Fast and Reliable Bootstrapping of Consistent Specification Tests

In this paper we investigate the applicability of reliable and fast bootstrap methods on two non-smoothing, consistent specification tests (Bierens, 1982; Escanciano, 2006). Through Monte Carlo experiments we compare the performance of these tests under the null when the null distribution is simulated by the bootstrap, the double bootstrap (Beran, 1988) and the fast double bootstrap (FDB, Davidson and MacKinnon (2007)) procedures. Based on theoretical considerations, the latter two are expected to yield refinements to the order in the error in rejection probabilities. Our main findings are: (1) The Rademacher distribution (Davidson and Flachaire, 2008) for the wild bootstrap should not be used to single bootstrap the investigated tests; (2) The two point distribution proposed by Mammen (1993) for the wild bootstrap is an adequate “omnibus” method for carrying out the bootstrap, double bootstrap and FDB; (3) The double bootstrap should not be used in small and moderate sized samples; (4) The FDB can generally be advised to be used for refining inference over the single bootstrap.