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This paper evaluates the effects of being an only child in a family onpsychological health, leveraging data on the One-Child Policy in China. We usean instrumental variable approach to address the potential unmeasuredconfounding between the fertility decision and psychological health, where theinstrumental variable is an index on the intensity of the implementation of theOne-Child Policy. We establish an analytical link between the localinstrumental variable approach and principal stratification to accommodate thecontinuous instrumental variable. Within the principal stratificationframework, we postulate a Bayesian hierarchical model to infer various causalestimands of policy interest while adjusting for the clustering data structure.We apply the method to the data from the China Family Panel Studies and findsmall but statistically significant negative effects of being an only child onself-reported psychological health for some subpopulations. Our analysisreveals treatment effect heterogeneity with respect to both observed andunobserved characteristics. In particular, urban males suffer the most frombeing only children, and the negative effect has larger magnitude if thefamilies were more resistant to the One-Child Policy. We also conductsensitivity analysis to assess the key instrumental variable assumption.

Is being an only child harmful to psychological health?: Evidence from an instrumental variable analysis of China's One-Child Policy