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Near exogeneity and weak identification in generalized empirical likelihood estimators: Many moment asymptotics

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  • Caner, Mehmet

Abstract

This paper investigates the Generalized Empirical Likelihood (GEL) estimators when there are local violations of the exogeneity condition (near exogeneity) in the case of many weak moments. We also examine the tradeoff between the degree of violation of the exogeneity and the number of nearly exogenous instruments. In this respect, this paper extends many weak moment asymptotics of Newey and Windmeijer (2009a). The overidentifying restrictions test can detect both mild and large violations of exogeneity. In the case of minor violations, the Anderson–Rubin (1949) and Wald tests are not size distorted.

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  • Caner, Mehmet, 2014. "Near exogeneity and weak identification in generalized empirical likelihood estimators: Many moment asymptotics," Journal of Econometrics, Elsevier, vol. 182(2), pages 247-268.
    • Handle: RePEc:eee:econom:v:182:y:2014:i:2:p:247-268
    DOI: 10.1016/j.jeconom.2014.05.001
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    1. Berkowitz, Daniel & Caner, Mehmet & Fang, Ying, 2008. "Are "Nearly Exogenous Instruments" reliable?," Economics Letters, Elsevier, vol. 101(1), pages 20-23, October.
    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. Michal Kolesár & Raj Chetty & John Friedman & Edward Glaeser & Guido W. Imbens, 2015. "Identification and Inference With Many Invalid Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 474-484, October.
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    6. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
    7. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    8. Bertille Antoine & Eric Renault, 2009. "Efficient GMM with nearly-weak instruments," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 135-171, January.
    9. Guggenberger, Patrik, 2012. "On The Asymptotic Size Distortion Of Tests When Instruments Locally Violate The Exogeneity Assumption," Econometric Theory, Cambridge University Press, vol. 28(2), pages 387-421, April.
    10. Berkowitz, Daniel & Caner, Mehmet & Fang, Ying, 2012. "The validity of instruments revisited," Journal of Econometrics, Elsevier, vol. 166(2), pages 255-266.
    11. 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.
    12. Mehmet Caner, 2010. "Testing, Estimation in GMM and CUE with Nearly-Weak Identification," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 330-363.
    13. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
    14. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
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    16. Doko Tchatoka, Firmin Sabro & Dufour, Jean-Marie, 2008. "Instrument endogeneity and identification-robust tests: some analytical results," MPRA Paper 29613, University Library of Munich, Germany.
    17. Guido W. Imbens, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(3), pages 359-383.
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    Cited by:

    1. Fan, Yanqin & Han, Fang & Li, Wei & Zhou, Xiao-Hua, 2020. "On rank estimators in increasing dimensions," Journal of Econometrics, Elsevier, vol. 214(2), pages 379-412.
    2. Lavergne, Pascal, 2015. "Assessing the Approximate Validity of Moment Restrictions," TSE Working Papers 15-562, Toulouse School of Economics (TSE), revised May 2020.
    3. Byunghoon Kang, 2018. "Higher Order Approximation of IV Estimators with Invalid Instruments," Working Papers 257105320, Lancaster University Management School, Economics Department.
    4. Shakeeb Khan & Xiaoying Lan & Elie Tamer & Qingsong Yao, 2021. "Estimating High Dimensional Monotone Index Models by Iterative Convex Optimization1," Papers 2110.04388, arXiv.org, revised Feb 2023.
    5. DiTraglia, Francis J., 2016. "Using invalid instruments on purpose: Focused moment selection and averaging for GMM," Journal of Econometrics, Elsevier, vol. 195(2), pages 187-208.
    6. Yanqin Fan & Fang Han & Wei Li & Xiao-Hua Zhou, 2019. "On rank estimators in increasing dimensions," Papers 1908.05255, arXiv.org.
    7. Mehmet Caner & Xu Han, 2021. "An upper bound for functions of estimators in high dimensions," Econometric Reviews, Taylor & Francis Journals, vol. 40(1), pages 1-13, January.
    8. Francis DiTraglia, 2011. "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM, Second Version," PIER Working Paper Archive 15-027, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 10 Aug 2015.

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    More about this item

    Keywords

    Violation of exogeneity; Anderson–Rubin test; Asymptotic size;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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