Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions
Susan Athey Professor of Economics, Stanford Graduate School of Business, and NBER, Guido W. Imbens Professor of Economics, Stanford Graduate School of Business, and NBER, Stefan Wager Assistant Professor of Operations, Information and Technology and of Statistics (by courtesy), Stanford Graduate School of Business,
Abstract
There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on pre-treatment variables. The unconfoundedness assumption is often more plausible if a large number of pre-treatment variables are included in the analysis, but this can worsen the performance of standard approaches to treatment effect estimation. In this paper, we develop a method for de-biasing penalized regression adjustments to allow sparse regression methods like the lasso to be used for $\sqrt{n}$ -consistent inference of average treatment effects in high-dimensional linear models. Given linearity, we do not need to assume that the treatment propensities are estimable, or that the average treatment effect is a sparse contrast of the outcome model parameters. Rather, in addition standard assumptions used to make lasso regression on the outcome model consistent under 1-norm error, we only require overlap, i.e., that the propensity score be uniformly bounded away from 0 and 1. Procedurally, our method combines balancing weights with a regularized
中文速览
在观察性研究中，研究者常需要控制大量协变量来让"条件无混淆"假设更可信，但变量维度一旦超过样本量，套索回归（lasso）等惩罚回归方法就会引入系统性偏差，让平均处理效应（ATE）的估计失准。现有的高维双重稳健方法虽能纠偏，却都要求能一致地估计倾向得分（propensity score），这在高维场景下往往难以保证。本文提出"近似残差均衡"（approximate residual balancing）两步法：第一步用套索拟合结果模型，第二步构造直接最小化协变量不均衡的重加权，将两者结合来消除正则化带来的偏差——关键在于，只要线性模型假设成立且倾向得分有界（即overlap条件满足），无需任何倾向得分的一致估计即可实现根号n收敛速率的有效推断。理论与模拟均表明该方法在高维线性模型下性能优于现有基准，突破了以往高维因果推断必须依赖倾向得分估计的限制，为实践中变量众多的观察性研究提供了更坚实的统计保障。
原文 arXiv:1604.07125;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1604.07125v5