Using Heteroscedasticity-Consistent Standard Errors for the Linear Regression Model with Correlated Regressors

Abstract

The use of heteroscedasticity-consistent covariance matrix (HCCM) estimators is very common in practice to draw correct inference for the coefficients of a linear regression model with heteroscedastic errors. However, in addition to the problem of heteroscedasticity, linear regression models may also be plagued with some considerable degree of collinearity among the regressors when two or more regressors are considered. This situation causes many adverse effects on the least squares measures and alternatively, the ordinary ridge regression method is used as a common practice. But in the available literature, the problems of multicollinearity and heteroscedasticity have not been discussed as a combined issue especially, for the inference of the regression coefficients. The present article addresses the inference about the regression coefficients taking both the issues of multicollinearity and heteroscedasticity into account and suggests the use of HCCM estimators for the ridge regression. This article proposes t- and F-tests, based on these HCCM estimators, that perform adequately well in the numerical evaluation of the Monte Carlo simulations.