Abstract
In this note, we analyze the sampling performance of the two-stage test that tests the linear hypothesis on regression coefficients after a pre-test for disturbance variance. It is shown that the two-stage test has a serious upward bias in size when the degrees of freedom is small, but it gets smaller as the degrees of freedom gets larger and the power of the two-stage test is higher than that of the conventional F test for the linear hypothesis which does not conduct the pre-test.
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