TESTS OF NONNESTED HYPOTHESES IN NONSTATIONARY REGRESSIONS WITH AN APPLICATION TO MODELING INDUSTRIAL PRODUCTION

Abstract

In the context of I(1) time series, we provide some asymptotic results for the Davidson-MacKinnon J-type test. We examine both the case where our regressor sets x_1t and x_2t are not cointegrated, and the case where they are. In the former case, the OLS estimator of the weighting coefficient from the artificial compound model converges at rate T to a mixed normal distribution, and the associated t-statistic has an asymptotic standard normal distribution. In the latter case, we find that the J-test also has power against violation of weak exogeneity (with respect to the short-run coefficients of the null model), which is caused by correlation between the disturbance of the null model and that of the cointegrating equation linking x_1t and x_2t. Moreover, unlike the previous case, the OLS estimator of the weighting coefficient from the artificial compound model converges at \sqrt{T} to an asymptotic normal distribution when the null model is specified correctly. In an empirical illustration, we use the tests to examine an industrial production data set for six countries.