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A GENERAL CLASS OF NON-NESTED TEST STATISTICS FOR MODELS DEFINED THROUGH MOMENT RESTRICTIONS

Published online by Cambridge University Press:  03 April 2017

Paulo M.D.C. Parente
Paulo M.D.C. Parente*
Affiliation:
Instituto Universitário de Lisboa (ISCTE-IUL) Business Research Unit (BRU-IUL)
*
*Address correspondence to Paulo M.D.C. Parente, BRU-IUL (Business Research Unit), ISCTE-IUL, Avenida das Forças Armadas, 1649-026 Lisboa, Portugal; e-mail: paulo.miguel.parente@iscte.pt.
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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 Journal 107, 503–519) and Ramalho and Smith (2002, Journal of Econometrics 107, 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 B 32, 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.

Type
ARTICLES
Information
Econometric Theory , Volume 34 , Issue 2 , April 2018 , pp. 477 - 507
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

I am grateful for the constructive comments and criticisms by the Editor, a co-Editor and three anonymous referees on previous drafts. Earlier versions of this paper were presented at the 2008 European Meeting of the Econometric Society, Bocconi University, Milan and the Third Meeting of the Portuguese Economic Journal, Funchal. This paper has also benefited from the comments of R. Dupleich, J.J.S. Ramalho, J.M.C. Santos Silva and R.J. Smith. The usual disclaimer applies. This work was supported by Fundação para a Ciência e a Tecnologia.

References

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