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Nonnested Testing In Models Estimated Via Generalized Method Of Moments


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  • Hall, Alastair R.
  • Pelletier, Denis


Rivers and Vuong (2002) develop a very general framework for choosing between two competing dynamic models. Within their framework, inference is based on a statistic that compares measures of goodness of fit between the two models. The null hypothesis is that the models have equal measures of goodness of fit; one model is preferred if its goodness of fit is statistically significantly smaller than its competitor. Under the null hypothesis, Rivers and Vuong (2002) show that their test statistic has a standard normal distribution under generic conditions that are argued to allow for a variety of estimation methods including Generalized Method of Moments (GMM). In this paper, we analyze the limiting distribution of Rivers and Vuong's (2002) statistic under the null hypothesis when inference is based on a comparison of GMM minimands evaluated at GMM estimators. It is shown that the limiting behaviour of this statistic depends on whether the models in question are correctly specified, locally misspecified or misspecified. Specifically, it is shown that: (i) if both models are correctly specified or locally misspecified then Rivers and Vuong's (2002) generic conditions are not satisfied, and the limiting distribution of the test statistic is non-standard under the null; (ii) if both models are misspecified then the generic conditions are satisfied, and so the statistic has a standard normal distribution under the null. In the latter case it is shown that the choice of weighting matrices affects the outcome of the test and thus the ranking of the models.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 27 (2011)
Issue (Month): 02 (April)
Pages: 443-456

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Handle: RePEc:cup:etheor:v:27:y:2011:i:02:p:443-456_00

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Cited by:
  1. Lee, Seojeong, 2014. "Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 178(P3), pages 398-413.
  2. Marmer, Vadim & Otsu, Taisuke, 2008. "Optimal Comparison of Misspecified Moment Restriction Models under a Chosen Measure of Fit," working papers vadim_marmer-2008-13, Vancouver School of Economics, revised 25 Jul 2011.
  3. Parente, Paulo M.D.C. & Santos Silva, J.M.C., 2012. "A cautionary note on tests of overidentifying restrictions," Economics Letters, Elsevier, vol. 115(2), pages 314-317.
  4. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2011. "Chi-squared tests for evaluation and comparison of asset pricing models," Working Paper 2011-08, Federal Reserve Bank of Atlanta.


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