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Optimal Comparison of Misspecified Moment Restriction Models under a Chosen Measure of Fit

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Abstract

Suppose that the econometrician is interested in comparing two misspecified moment restriction models, where the comparison is performed in terms of some chosen measure of fit. This paper is concerned with describing an optimal test of the Vuong (1989) and Rivers and Vuong (2002) type null hypothesis that the two models are equivalent under the given measure of fit (the ranking may vary for different measures). We adopt the generalized Neyman-Pearson optimality criterion, which focuses on the decay rates of the type I and II error probabilities under fixed non-local alternatives, and derive an optimal but practically infeasible test. Then, as an illustration, by considering the model comparison hypothesis defined by the weighted Euclidean norm of moment restrictions, we propose a feasible approximate test statistic to the optimal one and study its asymptotic properties. Local power properties, one-sided test, and comparison under the generalized empirical likelihood-based measure of fit are also investigated. A simulation study illustrates that our approximate test is more powerful than the Rivers-Vuong test.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1724.

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Length: 46 pages
Date of creation: Aug 2009
Date of revision: Jul 2011
Handle: RePEc:cwl:cwldpp:1724

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Keywords: Moment restriction; Model comparison; Misspecification; Generalized Neyman-Pearson optimality; Generalized method of moments;

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Cited by:
  1. Seojeong Lee, 2013. "Asymptotic Refinements of a Misspecification-Robust Bootstrap for Generalized Method of Moments Estimators," Discussion Papers 2013-09, School of Economics, The University of New South Wales.
  2. Jang, Tae-Seok, 2012. "Structural estimation of the New-Keynesian model: A formal test of backward- and forward-looking behavior," Economics Working Papers 2012-07, Christian-Albrechts-University of Kiel, Department of Economics.
  3. Jang, Tae-Seok, 2012. "Structural estimation of the New-Keynesian Model: a formal test of backward- and forward-looking expectations," MPRA Paper 39669, University Library of Munich, Germany.
  4. Jang, Tae-Seok, 2012. "Structural estimation of the New-Keynesian Model: a formal test of backward- and forward-looking expectations," MPRA Paper 40278, University Library of Munich, Germany.

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