A comparison of nonnested tests for misspecified models using the method of approximate slopes

Comparisons of the Cox, Wald, and J tests are conducted under a standard framework and in a misspecified setting - the data generation process includes a regressor that is not in either model. Most power comparisons have been carried out for 'local alternatives' but comparisons under a 'nonlocal alternatives' framework using the method of approximate slopes developed by Bahadur (1960, 1967) are made in this paper. Monte Carlo experiments are conducted and the Cox test is shown to have the highest small sample power and approximate slope for most of the cases considered. The results from response surface regressions provide strong evidence that the approximate slope is a good predictor of the small power of nonnested tests. It is also useful for directly comparing the small sample power of one degree of freedom tests of nonnested hypotheses.