A small sample study of some sandwich estimators to handle heteroscedasticity

Sammanfattning: This simulation study sets out to investigate Heteroscedasticity-Consistent Covariance Matrix Estimation using the sandwich method in relatively small sample sizes. The different estimators are evaluated on how accurately they assign confidence intervals around a fixed, true coefficient, in the presence of random sampling and both homo- and heteroscedasticity. A measure of Standard Error is also collected to further analyze the coefficients. All of the HC-estimators seemed to overadjust in most homoscedastic cases, creating intervals that way overlapped their specifications, and the standard procedure that assumes homoscedasticity produced the most consistent intervals towards said specifications. In the presence of heteroscedasticity the comparative accuracy improved for the HC-estimators and they were often better than the non-robust error estimator with the exception of estimating the intercept, which they all heavily underestimated the confidence intervals for. In turn, the constant estimator was subject to a larger mean error for said parameter - the intercept. While it is clear from previous studies that Sandwich estimation is a method that can lead to more accurate results, it was rarely much better than, and sometimes strictly worse than the non-robust, constant variance provided by the OLS-estimation. The conclusion is to stay cautious when applying HC-estimators to your model, and to test and make sure that they do in fact improve the areas where heteroscedasticity presents an issue.