Rescale a t-stat when only the SE ratio is given

Question

A colleague reports only that the White robust standard error is $1.8$ times the classical standard error, and that the classical t-statistic was $3.2$ . You do not have the coefficient or the raw standard errors.

What is the robust t-statistic, and is the effect still significant at 5 percent?

Accepted Answer

Use the ratio directly. The t-statistic is \hat\beta / 	ext{SE}. The coefficient is the same under both methods, so the robust t is the classical t scaled down by the same factor by which the standard error grew: t{	ext{robust}} = \frac{\hat\beta}{	ext{SE}{	ext{robust}}} = \frac{\hat\beta}{1.8 \cdot 	ext{SE}{	ext{classical}}} = \frac{t{	ext{classical}}}{1.8}. Plug in. t{	ext{robust}} = \frac{3.2}{1.8} \approx 1.78. Verdict. Since 1.78 < 1.96, the effect is no longer significant at the 5 percent level. You did not need the coefficient at all: the ratio of standard errors is enough to r…

Rescale a t-stat when only the SE ratio is given

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