Alternative HAC Covariance Matrix Estimators with Improved Finite Sample Properties

HAC estimators are known to produce test statistics that reject too frequently in finite samples. One neglected reason comes from using the OLS residuals when constructing the HAC estimator. If the regression matrix contains high leverage points, such as from outliers, then the OLS residuals will be negatively biased. This reduces the variance of the OLS residuals and the HAC estimator takes this to signal a more accurate coefficient estimate. Transformations to reflate the OLS residuals and offset the bias have been used in the related HC literature for many years, but these have been overlooked in the HAC literature. Using a suite of simulations I provide strong evidence in favour of replacing the OLS residual-based HAC estimator with estimators related to extensions of either of the two main HC alternatives. In an empirical application I show how different inference from using the alternative HAC estimators can be important, not only from a statistical perspective, but also from an economic one as well.