynasties to reflect the cultural heritage of and educational changes in various cities; furthermore, this factor is closely related to the “super high school” phenomenon in cities. With respect to exogeneity, historical data regarding the total number of Jinshi people in the Ming and Qing Dynasties can meet the relevant conditions to a large extent. Given that cross-sectional data concerning the total number of urban Jinshi residents during the Ming and Qing Dynasties are availableFootnote 6, this paper introduces the interaction term (Jinshi) between the original variable and the year dummy variable into the model as an instrumental variable and uses a two-stage regression method to estimate the model. The regression results regarding the instrumental variables are shown in Table 4.

Table 4 Regression results regarding the instrumental variables.
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Column (1) reports the regression results for the first stage. Jinshi is significantly positively correlated with Pilotrt at the 1% level, thus indicating that the higher the total number of Jinshi in the Ming and Qing Dynasties in a city is, the higher the probability of the existence of a “super high school” phenomenon in the city in question; thus, the instrumental variables meet the correlation conditions. In addition, the F statistic is 387.553, which is greater than the critical threshold of 16.38 at the 10% level with regard to the Stock–Yogo weak recognition test; thus, the possibility of a “weak instrumental variable” is excluded. The value of the LM statistic \(\rho\) is 0.000 is less than 0.01, thus rejecting the null hypothesis, which is not identifiable. All the test results indicate that the selected instrumental variables are suitable.

Column (2) reports the results of the two-stage regression. The estimated coefficient of Child_num is significantly negative and larger than that of the benchmark regression, thus indicating that the influence of Pilotrt on Child_num is underestimated in the benchmark regression due to the influence of endogeneity. Overall, the results of the estimation of the instrumental variables reveal that the existence of a “super high school” phenomenon in a city significantly inhibits the number of family births in that city, whereas ignoring the endogeneity problem can cause this effect to be underestimated.

Robustness test

To mitigate the randomness of the research results to the greatest extent possible, this paper tests the robustness of the estimated results of the benchmark regression by reducing the sample range and replacing both the measurement model and instrumental variables.

Reducing the sample range

In light of the problem of survival analysis, that is, the fact that the number of births produced by young women at the observation point does not represent their eventual number of births, it is possible to overestimate the effect of the “super high school” phenomenon in cities on the number of births in families in this case. Therefore, this paper relies on the research conducted by Zhu and Zhao (2022) by positing that the survival analysis problem can be addressed by limiting the age of married women; thus, the samples are recalculated to include married women between the ages of 31 and 40 years and subjected to a robustness test. The regression results are presented in Table 5a.

Table 5 a Robustness test. b Robustness test. c Robustness test.
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The regression results presented in column (2) of Table 5a reveal that the estimated coefficient of Pilotrt is significantly negative at the 1% level, thus indicating that after addressing the survival analysis problem, the “super high school” phenomenon in the city continues to have a significant negative effect on the number of family births, and the conclusions obtained in this context are consistent with the benchmark regression results.

Replacing the measurement model

Given that the dependent variable is a counting variable, this paper further uses the Poisson model for the robustness test. Table 5a (3) and (4) report the regression results regarding the effect of the “super high school” phenomenon on the number of family births according to the Poisson model. The estimated coefficients of Pilotrt are all significantly negative, thus indicating that the urban “super high school” phenomenon has a significant negative effect on the number of family births; this finding confirms the robustness of the estimated results.

Replacing the instrumental variables

In addition to the data concerning the number of Jinshi in the Ming and Qing Dynasties, some scholars have used the number of Confucian academies to reflect the cultural characteristics of a city. Therefore, this paper introduces the interaction term (Shuyuan) between the number of Confucian academies and the annual dummy variable in the model as an instrumental variable for the robustness test; the results are presented in Table 5b.

Column (1) presents the first-stage regression results. Shuyuan has a significantly positive effect on the existence of “super high schools” in cities, thus indicating a strong correlation between the number of Confucian academies and the existence of “super high schools” in cities. In addition, the F statistic is greater than the critical threshold at the 10% level with regard to the Stock–Yogo weak recognition test, and the LM statistic corresponds to a value of less than 0.01. Column (2) presents the second-stage regression results, according to which the estimated coefficient of Pilotrt is significantly negative at the 5% level, thus indicating that the presence of the “super high school” phenomenon in a city inhibits the number of family births in that city, thereby providing further support for the robustness of the benchmark regression results.

Performing other robustness tests

To ensure the reliability of the results, a robustness test is performed to take the following aspects into account. First, the winsorization process is applied to the continuous variables at the 5% and 95% levels. Second, this paper further introduces the interactive region and time fixed effects with the aim of controlling for the influence of regional characteristic factors, which may change dynamically over time, on the results. Finally, in light of the influence of regional differences on the estimation results, this paper divides the total sample into three subsamples: East, Central and West.

The results of winsorization are presented in Table 5c (1), and the estimated coefficient of Pilotrt is significantly negative at the 1% level. The results regarding the fixed effects are shown in Table 5c (2), and the estimated coefficient of Pilotrt does not change substantially; that is, the previous estimated result is reliable. The results pertaining to the regional dimension are shown in columns (3)–(5), respectively, of Table 5c. The estimated coefficients of Pilotrt are significantly negative, thus indicating that the conclusions obtained are consistent with the benchmark regression results after taking into account the influence of regional factors on the number of family births.

Mechanism analysis

According to the benchmark regression results, the “super high school” phenomenon in cities can reduce the number of family births. To verify the mechanism underlying the effect of this phenomenon on the number of family births in further detail, on the basis of the preceding theoretical analysis, this section tests whether this phenomenon in cities has a negative effect on the number of family births through increased family education costs, which are divided into two dimensions, i.e., the explicit and implicit costs of education for families. The regression results are presented in Table 6.

Table 6 Mechanism test.
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Column (1) reports the estimated effect of the “super high school” phenomenon on the explicit costs of education faced by families. The estimated coefficient of Pilotrt is significantly positive at the 5% level, thus indicating that this phenomenon increases the total annual education expenditure of families, that is, the explicit costs of education faced by families. Therefore, the “super high school” phenomenon in cities can reduce the number of family births by increasing the explicit costs of education faced by families.

Columns (2) and (3) report the estimated results of the effect of the “super high school” phenomenon in cities on the implicit education costs faced by families. The estimated coefficient of Pilotrt presented in column (2) is significantly negative at the 10% level, thus indicating that this phenomenon significantly reduces the labor availability of women and causes them to face income loss (i.e., an opportunity cost). The estimated coefficient of Pilotrt presented in column (3) is significantly positive at the 5% level, thus indicating that this phenomenon significantly improves women’s participation in children’s education; that is, it increases their time and energy investments in their children’s education. Therefore, the “super high school” phenomenon in cities can reduce the number of family births by increasing the costs of implicit education for families, thus supporting H2.

Heterogeneity analysis

In light of the heterogeneity of the influence of the “super high school” phenomenon on the number of family births, this paper conducts a subsample test on the basis of female education level, urban and rural classification and urban grade. The estimated results are presented in Tables 7a and 7b.

Table 7 a Heterogeneity test. b Heterogeneity test.
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Education level

Previous studies have suggested that the influence of female education level on the number of family births is influenced by the sum of the substitution and income effects (Amin and Behrman 2014). The substitution effect refers to the fact that the higher the education level women have obtained, the greater the opportunity costs they face with respect to having children. The income effect refers to the fact that the higher the education level women have obtained, the more likely they are to earn a high income and the less economic cost pressure they face due to bearing children. Therefore, this study divides the total sample into three groups, i.e., “primary education level”, “middle education level” and “higher education level”, with the goal of investigating the influence of the “super high school” phenomenon on the number of family births among women with different education levels.

Table 7a reports the differences in education level according to the effect of the “super high school” phenomenon on the number of family births in cities. With the exception of column (3), the estimated coefficients of all Pilotrt variables are significantly negative, thus indicating that for women with a primary education level or a middle education level, this phenomenon has an inhibitory effect on the number of family births. According to the regression results presented in column (3), the estimated coefficient of Pilotrt is negative but not significant; that is, for women with a higher education level, the influence of this phenomenon on the number of family births is statistically equivalent to zero.

Urban and rural classification

In this paper, the total sample is divided into rural and urban households on the basis of household registration location. The estimated results are reported in Table 7b. The estimated coefficient of Pilotrt presented in column (1) is negative but not significant, thus indicating that the “super high school” phenomenon in urban areas has no obvious inhibitory effect on the number of births among rural families. The estimated coefficient of Pilotrt presented in column (2) is significantly negative at the 1% level, thus indicating that for urban families, this phenomenon significantly inhibits the number of family births.

Urban grade

Given that cities at different levels exhibit tremendous differences in terms of their levels of economic development, educational resources and other aspects, these differences may cause the influence of the “super high school” phenomenon on the number of family births to be heterogeneous. Therefore, in line with the research conducted by Li and Yang (2019), this study divides the total sample into two groups, i.e., “general cities” and “key cities”, according to whether the cities in question are municipalities that are directly under the central government, provincial capitals or subprovincial cities; the regression results are shown in Columns (3) and (4) of Table 7b, respectively. The estimated coefficient of Pilotrt is significantly negative at the 1% level, thus indicating that the “super high school” phenomenon has an inhibitory effect on the number of family births in cities of different grades and that the impact on “key cities” is significantly stronger than the corresponding impact on “general cities”.

Extended analysis

In theory, educational inequality not only affects the number of family births but also may delay birth timing. Therefore, it is particularly important to examine the impact of educational inequality on families’ second-child birth interval in further detail. On the basis of the 2018 CFPS, this paper defines the birth interval of a family in terms of the time between the birth of the family’s first child and that of its second child (Interval). Moreover, in light of the studies conducted by Jin et al. (2019) and Yu and Han (2022), education level (Edu), birth cohort (Born), work status (Work), age of the woman at first birth (First_age), the first child’s gender (First_gender), residence (Urban), and family net income (Ln_finc) are included as control variables.

First, according to the preliminary test (Fig. 2), the survival curve associated with cities that are characterized by a “super high school” phenomenon is always greater than that of cities that are not characterized by such a phenomenon, thus indicating that the existence of the “super high school” phenomenon in cities extends families’ second-child birth interval. Moreover, the two survival curves do not intersect, thus indicating that the data satisfy the proportional risk assumption.

Fig. 2
figure 2

Kaplan–Meier survival curve for the second-child birth interval.

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Furthermore, this paper uses the Cox regression model to support its empirical analysis, and the regression results are presented in Table 8. No control variables are included in Model 1, whereas variables pertaining to individual and family characteristics are introduced into Models 2 and 3. When other factors remain unchanged, the coefficient of the independent variable is significantly negative at the 1% level, thus indicating that the “super high school” phenomenon in cities has a significant effect on families’ second-child interval. Moreover, the independent variable regression coefficient (risk ratio) in Model 3 is 0.842, thus indicating that this phenomenon reduces the likelihood of families having a second child by 15.8% and increases the second-child birth interval.

Table 8 Cox regression.
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Conclusions and discussion

Against the backdrop of increasingly prominent issues pertaining to educational inequality and fertility, this study examines whether a “super high school” phenomenon exists in cities; this phenomenon is then used as a representation of educational inequality. This study uses data drawn from the 2010–2018 CFPS to test the impact of educational inequality on family birth rates and the corresponding transmission mechanism empirically. Furthermore, on the basis of CFPS data from 2018, this study employs Cox regression models to analyze the effect of educational inequality on families’ second-child birth interval in further detail. Our findings can be summarized in terms of three aspects. First, educational inequality inhibits family birth rates by increasing both the explicit and the implicit costs associated with obtaining an education for families, and this conclusion remains valid after several robustness tests are conducted. Second, the negative effects of educational inequality are significantly heterogeneous and have a stronger inhibitory effect on women with primary or middle education levels and families in the urban area and key cities than on other women and families. Third, educational inequality not only inhibits the number of children within families but also prolongs the second-child birth interval.

The changes in family fertility decisions resulting from education can be explained by the quantity–quality trade-off model developed by Becker and Lewis (1973); that is, in modern society, under the assumption that families have limited disposable time and fixed incomes, to comply with the basic principle of utility maximization, parents pay more attention to the quality of their children than to the quantity of such children. This pursuit of high-quality children inevitably leads to an increase in families’ human capital investments in children and has become a foundation for research on the interaction between education and fertility. Most studies on this topic have verified the impacts of fertility decisions on educational inequality. For example, Chen and Yang (2015) used the educational Gini coefficient as a measure of educational inequality and reported that a decline in the urban fertility rate in China would exacerbate educational inequality in urban areas. With regard to male and female educational performance, Fors and Lindskog (2023) noted that gender-biased fertility strategies are more likely to cause gender inequality in education in India. The research conducted by Wei and Ren (2023) revealed that families with more children tend to dilute their family education investments; that is, parents’ expectations and investment in their children’s education is reduced, their children’s opportunities to obtain education are weakened, and educational inequality is ultimately exacerbated.

However, few scholars have focused on the influence of educational inequality on families’ fertility behavior, in which context the existence of “super high schools” is considered to be a typical example of educational inequality in China. This paper is the first to use such “super high schools” to characterize educational inequality. The research results, which were obtained from the perspective of educational inequality, supplement previous studies on the effects of fertility inhibition among families due to the high costs of education (Zhou and Chen 2023; Baizan and Nie 2024; Kim et al. 2024; Liu and Liu 2024). In other words, in China, the phenomenon of educational inequality results in vicious competition for education, a lack of high-quality education resources and unequal access to opportunities to participate in higher education, thus encouraging families to invest a great deal to address the explicit and implicit costs of education during the key stages of their children’s education. Therefore, families who have limited resources may make more conservative reproductive decisions for reasons related to good parenting. In this context, urban areas and key cities usually exhibit typical characteristics with regard to education and economic development or large populations; in these contexts, the prevalence of “super high schools” is high, the monopoly on opportunities to be admitted to elite universities is strong, and the competition for education is often more intense (Guo et al. 2021). Therefore, educational inequality has a more significant inhibitory effect on families in such areas. Women who have obtained higher education may be employed in relatively high-income jobs, and the opportunity cost of family‒wage conflict can be reduced by paying money, such as by hiring tutors as well as by procuring babysitting and other services (Hazan et al. 2023). Therefore, the inhibitory effect of educational inequality on the multichild behavior of women who have obtained higher education levels is limited.

Finally, in addition to quantitative measurement, considering the scope of fertility behavior from the perspective of the progress effect is also very important for attempts to address the issue of low fertility. Jin et al. (2023) reported that close birth spacing may intensify competition for family education resources among siblings. Therefore, in light of limitations to family resources, some couples are more likely to extend their birth intervals and have two or more children simultaneously when the cost inputs and work-family conflicts associated with this process are lower (Yu and Han 2022). Educational inequality in China encourages parents to compete fiercely for better and scarce educational resources. In order to avoid allowing their children to “lose at the starting line”, families’ educational expectations continue to rise, while they must simultaneously account for the need for family development and quality of life. In this process, the average family usually cannot afford to invest in the education of two or more children. In particular, women are also more likely to experience irreconcilable conflicts between work and family, thus extending families’ birth interval.

Recommendations

This paper not only enriches the research on family multichild behavior but also provides new ideas that can promote the optimization of fertility policies and help solve the dilemma of low fertility rates faced by China and most countries in East Asia. The policy recommendations made based on this paper are presented below.

First, educational inequality should be addressed, and an equitable distribution of educational resources should be ensured. The empirical evidence presented in this paper highlights the negative impact of the “super high school” phenomenon on family multichild behavior; thus, the government should attach a great deal of importance to the problem of educational inequality in the future. Primarily, “blood transfusion” should be treated equally. Moreover, the concept of “educational GDP” should be abandoned, the policy of providing “key support” for “super high schools” should be repealed, and each school should be given fair support in terms of educational funding. Furthermore, the skills of teachers should be strengthened with the goal of supporting sound educational development among children. The teacher rotation system should be strengthened, excellent teachers should be selected for teaching, the current problems of “weak rural areas and crowded urban areas” should be addressed, and the sharing of high-quality teacher resources should be promoted. Finally, the radiation effect of “super high schools” should be considered in, for example, attempts to foster teaching-related communication among schools; promote the digital transformation of education; and facilitate the joint construction and sharing of online courses, teaching, and management resources.

Second, the cost of family education should be reduced, and corresponding worries should be eliminated. Educational inequality significantly increases both the explicit and implicit costs of education for families. The task of implementing effective long-term support policies that can alleviate parents’ worries is key in this context. One way to reduce the explicit costs of family education is to improve family economic support policies and reduce the burden placed on families with regard to education. For example, clearer education subsidy policies should be implemented according to the different school stages of children and the number of children in different families, which can be considered with regard to subsidy adjustments. All educational expenses related to child care should be included in the personal income tax deduction. A second way of accomplishing this goal is to strengthen efforts to reform off-campus training institutions, standardize the training market, and guide families to consume off-campus education rationally. To reduce the implicit costs of education for families, one approach is to encourage schools to provide diverse after-school services, effectively connect students’ school time with parents’ work time, and alleviate time-related conflicts. Third, enterprises should ensure the flexibility of women’s workplaces and the effectiveness of their working hours, such as by implementing a “cloud” office at home, providing vacation care and other services to employees’ children, and eliminating employment discrimination against postpartum women, thus ensuring that these women have equal options for employment. In addition, the government should encourage the development of a gig economy and establish an employment environment that can help women balance their careers with their families more effectively.

Finally, preferential policies should be implemented for key groups to address the difficulties associated with educational inequality. Educational inequality has heterogeneous effects on multichild behavior in families, and relevant policies should be developed for women who have attained primary or middle education levels, urban families and families in key cities. First, the government should improve the guarantees it provides to women who have attained primary or middle education levels. On the one hand, women who have attained primary or middle education levels should be protected from discrimination in terms of employment, their training in vocational skills should be strengthened, and their competitiveness in terms of employment and income should be improved. On the other hand, preferential subsidies for their children’s education should be strengthened to reduce the cost of education. Second, given the uneven distribution of educational resources between urban and rural areas as well as between general and key cities, on the one hand, guidance should be given to parents to help them adopt a correct view of education and school choice, thus mitigating the irrational behavior of parents who blindly invest in education due to the pressure of competition for education. On the other hand, it is necessary to deepen educational reforms, expand the supply of high-quality education, and solve the problems of “hot school choice and high pressure” in cities.