Is being the only child harmful to psychological health?: Evidence from an instrumental variable analysis of China's One-Child Policy
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This paper evaluates the effects of being the 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 on the intensity of the implementation of the One-Child 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 we find small but statistically significant negative effects of being the only child on self-reported psychological health for some subpopulations. Our analysis also reveals treatment effect heterogeneity with respect to both observed and unobserved characteristics. We also conduct sensitivity analysis to assess the key instrumental variable assumptions, and carry out simulations to compare the proposed methods with common alternative methods.
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