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Exponential Tilting with Weak Instruments: Estimation and Testing

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  • Mehmet Caner

Abstract

This article analyses exponential tilting estimator with weak instruments in a nonlinear framework. Our paper differs from the previous literature in the context of consistency proof. Tests that are robust to the identification problem are also analysed. These are Anderson–Rubin and Kleibergen types of test statistics. We also conduct a simulation study wherein we compare empirical likelihood and continuous updating‐based tests with exponential tilting (ET)‐based ones. The designs involve GARCH(1,1) and contaminated structural errors. We find that ET‐based Kleibergen test has the best size among these competitors.

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  • Mehmet Caner, 2010. "Exponential Tilting with Weak Instruments: Estimation and Testing," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(3), pages 307-325, June.
    • Handle: RePEc:bla:obuest:v:72:y:2010:i:3:p:307-325
    DOI: 10.1111/j.1468-0084.2009.00579.x
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    1. Caner, Mehmet, 2007. "Boundedly pivotal structural change tests in continuous updating GMM with strong, weak identification and completely unidentified cases," Journal of Econometrics, Elsevier, vol. 137(1), pages 28-67, March.
    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. Otsu, Taisuke, 2006. "Generalized Empirical Likelihood Inference For Nonlinear And Time Series Models Under Weak Identification," Econometric Theory, Cambridge University Press, vol. 22(3), pages 513-527, June.
    4. Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(4), pages 667-709, August.
    5. Kocherlakota, Narayana R., 1990. "On tests of representative consumer asset pricing models," Journal of Monetary Economics, Elsevier, vol. 26(2), pages 285-304, October.
    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. 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.
    8. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    9. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
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    Cited by:

    1. Mehmet Caner, 2005. "Near Exogeneity and Weak Identification in Generalized Empirical Likelihood Estimators: Fixed and Many Moment Asymptotics," Econometrics 0509018, University Library of Munich, Germany.
    2. Richard Smith, 2005. "Weak instruments and empirical likelihood: a discussion of the papers by DWK Andrews and JH Stock and Y Kitamura," CeMMAP working papers CWP13/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," Cowles Foundation Discussion Papers 1530, Cowles Foundation for Research in Economics, Yale University.
    4. Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(4), pages 667-709, August.
    5. Paul Levine & Luis F. Martins & Vasco J. Gabriel, 2006. "Robust Estimates of the New Keynesian Phillips Curve," School of Economics Discussion Papers 0206, School of Economics, University of Surrey.
    6. Tang, Niansheng & Yan, Xiaodong & Zhao, Puying, 2018. "Exponentially tilted likelihood inference on growing dimensional unconditional moment models," Journal of Econometrics, Elsevier, vol. 202(1), pages 57-74.
    7. Alain Guay & Jean-Francois Lamarche, 2005. "The Information Content of Implied Probabilities to Detect Structural Change," Working Papers 0804, Brock University, Department of Economics, revised Oct 2008.
    8. Chaudhuri, Saraswata & Renault, Eric, 2020. "Score tests in GMM: Why use implied probabilities?," Journal of Econometrics, Elsevier, vol. 219(2), pages 260-280.
    9. Guggenberger, Patrik & Ramalho, Joaquim J.S. & Smith, Richard J., 2012. "GEL statistics under weak identification," Journal of Econometrics, Elsevier, vol. 170(2), pages 331-349.

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    More about this item

    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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