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On Standard Inference For Gmm With Local Identification Failure Of Known Forms

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  • Lee, Ji Hyung
  • Liao, Zhipeng

Abstract

This paper studies the GMM estimation and inference problem that occurs when the Jacobian of the moment conditions is rank deficient of known forms at the true parameter values. Dovonon and Renault (2013) recently raised a local identification issue stemming from this type of degenerate Jacobian. The local identification issue leads to a slow rate of convergence of the GMM estimator and a nonstandard asymptotic distribution of the over-identification test statistics. We show that the known form of rank-deficient Jacobian matrix contains nontrivial information about the economic model. By exploiting such information in estimation, we provide GMM estimator and over-identification tests with standard properties. The main theory developed in this paper is applied to the estimation of and inference about the common conditionally heteroskedastic (CH) features in asset returns. The performances of the newly proposed GMM estimators and over-identification tests are investigated under the similar simulation designs used in Dovonon and Renault (2013).

Suggested Citation

  • Lee, Ji Hyung & Liao, Zhipeng, 2018. "On Standard Inference For Gmm With Local Identification Failure Of Known Forms," Econometric Theory, Cambridge University Press, vol. 34(4), pages 790-814, August.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:04:p:790-814_00
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    Cited by:

    1. Yu Zhu, 2020. "Inference in nonparametric/semiparametric moment equality models with shape restrictions," Quantitative Economics, Econometric Society, vol. 11(2), pages 609-636, May.
    2. Ketz, Philipp, 2019. "On asymptotic size distortions in the random coefficients logit model," Journal of Econometrics, Elsevier, vol. 212(2), pages 413-432.
    3. Sentana, Enrique, 2024. "Finite underidentification," Journal of Econometrics, Elsevier, vol. 240(1).
    4. Prosper Dovonon & Firmin Doko Tchatoka & Michael Aguessy, 2019. "Relevant moment selection under mixed identification strength," School of Economics and Public Policy Working Papers 2019-04, University of Adelaide, School of Economics and Public Policy.
    5. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    6. Forneron, Jean-Jacques, 2024. "Detecting identification failure in moment condition models," Journal of Econometrics, Elsevier, vol. 238(1).
    7. Don S. Poskitt, 2020. "On GMM Inference: Partial Identification, Identification Strength, and Non-Standard," Monash Econometrics and Business Statistics Working Papers 40/20, Monash University, Department of Econometrics and Business Statistics.
    8. Hugo Kruiniger, 2023. "Large sample properties of GMM estimators under second-order identification," Papers 2307.13475, arXiv.org.

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