A review and comparison of methods of parameter estimation and inference for heteroskedastic linear regression models

Abstract

This article reviews methods of parameter estimation and inference in the linear regression model under heteroskedasticity. Several approaches to feasible weighted least squares estimation of the parameter vector are reviewed, along with various heteroskedasticity-consistent covariance matrix estimators, which are usually designed with inference as the end goal. A Monte Carlo experiment is designed to evaluate the ability of the reviewed methods to estimate three quantities: the variances of the random errors, the parameter vector, and the standard error of the ordinary least squares estimator thereof. Results of the experiment show that the homoskedastic variance estimator performs well at estimating error variances even in the heteroskedastic data-generating processes studied. Feasible weighted least squares approaches perform best for estimation of the parameter vector, whereas heteroskedasticity-consistent covariance matrix estimators perform best for estimation of the standard error thereof. This motivates a search for a method that would perform well in all three respects.