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Moderate Deviations of Generalized Method of Moments and Empirical Likelihood Estimators

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Abstract

This paper studies moderate deviation behaviors of the generalized method of moments and generalized empirical likelihood estimators for generalized estimating equations, where the number of equations can be larger than the number of unknown parameters. We consider two cases for the data generating probability measure: the model assumption and local contaminations or deviations from the model assumption. For both cases, we characterize the first-order terms of the moderate deviation error probabilities of these estimators. Our moderate deviation analysis complements the existing literature of the local asymptotic analysis and misspecification analysis for estimating equations, and is useful to evaluate power and robust properties of statistical tests for estimating equations which typically involve some estimators for nuisance parameters.

Suggested Citation

  • Taisuke Otsu, 2011. "Moderate Deviations of Generalized Method of Moments and Empirical Likelihood Estimators," Cowles Foundation Discussion Papers 1785, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1785
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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    3. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, January.
    4. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
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    6. Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
    7. Miguel Arcones, 2006. "Large deviations for M-estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(1), pages 21-52, March.
    8. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871549.
    9. Jens Jensen & Andrew Wood, 1998. "Large Deviation and Other Results for Minimum Contrast Estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(4), pages 673-695, December.
    10. Imbens, Guido W, 2002. "Generalized Method of Moments and Empirical Likelihood," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 493-506, October.
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    12. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871532.
    13. Guido W. Imbens, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," Review of Economic Studies, Oxford University Press, vol. 64(3), pages 359-383.
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    15. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    16. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    17. Yurinskii, V. V., 1976. "Exponential inequalities for sums of random vectors," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 473-499, December.
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    Cited by:

    1. Hwang, Jungbin & Kang, Byunghoon & Lee, Seojeong, 2022. "A doubly corrected robust variance estimator for linear GMM," Journal of Econometrics, Elsevier, vol. 229(2), pages 276-298.
    2. Seojeong Lee, 2018. "A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(3), pages 400-410, July.
    3. Jiang, Hui & Wang, Shaochen, 2017. "Moderate deviation principles for classical likelihood ratio tests of high-dimensional normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 57-69.
    4. 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.
    5. Byunghoon Kang, 2018. "Higher Order Approximation of IV Estimators with Invalid Instruments," Working Papers 257105320, Lancaster University Management School, Economics Department.

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    More about this item

    Keywords

    Generalized method of moments; Empirical likelihood; Moderate deviations; Large deviations;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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