Approximate inference in heteroskedastic regressions: A numerical evaluation

Abstract

The commonly made assumption that all stochastic error terms in the linear regression model share the same variance (homoskedasticity) is oftentimes violated in practical applications, especially when they are based on cross-sectional data. As a precaution, a number of practitioners choose to base inference on the parameters that index the model on tests whose statistics employ asymptotically correct standard errors, i.e. standard errors that are asymptotically valid whether or not the errors are homoskedastic. In this paper, we use numerical integration methods to evaluate the finite-sample performance of tests based on different (alternative) heteroskedasticity-consistent standard errors. Emphasis is placed on a few recently proposed heteroskedasticity-consistent covariance matrix estimators. Overall, the results favor the HC4 and HC5 heteroskedasticity-robust standard errors. We also consider the use of restricted residuals when constructing asymptotically valid standard errors. Our results show that the only test that clearly benefits from such a strategy is the HC0 test.

Keywords:

• covariance matrix estimation
• heteroskedasticity
• leverage point
• linear regression
• quasi-t test

Acknowledgements

The first author gratefully acknowledges partial financial support from CNPq. We also thank two anonymous referees for valuable comments and suggestions.

Notes

The original source of the data is the US Department of Commerce.

Wisconsin has been dropped from the data set since it had missing data, and Washington DC was included, hence n=50.

Note that, here (HC0), c depends on y through , and it is not possible to establish the unbiasedness of the resulting estimator.

Recall that .

Recall that these authors proposed using a=2 for MSE minimization.