Bootstrap J tests of nonnested linear regression models

The J test for nonnested regression models often overrejects very severely as an asymptotic test. We provide a theoretical analysis which explains why and when it performs badly. This analysis implies that, except in certain extreme cases, the J test will perform very well when bootstrapped. Using several methods to speed up the simulations, we obtain extremely accurate Monte Carlo results on the finite-sample performance of the bootstrapped J test. These results fully support the predictions of our theoretical analysis, even in contexts where the analysis is not strictly applicable.