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Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure

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  • Andrews, Donald W.K.
  • Cheng, Xu

Abstract

This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and confidence sets (CSs) in moment condition models in which some parameters are unidentified or weakly identified in part of the parameter space. The asymptotic distributions of GMM estimators are established under a full range of drifting sequences of true parameters and distributions. The asymptotic sizes (in a uniform sense) of standard GMM tests and CSs are established. The paper also establishes the correct asymptotic sizes of “robust” GMM-based Wald, t, and quasi-likelihood ratio tests and CSs whose critical values are designed to yield robustness to identification problems. The results of the paper are applied to a nonlinear regression model with endogeneity and a probit model with endogeneity and possibly weak instrumental variables.

Suggested Citation

  • Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(2), pages 287-333, April.
    • Handle: RePEc:cup:etheor:v:30:y:2014:i:02:p:287-333_00
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    Cited by:

    1. David T. Frazier & Eric Renault & Lina Zhang & Xueyan Zhao, 2020. "Weak Identification in Discrete Choice Models," Papers 2011.06753, arXiv.org, revised Jan 2021.
    2. Jean-Marie Dufour & Joachim Wilde, 2018. "Weak identification in probit models with endogenous covariates," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 611-631, October.
    3. Stépahne Auray & Nicolas Lepage-Saucier & Purevdorj Tuvaandor, 2018. "Doubly Robust GMM Inference and Differentiated Products Demand Models," Working Papers 2018-13, Center for Research in Economics and Statistics.
    4. Phillips, Peter C.B. & Kheifets, Igor L., 2024. "High-dimensional IV cointegration estimation and inference," Journal of Econometrics, Elsevier, vol. 238(2).
    5. Ketz, Philipp, 2019. "On asymptotic size distortions in the random coefficients logit model," Journal of Econometrics, Elsevier, vol. 212(2), pages 413-432.
    6. Gregory Cox, 2022. "A Generalized Argmax Theorem with Applications," Papers 2209.08793, arXiv.org.
    7. Jui-Chung Yang & Ke-Li Xu, 2013. "Estimation and Inference under Weak Identi cation and Persistence: An Application on Forecast-Based Monetary Policy Reaction Function," 2013 Papers pya307, Job Market Papers.
    8. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(2), pages 287-333, April.
    9. Forneron, Jean-Jacques, 2024. "Detecting identification failure in moment condition models," Journal of Econometrics, Elsevier, vol. 238(1).
    10. Woosik Gong & Myung Hwan Seo, 2022. "Bootstraps for Dynamic Panel Threshold Models," Papers 2211.04027, arXiv.org, revised Nov 2025.
    11. Gregory Fletcher Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org, revised Oct 2025.
    12. Peter C.B. Phillips & Igor Kheifets, 2021. "On Multicointegration," Cowles Foundation Discussion Papers 2306, Cowles Foundation for Research in Economics, Yale University.
    13. Frazier, David T. & Renault, Eric & Zhang, Lina & Zhao, Xueyan, 2025. "Weak identification in discrete choice models," Journal of Econometrics, Elsevier, vol. 248(C).
    14. Patrik Guggenberge & Frank Kleibergen & Sophocles Mavroeidis, 2021. "A Powerful Subvector Anderson Rubin Test in Linear Instrumental Variables Regression with Conditional Heteroskedasticity," Economics Series Working Papers 960, University of Oxford, Department of Economics.
    15. Jules Tinang & Nour Meddahi, 2016. "GMM estimation of the Long Run Risks model," 2016 Meeting Papers 1107, Society for Economic Dynamics.
    16. Ketz, Philipp, 2019. "Testing overidentifying restrictions with a restricted parameter space," Economics Letters, Elsevier, vol. 185(C).
    17. Chen, Heng & Fan, Yanqin & Liu, Ruixuan, 2016. "Inference for the correlation coefficient between potential outcomes in the Gaussian switching regime model," Journal of Econometrics, Elsevier, vol. 195(2), pages 255-270.
    18. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    19. Dakyung Seong, 2025. "Binary Response Model With Many Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 40(2), pages 214-230, March.
    20. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    21. Andrews, Donald W.K. & Cheng, Xu, 2013. "Maximum likelihood estimation and uniform inference with sporadic identification failure," Journal of Econometrics, Elsevier, vol. 173(1), pages 36-56.
    22. Fan, Yanqin & Shi, Xuetao, 2023. "Wald, QLR, and score tests when parameters are subject to linear inequality constraints," Journal of Econometrics, Elsevier, vol. 235(2), pages 2005-2026.
    23. Ketz, Philipp, 2018. "Subvector inference when the true parameter vector may be near or at the boundary," Journal of Econometrics, Elsevier, vol. 207(2), pages 285-306.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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