Selection on the basis of prior testing

We establish that under mild conditions, testing for the individual significance of an impulse indicator in the conditional model, selected on the basis of prior testing of its significance in the impulse saturated marginal model does not require bootstrapping critical values. Extensive Monte Carlo evidence shows that the real size of a joint F test in the conditional on the block of dummies retained from the marginal is independent of nominal size used for impulse saturation used in the marginal model. The findings are shown to hold for a plethora of dynamic models and sample sizes. Such results are fundamental not only in model selection theory, but also for the emerging class of automatically computable super exogeneity tests.