Correcting for Heteroscedasticity with Heteroscedasticity Consistent Standard Errors in the Linear Regression Model: Small Sample Considerations

In the presence of heteroscedasticity, OLS estimates are unbiased, but the usual tests of significance are inconsistent. However, tests based on a heteroscedasticity consistent covariance matrix (HCCM) are consistent. While most applications using a HCCM appear to be based on the asymptotic version of the HCCM, there are three additional, relatively unknown, small sample versions of the HCCM that were proposed by MacKinnon and White (1985), based on work by Hinkley (1977), Horn, Horn and Duncan (1975), and Efron (1982). Our objective in this paper is to provide more extensive evidence for the superiority of a version of the HCCM known as HC3. Using Monte Carlo simulations, we show that the most commonly used form of HCCM, known as HC0, results in incorrect inferences in small samples. We recommend that the data analyst should: a) correct for heteroscedasticity using HCCM whenever there is reason to suspect heteroscedasticity; b) the decision to correct for heteroscedasticity should not be based on a screening test for heteroscedasticity; and c) if the sample is less than 250, a small sample version of the HCCM known as HC3 should be used.