Asymptotic inference under heteroskedasticity of unknown form

This work focuses on the finite-sample behavior of heteroskedasticity-consistent covariance matrix estimators and associated quasi-t tests, and proposes a new estimator, which is tailored to take into account the effect of leverage points in the design matrix on associated quasi/t tests.

Abstract

We focus on the finite-sample behavior of heteroskedasticity-consistent covariance matrix estimators and associated quasi-t tests. The estimator most commonly used is that proposed by Halbert White. Its finite-sample behavior under both homoskedasticity and heteroskedasticity is analyzed using Monte Carlo methods. We also consider two other consistent estimators, namely: the HC3 estimator, which is an approximation to the jackknife estimator, and the weighted bootstrap estimator. Additionally, we evaluate the finite-sample behavior of two bootstrap quasi-t tests: the test based on a single bootstrapping scheme and the test based on a double, nested bootstrapping scheme. The latter is very computer-intensive, but proves to work well in small samples. Finally, we propose a new estimator, which we call HC4; it is tailored to take into account the effect of leverage points in the design matrix on associated quasi-t tests.