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Bootstrap Confidence Sets with Weak Instruments

Author

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  • Davidson, Russell
  • MacKinnon, James G.

Abstract

We study several methods of constructing confidence sets for the coefficient of the single right-hand-side endogenous variable in a linear equation with weak instruments. Two of these are based on conditional likelihood ratio (CLR) tests, and the others are based on inverting t statistics or the bootstrap P values associated with them. We propose a new method for constructing bootstrap confidence sets based on t statistics. In large samples, the procedures that generally work best are CLR confidence sets using asymptotic critical values and bootstrap confidence sets based on LIML estimates.

Suggested Citation

  • Davidson, Russell & MacKinnon, James G., 2012. "Bootstrap Confidence Sets with Weak Instruments," Queen's Economics Department Working Papers 274076, Queen's University - Department of Economics.
    • Handle: RePEc:ags:quedwp:274076
    DOI: 10.22004/ag.econ.274076
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. My "Must Read" List
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-09-27 06:33:00

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    Cited by:

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    2. Doko Tchatoka, Firmin & Wang, Wenjie, 2021. "Uniform Inference after Pretesting for Exogeneity with Heteroskedastic Data," MPRA Paper 106408, University Library of Munich, Germany.
    3. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    4. Wang, Wenjie & Kaffo, Maximilien, 2016. "Bootstrap inference for instrumental variable models with many weak instruments," Journal of Econometrics, Elsevier, vol. 192(1), pages 231-268.
    5. Wenze Li, 2025. "An Empirical Comparison of Weak-IV-Robust Procedures in Just-Identified Models," Papers 2506.18001, arXiv.org.
    6. James G. MacKinnon, 2020. "Wild cluster bootstrap confidence intervals," L'Actualité Economique, Société Canadienne de Science Economique, vol. 96(4), pages 721-743.
    7. Itay Saporta-Eksten & Ity Shurtz & Sarit Weisburd, 2021. "Social Security, Labor Supply, and Health of Older Workers: Quasi-Experimental Evidence from a Large Reform [Identification and Estimation of Local Average Treatment Effects]," Journal of the European Economic Association, European Economic Association, vol. 19(4), pages 2168-2208.
    8. Wang, Wenjie, 2020. "On Bootstrap Validity for the Test of Overidentifying Restrictions with Many Instruments and Heteroskedasticity," MPRA Paper 104858, University Library of Munich, Germany.
    9. Wenjie Wang & Qingfeng Liu, 2015. "Bootstrap-based Selection for Instrumental Variables Model," Economics Bulletin, AccessEcon, vol. 35(3), pages 1886-1896.
    10. Dennis Lim & Wenjie Wang & Yichong Zhang, 2024. "A Dimension-Agnostic Bootstrap Anderson-Rubin Test For Instrumental Variable Regressions," Papers 2412.01603, arXiv.org, revised Sep 2025.

    More about this item

    Keywords

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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