Heteroskedasticity-robust inference in linear regression models with many covariates

Abstract: We consider inference in linear regression models that is robust to heteroskedasticity and the presence of many control variables. When the number of control variables increases at the same rate as the sample size the usual heteroskedasticity-robust estimators of the covariance matrix are inconsistent. Hence, tests based on these estimators are size distorted even in large samples. An alternative covariance-matrix estimator for such a setting is presented that complements recent work by Cattaneo, Jansson and Newey (2018). We provide high-level conditions for our approach to deliver (asymptotically) size-correct inference as well as more primitive conditions for three special cases. Simulation results and an empirical illustration to inference on the union premium are also provided.