On pooling disturbance variances when the goal is testing restrictions on regression coefficients (Q1822178)

We examine the problem of pooling variances from the viewpoint of testing linear restrictions on regression coefficients. That is, we examine the sampling performance of the two-stage test which consists of the pre-test for equality of disturbance variances followed by the main-test for linear restrictions on regression coefficients. It is shown that the bias in the size of the two-stage test may not be important and the two-stage test can be more powerful than the usual test which does not conduct the pre-test, if the size of the pre-test is chosen appropriately.