Asymptotic power of the integrated conditional moment test against global and large local alternatives

In this paper we study further the asymptotic power properties of the integrated conditional moment (ICM) test of Bierens (1982) and Bierens and Ploberger (1994). First, we establish the relation between consistency against global alternatives and nontrivial local power, using the concept of potential consistency. Moreover, we study the asymptotic power of the test under a class of "large" local alternatives that shrink to the null at rate Op (c/..n), where n is the sample size and c is a large positive constant. We show that the local asymptotic power of the ICM test can be made arbitrarily close to 1 by choosing this constant c sufficiently large, where the rate of convergence is essentially independent of the instruments. Furthermore, we compare the asymptotic power of the ICM test against these large local alternatives with the asymptotic power of the parametric t-test. The asymptotic power function of the t-test under large local alternatives approaches 1 at the same rate as the consistent ICM test for c.. only if the local alternative is correctly specified up to a constant c. In all other cases the ICM test is asymptotically more powerful.