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

Shuxi Zeng, Fan Li+1 more|arXiv (Cornell University)|May 18, 2020

Demographic Trends and Gender Preferences40 references4 citations

TL;DR

This study uses instrumental variable analysis with the One-Child Policy's regional implementation intensity as an instrument to estimate the causal effect of being an only child on psychological health in China. Using a Bayesian hierarchical model within a principal stratification framework, it finds small but significant negative effects on self-reported psychological well-being, especially among urban males and families resistant to the policy, highlighting treatment effect heterogeneity due to unobserved and observed characteristics.

ABSTRACT

This 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 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 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 sensitivity analysis to assess the key instrumental variable assumption.

Motivation & Objective

• To evaluate the causal impact of being an only child on psychological health in China, addressing unmeasured confounding in fertility decisions.
• To address endogeneity from unobserved family characteristics that may simultaneously affect fertility choice and child psychological outcomes.
• To model treatment effect heterogeneity across observed (e.g., urban/rural) and unobserved (e.g., family resistance) characteristics.
• To develop and apply a local instrumental variable method for continuous instruments within a principal stratification framework.
• To incorporate clustering in data structure via a Bayesian hierarchical model for more accurate inference.

Proposed method

• Uses the intensity of One-Child Policy implementation as a continuous instrumental variable, derived from the Indicator of Family Planning Policy Resistance (IFPPR).
• Applies a local instrumental variable (IV) approach to estimate marginal treatment effects (MTE) and principal strata average causal effects.
• Establishes a formal analytical link between local IV and principal stratification to handle continuous instruments and unobserved heterogeneity.
• Employs a Bayesian hierarchical model to account for clustering in the data and to estimate causal estimands with uncertainty quantification.
• Conducts sensitivity analysis to test the validity of the exclusion restriction assumption under unobserved confounding.
• Uses simulation studies to validate the method’s performance under varying degrees of treatment effect heterogeneity.

Experimental results

Research questions

• RQ1 Does being an only child have a causal negative effect on self-reported psychological health in China?
• RQ2 How does the effect of being an only child vary across different subpopulations, such as urban versus rural residents?
• RQ3 What is the role of unobserved family resistance to the One-Child Policy in shaping treatment effect heterogeneity?
• RQ4 How does the intensity of policy implementation serve as a valid instrument for fertility choice in this context?
• RQ5 To what extent do clustering and unobserved heterogeneity bias standard IV estimators without proper adjustment?

Key findings

• Being an only child has a small but statistically significant negative effect on self-reported psychological health, particularly among urban males.
• The negative effect is more pronounced in families that were more resistant to the One-Child Policy, suggesting unobserved family-level resistance influences outcomes.
• Treatment effect heterogeneity is substantial, with larger variation in marginal treatment effects across principal strata defined by latent compliance behavior.
• The local IV method outperforms OLS and 2SLS in bias and root mean squared error, especially under high heterogeneity, validating its use in this context.
• Sensitivity analysis supports the plausibility of the instrumental variable assumption under plausible deviations from exclusion restriction.
• The results challenge the notion that reducing family size improves child well-being, indicating that sibling presence may contribute positively to psychological development.