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Abstract：
Structural equation models (SEMs) involving feedback loops may offer advantages over standard instrumental variables estimators in terms of modelling causal effects in the presence of bidirectional relationships. In the following note, we show that in the case of a single \"exposure\" and \"outcome\" variable, modelling relationships using a SEM with a simple bidirectional linear feedback loop offers no advantage over traditional instrumental variables estimators in terms of consistency (i.e. both approaches yield consistent estimates of the causal effect, provided that causal estimates are obtained in both directions). In the case of finite samples, traditional IV estimators and SEM exhibited similar power across many of the conditions we examined, although which method performed best depended on the residual correlation between variables and the strength of the instruments. In particular, the power of SEM was insensitive to the residual correlation between variables, whereas the power of the Wald estimator/2SLS improved (deteriorated) relative to SEM as the magnitude of the residual correlation increased (decreased) assuming a positive causal effect of the exposure on the outcome. The power of SEM improved relative to the Wald estimator/2SLS as the instruments explained more residual variance in the \"outcome\" variable.
摘要：
在存在双向关系的情况下对因果效应进行建模方面，涉及反馈回路的结构方程模型（SEM）可能比标准工具变量估计器具有优势。在以下注释中，我们表明，在单个“暴露”和“结果”变量的情况下，使用具有简单双向线性反馈回路的SEM建模关系在一致性方面没有传统工具变量估计器的优势（即两种方法都产生因果效应的一致估计，前提是在两个方向上获得因果估计)。在有限样本的情况下，传统的IV估计器和SEM在我们检查的许多条件下表现出相似的能力，尽管哪种方法效果最好取决于变量之间的残差相关性和仪器的强度。特别是,SEM的功效对变量之间的残差相关性不敏感，而Wald估计器/2SLS的功率相对于SEM改善(恶化),因为假设暴露对结果具有正的因果影响,残差相关性的大小增加(降低)。SEM的功效相对于Wald估计器/2SLS有所提高，因为这些仪器解释了“结果”变量中更多的残差方差。
