On Size and Power of Heteroskedasticity and Autocorrelation Robust Tests

TL;DR

This paper analyzes the size and power properties of heteroskedasticity and autocorrelation robust tests in linear regression, revealing limitations and proposing an adjustment method to improve test performance.

Contribution

It provides a comprehensive theory on the finite-sample behavior of robust tests and introduces an adjustment procedure to mitigate size distortions and enhance power.

Findings

Robust tests often have size equal to one or zero power under weak assumptions.

An adjustment procedure with artificial regressors can correct size distortions.

Adjusted tests maintain bounded power away from zero.

Abstract

Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. These procedures have been developed with the purpose of attenuating size distortions and power deficiencies present for the uncorrected F-test. We develop a general theory to establish positive as well as negative finite-sample results concerning the size and power properties of a large class of heteroskedasticity and autocorrelation robust tests. Using these results we show that nonparametrically as well as parametrically corrected F-type tests in time series regression models with stationary disturbances have either size equal to one or nuisance-infimal power equal to zero under very weak assumptions on the covariance model and under generic conditions on the design matrix. In addition we suggest an adjustment procedure based on artificial regressors. This adjustment resolves the problem in many cases in that the so-adjusted tests do not suffer from size distortions. At the same time their power function is bounded away from zero. As a second application we discuss the case of heteroskedastic disturbances.