Testing the Specification of Econometric Models in Regression and Non-Regression Directions

The asymptotic power of a statistical test depends on the model being tested, the (implicit) alternative against which the test is constructed, and the process which actually generated the data. The exact way in which it does so is examined for several classes of models and tests. First, we analyze the power of tests of nonlinear regression models in regression directions. Next, we consider the power of heteroskedasticity-robust variants of these tests. Finally, we examine the power of very general tests in the context of a very general class of models.