How educational inequality affects family multichild behavior—evidence from super high schools

China faces persistently low fertility despite successive relaxations of birth policies (two-child and three-child), with birth rates falling from 13.57‰ in 2016 to 6.77‰ in 2022. At the same time, demand for high-quality education has intensified concerns over educational inequality. The study asks: (1) Does educational inequality affect families’ fertility (multichild) behavior? (2) Through what mechanisms (explicit monetary costs vs. implicit opportunity/time costs)? (3) Is the effect heterogeneous by women’s education, urban/rural residence, and city grade? (4) Beyond the quantity of births, does educational inequality affect the timing (second-child birth interval)? The paper posits that educational inequality—proxied by the presence of city-level “super high schools”—raises both explicit and implicit education costs, thereby suppressing multichild behavior and potentially lengthening birth intervals. Hypotheses: H1, educational inequality negatively affects family multichild behavior; H2, it operates via increased explicit and implicit education costs.

Prior work links fertility to women’s characteristics (education, labor participation, wages, occupations), family traits (income, structure, marital satisfaction, childrearing costs, paternal involvement), and socio-economic factors (housing, education, healthcare costs). Progress-effect studies examine determinants of birth intervals, noting roles for health events, grandparental care, parental education, and women’s decision-making power. Education policy can shape fertility via costs and work-family compatibility; high education costs lower fertility intentions. The literature theorizes that educational inequality intensifies competition and raises both explicit and implicit costs, particularly burdening women. Gaps identified: few empirical studies quantify educational inequality’s impact on multichild behavior; common inequality measures emphasize education quantity, not quality; and most studies examine either number of births or spacing, not both. This study addresses these gaps by using “super high schools” as a city-level proxy for quality-focused educational inequality, testing effects on both birth number and second-child interval, and decomposing mechanisms into explicit and implicit education costs.

Data and samples: Microdata from CFPS 2010–2018 provide dependent variables and individual/household controls; city-level data (urbanization, GDP per capita, finance, housing prices, unemployment) come from the China Urban Statistical Yearbook; city-level indicators of “super high schools” are compiled from provincial/municipal education websites and school sites. The micro sample includes married women aged 20–50 with at least one child. Children counts are constructed from family rosters; education expenditures from CFPS family economy modules; children’s schooling information from the children’s database. City-level macrodata are matched to respondents’ prefecture-level cities. Extreme values are winsorized at 1% and 99% (some continuous variables log-transformed). Final matched data cover 80 cities; descriptive statistics show 16,054 observations for Child_num and varying N for mechanism variables.

Key variables: Dependent variable: Child_num (number of children in the family). Core independent variable: Pilotrt, a city–year indicator equal to 1 from the year a city first exhibits a “super high school” onward; zero otherwise. A “super high school” is defined (following Guo et al., 2021) as a high school with a top-university enrollment rate more than two standard deviations above its provincial average; the city is considered exposed if it hosts at least one such school. Mechanism variables: explicit education costs Ln_Cost (log of annual family education expenditures on nine categories: books, tuition/misc., accommodation, meals, study-related transport, school selection fees, ed-tech/software, after-school tutoring, other); implicit costs include women’s weekly working hours (Work_hrs; responses <30 or >84 hours excluded) and mothers’ participation in children’s education (Edu_time; sum of six Likert-scale items on monitoring and engagement, range 6–30). Controls: individual (Age, Age_sq, Edu, Ln_wage), household (Ln_finc, Urban), and city (Urb, Ln_eco, Fina, Ln_hou, Rate).

Empirical strategy: Baseline panel regressions use a two-way fixed effects model at the family–city–year level: Y_ijt = α + β·Pilotrt_jt + γ·Controls_ijt + μ_j + λ_t + ε_ijt, clustering SEs at the city level. Unit root (ADF) tests confirm stationarity for all variables. Hausman tests favor FE over RE. Endogeneity is addressed via 2SLS using historical cultural heritage as instruments: (i) the number of Jinshi (successful highest-level imperial exam candidates) in the Ming–Qing period by city, interacted with year dummies; (ii) robustness IV using the number of Confucian academies (Shuyuan) interacted with year. First-stage relevance (large F-statistics) and identification tests (Anderson LM) are reported. Robustness checks include: restricting the sample to women aged 31–40 (survival bias mitigation), Poisson count models, alternative IVs, winsorization at 5–95%, inclusion of region×time fixed effects, and regional subsamples (East/Central/West). Heterogeneity analyses split samples by women’s education (primary/junior high or below; middle: senior high/technical/vocational; higher: college+), by urban vs. rural hukou, and by city grade (general vs. key cities—municipalities, provincial capitals, subprovincial). Extended analysis: A Cox proportional hazards model (2018 CFPS) assesses effects on the second-child birth interval (time from first to second birth). Controls in Cox models include Edu, birth cohort (Born), employment (Work), age at first birth (First_age), first child’s gender (First_gender), Urban, and Ln_finc. Kaplan–Meier curves and non-crossing survival functions support proportional hazards.

• Baseline effects: Fixed effects regressions show a significant negative association between Pilotrt and the number of children. In the preferred FE specification with full controls, Pilotrt’s coefficient is significantly negative (e.g., −0.014, s.e. 0.002, p<0.01), indicating that the presence of a super high school at the city level reduces family fertility.
• Instrumental variables: Using Jinshi×year as IV, first-stage relevance is strong (Cragg–Donald F=387.533>16.38; Anderson LM p<0.001). Second-stage estimates show a larger negative effect on Child_num (−0.493, s.e. 0.166, p<0.01), suggesting baseline estimates may be downward biased due to endogeneity. Using Shuyuan×year as an alternative IV yields consistent negative effects (second stage: Pilotrt −1.199, s.e. 0.513, p<0.05; first-stage F=65.180).
• Mechanisms (Table 6): Educational inequality increases explicit costs (Pilotrt → Ln_Cost: +0.132, s.e. 0.057, p<0.05). It raises implicit costs by reducing women’s weekly working hours (−2.121, s.e. 1.185, p<0.10) and increasing mothers’ educational engagement (Edu_time: +0.557, s.e. 0.298, p<0.05).
• Robustness: Results hold when limiting to women aged 31–40 (Pilotrt −0.230, s.e. 0.069, p<0.01), using Poisson counts (−0.143, s.e. 0.042, p<0.01), after winsorization (−0.219, s.e. 0.066, p<0.01), with region×time FE (−0.222, s.e. 0.066, p<0.01), and across East (−0.286, s.e. 0.046, p<0.01), Central (−0.157, s.e. 0.090, p<0.10), and West (−0.835, s.e. 0.463, n.s.).
• Heterogeneity by women’s education: Stronger inhibition for primary/junior high (−0.213, s.e. 0.087, p<0.05) and middle (−0.312, s.e. 0.076, p<0.01); not significant for higher education (−0.048, s.e. 0.037, n.s.).
• Urban–rural: Urban households show significant negative effects (−0.264, s.e. 0.048, p<0.01); rural not significant (−0.050, s.e. 0.127).
• City grade: Negative in both general (−0.228, s.e. 0.071, p<0.01) and key cities (−0.376, s.e. 0.053, p<0.01), with stronger effects in key cities.
• Progress effect (timing): Cox models show Pilotrt hazard ratios ~0.842 (p<0.01), implying a 15.8% reduction in the hazard of having a second child at any time point, i.e., a longer second-child birth interval.

The study demonstrates that educational inequality—proxied by the emergence of city-level super high schools—dampens multichild behavior and delays second births. This addresses the research questions by confirming H1 (negative effect on fertility) and H2 (mechanism through costs). The explicit costs rise via greater outlays on tuition, tutoring, and school-choice expenditures, while implicit costs rise through reduced maternal labor supply and increased time spent on children’s education—particularly salient in competitive educational environments. Heterogeneity patterns suggest that women with lower education levels and urban residents in key cities are most affected, consistent with higher competitive pressures and fewer opportunities to outsource time costs. The progress-effect findings show that inequality impacts not only the number of children but also spacing, compounding low fertility through both quantity and timing channels. These results contribute to policy debates on fertility support and education equality by highlighting the intertwined nature of education market competition and family formation decisions.

The paper contributes by (1) introducing a city-level quality-oriented proxy for educational inequality (super high schools), (2) providing causal evidence that educational inequality reduces the number of children and lengthens the second-child interval, and (3) identifying explicit and implicit education costs as key mechanisms. The effects are stronger among women with primary/middle education, in urban areas, and in key cities. Policy implications include reducing educational inequality (more even resource allocation, teacher rotation, curbing preferential support for elite schools), lowering families’ explicit costs (targeted subsidies, tax deductions, regulating off-campus tutoring), and reducing implicit costs (after-school services, flexible work arrangements, anti-discrimination for mothers). Future research could refine measurement of educational inequality beyond the super high school proxy, assess impacts under the post-2021 three-child policy, and explore long-run family and child outcomes across cohorts.

• The measure of educational inequality relies on a proxy (presence of super high schools defined via top-university enrollment thresholds), which may not capture all dimensions of inequality.
• City coverage is limited to matched CFPS respondents across 80 cities; municipalities directly under the central government were excluded in some matching steps, potentially affecting generalizability.
• The main fertility analyses use 2010–2018 CFPS; the extended Cox analysis relies on 2018 data only, which may limit temporal variation for timing effects.
• The study focuses on first-to-second birth intervals; effects on third-birth intervals are not examined due to the timing of China’s three-child policy (post-2021) and small sample sizes for third births.
• Despite fixed effects and historical instruments (Jinshi, Confucian academies), residual unobserved factors or violations of IV assumptions cannot be fully ruled out.