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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 instrumental variable 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. This new pre-test is valid under heteroscedasticity and with many instruments.

Suggested Citation

  • Anna Mikusheva & Liyang Sun, 2022. "Inference with Many Weak Instruments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(5), pages 2663-2686.
    • Handle: RePEc:oup:restud:v:89:y:2022:i:5:p:2663-2686.
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    File URL: http://hdl.handle.net/10.1093/restud/rdab097
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    Cited by:

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    2. Wang, Wenjie & Zhang, Yichong, 2024. "Wild bootstrap inference for instrumental variables regressions with weak and few clusters," Journal of Econometrics, Elsevier, vol. 241(1).
    3. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    4. Angrist, Joshua & Kolesár, Michal, 2024. "One instrument to rule them all: The bias and coverage of just-ID IV," Journal of Econometrics, Elsevier, vol. 240(2).
    5. Matsushita, Yukitoshi & Otsu, Taisuke, 2024. "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.
    6. Allen, David, 2022. "Asset Pricing Tests, Endogeneity issues and Fama-French factors," MPRA Paper 113610, University Library of Munich, Germany.
    7. Anna Mikusheva & Liyang Sun, 2024. "Weak identification with many instruments," The Econometrics Journal, Royal Economic Society, vol. 27(2), pages -28.
    8. 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.
    9. Tom Boot & Johannes W. Ligtenberg, 2023. "Identification- and many instrument-robust inference via invariant moment conditions," Papers 2303.07822, arXiv.org, revised Sep 2023.
    10. Zhenhong Huang & Chen Wang & Jianfeng Yao, 2023. "The First-stage F Test with Many Weak Instruments," Papers 2302.14423, arXiv.org, revised Sep 2024.
    11. Dennis Lim & Wenjie Wang & Yichong Zhang, 2022. "A Conditional Linear Combination Test with Many Weak Instruments," Papers 2207.11137, arXiv.org, revised Apr 2023.
    12. 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.
    13. Aristide Houndetoungan & Abdoul Haki Maoude, 2024. "Inference for Two-Stage Extremum Estimators," Papers 2402.05030, arXiv.org, revised Nov 2024.
    14. Manu Navjeevan, 2023. "An Identification and Dimensionality Robust Test for Instrumental Variables Models," Papers 2311.14892, arXiv.org, revised Dec 2024.
    15. Zhenhong Huang & Chen Wang & Jianfeng Yao, 2023. "A specification test for the strength of instrumental variables," Papers 2302.14396, arXiv.org.
    16. Johannes W. Ligtenberg, 2023. "Inference in IV models with clustered dependence, many instruments and weak identification," Papers 2306.08559, arXiv.org, revised Mar 2024.
    17. Tom Boot & Didier Nibbering, 2024. "Inference on LATEs with covariates," Papers 2402.12607, arXiv.org, revised Nov 2024.
    18. 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.
    19. Lim, Dennis & Wang, Wenjie & Zhang, Yichong, 2024. "A conditional linear combination test with many weak instruments," Journal of Econometrics, Elsevier, vol. 238(2).
    20. Jochmans, Koen, 2023. "Many (Weak) Judges in Judge-Leniency Designs," TSE Working Papers 23-1481, Toulouse School of Economics (TSE).
    21. Thomas Wiemann, 2023. "Optimal Categorical Instrumental Variables," Papers 2311.17021, arXiv.org, revised May 2024.
    22. Johannes W. Ligtenberg & Tiemen Woutersen, 2024. "Multidimensional clustering in judge designs," Papers 2406.09473, arXiv.org.

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