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Bootstrapping the GMM overidentification test Under first-order underidentification

Author

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  • Prosper Dovonon
  • Sílvia Gonçalves

Abstract

The main contribution of this paper is to study the applicability of the bootstrap to estimating the distribution of the standard test of overidentifying restrictions of Hansen (1982) when the model is globally identified but the rank condition fails to hold (lack of first order local identification). An important example for which these conditions are verified is the popular test of common conditionally heteroskedastic features proposed by Engle and Kozicki (1993). As Dovonon and Renault (2013) show, the Jacobian matrix for this model is identically zero at the true parameter value, resulting in a highly nonstandard limiting distribution that complicates the computation of critical values. We first show that the standard bootstrap method of Hall and Horowitz (1996) fails to consistently estimate the distribution of the overidentification restrictions test under lack of first order identification. We then propose a new bootstrap method that is asymptotically valid in this context. The modification consists of adding an additional term that recenters the bootstrap moment conditions in a way as to ensure that the bootstrap Jacobian matrix is zero when evaluated at the GMM estimate.

Suggested Citation

  • Prosper Dovonon & Sílvia Gonçalves, 2014. "Bootstrapping the GMM overidentification test Under first-order underidentification," CIRANO Working Papers 2014s-25, CIRANO.
  • Handle: RePEc:cir:cirwor:2014s-25
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    File URL: http://www.cirano.qc.ca/files/publications/2014s-25.pdf
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    References listed on IDEAS

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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. Donald W. K. Andrews, 2002. "Higher-Order Improvements of a Computationally Attractive "k"-Step Bootstrap for Extremum Estimators," Econometrica, Econometric Society, vol. 70(1), pages 119-162, January.
    3. Angelo Melino, 1982. "Testing for Sample Selection Bias," Review of Economic Studies, Oxford University Press, vol. 49(1), pages 151-153.
    4. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
    5. Dovonon, Prosper & Renault, Eric, 2011. "Testing for Common GARCH Factors," MPRA Paper 40224, University Library of Munich, Germany.
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    Cited by:

    1. Guerron-Quintana, Pablo & Inoue, Atsushi & Kilian, Lutz, 2017. "Impulse response matching estimators for DSGE models," Journal of Econometrics, Elsevier, vol. 196(1), pages 144-155.
    2. Enrique Sentana, 2015. "Finite Underidentification," Working Papers wp2015_1508, CEMFI.
    3. Inoue, Atsushi & Kilian, Lutz, 2016. "Joint confidence sets for structural impulse responses," Journal of Econometrics, Elsevier, vol. 192(2), pages 421-432.
    4. Prosper Donovon & Alastair R. Hall, 2015. "GMM and Indirect Inference: An appraisal of their connections and new results on their properties under second order identification," The School of Economics Discussion Paper Series 1505, Economics, The University of Manchester.
    5. Prosper Donovon & Alastair R. Hall, 2017. "The Asymptotic Properties of GMM and Indirect Inference under Second Inference," The School of Economics Discussion Paper Series 1705, Economics, The University of Manchester.

    More about this item

    Keywords

    Bootstrapping; overidentification; overidentification;

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