Income inequality in China has widened despite rapid economic growth since 1978. Family contributions to children's education are increasingly significant, particularly through extracurricular activities. While FEI is crucial for human capital accumulation, excessive competition for resources can create adverse effects, widening the gap between social classes. This paper examines three key questions: 1) Does IGM, as a measure of opportunity inequality, affect FEI? 2) What are the underlying mechanisms? 3) Is this effect heterogeneous across socioeconomic statuses? The study uses data from the 2015 China 1 percent Population Sample Survey and the 2018 China Family Panel Studies to address these questions. The researchers measure IGM using an index of intergenerational educational rank correlation and FEI using extracurricular tutoring expenses. This study contributes to the literature by providing one of the first causal effect estimations of IGM on FEI, enriching our understanding of its mechanisms (considering incentive, anxiety, and status-seeking), and utilizing census data for a more accurate measurement of IGM.

Existing research on the impact of inequality on FEI offers varied insights. Some studies suggest that increased equality of opportunity incentivizes greater education investment, while others show inconsistent effects of income inequality on FEI, sometimes finding increased and sometimes decreased investment. The increased investment is sometimes explained by status-seeking behavior, and the decreased investment by credit constraints. Recent studies have also considered the role of educational anxiety, arguing that excessive anxiety can lead to overinvestment. While the literature explores the impact of inequality and anxiety, research directly examining the effect of regional IGM on FEI is limited. This study builds on previous work by focusing on the causal effect of IGM on FEI, considering multiple mechanisms, and employing a larger, more representative dataset.

The study employs data from three sources: the 2015 China 1 percent Population Sample Survey, the 2018 China Family Panel Studies (CFPS), and city-level databases. IGM is measured using the intergenerational educational rank correlation proposed by Dahl and DeLeire (2008), which calculates the correlation between parents' and children's educational rankings within their respective cohorts. FEI is measured using data from the CFPS child proxy questionnaire, specifically asking about extracurricular tutoring expenses in the past 12 months. The benchmark regression model takes the form: ln(FEIᵢⱼcₚ + 1) = β₀ + β₁IGM + βₓXᵢ + φXⱼ + γXₚ + νₚ + εᵢⱼcₚ, where FEIᵢⱼcₚ represents FEI for child i in family j in city c in province p, IGM is the intergenerational educational mobility of city c, and Xᵢ, Xⱼ, Xₚ are control variables for individual, family, and city characteristics, respectively. The study uses OLS and Tobit regression models. Robustness checks include replacing independent and dependent variables, controlling for omitted variables (GDP and Gini coefficient), assessing the impact of unobservable factors using the Altonji et al. (2005) method, and employing two-stage least squares (2SLS) regression with an instrumental variable to address endogeneity concerns. Heterogeneity analysis is conducted by separating samples based on urban/rural status and high/low economic and cultural capital. Mechanism analysis explores the roles of incentives (measured by agreement with "hard work can be rewarded"), excessive educational anxiety (binary variable based on CFPS data), and status-seeking behavior (calculated using the difference between self-assessed and actual economic status).

The baseline regression results show a significant negative relationship between IGM and FEI, with a 25.75% decrease in FEI for every 0.1-unit increase in IGM. This negative effect remains significant across various robustness tests, including the use of different models (OLS, Tobit, Probit, 2SLS), the inclusion of omitted variables, and accounting for unobservable factors. Heterogeneity analysis reveals that the negative effect is more prevalent in urban families and families with high socioeconomic status, where credit constraints and incentives are less of a concern. Mechanism analysis indicates that IGM reduces excessive educational anxiety and status-seeking behavior among parents, contributing to the lower FEI. The instrumental variable used in 2SLS regression was the average IGM of other cities in the same province. This instrument is negatively correlated with the city's IGM because of the competitive nature of educational resources across cities within a province.

The findings support the hypothesis that higher levels of IGM, indicating greater equality of opportunity, do not necessarily lead to increased FEI. Instead, the reduction in excessive anxiety and status-seeking behavior seems to outweigh any potential increase in incentive effects. This is particularly true for higher socioeconomic status families who are less constrained by financial factors and have less incentive to overinvest in education when the likelihood of upward mobility is higher. The results are significant in the context of rising inequality and competition in China's education system. The findings support the notion that policies aiming to reduce the burden of education (like China's "Double Reduction" policy) should be complemented by measures to improve equality of opportunity.

This study offers valuable insights into the complex relationship between IGM and FEI. The negative relationship found suggests that promoting equality of opportunity, rather than simply focusing on increased competition, is crucial for addressing excessive educational pressures and improving educational equity. Future research could explore other potential mechanisms, utilize panel data to enhance causal inference, and investigate how to effectively promote intergenerational mobility in the context of increasing class rigidity.

The study utilizes cross-sectional data, which limits the ability to establish definitive causal relationships. While the study examines several potential mechanisms, other factors such as the rate of return on education and family income might also play a role. The measurement of intergenerational mobility, while improved by using a large dataset, still relies on certain assumptions. The study primarily focuses on extracurricular tutoring, which may not fully capture all aspects of family education investment. Lastly, although robust tests were employed, some endogeneity may persist.