Is being an only child harmful to psychological health?: evidence from an instrumental variable analysis of China's one‐child policy

The paper evaluates the effects of being an only child in a family on psychological health, leveraging data on the one‐child policy in China. We use an instrumental variable approach to address the potential unmeasured confounding between the fertility decision and psychological health, where the instrumental variable is an index of the intensity of the implementation of the policy. We establish an analytical link between the local instrumental variable approach and principal stratification to accommodate the continuous instrumental variable. Within the principal stratification framework, we postulate a Bayesian hierarchical model to infer various causal estimands of policy interest while adjusting for the clustering data structure. We apply the method to the data from the China Family Panel Studies and find small but statistically significant negative effects of being an only child on self‐reported psychological health for some subpopulations. Our analysis reveals treatment effect heterogeneity with respect to both observed and unobserved characteristics. In particular, urban males suffer the most from being only children, and the negative effect has larger magnitude if the families were more resistant to the one‐child policy. We also conduct a sensitivity analysis to assess the key instrumental variable assumption.