# Robust Standard Errors

“Robust” standard errors is a technique to obtain unbiased standard errors of OLS coefficients under heteroscedasticity.  Remember, the presence of heteroscedasticity violates the Gauss Markov assumptions that are necessary to render OLS the best linear unbiased estimator (BLUE). You can find the consequences of heteroscedasticity on the OLS estimator here. Possible solutions to handle heteroscedasticity can be found here.

“Robust” standard errors have many labels that essentially refer all the same thing. Namely, standard errors that are computed with the sandwich estimator of variance. Typical terms for “robust” standard errors include White’s Standard Errors, Huber–White standard errors, Eicker–White or even Eicker–Huber–White standard errors.

The following equation estimates heteroscedasticity consistent standard errors:

$var_{r}(\hat{\beta}_{OLS}) = ( \frac{N}{N-K}) ( X^{'} X )^{-1} \sum_{i=1}^{N} (X_{i} X_{i}^{'} \hat{\epsilon}^{2}) ( X^{'} X )^{-1}$

“Robust” standard errors are usually larger than conventional standard errors. However, this is not always the case.

In STATA you can obtain robust standard errors simply by adding robust to your regression command. For instance

reg dependent_var independent_var, robust

It is also possible to estimate robust standard errors in R. However, in R there are several ways to compute heteroscedasticity consistent standard errors. Not all of them are easy to implement. I extended the summary() in order to simplify the computation of robust standard errors in R and make it easier to handle. My intention was to create a function that allows to compute robust standard errors in a similar fashion as in STATA. If you are interested in calculating robust standard errors in R click here. However, if you are more interested in the code and the exact extension of the summary() click here.