论文标题
具有治疗引起的选择的工具变量：确切的偏差结果
Instrumental Variables with Treatment-Induced Selection: Exact Bias Results
论文作者
论文摘要
当分析治疗条件时，仪器变量（IV）估计会遭受选择偏差。犹太珍珠对工具变量的早期图形定义明确禁止对治疗进行调节。尽管如此，这种做法仍然很普遍。在本文中，我们在一系列数据生成模型以及各种诱导过程中得出了精确的分析表达式。我们为线性模型提供了四组结果。首先，静脉选择偏置取决于调节过程（协方差调整与样品截断）。其次，由于协变量调整引起的静脉选择偏置是由于样品截断而引起的静脉选择偏置的限制情况。第三，在某些模型中，在选择下的IV和OLS估计量结合了大样本中的真正因果效应。第四，我们表征了尽管选择了治疗的情况，但尽管选择了治疗，但IV仍然比OLS更喜欢OL。这些结果扩大了超出样品截断的静脉选择偏差的概念，用精确的分析公式替换了先前的模拟发现，并实现了正式的灵敏度分析。
Instrumental variables (IV) estimation suffers selection bias when the analysis conditions on the treatment. Judea Pearl's early graphical definition of instrumental variables explicitly prohibited conditioning on the treatment. Nonetheless, the practice remains common. In this paper, we derive exact analytic expressions for IV selection bias across a range of data-generating models, and for various selection-inducing procedures. We present four sets of results for linear models. First, IV selection bias depends on the conditioning procedure (covariate adjustment vs. sample truncation). Second, IV selection bias due to covariate adjustment is the limiting case of IV selection bias due to sample truncation. Third, in certain models, the IV and OLS estimators under selection bound the true causal effect in large samples. Fourth, we characterize situations where IV remains preferred to OLS despite selection on the treatment. These results broaden the notion of IV selection bias beyond sample truncation, replace prior simulation findings with exact analytic formulas, and enable formal sensitivity analyses.
