Abstract
In this article, we introduce a new class of Cox’s non-nested test statistics for models defined through overidentifying moment restrictions that depend on a finite dimensional parameter vector. In addition to showing that the GEL test statistics proposed in Smith (1997,Economic Journal107, 503–519) and Ramalho and Smith (2002,Journal of Econometrics107, 99–125) are members of this class, we reveal that further members can be constructed using the artificial compound model approach, which was originally applied by Atkinson (1970,Journal of the Royal Statistical Society, Series B32, 323–335) in the parametric setting. We investigate the asymptotic properties of the statistics and propose tests based on modified versions of these statistics that have correct asymptotic size in a uniform sense, a requirement not satisfied by existing Cox’s non-nested tests. A Monte Carlo study examines the performance of the proposed tests.
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