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英文文献：Treatment Effects with Many Covariates and Heteroskedasticity-具有许多协变量和异方差的处理效果
英文文献作者：Matias D. Cattaneo,Michael Jansson,Whitney K. Newey
英文文献摘要：
The linear regression model is widely used in empirical work in Economics. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are obtained using high-dimensional approximations, where the number of covariates are allowed to grow as fast as the sample size. We find that all of the usual versions of Eicker-White heteroskedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroskedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroskedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: (i) parametric linear models with many covariates, (ii) semiparametric semi-linear models with many technical regressors, and (iii) linear panel models with many fixed effects.
线性回归模型广泛应用于经济学的实证研究中。研究人员经常在他们的线性模型规范中包括许多协变量，试图控制混杂因素。我们给出了允许许多协变量和异方差的推理方法。我们的结果是使用高维近似值获得的，其中协变量的数量允许增长与样本大小一样快。在此渐近下，我们发现线性模型中所有常用的Eicker-White异方差一致性标准误差估计量都是不一致的。然后，我们提出了一个新的异方差一致性标准误差公式，该公式对未知形式的异方差和可能包含许多协变量具有全自动和鲁棒性。我们将我们的发现应用于三种设置:(i)有许多协变量的参数线性模型，(ii)有许多技术回归的半参数半线性模型，和(iii)有许多固定效应的线性面板模型。
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