Subsampling tests of parameter hypotheses and overidentifying restrictions with possible failure of identification

Abstract

We introduce a general testing procedure inmodels with possible identification failure that has exactasymptotic rejection probability under the null hypothesis. The procedure iswidely applicable and in this paper we apply it to tests of arbitrary linear parameter hypotheses as well as to tests of overidentification in time series models given by unconditional moment conditions. The main idea is to subsample classical tests, like for example theWald or the J test.More precisely, instead of using critical values based on asymptotic theory,we compute data-dependent critical values based on the subsampling technique.
We show that under full identification the resulting tests are consistent against fixed alternatives and that they have exact asymptotic rejection probabilities under the null hypothesis independent of identification failure. Furthermore, the subsampling tests of parameter hypotheses are shown to have the same local power as the original tests under full identification. An algorithm is provided that automates the block size choice needed to implement the subsampling testing procedure. A Monte Carlo study shows that the tests have reasonable size properties and often outperform other robust tests in terms of power.