When robust standard errors are smaller, not larger

Question

Your OLS estimate is \hat\beta = 0.5 with a classical standard error of 0.30 (t-statistic 1.67, not significant). The White robust standard error comes out smaller, at 0.20. Recompute the t-statistic and state the new verdict. What does this say about the "robust SEs are always bigger" rule of thumb?

Accepted Answer

Recompute (coefficient unchanged). t = \frac{\hat\beta}{	ext{SE}{	ext{robust}}} = \frac{0.5}{0.20} = 2.5. The verdict flips the other way. Now 2.5 1.96, so the effect becomes significant under robust standard errors, the reverse of the usual story. Debunking the myth. Robust standard errors are not guaranteed to be larger than classical ones. They can be smaller when the observations with large residuals happen to have low leverage (small regressor values), so their heteroskedasticity actually reduces the true variance of \hat\beta relative to the constant-variance assumption. Robust SEs co…

When robust standard errors are smaller, not larger

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