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Bootstrap Confidence Sets with Weak Instruments

Author

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  • Russell Davidson

    (Department of Mining and Materials Engineering [Montréal] - McGill University = Université McGill [Montréal, Canada], GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • James G. Mackinnon

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 limited-information maximum likelihood (LIML) estimates.

Suggested Citation

  • Russell Davidson & James G. Mackinnon, 2014. "Bootstrap Confidence Sets with Weak Instruments," Post-Print hal-01463109, HAL.
    • Handle: RePEc:hal:journl:hal-01463109
    DOI: 10.1080/07474938.2013.825177
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    References listed on IDEAS

    as
    1. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    2. Zivot, Eric & Startz, Richard & Nelson, Charles R, 1998. "Valid Confidence Intervals and Inference in the Presence of Weak Instruments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1119-1146, November.
    3. Russell Davidson & James G. MacKinnon, 2014. "Confidence sets based on inverting Anderson–Rubin tests," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 39-58, June.
    4. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
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    6. Russell Davidson & James G. MacKinnon, 2008. "Bootstrap inference in a linear equation estimated by instrumental variables," Econometrics Journal, Royal Economic Society, vol. 11(3), pages 443-477, November.
    7. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
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    9. Mikusheva, Anna, 2010. "Robust confidence sets in the presence of weak instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 236-247, August.
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    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:

    1. MacKinnon, James G., 2020. "Wild cluster bootstrap confidence intervals," L'Actualité Economique, Société Canadienne de Science Economique, vol. 96(4), pages 721-743, Décembre.
    2. Wenjie Wang & Qingfeng Liu, 2015. "Bootstrap-based Selection for Instrumental Variables Model," Economics Bulletin, AccessEcon, vol. 35(3), pages 1886-1896.
    3. 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.
    4. 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.
    5. Doko Tchatoka, Firmin & Wang, Wenjie, 2021. "Uniform Inference after Pretesting for Exogeneity with Heteroskedastic Data," MPRA Paper 106408, University Library of Munich, Germany.
    6. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    7. 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.

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    More about this item

    Keywords

    Economie quantitative;

    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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