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Identification- and Singularity-Robust Inference for Moment Condition

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This paper introduces two new identification- and singularity-robust conditional quasi-likelihood ratio (SR-CQLR) test and a new identi"cation- and singularity-robust Anderson and Rubin (1949) (SR-AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2 + gamma bounded moments for some gamma > 0: No conditions are placed on the expected Jacobian of the moment functions, on the eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions. The SR-CQLR test is shown to be asymptotically e"icient in a GMM sense under strong and semi-strong identi"cation (for all k greater than or equal to p; where k and p are the numbers of moment conditions and parameters, respectively). The SR-CQLR test reduces asymptotically to Moreira�s CLR test when p = 1 in the homoskedastic linear IV model. The same is true for p greater than or equal to 2 in most, but not all, identi"cation scenarios. We also introduce versions of the SR-CQLR and SR-AR tests for subvector hypotheses and show that they have correct asymptotic size under the assumption that the parameters not under test are strongly identi"ed. The subvector SR-CQLR test is shown to be asymptotically e"icient in a GMM sense under strong and semi-strong identi"cation.

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  • Donald W. K. Andrews & Patrik Guggenberger, 2015. "Identification- and Singularity-Robust Inference for Moment Condition," Cowles Foundation Discussion Papers 1978R, Cowles Foundation for Research in Economics, Yale University, revised Oct 2018.
    • Handle: RePEc:cwl:cwldpp:1978r
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    3. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    4. 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.
    5. Jean-Jacques Forneron, 2019. "Detecting Identification Failure in Moment Condition Models," Papers 1907.13093, arXiv.org, revised Oct 2023.
    6. Zhongjun Qu & Denis Tkachenko, 2023. "Using arbitrary precision arithmetic to sharpen identification analysis for DSGE models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 644-667, June.
    7. Wenjie Wang & Yichong Zhang, 2021. "Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters," Papers 2108.13707, arXiv.org, revised Jan 2024.
    8. Woosik Gong & Myung Hwan Seo, 2022. "Bootstraps for Dynamic Panel Threshold Models," Papers 2211.04027, arXiv.org, revised Nov 2023.
    9. Gregory Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org, revised Dec 2022.
    10. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    11. Bertille Antoine & Pascal Lavergne, 2020. "Identification-Robust Nonparametric Interference in a Linear IV Model," Discussion Papers dp20-03, Department of Economics, Simon Fraser University.
    12. 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.
    13. Adam Lee & Geert Mesters, 2021. "Robust non-Gaussian inference for linear simultaneous equations models," Economics Working Papers 1792, Department of Economics and Business, Universitat Pompeu Fabra.
    14. Gregory Cox, 2022. "Weak Identification in Low-Dimensional Factor Models with One or Two Factors," Papers 2211.00329, arXiv.org, revised Mar 2024.
    15. Purevdorj Tuvaandorj, 2021. "Robust Permutation Tests in Linear Instrumental Variables Regression," Papers 2111.13774, arXiv.org, revised Jun 2023.
    16. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    17. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    18. Horowitz, Joel L., 2021. "Bounding the difference between true and nominal rejection probabilities in tests of hypotheses about instrumental variables models," Journal of Econometrics, Elsevier, vol. 222(2), pages 1057-1082.

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    More about this item

    Keywords

    Asymptotics; Conditional likelihood ratio test; Confidence set; Identification; Inference; Moment conditions; Robust; Singular variance; Test; Weak identification; Weak instruments;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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