We consider a situation where cause–effect relationships between variables can be described as a directed acyclic graph (DAG) and the corresponding linear structural equation model (linear SEM). When several pairs of instrumental variables (IVs) and covariates (IV-pairs; Pearl in: Proceedings of the 20th conference on uncertainty in artificial intelligence, AUAI Press, Arlington, Virginia, United States, UAI’04, 2004) are available, we propose (i) the graphical selection criteria of IV-pairs for total effects and (ii) an integrated estimator that combines them to estimate total effects with better accuracy. In this paper, in accordance with the paper by Brito and Pearl (in: Proceedings of the 18th conference on uncertainty in artificial intelligence, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, UAI’02, 2002), the proposed estimator is called an integrated generalized instrumental variable (iGIV) estimator. The proposed graphical selection criteria imply that (a) the back-door criterion achieves better estimation accuracy than the traditional instrumental variable (IV) method of estimating total effects even when the treatment and covariates are highly correlated and (b) the conditional IV method can be superior to the back-door criterion in some situations. The iGIV estimator provides a general class that includes both the ordinary least squares (OLS) estimator based on the back-door criterion and the two-stage least squares (2SLS) estimator based on the (conditional) IV method. We clarify the properties of the iGIV estimator, some of which can be read off from the DAG structure. Furthermore, through numerical experiments and an application to a case study, we show that the performance of the iGIV estimator is superior to those of the OLS and IV estimators. The iGIV estimator can be a powerful tool to estimate the total effect when the proposed graphical selection criteria of the IV-pairs are not satisfied.

中文翻译：

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用于估计总效应的广义工具变量的选择和整合

我们考虑一种情况，其中变量之间的因果关系可以描述为有向无环图（DAG）和相应的线性结构方程模型（线性 SEM）。当几对工具变量 (IV) 和协变量（IV 对；Pearl in：第 20 届人工智能不确定性会议论文集，AUAI 出版社，美国弗吉尼亚州阿灵顿，UAI'04，2004 年）可用时，我们提出 (i) 总效应的 IV 对的图形选择标准和 (ii) 一个综合估计器，将它们结合起来以更准确地估计总效应。在本文中，根据 Brito 和 Pearl 的论文（在：第 18 届人工智能不确定性会议的论文集，Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, UAI'02, 2002），建议的估计量称为综合广义工具变量 (iGIV) 估计量。所提出的图形选择标准意味着 (a) 即使在处理和协变量高度相关的情况下，后门标准也比传统的工具变量 (IV) 方法获得了更好的估计精度，并且 (b) 条件 IV 方法可以在某些情况下优于后门准则。iGIV 估计器提供了一个通用类，包括基于后门准则的普通最小二乘 (OLS) 估计器和基于（条件）IV 方法的两阶段最小二乘 (2SLS) 估计器。我们阐明了 iGIV 估计器的属性，其中一些可以从 DAG 结构中读出。此外，通过数值实验和案例研究的应用，我们表明 iGIV 估计器的性能优于 OLS 和 IV 估计器。当不满足建议的 IV 对图形选择标准时，iGIV 估计器可以成为估计总效果的强大工具。