A regression-based approach for bidirectional proximal causal inference
本文提出一种基于回归的双向近端因果推断方法，在存在未测量混杂因素时识别双向因果效应，并开发了敏感性分析方法，应用于美国州级面板数据分析堕胎率与谋杀率之间的双向因果效应。
Abstract Proxy variables are commonly used in causal inference when unmeasured confounding exists. While most existing proximal methods assume a unidirectional causal relationship between two primary variables, many social and biological systems exhibit complex feedback mechanisms that imply bidirectional causality. In this paper, using regression-based models, we extend the proximal framework to identify bidirectional causal effects in the presence of unmeasured confounding. We establish the identification of bidirectional causal effects and develop a sensitivity analysis method for violations of the proxy structural conditions. Building on this identification result, we derive bidirectional two-stage least squares estimators that are consistent and asymptotically normal under standard regularity conditions. Simulation studies demonstrate that our approach provides unbiased estimates across various scenarios and confirm the asymptotic properties. Sensitivity analyses further evaluate the robustness under violations of proxy structural conditions. Applying our methodology to a state-level panel dataset from 1985 to 2014 in the United States, we examine the bidirectional causal effects between abortion rates and murder rates. The analysis reveals a consistent negative effect of abortion rates on murder rates, while also finding a potential reciprocal effect from murder rates to abortion rates that conventional unidirectional analyses have not considered.