A result that survives the switch to robust standard errors

Question

Your OLS estimate is \hat\beta = 1.2 with a classical standard error of 0.3 (t-statistic 4.0). The White robust standard error comes out to 0.5. Recompute the t-statistic and state whether the result is still significant at 5 percent.

Accepted Answer

Recompute with the robust SE (coefficient unchanged). t = \frac{\hat\beta}{	ext{SE}{	ext{robust}}} = \frac{1.2}{0.5} = 2.4. The verdict holds. The critical value is about 1.96, and 2.4 1.96, so the coefficient remains significant at the 5 percent level, though less emphatically than the classical t = 4.0 suggested. The lesson. Robust standard errors weakened the result (the t-statistic fell from 4.0 to 2.4) but did not overturn it. A genuinely strong effect survives the correction; only borderline "significance" that leaned on the constant-variance assumption tends to vanish. Reporting the …

A result that survives the switch to robust standard errors

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