Robust standard errors erase a significant result

Question

Your OLS estimate is \hat\beta = 0.60 with a classical standard error of 0.20, a t-statistic of 3.0, comfortably "significant." Suspecting heteroskedasticity, you recompute White (heteroskedasticity-robust) standard errors and get 0.35. Recompute the t-statistic with the robust standard error and state whether the result is still significant at the 5 percent level.

Accepted Answer

The coefficient does not change. Robust standard errors correct the uncertainty, not the estimate. So \hat\beta stays at 0.60; only the denominator of the t-statistic changes. Recompute the t-statistic. t = \frac{\hat\beta}{	ext{SE}{	ext{robust}}} = \frac{0.60}{0.35} \approx 1.71. The verdict flips. The 5 percent two-sided critical value is about 1.96. Since 1.71 < 1.96, the coefficient is no longer significant. The original "significance" was an artifact of a too-small classical standard error, which assumed constant error variance that the data did not have. Why this matters. Under hetero…

Robust standard errors erase a significant result

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