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Inference with Many Weak Instruments

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  • Anna Mikusheva
  • Liyang Sun

Abstract

We develop a concept of weak identification in linear IV models in which the number of instruments can grow at the same rate or slower than the sample size. We propose a jackknifed version of the classical weak identification-robust Anderson-Rubin (AR) test statistic. Large-sample inference based on the jackknifed AR is valid under heteroscedasticity and weak identification. The feasible version of this statistic uses a novel variance estimator. The test has uniformly correct size and good power properties. We also develop a pre-test for weak identification that is related to the size property of a Wald test based on the Jackknife Instrumental Variable Estimator (JIVE). This new pre-test is valid under heteroscedasticity and with many instruments.

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  • Anna Mikusheva & Liyang Sun, 2020. "Inference with Many Weak Instruments," Papers 2004.12445, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2004.12445
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    References listed on IDEAS

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    1. Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012. "Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments," Econometric Theory, Cambridge University Press, vol. 28(1), pages 42-86, February.
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    Cited by:

    1. Joshua Angrist & Michal Kolesár, 2021. "One Instrument to Rule Them All: The Bias and Coverage of Just-ID IV," NBER Working Papers 29417, National Bureau of Economic Research, Inc.
    2. Chao, John C. & Swanson, Norman R. & Woutersen, Tiemen, 2023. "Jackknife estimation of a cluster-sample IV regression model with many weak instruments," Journal of Econometrics, Elsevier, vol. 235(2), pages 1747-1769.
    3. Dennis Lim & Wenjie Wang & Yichong Zhang, 2022. "A Conditional Linear Combination Test with Many Weak Instruments," Papers 2207.11137, arXiv.org, revised Apr 2023.
    4. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    5. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    6. Manu Navjeevan, 2023. "An Identification and Dimensionality Robust Test for Instrumental Variables Models," Papers 2311.14892, arXiv.org.
    7. Andrew Shephard & Xu Cheng & Alejándro Sanchez-Becerra, 2023. "How to weight in moments matchings: A new approach and applications to earnings dynamics," CeMMAP working papers 13/23, Institute for Fiscal Studies.
    8. Tom Boot & Johannes W. Ligtenberg, 2023. "Identification- and many instrument-robust inference via invariant moment conditions," Papers 2303.07822, arXiv.org, revised Sep 2023.
    9. Matsushita, Yukitoshi & Otsu, Taisuke, 2022. "A jackknife Lagrange multiplier test with many weak instruments," LSE Research Online Documents on Economics 116392, London School of Economics and Political Science, LSE Library.
    10. Zhenhong Huang & Chen Wang & Jianfeng Yao, 2023. "A specification test for the strength of instrumental variables," Papers 2302.14396, arXiv.org.
    11. Allen, David, 2022. "Asset Pricing Tests, Endogeneity issues and Fama-French factors," MPRA Paper 113610, University Library of Munich, Germany.
    12. Aristide Houndetoungan & Abdoul Haki Maoude, 2024. "Inference for Two-Stage Extremum Estimators," Papers 2402.05030, arXiv.org.
    13. Jochmans, Koen, 2023. "Many (Weak) Judges in Judge-Leniency Designs," TSE Working Papers 23-1481, Toulouse School of Economics (TSE).
    14. Johannes W. Ligtenberg, 2023. "Inference in IV models with clustered dependence, many instruments and weak identification," Papers 2306.08559, arXiv.org, revised Mar 2024.
    15. Zhenhong Huang & Chen Wang & Jianfeng Yao, 2023. "Assessing the strength of many instruments with the first-stage F and Cragg-Donald statistics," Papers 2302.14423, arXiv.org.
    16. Tom Boot & Didier Nibbering, 2024. "Inference on LATEs with covariates," Papers 2402.12607, arXiv.org.
    17. Aristide Houndetoungan & Abdoul Haki Maoude, 2024. "Inference for Two-Stage Extremum Estimators," THEMA Working Papers 2024-01, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    18. Anna Mikusheva & Liyang Sun, 2023. "Weak Identification with Many Instruments," Papers 2308.09535, arXiv.org, revised Jan 2024.
    19. Thomas Wiemann, 2023. "Optimal Categorical Instrumental Variables," Papers 2311.17021, arXiv.org.

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