We consider the accurate estimation of total causal effects in the presence of unmeasured confounding using conditional instrumental sets. Specifically, we consider the two-stage least squares estimator in the setting of a linear structural equation model with correlated errors that is compatible with a known acyclic directed mixed graph. To set the stage for our results, we fully characterise the class of conditional instrumental sets that result in a consistent two-stage least squares estimator for our target total effect. We refer to members of this class as valid conditional instrumental sets. Equipped with this definition, we provide three graphical tools for selecting accurate and valid conditional instrumental sets: First, a graphical criterion that for certain pairs of valid conditional instrumental sets identifies which of the two corresponding estimators has the smaller asymptotic variance. Second, a forward algorithm that greedily adds covariates that reduce the asymptotic variance to a valid conditional instrumental set. Third, a valid conditional instrumental set for which the corresponding estimator has the smallest asymptotic variance we can ensure with a graphical criterion.

中文翻译：

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用于选择准确有效的条件乐器组的图形工具

我们考虑使用条件工具集在存在无法测量的混杂的情况下准确估计总因果效应。具体来说，我们在线性结构方程模型的设置中考虑两阶段最小二乘估计器，该模型具有与已知的无环有向混合图兼容的相关误差。为了为我们的结果奠定基础，我们充分描述了条件工具集的类别，这些工具集为我们的目标总效应产生了一致的两阶段最小二乘估计量。我们将此类的成员称为有效的条件工具集。有了这个定义，我们提供了三个图形工具来选择准确和有效的条件乐器集：首先，一个图形标准，对于某些有效的条件工具集对，它可以识别两个相应估计量中的哪一个具有较小的渐近方差。第二，一种前向算法，贪婪地添加协变量，减少渐近方差到有效的条件工具集。第三，一个有效的条件工具集，其对应的估计量具有我们可以用图形标准确保的最小渐近方差。