China's demographic landscape has undergone significant changes, transitioning from strict birth control policies to policies encouraging larger families. Despite these changes, birth rates remain low, prompting concerns about the socioeconomic burden of an aging population and its impact on individual well-being. The recent emphasis on prioritizing population happiness necessitates understanding the relationship between family size and individual well-being. While the "quality-quantity" trade-off hypothesis suggests that fewer siblings lead to increased parental resource allocation per child, the relationship between sibling size and happiness in China remains unclear. Existing research presents conflicting findings, some showing positive correlations between sibling number and well-being due to social support, while others show negative correlations due to resource dilution. A critical gap in the existing literature is the lack of analysis considering indirect pathways through which sibling size might influence happiness, particularly through education and income. The endogeneity of sibling size, being a parental choice influenced by unobservable factors affecting education, income, and happiness, further complicates causal inference. This study aims to empirically examine both the direct and indirect effects of sibling size on happiness in China, using the 2008 Chinese General Social Survey (CGSS) data and instrumental variable techniques to address endogeneity. Provincial variations in the implementation of family planning policies in the 1970s are utilized as instrumental variables.

The literature on the relationship between sibling size and happiness presents mixed results. Some studies find a positive correlation, arguing that only children lack the support of siblings and face greater burdens. Other studies find a negative correlation, suggesting that only children benefit from increased parental investment, leading to better educational and economic outcomes and greater well-being. Studies in China also show conflicting findings with some showing positive and others negative relationships. A few studies have examined non-linear relationships, where moderate numbers of siblings are associated with higher happiness while extreme numbers (very few or many) are associated with lower happiness. However, these studies largely neglect the indirect effects of sibling size on happiness through channels like education and income. The impact of sibling size on income is often negatively correlated due to resource dilution, while the effect on education is debated, with the quantity-quality trade-off hypothesis suggesting a negative relationship. Studies in China often support the negative impact of larger family size on educational attainment.

This study uses data from the 2008 Chinese General Social Survey (CGSS), focusing on individuals born between 1968 and 1988. The dependent variable is individual happiness, measured on a 5-point scale. Key independent variables include sibling size, income (log-transformed), and years of education. Control variables include gender, birth year, health status, marital status, Communist party membership, and rural residence. Provincial fixed effects are included to account for regional variations. The study uses an ordered probit model for the happiness analysis and OLS and 2SLS regressions for income and education analyses. To address the endogeneity of sibling size, provincial variations in the implementation of family planning policies during the 1970s are used as instrumental variables. The instrumental variable is the difference between an individual's birth year and the year the Family Planning Leading Group (FPL) was established in their birth province. This approach leverages the staggered implementation of family planning policies across provinces to create exogenous variation in sibling size. The study tests the validity of the instrumental variable using the first-stage regression and a Hausman exogeneity test.

The study's key findings are as follows: 1. **Direct Effect of Sibling Size on Happiness:** The analysis reveals that after controlling for income and educational attainment, sibling size has no significant direct effect on happiness. This supports Hypothesis 1. 2. **Indirect Effect of Sibling Size on Happiness through Income:** OLS regression shows a significant negative correlation between sibling size and income. However, 2SLS estimation with instrumental variables reveals this negative relationship is not statistically significant, suggesting that observed negative correlation is not a causal one. Further investigation through decomposition of the total effect of sibling number on income into direct and indirect effects revealed that the direct effect of number of siblings on income is negative, suggesting that having more siblings dilutes family resources and directly reduces income. Thus, there is an indirect negative effect of sibling size on happiness via income, supporting Hypothesis 2. 3. **Indirect Effect of Sibling Size on Happiness through Education:** Both OLS and 2SLS regressions consistently show a significant negative relationship between sibling size and educational attainment. The 2SLS results, preferred due to rejection of the exogeneity test for the sibling size variable, show a stronger negative effect of sibling size on education than does the OLS model. This suggests a causal, negative relationship between the number of siblings and educational attainment. This supports Hypothesis 3 and indicates that resource dilution leads to reduced investment in each child's education, ultimately affecting happiness. The indirect negative effect of number of siblings on happiness through education was thus established. These findings consistently point towards indirect negative effects of sibling size on happiness through its impact on income and education.

The findings indicate that the negative association between sibling size and happiness in China is primarily driven by indirect effects operating through income and education. The lack of a significant direct effect suggests that the mere presence or absence of siblings does not inherently influence happiness. The negative impact on income is likely due to resource dilution within the family, while the negative impact on education is explained by the quantity-quality trade-off hypothesis. These findings have significant policy implications for China's efforts to increase birth rates. Policies aimed at boosting fertility should incorporate measures to mitigate the negative impacts on income and education. Such measures could include increased financial support for families, improved access to quality education, especially in rural areas, and initiatives to address gender inequalities in educational opportunities.

This study offers a nuanced understanding of the complex relationship between sibling size and happiness in China, highlighting the importance of considering indirect effects. The negative association between sibling size and happiness is largely indirect, operating through income and educational attainment. Future research should investigate the effects of recent changes in China's family planning policy on younger generations and explore additional factors influencing happiness beyond income and education, such as social capital.

The study's limitations include the reliance on cross-sectional data from 2008, which prevents a longitudinal analysis of the dynamic effects of sibling size. The study's focus on a specific age group (early and mid-adulthood) may limit the generalizability of the findings to other age groups. Additionally, unobserved family characteristics that influence both sibling size and happiness could remain even after controlling for parental occupation. The instrumental variable approach makes strong assumptions regarding exclusion restriction and no endogeneity, and any unmeasured correlation between this variable and happiness cannot be ruled out.