Power of Tests in Binary Response Models

Most hypotheses in binary response models are composite. The null hypothesis is usually that one or more slope coefficients are zero. Typically, the sequence of alternatives of interest is one in which the slope coefficients are increasing in absolute value. In this paper, we prove that the power goes to zero for this sequence of alternatives of interest in cases which often occur in practice. The practical implication is that for the sequence of alternatives of interest the power is nonmonotonic. This is true for any non-randomized test with size less than one and for a wide class of binary response models which includes the logit and probit models.