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Nearly Singular Design In Gmm And Generalized Empirical Likelihood Estimators

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  • MEHMET CANER

    (UNIVERSITY OF PITTSBURGH)

Abstract

Nearly-Singular design relaxes the nonsingularity assumption of the limit weight matrix in GMM, and the nonsingularity of the limit variance matrix for the first order conditions in GEL. The sample versions of these matrices are nonsingular, but in large samples we assume these sample matrices converge to a singular matrix. This can result in size distortions for the overidentifying restrictions test and large bias for the estimators. This nearly-singular design may occur because of the similar instruments in these matrices. We derive the large sample theory for GMM and GEL estimators under nearly-singular design. The rate of convergence of the estimators is slower than root n.
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  • Mehmet Caner, 2005. "Nearly Singular Design In Gmm And Generalized Empirical Likelihood Estimators," Econometrics 0509019, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0509019
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    Cited by:

    1. Stefan Boes, 2010. "Count Data Models with Correlated Unobserved Heterogeneity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 382-402, September.
    2. Antoine, Bertille & Renault, Eric, 2024. "GMM with Nearly-Weak Identification," Econometrics and Statistics, Elsevier, vol. 30(C), pages 36-59.
    3. Caner, Mehmet, 2008. "Nearly-singular design in GMM and generalized empirical likelihood estimators," Journal of Econometrics, Elsevier, vol. 144(2), pages 511-523, June.
    4. Caner, Mehmet & Yıldız, Neşe, 2012. "CUE with many weak instruments and nearly singular design," Journal of Econometrics, Elsevier, vol. 170(2), pages 422-441.
    5. Antoine, Bertille & Renault, Eric, 2012. "Efficient minimum distance estimation with multiple rates of convergence," Journal of Econometrics, Elsevier, vol. 170(2), pages 350-367.
    6. Tais Carestiato Da Silva & Helder Ferreira De Mendonça, 2011. "Setting The Interest Rate For Twooutlier Countries," Anais do XXXVIII Encontro Nacional de Economia [Proceedings of the 38th Brazilian Economics Meeting] 207, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    7. Richard, Patrick, 2019. "Residual bootstrap tests in linear models with many regressors," Journal of Econometrics, Elsevier, vol. 208(2), pages 367-394.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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