  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.
