The pseudo-true score encompassing test for non-nested hypotheses

Well-known encompassing tests are usually difficult to implement because it is difficult to compute the pseudo-true value of the quasi-maximum likelihood estimator. In this paper, we propose a more operational encompassing test that does not involve such pseudo-true value and is asymptotically equivalent to the Wald and score encompassing tests. Instead, the proposed test relies on the “pseudo-true score” which is relatively easy to evaluate. This test is not restricted to testing conditional mean specifications and hence extends the applicability of the conditional mean encompassing test of Wooldridge (J. Econom. 45 (1990b) 331). The proposed test is particularly useful when data characteristics can be fully incorporated into the likelihood function. Our simulations confirm that this test compares favorably with the J and JA tests in testing conditional mean specifications and outperforms the Cox test in testing conditional variance specifications.