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Bootstrapping the GMM overidentification test Under first-order underidentification

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  • Prosper Dovonon
  • Silvia 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 & Silvia 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: https://cirano.qc.ca/files/publications/2014s-25.pdf
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    References listed on IDEAS

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    Cited by:

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    3. Doko Tchatoka, Firmin & Wang, Wenjie, 2020. "Uniform Inference after Pretesting for Exogeneity," MPRA Paper 99243, University Library of Munich, Germany.
    4. 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.
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    6. Wang, Wenjie & Doko Tchatoka, Firmin, 2018. "On Bootstrap inconsistency and Bonferroni-based size-correction for the subset Anderson–Rubin test under conditional homoskedasticity," Journal of Econometrics, Elsevier, vol. 207(1), pages 188-211.
    7. Giuseppe Cavaliere & Rasmus Søndergaard Pedersen & Anders Rahbek, 2018. "The Fixed Volatility Bootstrap for a Class of Arch(q) Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 920-941, November.
    8. Prosper Dovonon & Alastair Hall, 2018. "The Asymptotic Properties of GMM and Indirect Inference under Second-order Identification," CIRANO Working Papers 2018s-37, CIRANO.
    9. Bing Su & Fukang Zhu & Ke Zhu, 2023. "Statistical inference for the logarithmic spatial heteroskedasticity model with exogenous variables," Papers 2301.06658, arXiv.org.
    10. Chen, Qihui & Fang, Zheng, 2019. "Inference on functionals under first order degeneracy," Journal of Econometrics, Elsevier, vol. 210(2), pages 459-481.
    11. Giovanni Angelini & Giuseppe Cavaliere & Luca Fanelli, 2022. "Bootstrap inference and diagnostics in state space models: With applications to dynamic macro models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(1), pages 3-22, January.
    12. 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," Economics Discussion Paper Series 1505, Economics, The University of Manchester.
    13. Prosper Dovonon & Alastair R. Hall, 2017. "The Asymptotic Properties of GMM and Indirect Inference Under Second-Order Identification," Economics Discussion Paper Series 1705, Economics, The University of Manchester.
    14. Dovonon, Prosper & Hall, Alastair R., 2018. "The asymptotic properties of GMM and indirect inference under second-order identification," Journal of Econometrics, Elsevier, vol. 205(1), pages 76-111.
    15. Sentana, Enrique, 2024. "Finite underidentification," Journal of Econometrics, Elsevier, vol. 240(1).
    16. Woosik Gong & Myung Hwan Seo, 2022. "Bootstraps for Dynamic Panel Threshold Models," Papers 2211.04027, arXiv.org, revised Sep 2024.

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    Keywords

    Bootstrapping; overidentification; overidentification;
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