Nonnested linear model selection revisited

In testing nonnested or separate hypotheses, statistical practitioners typically use the j-test, due to Davidson and MacKinnon (Estimation and Inference in Econometrics, Oxford University Press, New York, 1981), which is based on an artificial nesting approach. Results of a previous paper (Watnik and Johnson, The Behavior of Nonnested Linear Model Selection Tests Under the Alternative Hypothesis, UC Davis Technical Report, 2000) imply that the j-test is often asymptotically most efficient among the testing procedures in the literature. The j-test, however, is prone to making Type I errors (cf. Godfrey and Pesaran, J. Econometric. 1983, 84, 59-74). We formulate a different parameterization of the models, which facilitates comparisons of the various tests, and which provides a common framework for deriving asymptotic distribution theory. We also consider a finite-sample corrected j-test statistic, similar to the one considered by Royston and Thompson (Biometrics, 1995, 51, 114-27). This statistic greatly improves upon the small-sample performance of the j-test. We highlight that, when considering these tests for the purpose of model selection rather than for model specification, they should be treated as one-sided rather than two-sided tests. An illustrative example and simulations are provided.