Almost unbiased variance estimation in linear regressions with many covariates

We propose an adjustment to the variance estimator of Cattaneo, Jansson, and Newey (2018) when there are many covariates. The finite-sample correction in the spirit of Horn, Horn and Duncan (1975) makes the estimator exactly unbiased under homoskedasticity. Simulations show that the adjustment reduces test size distortions, especially with skewed regressors. We also verify whether further degrees-of-freedom adjustments in the spirit of Bell and McCaffrey (2002) bring improvements to the control over test size.