Commonly econometricians conduct inference based on covariance matrix estimates which are consistent in the presence of arbitrary forms of heteroskedasticity; the associated standard errors are referred to as “robust” (also, confusingly, White, or Huber-White, or Eicker-Huber-White) standard errors. These are easily requested in Stata with the “robust” option, as in the ubiquitous
reg y x, robust
Everyone knows that the usual OLS standard errors are generally “wrong,” that robust standard errors are “usually” bigger than OLS standard errors, and it often “doesn’t matter much” whether one uses robust standard errors. It is whispered that there may be mysterious circumstances in which robust standard errors are smaller than OLS standard errors. Textbook discussions typically present the nasty matrix expressions for the robust covariance matrix estimate, but do not discuss in detail when robust standard errors matter or in what circumstances robust standard errors will be smaller than OLS standard errors. This post attempts a simple explanation of robust standard errors and circumstances in which they will tend to be much bigger or smaller than OLS standard errors.